A minimum sample size of 64 business students must be randomly selected to estimate the mean monthly earnings with 95% confidence within $140 of the true population mean, given the population standard deviation of $569.
Explanation:To find the minimum sample size required to estimate an unknown population mean μ with a certain level of confidence, we can use the formula:
n = (Z*σ/E)^2
Where:
n is the sample sizeZ is the Z-score corresponding to the desired confidence levelσ (sigma) is the population standard deviationE is the margin of errorFor a 95% confidence level, the Z-score is approximately 1.96. The population standard deviation σ is given as $569. The margin of error E is $140.
Plugging these values into the formula, we get:
n = (1.96*569/140)^2
n = (1114.44/140)^2
n = (7.96)^2
n = 63.4
Since the sample size must be a whole number, we would round up to the next whole number which gives us a minimum sample size of 64 business students that must be randomly selected to estimate the mean monthly earnings of business students at one college with the desired precision and confidence level.
Final answer:
To estimate the population mean with a 95% confidence level and a margin of error of $140, we use the formula n = (Z*σ/E)^2 with σ = $569. Using the z-score for 95% confidence (1.96), the calculation yields 119.44, which we round up to 120 business students needed for the sample.
Explanation:
Calculating Minimum Sample Size for Estimating a Population Mean
To determine the minimum sample size needed to estimate the mean monthly earnings of business students at one college with 95% confidence and a margin of error of $140, we use the formula for the sample size (n). The formula is derived from the properties of a normal distribution and the central limit theorem and is as follows:
n = (Z*σ/E)^2
where:
Z is the z-score corresponding to the desired confidence level (1.96 for 95% confidence),
σ (sigma) is the population standard deviation, and
E is the desired margin of error.
Plugging in the given values of σ = $569 and E = $140, we find:
n = (1.96 * 569 / 140)^2
n ≈ (10.924)^2
n ≈ 119.44
Since we cannot survey a fraction of a person, we round up to the nearest whole number. Therefore, 120 business students must be randomly selected to achieve the desired precision.
An SAT coaching company claims it's course can raise SAT scores of high school students (thus, when they take it a second time after being coached). Of course, students who retake the SAT without paying for coaching generally raise their scores also. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were not coached. For both the coached group and the uncoached group, the gain in score was recorded. The SAT coaching company wishes to test to see if their coaching provided better second attempts on average. What case is best
Answer:
Check the explanation
Step-by-step explanation:
(a) The appropriate test is the matched-pairs test because a student’s score on Try 1 is certainly correlated with his/her score on Try 2. Using the differences, we have xbar = 29 and s = 59.
(b) To test H0: mu=0 vs. H1 mu > 0, we compute
[tex]t = (29-0)/((59/sqrt(427))=10.16[/tex]
with df = 426. This is certainly significant, with P < 0.0005. Coached students do improve their scores on average
(a) H0: μ1 = μ2 vs. Ha: μ1 > μ2, where μ1 is the mean gain among all coached students and μ2 is the mean gain among uncoached students. H0 and Ha. Using the conservative approach, df = 426 is rounded down to df = 100 in (t table) and we obtain 0.0025 < P < 0.005. Using software, df = 534.45 and P = 0.004. There is evidence that coached students had a greater average increase.
(b) 8 ± t*(3.0235) where t* equals 2.626 (using df = 100 with (t table) ) or 2.585 (df = 534.45 with software). This gives either 0.06 to 15.94 points, or 0.184 to 15.816 points, respectively.
(c) Increasing one’s score by 0 to 16 points is not likely to make a difference in being granted admission or scholarships from any colleges.
Serena is hitting golf balls at the driving range. When she hit a ball with her 9-iron, it stopped x yards in front of the 100-yard marker. She knows she can hit a ball twice that far if she uses her driver. Complete the steps below to see how far Serena can hit a golf ball with her driver.
Answer:
100-x represents the distance that Serena hit with her 9-iron. 2(100-x) represents the distance she can hit using her driver.
When the distance is given for the 9-iron, use the distributive property to find the simplified equation, so it will be much easier to solve after you are given the information on the 9-iron. Unsolvable without 9-iron distance.
Step-by-step explanation:
Hence, it is unsolvable without [tex]9[/tex] iron distance.
What is the yards?
A yard is a unit of length in both US Customary and British Imperial Systems of Measurement.
It is equivalent to [tex]3[/tex] feet or [tex]36[/tex] inches. Its symbol is yd. It is often used to measure the length of medium-sized objects.
Here, [tex]100-x[/tex] represents the distance that Serena hit with her [tex]9[/tex]-iron, and [tex]2(100-x)[/tex] represents the distance she can hit using her driver.
Now using the distributive property, it will be easier to solve about the information of nine-iron.
Hence, it is unsolvable without [tex]9[/tex] iron distance.
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Sophia and her brother combined to read a total of 40 books over the summer. Sophia read four times as many books as her brother. How many books did each person read?
Answer:
Brother read 8 books
Sophia read 32
Step-by-step explanation:
Number of book Sophia and her brother read is 32 and 8.
Distribution of books:Given that;
Total number of books = 40 books
Number of book Sophia read = 4[Number of book Sophia's brother read]
Find:
Number of books each person read
Computation:
Assume;
Number of book Sophia's brother read = a
So,
Number of book Sophia read = 4a
So,
a + 4a = 40
5a = 40
a = 8
Number of book Sophia's brother read = 8 books
So,
Number of book Sophia read = 32 books
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This year’s school population in Waterloo is 135 percent of last year’s school population. This year’s student population is 756. How many students did the school have last year?
Answer:560
Step-by-step explanation:
Let a be the number of students the school have last year
135% of a=756
135/100 x a=756
135a/100=756
Cross multiplying we get
135a=756 x100
135a=75600
Divide both sides by 135
135a/135=75600/135
a=560
What is the greatest common factor of 16 and 48
Answer:16
Step-by-step explanation:
prime factors of 16=2x2x2x2
Prime factors of 48=2x2x2x2x3
Their greatest common factor is:2x2x2x2=16
The greatest common factor of 16 and 48 is determined by listing the factors of each number and identifying the largest factor they share. In this case, the GCF of 16 and 48 is 16.
Explanation:The greatest common factor (GCF) is the highest number that divides exactly into two or more numbers. To find the GCF of 16 and 48, you can list the factors of each number and find the highest factor they share.
The factors of 16 are 1, 2, 4, 8, 16. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The largest number that appears in both lists is 16. Therefore, the GCF of 16 and 48 is 16.
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The GO transportation system of buses and commuter trains operates on the honor system. Train travelers are expected to buy their tickets before boarding the train. Only a small number of people will be checked on the train to see whether they bought a ticket. Suppose that a random sample of 200 train travelers was sampled and 24 of them had failed to buy a ticket. Estimate with 90% confidence the proportion of all train travelers who do not buy a ticket. Interpret the confidence interval you found.
Answer:
The 90% confidence interval for the population proportion of all train travelers who do not buy a ticket is (0.08, 0.16).
Step-by-step explanation:
The (1 - α)% confidence interval for the population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided is:
n = 200
X = 24
Confidence level = 90%
Compute the value of sample proportion as follows:
[tex]\hat p=\frac{X}{n}=\frac{24}{200}=0.12[/tex]
Compute the critical value of z for 90% confidence level as follows:
[tex]z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645[/tex]
Compute the 90% confidence interval for the population proportion of all train travelers who do not buy a ticket as follows:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]=0.12\pm 1.645\times\sqrt{\frac{0.12(1-0.12)}{200}}\\\\=0.12\pm0.038\\=(0.082, 0.158)\\\approx (0.08, 0.16)[/tex]
The 90% confidence interval for the population proportion of all train travelers who do not buy a ticket is (0.08, 0.16).
The 90% confidence interval (0.08, 0.16) for the population proportion of all train travelers who do not buy a ticket implies that there is a 0.90 probability that the true proportion lies in this interval.
Or if 100 such intervals are computed then 90 of those intervals will consist of the true proportion.
PLEASEEEEE HELPPPP MEEE WITHHH NUMBERR 20!!!!!
Angle 3 = 60°
Angle 4 = 60°
Step-by-step explanation:
To find angle 3 we have to use the straight angle that is formed with angle C. Angle C is the same value as angle 2 (120°) so all we have to do now is make an equation by subtracting angle C (120°) from 180°. 180°-120°=60°. So 60° is the value of angle 3.
Angle 4 is also 60° because it is the same angle as angle 3. So the value of angle 4 is 60°.
Another way to solve this problem (shown in the picture) is using the value of angle 1 (60°) and when you have the value 60° and there are triangles formed within the angle (highlighted in the picture) you know that all the angles within the triangle are going to be 60° because all angles within a triangle add up to 180°. So if we were to use this rule the equation would look like 60°+60°+60°=180°. Angle 3 in the green triangle would be equal to 60° because of the fact that one angle was already confirmed as being 60° so because of that all the angles in the triangle have to add up to 180° so the all the angles must be 60°. Angle 4 in the red triangle would also be equal to 60° for the same reason mentioned above.
So therefore the answer to this question is Angle 3 = 60° and Angle 4 = 60°
Hope this helps! If you have any more questions or you need further clarification please comment down below or message me! Good luck!
9/10 divided by (-6/5)
Answer:
-3/4
Step-by-step explanation:
9/10 ÷ (-6/5)
Copy dot flip
9/10 * -5/6
Rewriting
-5/10 * 9/6
-1/2 * 3/2
-3/4
Answer: -3/4
Step-by-step explanation: Remember that dividing by a fraction is the same thing as multiplying by the reciprocal of that fraction or that fraction flipped.
In other words we can rewrite 9/10 ÷ -6/5 as 9/10 · -5/6.
Before multiplying however, notice that we can cross-cancel
the 9 and 6 to 3 and 2 and the 5 and 10 to 1 and 2.
So we now have 3/2 · -1/2.
Now multiplying across the numerators
and denominators we get -3/4.
The probability that Lexie is on time for a given class is 98 percent. If there are 89 classes during the semester, what is the best estimate of the number of times out of 89 that Lexie is on time to class?
Answer:
87
Step-by-step explanation:
The expected value is the product of the probability and the outcome.
E = 0.98 (89)
E = 87.22
Rounded to the nearest integer, the expected number of classes is 87.
3y-9=-5x in slope intercept form
Answer:
y = (-5/3)x + 3
Step-by-step explanation:
slope intercept form: y = mx + b
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other.
First, add 9 to both sides:
3y - 9 (+9) = -5x (+9)
3y = -5x + 9
Next, divide 3 from both sides:
(3y)/3 = (-5x + 9)/3
y = (-5/3)x + 3
y = (-5/3)x + 3 is your answer.
~
Which of the following quadrilaterals are always parallelograms? Select all that apply. square rhombus trapezoid rectangle 2
Rectangle square rhombus
Step-by-step explanation:
Given the hyperbola y = 1/x, find the area under the curve between x = 5 and x = 33 to 3 sig. dig. namely: integral subscript 5 superscript 33 1 over x d x space equals . State the definite integral and evaluate it:Given the hyperbola y = 1/x, find the area under the curve between x = 5 and x = 33 to 3 sig. dig. namely: integral subscript 5 superscript 33 1 over x d x space equals . State the definite integral and evaluate it:
Answer:
[tex]\displaystyle A = \int\limits^{33}_{5} {\frac{1}{x}} \, dx[/tex]
[tex]\displaystyle A = \ln \frac{33}{5}[/tex]
General Formulas and Concepts:
Algebra II
Logarithmic PropertiesCalculus
Integration
IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{1}{x}[/tex]
Bounds: [5, 33]
Step 2: Find Area
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^{33}_{5} {\frac{1}{x}} \, dx[/tex][Integral] Integrate [Logarithmic Integration]: [tex]\displaystyle A = \ln |x| \bigg| \limits^{33}_5[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle A = \ln |33| - \ln |5|[/tex]Condense: [tex]\displaystyle A = \ln \frac{33}{5}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Bonnie knits 3 centimeters of
scarf each night. After 12 nights
of knitting, how many
centimeters of scarf will Bonnie
have knit in total?
Answer:
3 x 12 = 36
Step-by-step explanation:
help me please it is math
Maria pulls colored marbles out of a bag one at a time. Her results are shown in the table below. Based on the outcomes, if 20 more marbles are pulled out of the bag and replaced, how many marbles can be expected to be white?
To find the expected number of white marbles in future pulls, calculate the probability of pulling a white marble from the current results, then multiply this probability by the number of new pulls.
Explanation:To solve this problem, we will first identify the probability of pulling a white marble out of the bag based on Maria's results. Then, we will multiply this probability by the number of new marbles being pulled out (20) to determine the expected number of white marbles.
Calculate the total number of marbles Maria pulled out and the number of those marbles that were white.Divide the number of white marbles by the total number of marbles to find the probability of pulling a white marble.Multiply this probability by 20 (the number of additional pulls) to find the expected number of white marbles.Note: Since the outcomes are being replaced, the probabilities don't change after each pull.
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A farmer sells 7.7 kilograms of apples and pears.3/5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmers market?
Answer:
The weight of pears is 3.08 kg
Step-by-step explanation:
A farmer sells 7.7 kilograms of apples and pears.
3/5 of this weight is apples.
This means that the weight of apples is:
3/5 of 7.7
=> [tex]\frac{3}{5} * 7.7 = 4.62kg[/tex]
The weight of apples is 4.62 kg.
The weight of pears will therefore be:
[tex]7.7 - 4.62 = 3.08 kg[/tex]
The weight of pears is 3.08 kg.
Which formula is used to calculate the standard deviation of sample data?
cok
n-1
100. ()*(3*3)*==(x-)
0 /6 -> * (37)*(
n-1
Answer:
[tex]s=\sqrt{\frac{\sum (x_{i} -\mu)^{2} }{N-1} }[/tex]
Step-by-step explanation:
In statistics, the standard deviation is a measure about the amount of variation of a dataset.
The variation is measured through comparison between each data and the mean of the dataset. This way, we could get a numerical information about how far are those values form the mean (which represents the central value).
The formula to find the standard deviation of a sample is
[tex]s=\sqrt{\frac{\sum (x_{i} -\mu)^{2} }{N-1} }[/tex]
Where [tex]\mu[/tex] is the sample mean and [tex]N[/tex] is the total number of values there are.
In the formula you can notice the difference between each value ([tex]x_{i}[/tex]) and the mean ([tex]\mu[/tex]), That's why the standard deviation is commonly use to measure variation.
Therefore, the answer is
[tex]s=\sqrt{\frac{\sum (x_{i} -\mu)^{2} }{N-1} }[/tex]
Which of the following statements is true in a one-way ANOVA? a. The critical value of the test will be a value obtained from the F-distribution. b. If the null hypothesis is rejected, it may still be possible that two or more of the population means equal. c. The degrees of freedom associated with the sum of squares for treatments is equal to one less than the number of populations. d. All of these. e. None of these.
Answer:
d) All of the above
Step-by-step explanation:
A one way analysis of variance (ANOVA) test, is used to test whether there's a significant difference in the mean of 2 or more population or datasets (minimum of 3 in most cases).
In a one way ANOVA the critical value of the test will be a value obtained from the F-distribution.
In a one way ANOVA, if the null hypothesis is rejected, it may still be possible that two or more of the population means are equal.
This one way test is an omnibus test, it only let us know 2 or more group means are statistically different without being specific. Since we mah have 3 or more groups, using post hoc analysis to check, it may still be possible it may still be possible that two or more of the population means are equal.
The degrees of freedom associated with the sum of squares for treatments is equal to one less than the number of populations.
Let's say we are comparing the means of k population. The degree of freedom would be = k - 1
The correct option here is (d).
All of the above
The correct answer is all of the statements are true in a one-way ANOVA: the test uses the F-distribution, rejecting the null can mean two or more population means are equal, and degrees of freedom for treatment sum of squares is the number of groups minus one.
Explanation:The correct answer to which statement is true in a one-way ANOVA is d. All of these.
The critical value of the test comes from the F-distribution.If the null hypothesis is rejected, it is still possible that two or more of the population means equal, as rejecting the null suggests at least two means are different, not necessarily all.The degrees of freedom associated with the sum of squares for treatments equals one less than the number of populations (dfbetween = number of groups - 1).One-way ANOVA is used to determine if there are any statistically significant differences between the means of three or more independent (unrelated) groups. The F statistic in ANOVA is always right-tailed because larger F values fall in the right tail of the F-distribution curve, leading to the rejection of the null hypothesis.
Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type-A vessel has 60 deluxe cabins and 160 standard cabins, whereas a type-B vessel has 80 deluxe cabins and 120 standard cabins. Under a charter agreement with Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 360 deluxe and 680 standard cabins for their 15-day cruise in May. It costs $42,000 to operate a type-A vessel and $51,000 to operate a type-B vessel for that period. How many of each type of vessel (x type-A and y type-B) should be used in order to keep the operating costs to a minimum
Answer: It should be used 2 for type-A and 3 for type-B to minimize the cost.
Step-by-step explanation: As it is stipulated, x relates to type-A and y to type-B.
Type-A has 60 deluxe cabins and B has 80. It is needed a minimum of 360 deluxe cabins, so:
60x + 80y ≤ 360
For the standard cabin, there are in A 160 and in B 120. The need is for 680, so:
160x + 120y ≤ 680
To calculate how many of each type you need:
60x + 80y ≤ 360
160x + 120y ≤ 680
Isolating x from the first equation:
x = [tex]\frac{360 - 80y}{60}[/tex]
Substituing x into the second equation:
160([tex]\frac{360 - 80y}{60}[/tex]) + 120y = 680
-3200y+1800y = 10200 - 14400
1400y = 4200
y = 3
With y, find x:
x = [tex]\frac{360 - 80y}{60}[/tex]
x = [tex]\frac{360 - 80.3}{60}[/tex]
x = 2
To determine the cost:
cost = 42,000x + 51,000y
cost = 42000.2 + 51000.3
cost = 161400
To keep it in a minimun cost, it is needed 2 vessels of Type-A and 3 vessels of Type-B, to a cost of $161400
Halle drives 2.41 kilometers to the train station. Then she travels 15.8 kilometers on the train. Finally, she walks 0.45 kilometers to the building where she works.
How many kilometers does Halle travel in all?
Answer:
18.66
Step-by-step explanation:
2.41 + 15.8 + 0.45
Suppose that the price per unit in dollars of a cell phone production is modeled by p= $45 -0.0125x, where x is in thousands of phones produced, and the revenue represented by
thousands of dollars is R X .p. Find the production level that will maximize revenue.
Answer:
The production level that will maximize the revenue is 1800 (in thousands of phones produced), that is, production of 1,800,000 phones will maximize the revenue.
Step-by-step explanation:
The price per unit of phone is given as
p = 45 - 0.0125x
where x is in thousands of phones produced
Revenue = (price per unit) × (number of units)
Revenue = (45 - 0.0125x) × x
= (45x - 0.0125x²)
To find the maximum revenue, we need to obtain the maximum value of the revenue function.
R(x) = (45x - 0.0125x²)
At maximum point, (dR/dx) = 0 and (d²R/dx²) < 0
R(x) = (45x - 0.0125x²)
(dR/dx) = 45 - 0.025x
at maximum point, (dR/dx) = 0
(dR/dx) = 45 - 0.025x = 0
0.025x = 45
x = (45/0.025) = 1800
Hence, the production level that will maximize the revenue is 1800 (in thousands of phones produced)
That maximum revenue is thus
R(x) = (45x - 0.0125x²)
R(1800) = (45×1800) - (0.0125×1800²)
= 40,500
Hope this Helps!!!
To find the production level that will maximize revenue, we need to find the critical point of the revenue equation and determine if it is a maximum or minimum. Then we can find the corresponding production level.
Explanation:To find the production level that will maximize revenue, we need to find the value of x that maximizes the revenue equation R(X)=X*p. The revenue equation can be written as R(X) = X*(45 - 0.0125x). To maximize revenue, we can find the x-value where the derivative of the revenue equation is equal to zero. After finding this critical point, we can check if it is a maximum or minimum by analyzing the second derivative. Finally, we can substitute this x-value back into the original equation to find the corresponding production level.
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will the product be greater or less then each factor? 56.9×2.01
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n=83, x=45, 98 percent
Could you please explain the steps and how to get to an answer? Thank you!
Answer:
The 98% confidence interval for the population proportion p is (0.4149, 0.6695).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 83, \pi = \frac{45}{83} = 0.5422[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5422 - 2.327\sqrt{\frac{0.5422*0.4578}{83}} = 0.4149[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5422 + 2.327\sqrt{\frac{0.5422*0.4578}{83}} = 0.6695[/tex]
The 98% confidence interval for the population proportion p is (0.4149, 0.6695).
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 6.2 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 180 engines and the mean pressure was 6.3 pounds/square inch. Assume the standard deviation is known to be 0.9. A level of significance of 0.05 will be used. Make a decision to reject or fail to reject the null hypothesis. Make a decision.
Answer:
Given:
mean, u = 6.2
sample size, n = 180
Sample mean, X' = 6.3
s.d [tex] \sigma [/tex] = 0.9
Significance level = 0.05
The null and alternative hypothesis will be:
H0 : u = 6.2
H1 : u > 6.2
Degree of freedom = 180 - 1 = 179
Using t table, the t critical value,
t> t(0.05, 179) = 1.6534
The test statistic:
[tex] t = \frac{X' - u}{\frac{\sigma}{\sqrt{n}}} [/tex]
[tex] T = \frac{6.3 - 6.2}{\frac{0.9}{\sqrt{180}}} = 1.4907 [/tex]
Since the test statistic(t calculated value) 1.4907 < t critical value (1.6534), we fail to reject the null hypothesis H0.
what is the answer of this question?
Answer:
116
Step-by-step explanation:
8.2 / 2 = 4.1
a = [tex]\sqrt{7^{2}-4.1^{2} } = 5.6736[/tex]
0.5 x 8.2 x 5.6736 = 23.2618
23.2618 x 5 = 116.309 = 116
Reginald read his novel three nights in a row. Each night, he read for
3/4 of an hour.
How many hours did Reginald read his novel altogether?
9 hours
2 1/2 hours
2 1/4 hours
4 hours
Answer:
2 1/4 hours
Step-by-step explanation:
Each night, he read for 3/4 hours = 3*60/4 = 45 minutes.
He read for 3 days.
So in total, he read for:
3*45 = 135 minutes.
135 minutes is 2 hours and 15 minutes. 15 minutes is 1/4 of an hour.
So the correct answer is:
2 1/4 hours
How many different 5-letter radio station call letters can be made a. if the first letter must be Upper C comma Upper X comma Upper T comma or Upper M and no letter may be repeated? b. if repeats are allowed (but the first letter is Upper C comma Upper X comma Upper T comma or Upper M)? c. How many of the 5-letter radio station call letters (starting with Upper C comma Upper X comma Upper T comma or Upper M) have no repeats and end with the letter Upper S?
Answer:
a) 1,518,000
b) 2,284,880
c) 60,720
Step-by-step explanation:
a) a. if the first letter must be Upper C comma Upper X comma Upper T comma or Upper M and no letter may be repeated?
We draw 5 boxes, and based on that we will see the total possible cases. There are 26 alphabets
The first box should have C or X or T or M .No letter may be repeated.
Any Any Any Any Any
5 alphabets of the of the of the of the
C,X , T , M remaining remaining remaining remaining
25 alphabets 24 alphabets 23 alphabets 22 alphabets
Therefore; total possible call letters = 5 × 25 × 24 × 23 × 22 = 1,518,000
b)
The first box should have C or X or T or M Repeats as allowed
Any Any Any Any Any
5 alphabets of the of the of the of the
C,X , T , M remaining remaining remaining remaining
26 alphabets 26 alphabets 26 alphabets 26 alphabets
Therefore Total possible call letters = 5 × 26 × 26 × 26 × 26 = 2,284,880
c) The first box should have C,X , T , M and end with S
So the last place if fixed, and we now have 25 alphabets. The first box can go in 5 ways. The next box then will have only 24 letters to choose from, as the first box has taken a letter and the last box already has S in it. Repetition not allowed
Any Any Any Any S
5 alphabets of the of the of the is fixed
C,X , T , M remaining remaining remaining here
24 alphabets 23 alphabets 22 alphabets
Therefore Total possible call letters = 5 × 24 × 23 × 22 × 1 = 60,720
a. 30,240 different call letters can be made if the first letter must be C, X, T, or M and no letter may be repeated. b. 11,881,376 different call letters can be made if repeats are allowed. c. 22,464 different call letters can be made if the call letters start with C, X, T, or M, have no repeats, and end with S.
Explanation:a. If the first letter must be C, X, T, or M, and no letter may be repeated, the options for the first letter are 4. For the remaining 4 positions, we can choose from 25 letters (all except the first letter chosen). Therefore, the total number of different 5-letter radio station call letters is 4 * 25 * 24 * 23 * 22 = 30,240.
b. If repeats are allowed, including the first letter being C, X, T, or M, we still have 26 options for each position (including the possibility of repeating the first letter chosen). Therefore, the total number of different 5-letter radio station call letters is 26 * 26 * 26 * 26 * 26 = 26^5 = 11,881,376.
c. To have no repeats and end with the letter S, we have 24 options for the first position (all letters except C, X, T, or M) and 1 option for the last position (the letter S). For the remaining 3 positions, we can choose from 24 letters (all except the first and last position chosen). Therefore, the total number of different 5-letter radio station call letters starting with C, X, T, or M and ending with S is 4 * 24 * 24 * 24 * 1 = 22,464.
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Use x for your variable.
The sum of four times a number and seven is ten more than the number.
Answer:
4x + 7 = x + 10: x = 1!
Step-by-step explanation:
Not sure if you wanted me to solve as well; but I figured I would do it just in case!
To solve this, use the following steps!:
[tex]4x+7=x+10\\-7\\4x=x+3\\-x\\3x=3\\x=1![/tex]
x = 1 Should be the correct answer!
The sum of four times a number and seven is ten more than the number can be express as follows:
4x - 3
let
the number = x
Therefore,
Four times the number = 4x
Seven is ten more than the number is as follows:
7 - x = 10x = 7 - 10x = -3Therefore, the sum of four times a number and seven is ten more than the number is as follows:
4x + (-3)4x - 3Algebraic expression4x - 3learn more on variable here: https://brainly.com/question/18681264
Maria put trim around a banner that is the shape of a triangle. Each side is 21 inches long. Maria has 3 4 foot of trim left. What was the length of the trim when she started? Enter your answer in yards.
We have been given that Maria put trim around a banner that is the shape of a triangle. Each side is 21 inches long.
The amount of trim will be equal to perimeter of triangle. The perimeter of given triangle will be 3 times each side length that is [tex]3\times 21=63[/tex] inches.
Now we need to convert 63 inches into feet.
12 inches = 1 feet
63 inches = [tex]\frac{63}{12}[/tex] feet = 5.25 feet.
We are also told that Maria has [tex]\frac{3}{4}[/tex] foot of trim left, so total length of trim would be trim used plus trim left that is [tex]5.25+\frac{3}{4}=5.25+0.75=6[/tex] feet.
Since we need to find length of trim in yards, so we will convert 6 feet into yards.
3 feet = 1 yard
6 feet = [tex]\frac{6}{3}[/tex] yards = 2 yards
Therefore, the length of the trim was 2 yards.
Patricia got a 5/25 balloon mortgage and her initial payments were $965. She
decided to refinance her balloon payment with a 30-year mortgage and her
new payments were $925. What is the total financed cost she paid for her
house?
Answer:
$390,900
Step-by-step explanation:
Given:
Initial payment = $965
New rapayment = $925 when she decided to refinance her ballon payment with a 30 year mortgage
In this case, a 5/25 ballon mortgage simply means loan repayment for the first 5 years is at a fixed rate.
Which means the total amount she paid in the first five years was=
12 * 5 * $965 = $57,900
When she refinanced the payment with a 30 year mortgage, her total payment = $925 * 12 * 30years = $333,000
Total financed cost Patricia paid =
$57,900 + $333,000 = $390,900
A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. Find the residuals from the regression and verify that the residuals are approximately normally distributed. Height (inches), x 26.75 25.5 26.5 27 25 Head Circumference (inches), y 17.3 17.1 17.3 17.5 16.9
Answer:
[tex]y=0.259 x +10.447[/tex]
Now we can find the residulls like this:
[tex] e_1 = 17.3 - 17.375 = -0.075[/tex]
[tex] e_2 = 17.1 - 17.052 = 0.049[/tex]
[tex] e_3 = 17.3 - 17.311 = -0.011[/tex]
[tex] e_4 = 17.5 - 17.440 = 0.06[/tex]
[tex] e_5 = 16.9 - 16.922 = -0.022[/tex]
So then we can see that the residuals are not with an specified pattern (alternating sign) so then we can conclude that are distributed normally
Step-by-step explanation:
We have the following data given:
Height (inches), x 26.75 25.5 26.5 27 25
Head Circumference (inches), y 17.3 17.1 17.3 17.5 16.9
We need to find a linear model [tex] y = mx +b[/tex]
For this case we need to calculate the slope with the following formula:
[tex]m=\frac{S_{xy}}{S_{xx}}[/tex]
Where:
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]
So we can find the sums like this:
[tex]\sum_{i=1}^n x_i =130.75[/tex]
[tex]\sum_{i=1}^n y_i =86.1[/tex]
[tex]\sum_{i=1}^n x^2_i =3422.06[/tex]
[tex]\sum_{i=1}^n y^2_i = 1482.85[/tex]
[tex]\sum_{i=1}^n x_i y_i =2252.28[/tex]
With these we can find the sums:
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=3422.06-\frac{130.75^2}{5}=2.95[/tex]
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=2252.28-\frac{130.75*86.1}{5}=0.765[/tex]
And the slope would be:
[tex]m=\frac{0.765}{2.95}=0.259[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{130.75}{5}=26.15[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{86.1}{5}=17.22[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=17.22-(0.259*26.15)=10.447[/tex]
So the line would be given by:
[tex]y=0.259 x +10.447[/tex]
Now we can find the residulls like this:
[tex] e_1 = 17.3 - 17.375 = -0.075[/tex]
[tex] e_2 = 17.1 - 17.052 = 0.049[/tex]
[tex] e_3 = 17.3 - 17.311 = -0.011[/tex]
[tex] e_4 = 17.5 - 17.440 = 0.06[/tex]
[tex] e_5 = 16.9 - 16.922 = -0.022[/tex]
So then we can see that the residuals are not with an specified pattern (alternating sign) so then we can conclude that are distributed normally