Answer:
Step-by-step explanation:
Hello!
To study time perception, 8 students measured one minute (counted to 60), the given data show the actual time (in seconds) it took each student to measure one minute:
53, 52, 75, 62, 68, 58, 49, 49
8 observations make this sample, n=8
You can summarize the observed data using descriptive statistics:
Central tendency measures:
Median (Me):
The median is the value that separates the sample in a half ( the bottom 50% from the top 50%). To calculate it you have to calculate its position:
(for even samples) PosMe: n/2= 8/2= 4
Then you arrange the data from least to greatest and identify the 4th value:
49, 49, 52, 53, 58, 62, 68, 75
Me= 53s
Mode (Md):
The mode is the most observed value, i.e. the value with the most absolute frequency:
In this data set, the only value that was observed more than once is 49, so that is the value of the mode
Md= 49s
Mean (X[bar]):
Is the average or expected value of the data set, it is always within the range of definition of the variable but it doesn't necessarily correspond to and observation. You calculate it as:
X[bar]= ∑X/n= (53+52+75+62+68+58+49+49)/8= 466/8= 58.25s
Measures of dispersion:
Range (R):
The is the difference between the minimum and maximum observations of the sample.
R= max - min = 75 - 49= 26s
Standard deviation (S):
It shows the variability between the values of the sample. A low standard deviation tells that the observations are close to the meanwhile a high standard deviation show that the values are further away from the mean.
∑X= 466
∑X²= 27772
[tex]S= \sqrt{(\frac{1}{n-1})[sumX^2-\frac{(sumX)^2}{n} ]= \sqrt{(\frac{1}{7} )[27772-\frac{(466)^2}{8} ]} = \sqrt{\frac{1255}{14} } = 9.47s[/tex]
S= 9.47s
I hope this helps!
Which is the unit rate if 4 tuna cans are sold for $6
Answer:
$1.50 per can
Step-by-step explanation:
6/4 = 1.5
to check your answer, do 1.50*4, and you get $6
hope this helps :)
Answer:
The unit rate is $1.50 per can.
Step-by-step explanation:
Price: $6
Number of Cans Purchased at This Price: 4
$6/4 cans=$1.50 per can
The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as
ere'o - 10
and is the least intense sound a human ear can hear. What is the approximate loudness of a
dinner conversation with a sound intensity of 10-7?
O -58 Db
O -50 Db
O 9 Db
O 50 Db
Answer:
[tex]I_o = 10^{-12} \frac{W}{m^2}[/tex] represent the minimum audible intensity by the humans
[tex] I= 10^{-7} \frac{W}{m^2}[/tex] represent the intensity for the dinner conversation
And replacing this into the formula we got:
[tex] dB = 10 log_{10} (\frac{10^{-7}}{10^{-12}})= 10 log_{10} (100000) = 50 dB[/tex]
So then the best answer for this case would be:
O 50 Db
Step-by-step explanation:
For this case we can use the following equation for decibels:
[tex] dB = 10 log_{10} (\frac{I}{I_o})[/tex]
Where:
[tex]I_o = 10^{-12} \frac{W}{m^2}[/tex] represent the minimum audible intensity by the humans
[tex] I= 10^{-7} \frac{W}{m^2}[/tex] represent the intensity for the dinner conversation
And replacing this into the formula we got:
[tex] dB = 10 log_{10} (\frac{10^{-7}}{10^{-12}})= 10 log_{10} (100000) = 50 dB[/tex]
So then the best answer for this case would be:
O 50 Db
The approximate loudness of a dinner conversation with a sound intensity of 10^-7 is -50Db
Logarithm functionsGiven the general expression for calculating the loudness, L, measured in decibels (Db), of sound intensity, I as:
L = 10log(I0/I)
Given the following parameters
I0 = 10^-12 Wb/m²
I = 10^-7 Wb/m²
Substitute
L = 10log(10^-12/10^-7)
L = 10log(10^-5)
L = -5(10)log10
L = -50Db
Hence the approximate loudness of a dinner conversation with a sound intensity of 10^-7 is -50Db
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The large exhibit at the aquarium has a viewing window that is 22 feet long 58.25 feet high and 13 inches thick estimate its volume in cubic feet remember remember 12 inches equal 1 foot
Answer:
Step-by-step explanation: convert feet to inches then multiply all 3 numbers. 264 x 699x13 = 2398968. Then decide that by 12 the amount of inches in a foot and get 199,914 ft^3
Suppose Julio is a veterinarian who is doing research into the weight of domestic cats in his city. He collects information on 174 cats and finds the mean weight for cats in his sample is 10.75 lb with a standard deviation of 4.30 lb. What is the estimate of the standard error of the mean (SE)
Answer:
The standard error of the mean (SE) is of 0.326lb.
Step-by-step explanation:
The standard error of the mean is given by the following formula:
[tex]SE = \frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
In this problem, we have that:
[tex]s = 4.3, n = 174[/tex]
Then
[tex]SE = \frac{s}{\sqrt{n}} = \frac{4.3}{\sqrt{174}} = 0.326[/tex]
The standard error of the mean (SE) is of 0.326lb.
Suppose seven pairs of similar-looking boots are thrown together in a pile. What is the minimum number of individual boots that you must pick to be sure of getting a matched pair? Why?Since there are 7 pairs of boots in the pile, if at most one boot is chosen from each pair, the maximum number of boots chosen would be . It follows that if a minimum of Incorrect: Your answer is incorrect. boots are chosen, at least two must be from the same pair.
Answer:
We must pick at least 8 individual boots to be sure of picking at least one matching pair as explained from the pigeon hole principle.
Step-by-step explanation:
From pigeonhole principle, if k is a positive integer and k + 1 or more objects are placed into k boxes, then there is at least one box containing 2 or more objects.
Now, since we have 7 pairs of similar looking boots, thus, number of single boots we have will be;
Number of single boots = 7 x 2 = 14
Now, if we select 7 boots from the 14,then there's a possibility of selecting exactly 1 from each pair. Thus, we will not get a matching pair.
Whereas if we select 8 boots from the 14 single boots, then by the pigeon hole principle, at least 2 of the boots will need to be from the same pair. Hence we can pick at least 8 individual boots to be sure of picking at least one matching pair.
To ensure getting a matched pair from a pile of 7 pairs of boots, you would need to pick eight individual boots. This is based on the counting principle in mathematics where in the worst-case scenario, each boot you pick could be from a different pair.
Explanation:The question is about probability and counting principles in mathematics, specifically about how to identify a matched pair of boots from a pile of similar looking pairs. In the pile, there are seven pairs of boots, which means there are 14 individual boots from seven different pairs.
Now, if you randomly pick one boot, it could be from any pair. If you pick a second boot, it could also be from any pair, including the same pair as the first one. But to be sure that you get a matched pair, you will have to pick up eight boots. This is because, in the worst-case scenario, you might pick seven different boots each from a different pair. Once you pick the eighth boot, it is guaranteed to match one of the earlier seven because there are only seven pairs.
The minimum number of individual boots that you must pick to be sure of getting a matched pair is eight.
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What is the height of the following triangle if the area is 60 square meters? Do not round your answer.
Answer:
The height of the triangle, h, is 8 m
Step-by-step explanation:
The formula for the area of a triangle of base b and height h is A = (1/2)(b)(h).
Here b = 15 m and A = 60 m^2. We want the measure of the height, h.
First we solve the area equation (above) for h: 2A = bh, or h = 2A/b,
and then substitute the given values for b and A:
2(60 m^2)
h = ------------------ = 8 m
15 m
The height of the triangle, h, is 8 m
Answer:
Answer is 8 because I did the quiz on my online school.
Hope it helps
Given the graph of a system of equations, which
statements are true about the solution? Check all that
apply.
V
The x-value is an integer.
2
The x-value is between 3 and 4.
-4
2.
2
The y-value is between-2 and -1.
The x-value is positive.
The x- and y-values have the same sign.
-2
-4
Answer:
B. The x-value is between 3 and 4.
C. The y-value is between –2 and –1.
D. The x-value is positive.
Step-by-step explanation:
I did the Assignment on Edg.
The true options are: The x-value is between 3 and 4, the y-value is between –2 and –1 and the x-value is positive.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
From the graph, we have the following highlights
The point of intersection of the two lines is in the fourth quadrant.
The value of x is between 3 and 4.
The value of y is between -1 and -2.
x is positive, and y is negative.
x is not an integer.
x is between 3 and 4, while y is between -1 and -2
Hence, the true options are: The x-value is between 3 and 4.
the y-value is between –2 and –1 and the x-value is positive.
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Theme park spending In a random sample of 40 visitors to a certain theme park, it was determined that the mean amount of money spent per person at the park (including ticket price) was $93.43 per day with a standard deviation of $15. Construct and interpret a 99% confidence interval for the mean amount spent daily per person at the theme park.
Answer:
The 99% confidence interval for the mean amount spent daily per person at the theme park is between $52.81 and $134.05.
This means that we are 99% sure that the true mean amount spent daily per person at the theme park is between $52.81 and $134.05.
Step-by-step explanation:
We have the sample standard deviation, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 40 - 1 = 39
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 39 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.7079
The margin of error is:
M = T*s = 2.7079*15 = 40.62
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 93.43 - 40.62 = $52.81.
The upper end of the interval is the sample mean added to M. So it is 93.43 + 40.62 = $134.05
The 99% confidence interval for the mean amount spent daily per person at the theme park is between $52.81 and $134.05.
This means that we are 99% sure that the true mean amount spent daily per person at the theme park is between $52.81 and $134.05.
Dean mixed together different kind of nuts as a snack. There were 9 nuts in the bowl, 7 of
which were hazelnuts.
If Dean randomly chose to eat 6 of the nuts, what is the probability that all of them are
hazelnuts?
Write your answer as a decimal rounded to four decimal places.
Answer:
0.0833
Step-by-step explanation:
There are 7C6 = 7 ways to choose 6 hazelnuts from the 7 present.
There are 9C6 = 84 ways to choose 6 nuts from the 9 present.
The probability of choosing 6 hazelnuts from the 9 present is ...
7/84 = 1/12 = 0.0833...(repeating)
The probability of interest is 0.0833.
____
Comment on the notation
The notation nCk means n!/(k!(n-k)!). It is the number of ways k items can be chosen from n items without regard to order. It can be pronounced "n choose k."
Como podríamos saber cuantos camellos le corresponden a cada hermano en realidad
Answer:
Eldest brother = 18 camels
2nd brother = 12 camels
Youngest brother = 4 camels
Step-by-step explanation:
Question posted:
How could we know how many camels actually correspond to each brother?
It is from "the man who calculated":
The question is incomplete without the background information.
Based on the question, It has to do with sharing an inheritance of 35 camels among 3 brothers.
"The man who calculated", by Malba Tahan.
Since the complete question isn't available, we are going to look at the following question to understand how to do the calculation.
Question:
How can an inheritance of 35 camels be divided among three brothers in such a way that the eldest brother gets half of them, the second one gets 1/3 of the total and the youngest brother gets 1/9 of the total camels?
Solution:
Total number of camels= 35
Eldest brother gets half: 1/2 of 35 gives a fraction and not an whole number
2nd brother = 1/3 of 35 (gives a fraction)
3rd brother = 1/9 of 35 (gives a fraction)
Since we can't have a camel in fraction except in whole number, we would look for the closest number to 35 that would be divided by 2, 3 and 9 respectively without giving a fraction.
Number 36 is the closest number to 35 that satisfies this condition.
1st brother = 1/2 × 36 = 18 camels
2nd brother = 1/3 × 36 = 12 camels
3rd brother = 1/9 × 36 = 4 camels
Now let's add the camels the 3 brother got together = 18 + 12 + 4 = 34 camels
Total camels - amount shared = 35 -34 = 1
Meaning one camel is remaining. The distributor would keep the remaining one as that's the way such distributions could be achieved.
A researcher is studying the monthly gross incomes of drivers for a ride sharing company. (Gross incomes represent the amount paid to drivers before accounting for the costs associated with driving.) The researcher obtains a list of all the drivers in San Francisco and randomly selects 200 of them to contact. The list of incomes in the sample has an average of $800 per month, with an SD of $1000. (a) Does the histogram of the sample incomes follow the normal curve? Explain why or why not.
Answer:
The histogram of the sample incomes will follow the normal curve.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
In this case the researches wants to determine the monthly gross incomes of drivers for a ride sharing company.
He selects a sample of n = 200 drivers and ask them their monthly salary.
As the sample selected is quite large, i.e. n = 200 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the Normal distribution.
Thus, the histogram of the sample incomes will follow the normal curve.
-)) In a right triangle, a and b are the lengths of the legs and c is the length of the
hypotenuse. If b = 5.4 millimeters and c = 8.3 millimeters, what is a? If necessary, round to
the nearest tenth
Answer:
a = 6.3mm
Step-by-step explanation:
Use Pythagoras theorem here
[tex]a^{2} + b^{2} = c^{2}[/tex]
Rearrange for a by subtracting [tex]b^{2}[/tex] from both sides of the equation
[tex]a^{2} + b^{2} -b^{2} = c^{2} -b^{2}[/tex]
Simplify
[tex]a^{2} = c^{2} -b^{2}[/tex]
Substitute in our numbers and solve for a
[tex]a^{2}[/tex] = [tex]8.3^{2} - 5.4^{2}[/tex]
[tex]a^{2}[/tex] = 68.89 - 29.16
[tex]a^{2}[/tex] = 39.73
a = [tex]\sqrt{39.73}[/tex]
a = 6.3mm
Final answer:
To find the length of leg a when b = 5.4 mm and c = 8.3 mm in a right triangle, we use the Pythagorean theorem a^2 + b^2 = c^2. We solve for a, yielding a ≈ 6.3 mm (rounded to the nearest tenth).
Explanation:
The student is asking how to find the length of leg a in a right triangle where the lengths of leg b and the hypotenuse c are given. Since b = 5.4 millimeters and c = 8.3 millimeters, we can use the Pythagorean theorem to find leg a.
First, we'll apply the theorem: a2 + b2 = c2. To solve for a, we rearrange it: a2 = c2 - b2.
Substitute the given values:
a2 = c2 - b2
= 8.32 - 5.42
= 68.89 - 29.16
= 39.73
Now, we take the square root of both sides to find a:
a =
√39.73
≈ 6.3 millimeters (rounded to the nearest tenth)
Therefore, the length of leg a is approximately 6.3 millimeters.
Question 1
State the value of the discriminant for y = x2 – 8x + 10.
a) 10.2
b) 4.9
c) 104
d) 24
Answer:
D = 24
Step-by-step explanation:
The given quadratic equation is [tex]y=x^2-8x+10[/tex].
It is required to find the value of the discriminant. The value of discriminant of any quadratic equation is given by :
[tex]D=b^2-4ac[/tex]
Here, a = 1, b = -8 and c = 10
On plugging all the values, we get :
[tex]D=(-8)^2-4\times 1\times 10\\\\D=24[/tex]
So, the value of discriminant for y is 24.
The domain of the following relation R {(6, −2), (1, 2), (−3, −4), (−3, 2)} is (1 point)
Answer:
Domain: { -3,1,6}
Step-by-step explanation:
The domain is the input values
Domain: { 6,1,-3,-3}
We usually put them in numerical order and we do not list the same value twice
Domain: { -3,1,6}
I need help asap !!! please !!!
Answer:
2^-84
Step-by-step explanation:
First simplify inside the parentheses
2^-10 / 4^2
Rewriting 4 as 2^2
2^-10 / 4^2^2
We know that a^b^c = a^(b*c)
2^-10 / 2^(2*2) = 2^-10 / 2^4
We know that a^b / a^c = a^(b-c)
2^-10 / 2^4 = 2^(-10-4) = 2^-14
Replace the term in side the parentheses with 2^-14
2^-14 ^7
We know that a^b^c = a^(b*c)
2^(-14*7)
2^-84
Triangle D E F. Side D F is 6 inches, side F E is 10 inches, and side E D is question mark.
Which could be a possible length of side DE?
2 in.
3 in.
7 in.
16 in.
Answer:
7
Step-by-step explanation:
THe Triangle Inequality Theorem states that the sum of the two least sides of a triangle must be greater than the third side. In this case, 2 and 6 are less than 10, 3 and 6 are less than 10, 6 and 10 are greater than 16, so the only number left is 7. The sum of seven and six is greater than ten so seven would be the correct answer.
Question:
Triangle D E F. Side D F is 6 inches, side F E is 10 inches, and side E D is question mark.
Which could be a possible length of side DE?
2 in.
3 in.
7 in.
Answer:
C.) 7 in.
Step-by-step explanation:
To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c. Remember the formula for finding the perimeter of a triangle. For a triangle with sides a, b and c, the perimeter P is defined as: P = a + b + c. What this formula means in simpler terms is that to find the perimeter of a triangle, you just add together the lengths of each of its 3 sides. Since all the three sides of the triangle are of equal length, we can find the perimeter by multiplying the length of each side by 3. 20 + 20 + 20 = 3 × 20 = 60 cm. Thus, the perimeter of an equilateral triangle is 3 times the length of each side. Area of a two-dimensional shape is the space occupied by the shape.
Have a Nice day! <3
If "f" varies directly with "m," and f=-19 when m=14, what is "f" when m=2?if
Answer:-19/7
Step-by-step explanation:
f varies directly as m
f=k x m
When f=-19,m=14
-19=k x 14
k=-19/14
Relationship is f=-19m/14
When m is 2
f=(-19x2) ➗ 14
f=-38 ➗ 14
f=-19/7
Which expression shows 20% of 60! Please give the right answer tryna pass
Answer:
1/5 - 60 or b
Step-by-step explanation:
The expression that shows 20% of 60 is 1/5 * 60
How to determine the correct expression?The expression is given as:
20% of 60
Express of as *
20% * 60
Express the percentage as fraction
20/100 * 60
Simplify the fraction
1/5 * 60
Hence, the expression that shows 20% of 60 is 1/5 * 60
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Pls help me Idk what to do
Answer:
6
Step-by-step explanation:
The line in the middle of the box is the median
Which of the following is the correct interpretation of the p-value? A. The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is no difference in the mean number of partners. B. The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is a difference in the mean number of partners. C. The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is no difference in the sample mean number of partners. D. The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is a difference in the sample mean number of partners.
Answer:
The correct option is (A).
Step-by-step explanation:
The p-value is well defined as the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.
From the provided options we can guess that the hypothesis was defined as follows:
H₀: There is no difference in the mean number of partners, i.e. μ₁ - μ₂ = 0.
Hₐ: There is difference in the mean number of partners, i.e. μ₁ - μ₂ ≠ 0.
The test is two tailed mean difference test.
A z-test or a t-test can be used to conclude the result.
In this case the p-value can be defined as the probability of obtaining a test statistic value equal to or more extreme that the results obtained from the sample, when the difference between the mean number of partners is 0.
Thus, the correct interpretation of the p-value is provided by statement (A).
The p-value represents the likelihood of obtaining a test statistic as extreme as our observed data, assuming the null hypothesis is true. The null hypothesis usually posits there's no difference or effect. A small p-value would suggest rejecting the null hypothesis in favor of the alternative hypothesis, indicating a significant effect or difference.
Explanation:The correct interpretation of the p-value is: The p-value is the probability of getting a test statistic equal to or more extreme than the sample result if there is no difference in the mean number of partners.
In other words, the p-value measures how likely you are to get the observed data if the null hypothesis is true. The null hypothesis typically represents a theory that there is no effect or no difference between the groups you're comparing. Hence, if there's no difference in the mean number of partners (which is our null hypothesis here), then the p-value tells how likely we are to observe a test statistic as extreme as our sample result.
For example, if the p-value is very small, it might be less than our significance level (commonly 0.05 or 5%). In such a case, we have evidence to reject our null hypothesis in favor of the alternative hypothesis. The alternative hypothesis generally represents a theory that there is an effect or a difference between the groups. So, in this case, a small p-value would indicate a statistically significant difference in the mean number of partners.
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Suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $20. The population standard deviation is $5. What is the probability that a sample of 100 steady smokers spend between $19 and $21
Answer:
95.44% probability that a sample of 100 steady smokers spend between $19 and $21
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 20, \sigma = 5, n = 100, s = \frac{5}{\sqrt{100}} = 0.5[/tex]
What is the probability that a sample of 100 steady smokers spend between $19 and $21
This is the pvalue of Z when X = 21 subtracted by the pvalue of Z when X = 19. So
X = 21
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{21 - 20}{0.5}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 19
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{19 - 20}{0.5}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
95.44% probability that a sample of 100 steady smokers spend between $19 and $21
To find the probability that a sample of 100 steady smokers spend between $19 and $21, calculate the Z-score and use a standard normal distribution table or calculator. The probability is approximately 0.3413.
Explanation:To find the probability that a sample of 100 steady smokers spend between $19 and $21, we can use the Z-score formula. The Z-score is calculated as the difference between the sample mean and the desired value (in this case, $20), divided by the population standard deviation, multiplied by the square root of the sample size.
Z = (x - μ) / (σ / √n)
Plugging in the values we have:
Z = (21 - 20) / (5 / √100) = 1
We can then use a standard normal distribution table or a calculator to find the probability associated with a Z-score of 1. The probability of obtaining a Z-score of 1 or less is approximately 0.8413. Since we want the probability between $19 and $21, we subtract the probability of getting a Z-score of less than 1 from the probability of getting a Z-score of less than or equal to 0. This gives us:
Probability = 0.8413 - 0.5000 = 0.3413
Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 43.8 months and a standard deviation of 6.5 months.
(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace?
(b) If quick Start does not want to make refunds for more than 10% of its batteries under the full refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
Answer:
a) The company should expect to replace 11.51% of its batteries.
b) 35 months.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 43.8, \sigma = 6.5[/tex]
(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace?
This is the pvalue of Z when X = 36. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{36 - 43.8}{6.5}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a pvalue of 0.1151.
The company should expect to replace 11.51% of its batteries.
(b) If quick Start does not want to make refunds for more than 10% of its batteries under the full refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
The warranty should be the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 43.8}{6.5}[/tex]
[tex]X - 43.8 = -1.28*6.5[/tex]
[tex]X = 35.48[/tex]
To the nearest month, 35 months.
Final answer:
To calculate the percentage of batteries that will be expected to be replaced within the 36-month period, we need to find the area under the normal distribution curve from 0 to 36.
Explanation:
In this question, we are given information about the average life of a Quick Start car battery, which follows a normal distribution with a mean of 43.8 months and a standard deviation of 6.5 months.
(a) To calculate the percentage of batteries that will be expected to be replaced within the 36-month period, we need to find the area under the normal distribution curve from 0 to 36. We can use the z-score formula to standardize the value of 36 and then use a standard normal distribution table to find the corresponding area. The percentage of batteries that will be expected to be replaced is the same as the percentage of batteries that fall within the range of 0 to 36 months.
Subtract the mean from 36: 36 - 43.8 = -7.8Divide the result by the standard deviation: -7.8 / 6.5 = -1.2Using the z-score -1.2, find the corresponding area under the standard normal distribution curve using a standard normal distribution table or a calculator with standard normal distribution capabilities.You are in an airplane 5.7 miles above the ground. What is the measure of BD⌢
the portion of Earth that you can see? Round your answer to the nearest tenth. (Earth's radius is approximately 4000 miles.)
The measure of the portion of Earth that can be seen from an airplane 5.7 miles above the ground is approximately 0.163 degrees, when rounded to the nearest tenth. This is found using the formula for the angle subtended by an arc, and then converting from radians to degrees.
Explanation:To solve this problem, we can use the properties of a circle, since the Earth is approximately spherical in shape. The formula to calculate the angle subtended by an arc (BD⌢) on the Earth's surface is as follows: θ = 2 * arcsin((distance_to_object)/(2 * radius_of_earth)).
So inserting the given values:
The distance to the airplane is 5.7 miles above groundThe Earth's radius is roughly 4000 milesWe get: θ = 2 * arcsin((5.7)/(2 * 4000)). This will give you an answer in radians, to convert this to degrees multiply by 180/π. In this case, the answer is approximately 0.163 degrees, rounded to the nearest tenth.
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Problem 3: Sampling methods
Willy wants to find what percent of students at his school drink the milk after
they finish their cereal. He is considering the following sampling methods:
QUESTION
He selects every tenth person who enters the school. What type of sampling
is this?
Choose 1 answer:
Willy is using a systematic sampling method by selecting every tenth person entering the school to understand milk consumption habits after cereal.
Explanation:When Willy selects every tenth person who enters the school to determine what percent of students drink the milk after they finish their cereal, he is using a systematic sampling method. This type of sampling involves selecting subjects at regular intervals from an ordered list.
It's a form of probability sampling where the first unit is selected randomly and the subsequent units are selected using a fixed periodic interval.
In the context of the situation provided, this method could potentially provide a more representative sample compared to methods like convenience sampling, but there could be inherent biases if there are underlying patterns in the student arrivals at school that correlate with milk drinking habits after cereal.
graph the two lines y=2x + 5 and y= x -1 what is the the x-value of the point where they intersect
Answer:
x=-6
Step-by-step explanation:
y=2x + 5
y= x -1
Plug in the equation for y
x-1=2x+5
Combine like terms
-1=x+5
-6=x
Hope this helps! Please mark brainliest :)
Consider a drug testing company that provides a test for marijuana usage. Among 317 tested subjects, results from 25 subjects were wrong (either a false positive or a falsenegative). Use a 0.05 significance level to test the claim that less than 10 percent of the test results are wrong. Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0H0: pequals=0.10.1 Upper H 1H1: pless than<0.10.1 B. Upper H 0H0: pless than<0.10.1 Upper H 1H1: pequals=0.10.1 C. Upper H 0H0: pequals=0.10.1 Upper H 1H1: pgreater than>0.10.1 D. Upper H 0H0: pequals=0.10.1 Upper H 1H1: pnot equals≠0.10.1 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is nothing. (Round to two decimal places as needed.) Identify theP-value for this hypothesis test. The P-value for this hypothesis test is nothing. (Round to three decimal places as needed.) Identify the conclusion for this hypothesis test. A. Fail to rejectFail to reject Upper H 0H0. There is notis not sufficient evidence to warrant support of the claim that less than 1010 percent of the test results are wrong. B. RejectReject Upper H 0H0. There is notis not sufficient evidence to warrant support of the claim that less than 1010 percent of the test results are wrong. C. RejectReject Upper H 0H0. There isis sufficient evidence to warrant support of the claim that less than 1010 percent of the test results are wrong. D. Fail to rejectFail to reject Upper H 0H0. There isis sufficient evidence to warrant support of the claim that less than 1010 percent of the test results are wrong. Click to select your answer(s).
Answer:
The null and alternative hypothesis are:
[tex]H_0: \pi=0.1\\\\H_a:\pi<0.1[/tex]
The test statistic for this hypothesis test is z=-1.15.
The P-value for this hypothesis test is P-value=0.124.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that less than 10 percent of the test results are wrong.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that less than 10 percent of the test results are wrong.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.1\\\\H_a:\pi<0.1[/tex]
The significance level is 0.05.
The sample has a size n=317.
The sample proportion is p=0.079.
[tex]p=X/n=25/317=0.079[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{317}}\\\\\\ \sigma_p=\sqrt{0.000284}=0.017[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.079-0.1+0.5/317}{0.017}=\dfrac{-0.019}{0.017}=-1.153[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z<-1.153)=0.124[/tex]
As the P-value (0.124) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that less than 10 percent of the test results are wrong.
what is the derivative of 66lnx +135
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{66}{x}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = 66 \ln x + 135[/tex]
Step 2: Differentiate
Derivative Property [Addition/Subtraction]: [tex]\displaystyle y' = \frac{d}{dx}[66 \ln x] + \frac{d}{dx}[135][/tex]Derivative Property [Multiplied Constant]: [tex]\displaystyle y' = 66\frac{d}{dx}[\ln x] + \frac{d}{dx}[135][/tex]Logarithmic Differentiation: [tex]\displaystyle y' = \frac{66}{x}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
The function s(t) describes the motion of a particle along a line. s(t) = 14t − t2 (a) Find the velocity function v(t) of the particle at any time t ≥ 0. v(t) = 14−2t (b) Identify the time interval on which the particle is moving in a positive direction. (Enter your answer using interval notation.) (c) Identify the time interval on which the particle is moving in a negative direction. (Enter your answer using interval notation.) (7,[infinity]) (d) Identify the time at which the particle changes direction.
a. The velocity function is v(t) = 14 - 2t. b. The particle is moving in a positive direction on the interval (0, 7). c. The particle is moving in a negative direction on the interval (7, infinity). d. The particle changes direction at t = 7.
Explanation:a. The velocity function can be found by taking the derivative of the position function, s(t). The derivative of s(t) with respect to t is v(t) = 14 - 2t.
b. To determine the time interval on which the particle is moving in a positive direction, we need to find the values of t that make v(t) > 0. Solving the inequality 14 - 2t > 0, we get t < 7. Therefore, the particle is moving in a positive direction on the interval (0, 7).
c. Similarly, to determine the time interval on which the particle is moving in a negative direction, we need to find the values of t that make v(t) < 0. Solving the inequality 14 - 2t < 0, we get t > 7. Therefore, the particle is moving in a negative direction on the interval (7, infinity).
d. The particle changes direction at the time t = 7. This can be determined from the fact that v(t) changes sign at this time.
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For the graffiti cat sweater on page 9, Dodd knit
12 stitches to make 2 inches in width. The sweater is
9 inches wide from the left edge to the beginning of the
black smile. How many stitches wide is that?
Answer: 54 stitches
Step-by-step explanation:
12/2=6
6 stitches= 1 inch
X stitches=9 inches
X=54 stitches
Use properties of power series, substitution, and factoring of constants to find the first four nonzero terms of the Taylor series centered at 0 for the function given below. Use the Taylor series (1 plus x )Superscript negative 2 Baseline equals 1 minus 2 x plus 3 x squared minus 4 x cubed plus times times times, for negative 1 less than x less than 1. (1 plus 9 x )Superscript negative 2 The first term is nothing. The second term is nothing. The third term is nothing. The fourth term is nothing.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.