Consider the linear system 211 + 3x2 - 5.23 = b 7.01 + 2.02 + 813 = b2 -X1 + 12 - 5.23 = b3

(a) Find the echelon form of the augmented matrix of the above system.

(b) Find the conditions on b1,b2, b3 for which this system has a solution.

(c) Do you see the shape of the points (61, 62, 63) for which the above system has a solution?

(d) If you randomly picked a (61, 62, 63) in R3, do you expect the above system to have a solution?

Answers

Answer 1

Answer:

The answers are shown in the step by step explanation that is attached

Step-by-step explanation:

The step by step calculation is as shown in the attachment below

Consider The Linear System 211 + 3x2 - 5.23 = B 7.01 + 2.02 + 813 = B2 -X1 + 12 - 5.23 = B3 (a) Find

Related Questions

simplify -1/64........

Answers

Answer:

- 2⁻⁶

Step-by-step explanation:

To simplify this we have to know the following rules.

(i) (xᵃ)ᵇ = xᵃᵇ

(ii) 1/xᵃ = x⁻ᵃ

Given: [tex]$ \frac{-1}{64} $[/tex]

= [tex]$ \frac{-1}{4^3} $[/tex]

= [tex]$ \frac{-1}{(2^2)^3} $[/tex]

= [tex]$ \frac{-1}{2^6} \hspace{10mm} $[/tex]               [using (i)]

= [tex]$ 2^{-6} $[/tex]              [using (ii)]

Hence, the simplified form would be: [tex]$ 2^{-6} $[/tex]

Which equation represent the relationship between the total number of pages N that Ronalds can read in M minutes?

Answers

Answer:option A is the correct answer.

Step-by-step explanation:

Ronald can read at a constant rate of p pages per minute.

If Roland can read a total number of N pages in minutes, then the equation representing the relationship between the number of pages, N and the time, m minutes would be

p pages = 1 minute

N pages = m minutes

Crossmultiplying, it becomes

p × m = N × 1

N = pm

Find the expression for the electric field, E [infinity] , of the ring as the point P becomes very far from the ring ( x ≫ R ) in terms of the radius R , the distance x , the total charge on the ring q , and the constant k = 1 / ( 4 π ϵ 0 ).

Answers

Answer:

The expression of the field E as the point P becomes very far from the ring is:

[tex]\vec{E}(x)=\displaystyle\frac{q}{4\pi\epsilon_0} \frac{sgn(x)}{x^2}\vec{x} \\\left \{ {{\vec{E}(x)=\frac{q}{4\pi\epsilon_0} \frac{1}{x^2}\vec{x} \mapsto x>0} \atop {\vec{E}(x)=\frac{q}{4\pi\epsilon_0} \frac{-1}{x^2}\vec{x} \mapsto x< 0 }} \right.[/tex]

Step-by-step explanation:

The Electric field expression is:

[tex]\vec{E}(x)=\displaystyle\frac{q}{4\pi\epsilon_0} \frac{x}{(R^2+x^2)^{\frac{3}{2}}}\vec{x}[/tex]

To determine the asked expression we use limits. If we consider that x≫R, this is the same as considering the radius insignificant respect the x distance. Therefore we can considerate than from this distance X, the radius R tends to zero:

[tex]\displaystyle\lim_{R \to{}0}{\vec{E}(x)}=\lim_{R \to{}0}{\frac{q}{4\pi\epsilon_0} \frac{x}{(R^2+x^2)^{\frac{3}{2}}}\vec{x}}\rightarrow\frac{q}{4\pi\epsilon_0} \frac{x}{(0^2+x^2)^{\frac{3}{2}}}\vec{x}=\frac{q}{4\pi\epsilon_0} \frac{x}{(x^2)^{\frac{3}{2}}}\vec{x}=\frac{q}{4\pi\epsilon_0} \frac{\cancel{x}}{|x|^{\cancel{3}}}\vec{x}=\displaystyle\frac{q}{4\pi\epsilon_0} \frac{sgn(x)}{x^2}\vec{x}[/tex]

The expression for the electric field of the ring as the point P becomes very far from the ring is [tex]E_{z} = \frac{k\cdot Q}{x^{2}}[/tex].

How to estimate an electric field for a ring with an uniform charge

Let suppose that the ring has an uniform linear electric density ([tex]\lambda[/tex]). A formula for the electric field at point P ([tex]E[/tex]) in rectangular coordinates is shown below:

[tex]\vec E = (E_{x}, E_{y}, E_{z})[/tex] (1)

Where:

[tex]E_{x}[/tex] - Electric field in the x-direction.[tex]E_{y}[/tex] - Electric field in the y-direction.[tex]E_{z}[/tex] - Electric field in the z-direction.

Each component of the electric field are defined by the following integral formulae:

[tex]E_{x} = \int\limits^{2\pi}_{0} {\sin \theta \cdot \cos \phi} \, dE[/tex] (2)

[tex]E_{y} = \int\limits^{2\pi}_{0} {\sin \theta\cdot \sin\phi} \, dE[/tex] (3)

[tex]E_{z} = \int\limits^{2\pi}_{0} {\cos \theta} \, dE[/tex] (4)

Where:

[tex]\theta[/tex] - Axial angle, in radians.[tex]\phi[/tex] - Radial angle, in radians.

By Coulomb's law and trigonometric and geometric relationships, we expand and solve each integral as following:

[tex]E_{x} = \frac{R}{\sqrt{x^{2}+R^{2}}}\int\limits^{2\pi}_{0} {\cos \phi} \, dE = \frac{k\cdot \lambda\cdot R^{2}}{(x^{2}+R^{2})^{3/2}}\int\limits^{2\pi}_{0} {\cos \phi} \, d\phi = 0[/tex]

[tex]E_{y} = \frac{R}{\sqrt{x^{2}+R^{2}}}\int\limits^{2\pi}_{0} {\sin \phi} \, dE = \frac{k\cdot \lambda\cdot R^{2}}{(x^{2}+R^{2})^{3/2}}\int\limits^{2\pi}_{0} {\sin \phi} \, d\phi = 0[/tex]

[tex]E_{z} = \frac{k\cdot \lambda\cdot x \cdot R}{(x^{2}+R^{2})^{3/2}} \int\limits^{2\pi}_{0}\, d\phi = \frac{x\cdot k \cdot (2\pi\cdot \lambda\cdot R)}{(x^{2}+R^{2})^{3/2}} = \frac{x\cdot k\cdot Q}{(x^{2}+R^{2})^{3/2}}[/tex] (5)

 Where [tex]k[/tex] is the electrostatic constant.

If [tex]x >> R[/tex], (5) is simplified into the following expression:

[tex]E_{z} = \frac{k\cdot Q}{x^{2}}[/tex] (6)

Where [tex]Q[/tex] is the electric charge of the entire ring.

Please notice that (6) tends to be zero when [tex]x \to \infty[/tex]. The expression for the electric field of the ring as the point P becomes very far from the ring is [tex]E_{z} = \frac{k\cdot Q}{x^{2}}[/tex]. [tex]\blacksquare[/tex]

To learn more on electric fields, we kindly invite to check this verified question: https://brainly.com/question/12757739

Determine whether the value given is a parameter or statistic. Two thirds of all the students in this class are womena. Parameterb. Statistic

Answers

Answer: a. Parameter

Step-by-step explanation:

Parameter can be defined as a fact/characteristic about a whole population.

For example:

i. 20% of my class are boys

ii. 40% of Canadian senators are women.

Parameter usually deal with a small measurable population.

While statistic is a characteristic/fact about the sample.

Therefore the case above is a parameter because the students in the class is the population and the stated (Two thirds of all the students in this class are women) is a fact about the population.

Answer:

Parameter

Step-by-step explanation:

The given value is Parameter because it contains the measurement of population. In short, the given value 2/3 is the estimated value of population.

The population consists of all the students in the class. If the ratio of women from all the students in the class is calculated, then it is a measure of population. Thus, the given value is parameter.

An engineer in charge of water rationing for the U.S. Army wants to determine if the average male soldier spends less time in the shower than the average female soldier. Let μm represent the average time in the shower of male soldiers and μf represent the average time in the shower of female soldiers.

a) What are the appropriate hypotheses for the engineer?
H0: μm = μf versus Ha: μm > μf
H0: σm = σf versus Ha: σm > σf
H0: μm = μf versus Ha: μm ≠ μf
H0: μm = μf versus Ha: μm < μf

b) Among a sample of 66 male soldiers the average shower time was found to be 2.68 minutes and the standard deviation was found to be 0.65 minutes. Among a sample of 69 female soldiers the average shower time was found to be 2.7 minutes and the standard deviation was found to be 0.5 minutes. What is the test statistic? Give your answer to three decimal places.
c) What is the P-value for the test? Give your answer to four decimal places.
d) Using a 0.1 level of significance, what is the appropriate conclusion?
Reject the claim that the average shower times are different for male and female soldiers because the P-value is greater than 0.1.
Conclude that the average shower time for males is less than the average shower time for females because the P-value is less than 0.1.
Fail to reject the claim that the average shower times are the same for male and female soldiers because the P-value is greater than 0.1.
Conclude that the average shower time for males is equal to the average shower time for females because the P-value is less than 0.1.

Answers

Answer:

a) H0: μm = μf versus Ha: μm < μf

b) [tex]t=\frac{(2.68-2.7)-0}{\sqrt{\frac{0.65^2}{66}+\frac{0.5^2}{69}}}}=-0.200[/tex]

c) [tex]p_v =P(t_{133}<-0.200)=0.421[/tex]  

d) Fail to reject the claim that the average shower times are the same for male and female soldiers because the P-value is greater than 0.1.

Step-by-step explanation:

Data given and notation  

[tex]\bar X_{m}=2.68[/tex] represent the mean for the sample male

[tex]\bar X_{f}=2.7[/tex] represent the mean for the sample female

[tex]s_{m}=0.65[/tex] represent the sample standard deviation for the males

[tex]s_{f}=0.5[/tex] represent the sample standard deviation for the females  

[tex]n_{m}=66[/tex] sample size for the group male  

[tex]n_{f}=69[/tex] sample size for the group female  

t would represent the statistic (variable of interest)  

Part a

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the average male soldier spends less time in the shower than the average female soldier, the system of hypothesis would be:  

Null hypothesis:[tex]\mu_{m}-\mu_{f}\geq 0[/tex]  

Alternative hypothesis:[tex]\mu_{m} - \mu_{f}< 0[/tex]  

Or equivalently:

Null hypothesis:[tex]\mu_{m}-\mu_{f}= 0[/tex]  

Alternative hypothesis:[tex]\mu_{m} - \mu_{f}< 0[/tex]  

And the best option is:

H0: μm = μf versus Ha: μm < μf

Part b

We don't have the population standard deviation, so for this case is better apply a t test to compare means, and the statistic is given by:  

[tex]t=\frac{(\bar X_{m}-\bar X_{f})-\Delta}{\sqrt{\frac{s^2_{m}}{n_{m}}+\frac{s^2_{f}}{n_{f}}}}[/tex] (1)

And the degrees of freedom are given by [tex]df=n_m +n_f -2=66+69-2=133[/tex]  

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

What is the test statistic?

With the info given we can replace in formula (1) like this:  

[tex]t=\frac{(2.68-2.7)-0}{\sqrt{\frac{0.65^2}{66}+\frac{0.5^2}{69}}}}=-0.200[/tex]

Part c What is the p-value?

Since is a left tailed test the p value would be:  

[tex]p_v =P(t_{133}<-0.200)=0.421[/tex]  

Part d

The significance level given is [tex] \alpha =0.1[/tex] since the p value is higher than the significance level we can conclude:

Fail to reject the claim that the average shower times are the same for male and female soldiers because the P-value is greater than 0.1.

Final answer:

The question relates to hypothesis testing in statistics, insights into average shower times for male and female soldiers. After formulating the hypotheses, we calculate the test statistic using the provided sample data, and then find the corresponding P-value. If the P-value is less than our significance level, we reject the null hypothesis and side with the alternative hypothesis.

Explanation:

The subject of this question falls under Mathematics, specifically it deals with hypothesis testing statistics.

a) The appropriate hypotheses for the engineer to consider would be: H0: μm = μf versus Ha: μm > μf

b) To calculate the test statistic, we use the formula for the test statistic in a independent two-sample t-test which incorporates the sample sizes, means, and standard deviations from the two groups. The formula is (avg(male soldiers)-avg(female soldiers))/sqrt(((sd(male soldiers))^2/number(male soldiers))+((sd(female soldiers))^2/number(female soldiers))). Plug in given values, we can obtain the test statistic.

c) The P-value can be obtained by looking up the test statistic in the T distribution table.

d) If the P-value is greater than the level of significance (0.1), we would fail to reject the null hypothesis. If the P-value is less than the level of significance, we would reject the null hypothesis. The conclusion is based on the specific P-value we computed.

Learn more about Hypothesis Testing here:

https://brainly.com/question/34171008

#SPJ3

Find the sample standard deviation s for the following sample data. Round your answer to the nearest hundredth. 23 20 14 35 28

Answers

Answer:

The standard deviation for given sample is 7.97          

Step-by-step explanation:

We are given the following data set:

23, 20, 14, 35, 28

Formula:

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.  

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{120}{5} = 24[/tex]

Sum of squares of differences = 1 + 16 + 100 + 121 + 16 = 254

[tex]S.D = \sqrt{\dfrac{254}{4}} = 7.97[/tex]

The standard deviation for given sample is 7.97

To find the sample standard deviation for the data sets 23, 20, 14, 35, 28, we calculate the mean, subtract the mean from each data point and square the result, sum these squares, divide by one less than the sample size to find the variance, and finally take the square root to find the standard deviation which is approximately 7.97.

To calculate the sample standard deviation (s), follow these steps:

Find the mean (average) of the sample data.

Subtract the mean from each data point and square the result.

Sum all the squared values.

Divide this sum by the sample size minus one (n-1) to get the sample variance.

Take the square root of the sample variance to find the sample standard deviation.

Let's apply these steps to the given data: 23, 20, 14, 35, 28.

Mean = (23 + 20 + 14 + 35 + 28) / 5 = 120 / 5 = 24.

Subtract the mean and square: (23 - 24)² = 1, (20 - 24)² = 16, (14 - 24)² = 100, (35 - 24)² = 121, (28 - 24)² = 16.

Sum of squares = 1 + 16 + 100 + 121 + 16 = 254.

Variance = 254 / (5 - 1) = 254 / 4 = 63.5.

Standard Deviation = √63.5 ≈ 7.97 (rounded to the nearest hundredth).

The sample standard deviation s is approximately 7.97.

Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.5 millimeters (mm) and a standard deviation of 1.7 mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.)

(a) the thickness is less than 3.0 mm.

(b) the thickness is more than 7.0 mm.

(c) the thickness is between 3.0 mm and 7.0 mm.

Answers

Answer:

a) [tex]P(X<3.0)=P(\frac{X-\mu}{\sigma}<\frac{3-\mu}{\sigma})=P(Z<\frac{3-4.5}{1.7})=P(z<-0.882)[/tex]

[tex]P(z<-0.882)=0.189[/tex]

b) [tex]P(X>7.0)=P(\frac{X-\mu}{\sigma}>\frac{7-\mu}{\sigma})=P(Z<\frac{7-4.5}{1.7})=P(z>1.47)[/tex]

[tex]P(z>1.47)=1-P(z<1.47) = 1-0.929=0.071[/tex]

c)  [tex]P(3<X<7)=P(\frac{3-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{7-\mu}{\sigma})=P(\frac{3-4.5}{1.7}<Z<\frac{7-4.5}{1.7})=P(-0.882<z<1.47)[/tex]

[tex]P(-0.882<z<1.47)=P(z<1.47)-P(z<-0.882)=0.929-0.189=0.740[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the thickness of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(4.5,1.7)[/tex]  

Where [tex]\mu=4.5[/tex] and [tex]\sigma=1.7[/tex]

We are interested on this probability

[tex]P(X<3.0)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X<3.0)=P(\frac{X-\mu}{\sigma}<\frac{3-\mu}{\sigma})=P(Z<\frac{3-4.5}{1.7})=P(z<-0.882)[/tex]

And we can find this probability using excel or the normal standard table:

[tex]P(z<-0.882)=0.189[/tex]

Part b

We are interested on this probability

[tex]P(X>3.0)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(X>7.0)=P(\frac{X-\mu}{\sigma}>\frac{7-\mu}{\sigma})=P(Z<\frac{7-4.5}{1.7})=P(z>1.47)[/tex]

And we can find this probability using excel or the normal standard table:

[tex]P(z>1.47)=1-P(z<1.47) = 1-0.929=0.071[/tex]

Part c

[tex]P(3<X<7)=P(\frac{3-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{7-\mu}{\sigma})=P(\frac{3-4.5}{1.7}<Z<\frac{7-4.5}{1.7})=P(-0.882<z<1.47)[/tex]

And we can find this probability using excel or the normal standard table liek this:

[tex]P(-0.882<z<1.47)=P(z<1.47)-P(z<-0.882)=0.929-0.189=0.740[/tex]

For each of the following questions, select a research technique that is likely to yield a useful answer. For instance, if the question is "Which companies within a 20-mile radius of our company headquarters sell recycled paper?" a search of the web is likely to provide a useful answer.
a. Does the Honda CR-V include traction control as a standard feature?
b. How much money has our company's philanthropic foundation donated to colleges and universities in each of the last three years?
c. How does a 3D printer work?
d. Could our Building 3 support a rooftop green space?
e. How can we determine whether we would save more money by switching to LED lighting in our corporate offices?

Answers

Answer:

Web searching, specialists consultations and comparisons.

Step-by-step explanation:

a. Does the Honda CR-V iclude traction control as a standard feature?

Research about the Honda CR-V on the internet, or reading an article about it.

b. How much money has our company´s philanthropic foundation donated to colleges and universities in each of the last three year?

Look over the company´s administrative records.

c.How does a 3D printer work?

Search on the web about the 3D printer function.

d. Could our Building 3 support a rooftop green space?

Consultation with an architect.

e. How can we determine whether we would save more money by switching to LED lighting in our corporate offices?

Search on the web about the LED lighting use of electricty and the use of electricty of the type of lighting that the company is already using and compare for the best one.

The California State University (CSU) system consists of 23 campuses, from San Diego State in the south to Humboldt State near the Oregon border. A CSU administrator wishes to make an inference about the average distance between the hometowns of students and their campuses. Describe and discuss several different sampling methods that might be employed. (Select all that apply.)
a. One could take a simple random sample of students from all students in the California State University system and ask each student in the sample to report the distance from their hometown to campus.
b. There are no potential problems with self reporting of distances.
c. Certain problems arise with self reporting of distances, such as recording error or poor recall.
d. Instead of taking a random sample, every student should be included in the study.
e. The sample could be generated by taking a stratified random sample by taking a simple random sample from each of the 23 campuses and again asking each student in the sample to report the distance from their hometown to campus.

Answers

Final answer:

A Simple Random Sample or a Stratified Random Sample of students across the CSU campuses would allow for reliable data collection on the average distance between student hometowns and their campus, taking into account that self-reporting may introduce errors.

Explanation:

When considering methods to sample the average distance between the hometowns of students and their California State University (CSU) campuses, there are several sampling techniques that can be considered:

(a) Simple Random Sample - This involves randomly selecting students from the entire CSU system, which could help ensure that each student has an equal chance of being included in the sample.(c) Self-reporting issues – When students report distances, errors can occur due to recording mistakes or poor recall. This is an important consideration that can affect data accuracy.(e) Stratified Random Sample - This method involves taking a simple random sample from each of the 23 campuses to avoid overrepresentation or underrepresentation of any single campus and can provide a more accurate reflection of the entire system.

Option (b) is incorrect as there are potential problems with self-reporting of distances, and option (d) is impractical for such a large population and not necessary for making inferences. Therefore, options (a), (c), and (e) are relevant to the question.

What is next in this sequence of numbers: 1, 11, 21, 1211, 111221, 312211, ...?

Answers

Answer:

13112221

Step-by-step explanation:

Each sequence of numbers is a verbal representation of the sequence before it. Thus, starting with 1, the next sequence would be "one one," or "11." That sequence is followed by "two one," or "21," and so on and so forth.

This may also be a good explanation:

The first number is just ONE (amount) "1" (0-9 numeral). So if you say there's ONE "1" (seriously just say it aloud) the next number would be an 11. Then there are TWO "1's", creating 21. Then ONE "2" and ONE "1" which creates 1,211. Then ONE "1", ONE "2", and TWO "1's" creating 111,221 ... and so on.

The first number 1 is read as one one, so the second number is written as 11, this is read as two ones, so the next number is written as 21 ( two ones)

This continues throughout the sequence.

The last number written is 312211 which is read as one three, one one, two twos, two ones

This gets written as 13112221

4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

Answers

Answer:

[tex]\sum_{n=0}^9cos(\frac{\pi n}{2})=1[/tex]

[tex] \sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0[/tex]

[tex] \sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}[/tex]

Step-by-step explanation:

[tex] \sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))[/tex]

[tex]=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})[/tex]

[tex]=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1[/tex]

2nd

[tex]\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}[/tex]

[tex]=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0[/tex]

3th

[tex] \sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))[/tex]

[tex]=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}[/tex]

What we use?

We use that

[tex] e^{i\pi n}=cos(\pi n)+i sin(\pi n)[/tex]

and

[tex]\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}[/tex]

Final answer:

Geometric sum formulas are used to evaluate sums of a geometric series, with the result expressed in Cartesian form (a + bi) where a is the real part and bi is the imaginary part. The sum of a geometric series is calculated with the formula: Sum = a * (1 - r^n) / (1 - r), where a is the first term and r is the ratio. Please provide the specific sums for a detailed step-by-step calculation.

Explanation:

The problem at hand revolves around the usage of geometric sum formulas to evaluate sums and to express the result in Cartesian form. The critical point to remember is that a geometric series is a series with a constant ratio between successive terms. The sum of the first 'n' terms of a geometric sequence can be calculated using the formula:

Sum = a * (1 - rⁿ) / (1 - r)

Assuming 'a' represents the first term in the series and 'r' is the ratio.To convert a complex number into Cartesian form, you simply map the real and imaginary parts of the number 'a + bi', where 'a' is the real part, and 'bi' is the imaginary part.Unfortunately, without the specifics of the sums you're looking to evaluate, it's impossible to give a concrete step-by-step calculation. However, understanding the formulas and how they're applied should provide you with a good start.

Learn more about Geometric Sum Formulas and Cartesian Form here:

https://brainly.com/question/35501415

#SPJ3

Marian went shopping and bought clothes for $76.17 and books for $44.98. She then had a meal at the mall for $19.15. Which is the best estimate of the total cost of her shopping trip?

A. $130
B. $120
C. $150
D. $140

Answers

Answer:

D. $140.

Step-by-step explanation:

Given:

Cost of clothes = $76.17

Cost of books = $44.98

Cost of meal = $19.15

We need to find the best estimate of total cost of her shopping trip.

Solution:

First we will find the total cost of her shopping trip.

total cost of her shopping trip is equal to sum of Cost of clothes, Cost of books and Cost of meal.

framing in equation form we get;

total cost of her shopping trip = [tex]76.17+44.98+19.15 = \$140.3[/tex]

Now we can say that;

140.3 is close to 140

Hence Best estimate of total cost of shopping trip is $140.

An article reported the following data on oxygen consumption (mL/kg/min) for a sample of ten firefighters performing a fire-suppression simulation: 28.6 49.4 30.3 28.2 28.9 26.4 33.8 29.9 23.5 30.2Compute the following. (Round your answers to four decimal places.) a. The sample range mL/kg/minb. The sample variance s2 from the definition (i.e., by first computing deviations, then squaring them, etc.) mL2/kg2/min2c. The sample standard deviation mL/kg/mind. s2 using the shortcut method mL2/kg2/min

Answers

Answer:

a) The sample range 25.9 [tex]ml\slash kg\slash \min[/tex]

b) The sample variance is 49.344 [tex]ml^2 \slash kg^2 \slash min^2[/tex]

c) The sample standard deviation 7.0245 [tex]ml\slash kg\slash \min[/tex]                  

Step-by-step explanation:

We are given the following data on oxygen consumption (mL/kg/min):

28.6, 49.4, 30.3, 28.2, 28.9, 26.4, 33.8, 29.9, 23.5, 30.2

a) The sample range

Range = Maximum - Minimum

[tex]\text{Range} = 49.4 - 23.5 = 25.9[/tex]

The sample range 25.9 [tex]ml\slash kg\slash \min[/tex]

b) The sample variance

[tex]\text{Variance} = \displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.  

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{309.2}{10} = 30.92[/tex]

Sum of squares of differences =

5.3824 + 341.5104 + 0.3844 + 7.3984 + 4.0804 + 20.4304 + 8.2944 + 1.0404 + 55.0564 + 0.5184 = 444.096

[tex]s^2 = \dfrac{444.096}{9} = 49.344[/tex]

The sample variance is 49.344 [tex]ml^2 \slash kg^2 \slash min^2[/tex]

c)  The sample standard deviation

It is the square root of sample variance.

[tex]s = \sqrt{s^2} = \sqrt{49.344} = 7.0245[/tex]

The sample standard deviation 7.0245 [tex]ml\slash kg\slash \min[/tex]

Help me plsss I need it by tonight

Answers

Answer:

[tex]y=2x+2[/tex]

Step-by-step explanation:

we know that

The equation of a linear function has no exponents higher than 1, and the graph of a linear function is a straight line.

Verify each case

case 1) we have

[tex]y=2x+2[/tex]

Is the equation of a line in slope intercept form

so

Is a straight line and has no exponents higher than 1

therefore

Is a linear equation

case 2) we have

[tex]y=2x^{2}+2[/tex]

Is a quadratic equation

Is a curved line and has at least one exponent higher than 1,

therefore

Is a non-linear equation

case 3) we have

[tex]y=2x^{3}+2[/tex]

Is a cubic equation

Is a curved line and has at least one exponent higher than 1,

therefore

Is a non-linear equation

case 4) we have

[tex]y=2x^{4}+2[/tex]

Is a quartic equation

Is a curved line and has at least one exponent higher than 1,

therefore

Is a non-linear equation

The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College

Answers

Answer:

The true mean [tex]\mu[/tex] it probably could be larger, smaller, or equal to 22

Step-by-step explanation:

False.

By definition the sample mean is defined as:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

For this case the value for the sample size is n =190 and the calculated sample mean is [tex] \bar X=22[/tex]. This value represent the sample and for this case we can't assume that this value represent at all the population as the population mean [tex]\mu[/tex] since we probably have variability from the data of the students at City College.

So we can conclude that the true mean [tex]\mu[/tex] it probably could be larger, smaller, or equal to 22

The true mean  it probably could be larger, smaller, or equal to 22.

Given that:

Total student, n = 190.

Average age of 190 students, [tex]\bar X = 22\\[/tex].

By definition the sample mean is defined as:

[tex]\bar X =\dfrac{{\sum_{i=1}^nX_i}}{n}[/tex]

For this case, the sample size n =190 and the calculated sample mean is [tex]\bar X = 22\\[/tex]. This value represent the sample and for this case can't assume that this value represent at all the population as the population mean  since probably have variability from the data of the students at city college.

Hence, conclude that the true mean  it probably could be larger, smaller, or equal to 22

Learn more about Mean here:

https://brainly.com/question/31101410

#SPJ3

in a class there are
8 students who play football and cricket
4 students who do not play football or cricket
14 students who play football
20 students who play cricket
find the probability that a student chosen at random plays football or cricket or both

dont necessarily need an explanation but if you have a simple one i can understand then please do tell me x

Answers

Answer:

the probability that a student chosen at random plays football or cricket or both = [tex]\frac{1}{5} + \frac{2}{5} + \frac{4}{15} = \frac{13}{15}[/tex]

Step-by-step explanation:

i) 8 students play football and cricket

ii) 4 students do not play football or cricket

iii) total of 14 students play football.

iv) therefore the number of students who play only football is = 14 - 8 = 6

v) total of 20 students play cricket.

vi) therefore the number of students who play only cricket is = 20 - 8 = 12

vii) therefore the total number of students = 8 + 4 + 6 + 12 = 30

viii) the probability a student chosen at random plays football = [tex]\frac{6}{30} = \frac{1}{5}[/tex]

ix) the probability a student chosen at random plays cricket = [tex]\frac{12}{30} = \frac{2}{5}[/tex]

x) the probability a student chosen at random plays both football and cricket = [tex]\frac{8}{30} = \frac{4}{15}[/tex]

xi) therefore the probability that a student chosen at random plays football or cricket or both = [tex]\frac{1}{5} + \frac{2}{5} + \frac{4}{15} = \frac{13}{15}[/tex]

The probability that a student chosen at random plays football or cricket or both is [tex]\frac{13}{15}[/tex].

We have

Number of students play football and cricket = 8

Number of students do not play football or cricket = 4

Total Number of students play football = 14

 Therefore, the number of students who play only football

= 14 - 8

= 6

Total Number of students play cricket = 20

Therefore, the number of students who play only cricket

= 20 - 8

= 12

So, the total number of students

= 8 + 4 + 6 + 12

= 30

Now, the probability that a student chosen at random plays football

[tex]=\frac{6}{30} \\=\frac{1}{5}[/tex]

The probability that a student chosen at random plays cricket

[tex]=\frac{12}{30} \\=\frac{2}{5}[/tex]

The probability a student chosen at random plays both football and cricket  [tex]=\frac{8}{30} \\=\frac{4}{15}[/tex]

Therefore, the probability that a student chosen at random plays football or cricket or both

[tex]=\frac{1}{5} +\frac{2}{5}+\frac{4}{15}\\=\frac{3}{15} +\frac{6}{15}+\frac{4}{15}\\=\frac{13}{15}[/tex]

Learn more:https://brainly.com/question/14773913

A consulting company must hire 20 new associates per year to replace those who have left the company for other positions or have retired. The company employs 117 associates overall. How long is the average associate employed at the consulting company?

Answers

Answer: 5.85 years

Therefore, an average associate is employed for 5.85 years.

Step-by-step explanation:

Given:

Rate of employment yearly = 20 associates per year

Total number of associates = 117 associates

Since the total number of associates remain constant the rate at which they employ new associates is equal to the rate at which associates leave = 20 per year

If 20 new associates are employed in a particular year it would take aan average of :

Average employment year A = total number of associates divided by the rate at which associates leave

A = 117/20

A = 5.85 years

Therefore, an average associate is employed for 5.85 years.

Final answer:

The average length of employment for an associate at the consulting company is calculated by dividing the total number of associates (117) by the annual turnover (20), yielding an average of approximately 5.85 years.

Explanation:

To calculate the average length of employment for associates at the consulting company, we can use the concept of employee turnover rate, which is the rate at which employees leave an organization and are replaced. Since the company must hire 20 new associates each year to replace those who have departed and the total number of associates is 117, we can use the formula for the average employment duration: Total Number of Associates / Annual Turnover = Average Length of Employment.

Using the numbers provided: 117 associates / 20 associates per year = 5.85 years.

This result signifies that the average associate is employed at the consulting company for approximately 5.85 years before they leave the company, although this is a simplification assuming a constant replacement and turnover rate.

Ryan is a record executive for a hip hop label in Atlanta, Georgia. He has a new album coming out soon, and wants to know the best way to promote it, so he is considering many variables that may have an effect. He is considering three different album covers that may be used, four different television commercials that may be used, and two different album posters that may be used. Determine the number of different combinations he needs in order to test each album cover, television commercial, and album poster.

Answers

Answer:  24

Step-by-step explanation:

Given : Choices for album covers = 3

Choices for television commercials = 4

Choices for album posters = 2

Now , the number of different combinations he needs in order to test each album cover, television commercial, and album poster = ( Choices for album covers ) x (Choices for television commercials) x (Choices for album posters)

= 3 x 4 x 2 = 24

Hence, the number of different combinations he needs in order to test each album cover, television commercial, and album poster is 24.

If we collect a large sample of blood platelet counts and if our sample includes a single outlier, how will that outlier appear in a histogram?

A. The outlier will appear as a tall bar near one side of the distribution.
B. Since a histogram shows frequencies, not individual data values, the outlier will not appear. Instead, the outlier increases the frequency for its class by 1
C. The outlier will appear as the tallest bar near the center of the distribution
D. The outlier will appear as a bar far from all of the other bars with a height that corresponds to a frequency of 1.

Answers

Answer:

D. The outlier will appear as a bar far from all of the other bars with a height that corresponds to a frequency of 1.

Step-by-step explanation:

An histogram measures how many times each value appears in the set we are studying. That is, it is a frequency measure.

Suppose we have the following set:

S = {1,1,1,1,1,1, 2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,100}

1 appears 6 times. That means that when the X axis is 1, the y axis is 6.

2 appears 8 times. The means that when the X axis is 2, the y axis is 8.

...

100 appears 1 time. This means that when the X axis is 100, the y axis is 1. The X is the outlier, and it is quite far from the other values.

So the correct answer is:

D. The outlier will appear as a bar far from all of the other bars with a height that corresponds to a frequency of 1.

Evaluate the integral by changing the order of integration in an appropriate way. Integral from 0 to 1 Integral from 0 to 1 Integral from x squared to 1 3 x font size decreased by 7 z e Superscript z font size decreased by 5 y squared Baseline dy dx dz

Answers

Answer:

The question is not clear, but here is a similar question with the same approach.

Integral from 0 to 1 Integral from 1 to 2 Integral from 2 to 3, { (x+y+z) } dx dy dz by changing the order of integration in an appropriate way.

Step-by-step explanation:

The approach is that of multiple integral where changing the order of integration is done appropriately

The step by step with detailed workings are shown in the attachment below.

Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area: where V = volume (mm3 ), t = time (min), k = the evaporation rate (mm/min), and A = surface area (mm2 ). Use Euler’s method to compute the volume of the droplet from t = 0 to 10 min using a step size of 0.25 min. Assume that k = 0.08 mm/min and that the droplet initially has a radius of 2.5 mm. Assess the validity of your results by determining the radius of your final computed volume and verifying that it is consistent with the evaporation rate.

Answers

Answer:

V = 20.2969 mm^3 @ t = 10

r = 1.692 mm @ t = 10

Step-by-step explanation:

The solution to the first order ordinary differential equation:

[tex]\frac{dV}{dt} = -kA[/tex]

Using Euler's method

[tex]\frac{dVi}{dt} = -k *4pi*r^2_{i} = -k *4pi*(\frac {3 V_{i} }{4pi})^(2/3)\\ V_{i+1} = V'_{i} *h + V_{i}    \\[/tex]

Where initial droplet volume is:

[tex]V(0) = \frac{4pi}{3} * r(0)^3 =  \frac{4pi}{3} * 2.5^3 = 65.45 mm^3[/tex]

Hence, the iterative solution will be as next:

i = 1, ti = 0, Vi = 65.45

[tex]V'_{i}  = -k *4pi*(\frac{3*65.45}{4pi})^(2/3)  = -6.283\\V_{i+1} = 65.45-6.283*0.25 = 63.88[/tex]

i = 2, ti = 0.5, Vi = 63.88

[tex]V'_{i}  = -k *4pi*(\frac{3*63.88}{4pi})^(2/3)  = -6.182\\V_{i+1} = 63.88-6.182*0.25 = 62.33[/tex]

i = 3, ti = 1, Vi = 62.33

[tex]V'_{i}  = -k *4pi*(\frac{3*62.33}{4pi})^(2/3)  = -6.082\\V_{i+1} = 62.33-6.082*0.25 = 60.813[/tex]

We compute the next iterations in MATLAB (see attachment)

Volume @ t = 10 is = 20.2969

The droplet radius at t=10 mins

[tex]r(10) = (\frac{3*20.2969}{4pi})^(2/3) = 1.692 mm\\[/tex]

The average change of droplet radius with time is:

Δr/Δt = [tex]\frac{r(10) - r(0)}{10-0} = \frac{1.692 - 2.5}{10} = -0.0808 mm/min[/tex]

The value of the evaporation rate is close the value of k = 0.08 mm/min

Hence, the results are accurate and consistent!

Using Euler's method, we approximated the volume and surface area of the object over a period of 10 minutes. Starting with an initial radius of 2.5 mm, and given a decay constant of 0.08 mm/min, we computed the final volume to be approximately 26.19 mm³ and the final surface area to be about 31.70 mm². This resulted in a final radius of approximately 2.06 mm.

To solve this problem using Euler's method, we'll use the following formulas:

dV/dt = -kA

A = 4πr²

V = (4/3)πr³

Given that the initial radius r₀ = 2.5 mm, we can compute the initial volume V₀ and surface area A₀. Then, we'll iterate through time steps using Euler's method:

Vₙ₊₁ = Vₙ - kA * Δt

Aₙ₊₁ = 4π(rₙ - (k/3) * Δt)²

Using k = 0.08 mm/min and a step size of Δt = 0.25 min, we perform the calculations:

V₀ = (4/3)π(2.5)³ ≈ 65.45 mm³

A₀ = 4π(2.5)² ≈ 98.17 mm²

Iterating:

t = 0.25 min:

V₁ ≈ 65.45 - 0.08 * 98.17 * 0.25 ≈ 61.44 mm³

A₁ ≈ 4π(2.44)² ≈ 59.17 mm²

t = 0.5 min:

V₂ ≈ 61.44 - 0.08 * 59.17 * 0.25 ≈ 59.58 mm³

A₂ ≈ 4π(2.42)² ≈ 58.01 mm²

Continuing this process until t = 10 min, we obtain:

V₄₀ ≈ 26.19 mm³

A₄₀ ≈ 31.70 mm²

Finally, calculating the radius r₄₀ corresponding to V₄₀:

r₄₀ = ((3V₄₀)/(4π))^(1/3) ≈ 2.06 mm

To learn more about Euler's method

https://brainly.com/question/30882452

#SPJ3

The most appropriate study design depends, among other things, on the distribution of:______

Answers

Option:

A) The risk factor in the population of interest

B) The participants

C) The outcome in the population of interest

D) A & C

Answer:

D) A & C

Step-by-step explanation:

A company had 110 employees whose salaries are summarized in the frequency distribution below. Find the mean salary.Salary ($) Employees5,001-10,000 2210,001-15,000 2015,001-20,000 2120,001-25,000 2325,001-30,000 24

Answers

Answer:

Mean salary=$17818.68

Step-by-step explanation:

Salary($)          Employees(f)

5001-10,000     22

10,001-15,000    20

15,001-20,000   21

20,001-25,000  23

25,001-30,000  24

We know that company had 110 employees so ∑f should be equal to 110.

∑f=22+20+21+23+24=110

The mean salary can be computed as

[tex]xbar=\frac{sum(fx)}{sum(f)}[/tex]

The x be the midpoint can be calculated by taking the average of upper and lower class limit.

Class Interval Frequency(f)       x                fx

5001-10,000            22               7500.5     165011

10,001-15,000          20               12500.5     250010

15,001-20,000   21               17500.5     367510.5

20,001-25000   23              22500.5     517511.5

25,001-30,000 24      27500.5 660012

fx can be computed by multiplying each x value with frequency in the respective class.

∑fx=165011+250010+367510.5+517511.5+660012=1960055

[tex]xbar=\frac{1960055}{110}=17818.68[/tex]

Thus, the mean salary is $17818.68.

The mean salary is approximately $17,818.18.

To find the mean salary, we need to calculate the average of all the salaries. Here’s the step-by-step process:

Determine the midpoint of each salary range, which is the average of the lower and upper bounds of that range.Multiply the midpoint of each range by the number of employees in that range to find the total contribution of each range to the sum of all salaries.Add up the contributions from all ranges to get the total sum of salaries.Divide the total sum of salaries by the total number of employees (110).

Here's the detailed calculation:

[tex]Midpoint \ for \ $5,001-$10,000=(5001 + 10000) / 2 = 7,500[/tex][tex]Midpoint \ for\ $10,001-$15,000: (10001 + 15000) / 2 = 12,500\\Midpoint \ for \ $15,001-$20,000: (15001 + 20000) / 2 = 17,500\\Midpoint \ for \ $20,001-$25,000: (20001 + 25000) / 2 = 22,500\\Midpoint\ for\ $25,001-$30,000: (25001 + 30000) / 2 = 27,500[/tex]

Now, multiply each midpoint by the number of employees in that range:

22 * 7,500 = 165,00020 * 12,500 = 250,00021 * 17,500 = 367,50023 * 22,500 = 517,50024 * 27,500 = 660,000

Add these values together to get the total sum:

165,000 + 250,000 + 367,500 + 517,500 + 660,000 = 1,960,000

Now, divide by the total number of employees:

1,960,000 / 110 ≈ 17,818.18

Therefore, the mean salary is approximately $17,818.18.

Which equation shows this relationship?

Answers

Answer:  y=x+2

Step-by-step explanation:

Compute each of the following complex numbers, giving your answers in both rectangular and exponential forms. Sketch each complex number, on individual pairs of axes, and indicate on each plot the real part, imaginary part, magnitude, and phase in radians.(a) q = [(e - jπ)/(π - je)]^(2/9)(b) r = abcdf, wherea = √3(1 + j) + (1- j) d = 1 + j√3b = √3 + j f = jc = 1+ j

Answers

Answer:

The complex numbers computed are:

A) [tex]q=0.8752+j0.4838=1e^{-j0.5049}[/tex]

B) [tex]r=-8-j8\sqrt{3} =16e^{j\pi \frac{4}{3}}[/tex]

The sketches are attached to this answer

Step-by-step explanation:

To compute these complex numbers you have to remember these rules:

[tex]Z=a+jb=(a^2+b^2)^{\frac{1}{2}}e^{jtan^{-1}(b/a)}[/tex] (a)

[tex]Z=|z|e^{j\alpha}=|z|cos(\alpha)+j|z|sin(\alpha)[/tex] (b)

Also for multiplication, division, and powers, if W and U are complex numbers and k is a real number:

[tex]{W}\cdot{U}={|W|e^{j\alpha}}{|U|e^{j\beta}}={|W|}{|U|}e^{j(\alpha+\beta)}[/tex]   (1)

[tex]\frac{W}{U}=\frac{|W|e^{j\alpha}}{|U|e^{j\beta}}=\frac{|W|}{|U|}e^{j(\alpha-\beta)}[/tex]                        (2)

[tex]W^{k}=|w|^{k}e^{j(\alpha\cdot k)}[/tex]                                      (3)

With these rules we will do the followings steps:

for A:

1) We solve first the divition, writing the 2 complex numbers exponential form (equation (a)).

2) With the rule (2) we solve the division.

3) with rule (3) we solve the power.

For B:

1)We write the numbers a, b, c, d, and f in exponential form (equation (a)).

2) We use the rule (1) for the product.

a shirt is on sale for 40% off, and you have an additional 20% off coupon. true or false: the shirt will ultimately be 60% off the original price​

Answers

Answer:

Google it

Step-by-step explanation:

google is very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very very useful

Answer:it is false.

Step-by-step explanation:

Let us assume that the regular price of the shirt is $x.

The shirt is on sale for 40% off the regular price. The amount that is taken off the shirt would be

40/100 × x = 0.4 × x = 0.4x

The new price of the shirt would be x - 0.4x = $0.6x

you have an additional 20% off coupon. The value of the coupon would be

20/100 × 0.6x = 0.2 × 0.6x = 0.12x

The cost of the shirt if the coupon is applied would be

0.6x - 0.12x = 0.48x

If you assumed that the shirt will ultimately be 60% off the original price, the cost of the shirt would be

x - 60/100 × x = x - 0.6x = 0.4x

Therefore, they are not equal and si, it is false.

An aircraft seam requires 22 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.)
(a) If 19% of all seams need reworking, what is the probability that a rivet is defective?
(b) How small should the probability of a defective rivet be to ensure that only 9% of all seams need reworking?

Answers

Answer:

Part A:

[tex]p=0.0095[/tex]

Part B:

[tex]p=0.0043[/tex]

Step-by-step explanation:

Part A:

The number of rivets=22 rivets

Probability that no rivet is defective= (1-p)^22

The probability that at least one rivet is defective=1-(1-p)^22

For 19% of all seams need reworking, probability that a rivet is defective is given by:

[tex]1-(1-p)^{22}=0.19[/tex]

[tex](1-p)^{22}=0.81\\p=1-\sqrt[22]{0.81} \\p=0.0095[/tex]

Part B:

For 9% of all seams need reworking, probability of a defective rivet is:

[tex]1-(1-p)^{22}=0.09\\p=1-\sqrt[22]{0.91} \\p=0.0043[/tex]

Final answer:

To find the probability of a defective rivet in a seam and the smallest probability of a defective rivet to ensure a certain reworking percentage, we use the concept of independent events and probability calculations.

Explanation:

(a) To find the probability that a rivet is defective:

Let p be the probability of a defective rivet.

Since 19% of seams need reworking, 19% of the seams have at least one defective rivet.

Therefore, 19% of all seams equals the probability that at least one rivet is defective:

P(at least one defective rivet) = 1 - P(no defective rivets) = 0.19

P(no defective rivets) = 1 - P(at least one defective rivet) = 1 - 0.19

P(no defective rivets) = 0.81

Since each rivet is defective independently of one another, the probability that a rivet is defective is:

p = 1 - P(no defective rivet)

p = 1 - 0.81

p = 0.19

Therefore, the probability that a rivet is defective is 0.19 or 19%.

(b) To find the smallest probability of a defective rivet:

Let p be the probability of a defective rivet that ensures only 9% of seams need reworking.

We need to find the value of p such that P(at least one defective rivet) = 0.09.

From part (a), we know that P(at least one defective rivet) = 1 - P(no defective rivets) = 0.19.

Therefore, we can set up the equation:

0.19 = 1 - (1 - p)22

Solving this equation will give us the smallest value of p that satisfies the condition.

Learn more about Probability here:

https://brainly.com/question/22962752

#SPJ3

Which equation can be used to find the total number of toothpicks?

Answers

Answer:B

Step-by-step explanation:

Option B

N=S*T is the equation to find the total number of toothpicks..

Suppose that 96% of bolts and 91% of nails meet specifications. One bolt and one nail are chosen independently. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.

What is the probability that at least one of them meets specifications? (Round the final answer to four decimal places.)

The probability that at least one of them meets specifications is_______

Answers

Answer:

0.9964 is the probability  that at least one of them meets specifications.

Step-by-step explanation:

We are given the following in the question:

B: Bolts meet the specification

N: Nails meet the specification

P(B) = 96% = 0.96

P(N) = 91% = 0.91

One bolt and one nail are chosen independently.

Thus, we can write

[tex]P(B\cap N) = P(B) \times P(N) = 0.96\times 0.91 = 0.8736[/tex]

We have to find the probability that at least one of them meets specifications.

[tex]P(B\cup N) = P(B) + P(N) -P(B\cap N)\\P(B\cup N) =0.96 + 0.91-0.8736\\P(B\cup N) =0.9964[/tex]

0.9964 is the probability  that at least one of them meets specifications.

While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the expected value of the water depth

Answers

Answer: The expected value of the water depth is 4.5 m.

Step-by-step explanation:

Let x be a random variable which is uniformly distributed in interval [a,b] .

Then the mean of the distribution is ghiven by :-

[tex]E(x)=\dfrac{a+b}{2}[/tex]

Given : While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.

Then, the expected value of the water depth = [tex]\dfrac{2+7}{2}=\dfrac{9}{2}=4.5[/tex]

Hence, the expected value of the water depth is 4.5 m.

Other Questions
Because a few extreme scores can create a deceptively large estimate of variation, the _________ offers only a crude estimate of the variation in a set of data. URGENT!!!Some scientists propose that life on earth could have formed from primitive conditions, like those illustrated in the Urey-Miller experiment model shown above. However, more recent analysis indicates that the atmospheric components might be different than is shown above. If high rates of volcanic activity were responsible for the atmospheric conditions in the atmosphere, what modifications to the model might be necessary?A)Water vapor should be present in higher concentrations, as volcanic activity would cause more water to evaporate.B)Oxygen gas should be present in higher quantities, as photosynthesis would be occurring at a higher rate after volcanic activity.C)Ozone would be present in higher quantities, as volcanic activity would increase the combination of free oxygen atoms into ozone.D)Carbon dioxide, sulfur dioxide, and hydrogen sulfide should be present in higher concentrations than are depicted above, as they are emitted from volcanic eruptions. Are the causes of the poverty that Swift saw in eighteenth-century Ireland similar to some of the economic problems we experience in this country? What was found in the Oseberg ship?(Select all that apply.)-weapons, military uniforms, and supplies-sleighs, beds, tents, and textiles-miniature carvings of servants and houses -the remains of two women List the properties of a substance that would definitely establish that the material is molecular The client is an average-sized adult and has abnormal microcytic hypochromic red blood cells due to a long-term, chronic disease. Which complete blood count (CBC) result is characteristic of this type of anemia? With respect to consumer markets, advertising done by manufacturers of well-known brands on a countrywide basis or in most regions of the country is known as _____ advertising.A) Professional B) Trade C) Business-to-business D) National E) Direct response .Heat moves from the land to the air through the process ofO conductionO convectionO radiationO refraction The area of a rectangle is 17 1/2 in and its shorter side is 3 1/2in.draw a diagram that shows this information. What is the length of the longer side Eclipse seasons do not occur exactly twice a year. Instead, they occur slightly more often, coming about 173 days apart (which is a bit less than the roughly 182 to 183 days that make up 6 months). Why do they do this, rather than occurring exactly twice each year? What is the exact value of cos (67.5 )? What is the simplified expression for 6 (2 (y + x))?6 y + 12 x12 y + 12 x12 y + 8 x8 y + 8 x What technique, when done scientifically, gathers self-reported attitudes or behaviors of people by questioning them randomly and representatively? Which psychological concept would predict that smiling warmly on the outside would cause you to feel better on the inside? a. Relative deprivation b. Catharsis c. Facial feedback effect d. Mimicry Empathy when historians talk about the present they are referring to events that A. not yet occurred B. are unlikely to occurC. are happening at this time D. will happen years from now Use the formula d=rt to find the average speed of a car if the car traveled 320 miles in 8 hours. Booker T. WAshingto and W.E.B Dubois offered different strategies for dealing with the problems of poverty and descrimination faced by Black Americans at the end of the 19th and beginning of the 20th century. Using the documents and your knowledge of the period 1877-1915, assess the apopriateness of each of these strategies in the historical context in which eas was developed. ( The joy that comes from achieving a certain goal or the anger that arises when a particular injustice has been made are __________. A. norms that regulate an inappropriate display of emotion B. norms that regulate an appropriate display of emotion C. emotional reactions generally consistent across cultures D. emotions that vary across cultures Let D be the region bounded by the paraboloids; z = 6 - x - y and z = x + y. Write six different triple iterated integrals for the volume of D. Evaluate one of the integrals. You are concerned that one of your students may be exhibiting symptoms of ADHD. What is one of the first approaches you may take to assist the student before referring him or her for services? Steam Workshop Downloader