Mr. Good Wrench advertises that a customer will have to wait no more than 30 minutes for an oil change. A sample of 26 oil changes had a standard deviation of 4.8 minutes. Use this information to calculate a 90% confidence interval for the population standard deviation waiting time for an oil change.
Answers
Answer:
The 90% confidence interval for the population standard deviation waiting time for an oil change is (3.9, 6.3).
Step-by-step explanation:
The (1 - α)% confidence interval for the population standard deviation is:
[tex]CI=\sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1)}}}\leq \sigma\leq \sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2, (n-1)}}}[/tex]
The information provided is:
n = 26
s = 4.8 minutes
Confidence level = 90%
Compute the critical values of Chi-square as follows:
[tex]\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.10/2, (26-1)}=\chi^{2}_{0.05, 25}=37.652[/tex]
[tex]\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{1-0.10/2, (26-1)}=\chi^{2}_{0.95, 25}=14.611[/tex]
*Use a Chi-square table.
Compute the 90% confidence interval for the population standard deviation waiting time for an oil change as follows:
[tex]CI=\sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1)}}}\leq \sigma\leq \sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2, (n-1)}}}[/tex]
[tex]=\sqrt{\frac{(26-1)\times 4.8^{2}}{37.652}}\leq \sigma\leq \sqrt{\frac{(26-1)\times 4.8^{2}}{14.611}}\\\\=3.9113\leq \sigma\leq 6.2787\\\\\approx 3.9 \leq \sigma\leq6.3[/tex]
Thus, the 90% confidence interval for the population standard deviation waiting time for an oil change is (3.9, 6.3).
Related Questions
According to a 2014 research study of national student engagement in the U.S., the average college student spends 17 hours per week studying. A professor believes that students at her college study less than 17 hours per week. The professor distributes a survey to a random sample of 80 students enrolled at the college. From her survey data the professor calculates that the mean number of hours per week spent studying for her sample is 15.6 hours per week with a standard deviation of 4.5 hours per week. The professor chooses a 5% level of significance. What can she conclude from her data? Group of answer choices The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week. The professor cannot conclude that the average number of hours per week spent studying for students at her college is less than 17 hours per week. The sample mean of 15.6 is not significantly less than 17. Nothing. The conditions for use of a T-model are not met. The professor cannot trust that the p-value is accurate for this reason.
Answers
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 17
For the alternative hypothesis,
µ < 17
This is a left tailed test.
Since the population standard deviation is not given, the distribution is a student's t.
Since n = 80,
Degrees of freedom, df = n - 1 = 80 - 1 = 79
t = (x - µ)/(s/√n)
Where
x = sample mean = 15.6
µ = population mean = 17
s = samples standard deviation = 4.5
t = (15.6 - 17)/(4.5/√80) = - 2.78
We would determine the p value using the t test calculator. It becomes
p = 0.0034
Since alpha, 0.05 > than the p value, 0.0043, then we would reject the null hypothesis.
The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week.
The perimeter of a square is equal to the perimeter of an equilateral triangle. The length of a side of the square is given by x, and the length of a side of the equilateral triangle is given by x + 1. Which equation can be used to find the value of x?
Answers
Answer: The equation you could use is 4x = 3x + 3
Step-by-step explanation:
THE SQUARE
A square has sides with 4 equal sides. If one side is equal to x, then every other side is also x.
Add x + x + x + x to get the square’s perimeter.
The sqaure’s perimeter is 4x.
THE TRIANGLE
An equilateral triangle has equal sides too. If one side is x + 1, every other side is x + 1 too.
Add, (x + 1) + (x + 1) + (x + 1)
the triangles perimeter is 3x + 1
BOTH
The triangle and the square have the same perimeter. Therefore,
4x = 3x + 3. That is the equation.
( The solution would be x = 3, by the way)
[tex] \sqrt{2x + 3 } - \sqrt{x - 2} = 2 [/tex]
find x
Answers
Answer:
Step-by-step explanation:
hello : here is an solution
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that the mean income is found to be $21.1 for a random sample of 717 people. Assume the population standard deviation is known to be $12.6. Construct the 85% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
Answers
Answer:
The 85% confidence interval for the mean per capita income in thousands of dollars is between $20.4 and $21.8.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.85}{2} = 0.075[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.075 = 0.925[/tex], so [tex]z = 1.44[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.44\frac{12.6}{\sqrt{717}} = 0.7[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 21.1 - 0.7 = $20.4.
The upper end of the interval is the sample mean added to M. So it is 21.1 + 0.7 = $21.8.
The 85% confidence interval for the mean per capita income in thousands of dollars is between $20.4 and $21.8.
samuel wants to buy a snake for 288 and the pet store owner wants hin to make 6 equal payments of 49 what error did the pet store owner make
Answers
Answer:
There is a multiplication error. The payment should be $48 per month.
Step-by-step explanation:
i took the assignment hopes this help can i get brainliest plzzzzz
The pet store owner made an error in his calculation. When you multiply the amount of each payment ($49) by the number of payments (6), the result is $294, not $288.
Explanation:The information provided in the question implies a situation that involves simple mathematics; specifically, multiplication and addition. To determine the total cost of the snake, it would be necessary to multiply the number of payments (6) by the individual amount of each payment ($49).
Here's how:
This means that
the pet store owner is asking for $294 in total
, not $288. Thus, the error that the pet store owner made was in the calculation of the total amount due for the snake.
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What is the volume of a square pyramid if the length of an edge of the base is 7 and the altitude
of the pyramid is 12?
(1) 28
(2) 56
(3) 196
(4) 588
Answers
We have been given that the length of an edge of a square pyramid is 7 and altitude of the pyramid is 12. We are asked to find the volume of the pyramid.
We will use volume of pyramid formula to solve our given problem.
[tex]V=\frac{1}{3}\cdot b\cdot h[/tex], where,
b = Area of base of pyramid,
h = Height of pyramid.
We know that area of a square is square of its side length, so area of the base of pyramid would be [tex]7^2=49[/tex].
The height of the pyramid will be equal to altitude.
[tex]V=\frac{1}{3}\cdot 49\cdot 12[/tex]
[tex]V=49\cdot 4[/tex]
[tex]V=196[/tex]
Therefore, the volume of the given pyramid would be 196 cubic units and 3rd option is the correct choice.
A coach of a baseball team orders hats for the 12 players on his team. Each hat costs $9.95. The shipping charge for the entire order is $5.00. There is no tax on the order. What is the total cost of the coach’s order ?
Answers
Answer:
124.4
Step-by-step explanation:
12 x 9.95 = 119.4 dollars
119.4+5.00=124.4
The total cost is $124.40.
Answer:
Step-by-step explanation:
Answer:
124.4
Step-by-step explanation:
12 x 9.95 = 119.4 dollars
119.4+5.00=124.4
The total cost is $124.40.
Which words or phrases describe some advantages of nonrenewable resources? Check all that apply.
easy to produce
habit-forming
finite
affordable
abundant
Answers
Answer:
a.)Easy to produce, d.)affordable, and e.)abundant
Step-by-step explanation:
i got it correct on the instructions
The correct options are easy to produce, affordable, and abundant.
What are nonrenewable resources?A nonrenewable resource is a natural substance that is not replenished with the speed at which it is consumed.
A non-renewable resource is defined as the natural resources which are not readily replaced through natural means and it takes thousands of years for their renewal.
Examples of non-renewable resources include Fossil fuels such as natural gas, oil, and coal.
There are many advantages of non-renewable resources such as:
Easy to produce: non-renewable resources are easy to produce because processing stations can be easily developed for refinement and distillation of non-renewable resources.Affordable and abundant: nonrenewable resources are affordable and abundant on the earth. for example, diesel and oil are good choices for powering vehicles.Hence, the correct options are easy to produce, affordable, and abundant.
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Mrs. Duncan measured the lengths of a crayon and a pencil. The pencil is double the length of the crayon. The sum of their length is 24 centimeters. What are their lengths?
Answers
Answer: The length of pencil is 16 centimetres and length of crayons is 8 centimetres
Step-by-step explanation:
Let the length of crayon =[tex]x[/tex]
Length of a pencil =[tex]2x[/tex]
As according to question that the sum of their length is 24 centimetres
So we have
[tex]x+2x=24\\\\\Rightarrow 3x= 24 \\\\\Rightarrow x= \dfrac{24}{3} =8[/tex]
Therefore the length of crayon = 8 centimetres
Length of pencil= [tex]2x= 2\times x = 2\times 8 =16[/tex] centimetres
Hence, the length of pencil is 16 centimetres and length of crayons is 8 centimetres
Which rules give a repeating pattern that has a 7 as the 15th number? Select all that apply.
a) 1, 7
b) 1, 7, 9
c) 1, 9, 7
d) 1, 7, 7
e) 7, 1, 9
Answers
Jasmine walked 15 blocks. She stopped at the store 3/5 of the way into her walk. How many blocks did she walk to the store?
Answers
Answer:
8
Step-by-step explanation:
MacGyver wants to estimate the width of a river so he can get to the other side to save the world. He makes the measurements pictured. How wide is the river? Will he be able to do it?
Answers
Answer:
Wideness ≈ 40 m
He will be able to do it .
Step-by-step explanation:
He wants to estimate the width of a river so he can get to the other side to save the world . The width of the river is the side AB. From the scale above 2 right angle triangle are formed . The smaller triangle is CDE and the larger triangle is CAB.
The angle ECD can be gotten below
tan C = opposite/adjacent
tan C = 8/6
tan C = 1.3333
C = tan⁻¹ 1.333
C = 53.1301022854
C = 53. 13°
∠ACB = ∠ECD (vertically opposite angles)
Using the angle to find the wideness of the river AB in triangle CAB.
tan C = opposite/adjacent
tan 53.13° = AB/30
AB = 30 tan 53.13
AB = 30 × 1.33332837108
AB = 39.9998511323
AB ≈ 40 m
He will be able to do it.
A Nissan Motor Corporation advertisement read, "The average man's I.Q. is 107. The average brown trout's I.Q. is 4. So why can't man catch brown trout?" Suppose you believe that the brown trout's mean I.Q. is greater than four. You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5; 4; 7; 3; 6; 4; 5; 3; 6; 3; 8; 5. Conduct a hypothesis test of your belief. (Use a significance level of 0.05.)
Answers
Answer:
We conclude that the brown trout's mean I.Q. is greater than four.
Step-by-step explanation:
We are given that the average brown trout's I.Q. is 4. Suppose you believe that the brown trout's mean I.Q. is greater than four.
You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5, 4, 7, 3, 6, 4, 5, 3, 6, 3, 8, 5.
Let [tex]\mu[/tex] = the brown trout's mean I.Q.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 4 {means that the brown trout's mean I.Q. is smaller than or equal to four}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 4 {means that the brown trout's mean I.Q. is greater than four}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean I.Q. of brown tout = [tex]\frac{\sum X}{n}[/tex] = 4.92
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X- \bar X)^{2} }{n-1} }[/tex] = 1.62
n = sample of brown trout = 12
So, the test statistics = [tex]\frac{4.92-4}{\frac{1.62}{\sqrt{12} } }[/tex] ~ [tex]t_1_1[/tex]
= 1.967
The value of t test statistics is 1.967.
Now, at 5% significance level the t table gives critical value of 1.796 at 11 degree of freedom for right-tailed test.
Since our test statistic is more than the critical value of t as 1.967 > 1.796, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the brown trout's mean I.Q. is greater than four.
To conduct a hypothesis test, compare the sample mean IQ of 12 brown trout to the hypothesized mean of 4 using a one-sample t-test at a 0.05 significance level.
Explanation:To conduct a hypothesis test of the belief that the brown trout's mean IQ is greater than four, we can use a one-sample t-test. The null hypothesis (H0) is that the mean IQ of brown trout is equal to four. The alternative hypothesis (Ha) is that the mean IQ is greater than four.
Using a proper significance level of 0.05, we can compare the sample mean IQ of the 12 brown trout to the hypothesized mean of four. If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence to support the belief that the brown trout's mean IQ is greater than four.
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A baker packages 12 cupcakes to a box. Sean orders 5 boxes for his sister’s graduation party and 3.5 boxes for the Variety Show Party. Write an expression that shows the calculations you could use to find the number of cupcakes Sean Orders
Answers
Answer:
The expression isTotal number of cupcakes Sean orders=5 boxes (12 cupcakes)+ 3.5 boxes (12 cupcakes)
Step-by-step explanation:
A box= 12 cupcakes
Sean's order
Sister's graduation=5 boxes
Variety show party=3.5 boxes
Total number of cupcakes Sean orders=5 boxes (12 cupcakes)+ 3.5 boxes (12 cupcakes)
Total number of cupcakes Sean orders=5(12)+3.5(12)
=60+42
=102 cupcakes
6th grade math please help !
Answers
Answer:
okay my daughter is in 6th grade so the answer is c 45 dollars per 3 hours
Step-by-step explanation:
A stream traverses two lakes flowing downstream, and carrying fresh water as it enters the upper lake. The upper lake contains 4∗109 gallons of water, and the lower lake contains 2 ∗109 gallons of water. The flow rate of the stream is the same at all points and is 4 ∗ 106 gallons per day. A factory situated at the upper lake releases a pollutant at a rate of 200 lbs. per day. Let Q1(t) and Q2(t) be the amount, in pounds, of pollutant in the upper and lower lakes, respectively, where time t is measured in days. Assuming that each lake is well mixed, Q1 and Q2 obey the system(a) Q'1 = 4 ∗ 106 (200 − Q1), Q'2 = 4 ∗ 106 (Q1 − Q2).(b) Q'1 = 200 − Q1/1000, Q'2 = Q1/1000 − Q2/500.(c) Q'1 = 200 − 4 ∗ 106Q1, Q'2 = 4 ∗ 106 (Q1 − Q2).
(d) Q'1 = 200t − 4 ∗ 106Q1, Q'2 = 4 ∗ 106 (Q1 − Q2).
Answers
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images for the step by step explanation to the question
5 95 8,994 + 11 11 9,010 =
Answers
Answer:
5,95,9005,11,9010
Step-by-step explanation:
Which set of statements shows the correct steps to find 70 percent of 82? Write 70 percent as 7 ´ 1 percent. Write 1 percent as StartFraction 1 Over 100 EndFraction. Then, find StartFraction 1 Over 100 EndFraction of 82: 82 times StartFraction 1 Over 100 EndFraction = StartFraction 82 Over 100 EndFraction = 0.82. Multiply 0.82 by 7 to get 5.74. So, 70 percent of 82 is 5.74. Write 70 percent as StartFraction 1 Over 7 EndFraction. Then, find StartFraction 1 Over 7 EndFraction of 82: 82 times StartFraction 1 Over 7 EndFraction = StartFraction 82 Over 7 EndFraction = 11.71. So, 70 percent of 82 is 11.71. Write 70 percent as 7 ´ 10 percent. Write 10 percent as StartFraction 1 Over 10 EndFraction. Then, find StartFraction 1 Over 10 EndFraction of 82: 82 times StartFraction 1 Over 10 EndFraction = StartFraction 82 Over 10 EndFraction = 8.2. Multiply 8.2 by 7 to get 57.4. So, 70 percent of 82 is 57.4. Write 70 percent as StartFraction 1 Over 70 EndFraction. Then, find StartFraction 1 Over 70 EndFraction of 82: 82 times StartFraction 1 Over 70 EndFraction = StartFraction 82 Over 70 EndFraction = 1.17. So, 70 percent of 82 is 1.17.
Answers
Answer:
(C)
Step-by-step explanation:
To find 70 percent of 82
Write 70 percent as 7*10 percent.
Write 10 percent as [tex]\frac{10}{100}= \frac{1}{10}[/tex].
Then, find [tex]\frac{1}{10}$ of 82[/tex]
[tex]82 X\frac{1}{10}=8.2[/tex]
Multiply 8.2 by 7: 8.2 X 7 =57.4
Therefore, 70 percent of 82 is 57.4.
The steps in Option C are the correct steps.
Answer:
The answer to ur question is C
Step-by-step explanation:
A food truck caters an event attended by 100 guests. Every guest orders one of two possible dishes: a salad or a turkey plate. The price of each meal decreases as more of that particular type are ordered. The price of a salad is $ 10.00 minus $ 0.04 for each salad ordered. The price of a turkey plate is $ 12.00 minus $ 0.02 multiplied by the square of the number of turkey plates ordered. Guests pay for their meal only after everyone has placed their order. Using differentiation, find the maximum revenue for the food truck. Remember that the number of meals is a positive integer. Round revenue to the nearest cent.
Answers
Answer:
Max revenue: R = $679.73
Step-by-step explanation:
total people = 100
each person orders 1 of 2 dishes
salad price = $10 - 0.04x
turkey price = $12 - 0.02*y^2
so x + y = 100
s = 10 - 0.04x
t = 12 - 0.02*y^2
Revenue = s*x + t*y
Revenue = (10 - 0.04x)*x + (12 - 0.02y^2)*y
y = 100 - x
so
Revenue = (10 - 0.04x)*x + (12 - 0.02*(100 - x)^2 )*(100 - x)
R =
R = (10 - 0.04x)*x + (12 - 0.02*(100 - x)^2 )*(100 - x)
R = 10x - 0.04x*x + (12 - 0.02*(10000 - 200x + xx) )*(100 - x)
R = 10x - 0.04x*x + (12 - 200 + 4x -0.02 xx )*(100 - x)
R = 10x - 0.04x*x + (-188 + 4x -0.02 xx )*(100 - x)
R = 10x - 0.04x*x + (-188 + 4x -0.02 xx )*100 -x (-188 + 4x -0.02 xx )
R = 10x - 0.04x*x + -18800 + 400x -2 xx -x (-188 + 4x -0.02 xx )
R = 10x - 0.04x*x + -18800 + 400x -2 xx + 188x - 4xx +0.02 xxx
R = 10x - 0.04x*x + -18800 + 588x -6 xx + 0.02 xxx
R = -18800 + 598x -6.04 xx + 0.02 xxx
dR/dx = 598 - 12.08x + 0.06 x^2
set = 0
598 - 12.08x + 0.06xx = 0
299 - 6.04x + 0.03xx = 0
x = -(-6.04)/(2*0.03) + root((-6.04)^2 - 4*0.03*299) / 2*0.03
x = 100.6667 - root(36.4816 - 35.88) / 0.06
x = 100.6667 - 12.927
x = 87.739
so that is where you get the maximum revenue, when you sell 87.7 salad plates and 12.2605 turkey dishes
Revenue = (10 - 0.04*87.739)*87.739 + (12 - 0.02(12.2605)^2)*12.2605
Revenue = 569.464715 + 110.266
R = $679.7307
R = $679.73
To find the maximum revenue, differentiate the revenue functions of salads and turkey plates with respect to the number of salads sold, considering a total of 100 guests, find critical points, and use the second derivative test or sign changes to identify the maximum revenue. Ensure that the number of meals are integers.
Explanation:To determine the maximum revenue for the food truck, we need to derive the revenue functions for salad and turkey plates and then find the total revenue function. Assuming s salads and t turkey plates are sold, the price functions are Ps(s) = 10 - 0.04s for salads and Pt(t) = 12 - 0.02t2 for turkey plates. The revenue functions would be Rs(s) = s × Ps(s) and Rt(t) = t × Pt(t). Because there are 100 guests, s + t = 100, hence t = 100 - s. We substitute t in Rt and add Rs and Rt for the total revenue R(s). To find the maximum revenue, we differentiate R(s) with respect to s, find critical points, and check these for the maximum value using the second derivative test or analyzing the sign changes of R'(s). Remember to check if the critical points result in s and t being positive integers, as per the conditions given.
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 6262 minutes with a mean life of 606606 minutes. If the claim is true, in a sample of 9999 batteries, what is the probability that the mean battery life would be greater than 619619 minutes? Round your answer to four decimal places.
Answers
Answer:
0.0183 = 1.83% probability that the mean battery life would be greater than 619 minutes
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 = 606, \sigma = 62, n = 99, s = \frac{62}{\sqrt{99}} = 6.23[/tex]
What is the probability that the mean battery life would be greater than 619 minutes?
This is 1 subtracted by the pvalue of Z when X = 619. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{619 - 606}{6.23}[/tex]
[tex]Z = 2.09[/tex]
[tex]Z = 2.09[/tex] has a pvalue of 0.9817
1 - 0.9817 = 0.0183
0.0183 = 1.83% probability that the mean battery life would be greater than 619 minutes
Translate this into an equation
Answers
Answer:
r + 6 = 90
Step-by-step explanation:
Answer:
90 = r6
Step-by-step explanation:
90 is the answer or product (multiplication) of Rita's age (r) and 6.
Meaning r times 6 = 90
If necessaly, combine like terms.
(3x+8)2
Answers
Step-by-step explanation:
multiply 2 with the bracket numbers
6x+16=0
6x= - 16
x=-16/6
x= - 8/3
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm3
What is the volume of the sphere?
Answers
Answer:
12 cm³
Step-by-step explanation:
Let's say the radius of the sphere and cylinder is r and the height is h. However, notice that the "height" of the sphere is the same thing as the diameter, which is 2r, so h = 2r.
The volume of a sphere is denoted by: [tex]V=\frac{4}{3} \pi r^3[/tex] , where r is the radius.
The volume of a cylinder is denoted by: [tex]V=\pi r^2h[/tex], where r is the radius and h is the height. Plug in 2r for h and 18 for V:
[tex]V=\pi r^2h[/tex]
[tex]18=\pi r^2*2r=2\pi r^3[/tex]
[tex]\pi r^3=18/2=9[/tex]
Now plug in 9 for πr³ in the volume formula for the sphere:
[tex]V=\frac{4}{3} \pi r^3[/tex]
[tex]V=\frac{4}{3} *9=12[/tex]
The volume of the sphere is 12 cm³.
The chance of winning a certain game at a carnival is 2 in 5. If Andy plays the game 12 times, what is the probability that he loses AT MOST 3 times?
Answers
Answer:
1.5267% probability that he loses AT MOST 3 times
Step-by-step explanation:
For each game that Andy plays, there are only two possible outcomes. Either he wins, or he loses. The probability of winning a game is independent of other games. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The chance of winning a certain game at a carnival is 2 in 5.
So the chance of losing is (5-2) in 5, that is 3 in 5.
So [tex]p = \frac{3}{5} = 0.6[/tex]
12 games:
This means that [tex]n = 12[/tex].
What is the probability that he loses AT MOST 3 times?
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex].
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.6)^{0}.(0.4)^{12} = 0.000017[/tex]
[tex]P(X = 1) = C_{12,1}.(0.6)^{1}.(0.4)^{11} = 0.000302[/tex]
[tex]P(X = 2) = C_{12,2}.(0.6)^{2}.(0.4)^{10} = 0.002491[/tex]
[tex]P(X = 3) = C_{12,3}.(0.6)^{3}.(0.4)^{9} = 0.012457[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.000017 + 0.000302 + 0.002491 + 0.012457 = 0.015267[/tex]
1.5267% probability that he loses AT MOST 3 times
Evaluate the expression 2x - 5 when x =3?
A) -4
B) 1
C) 6
D) 11
Answers
Answer:
Step-by-step explanation:
2x - 5
2(3) - 5
2 times 3 = 6
6-5=1
B) is the answer
I think the answer is B because you have to plug in 1 for the expression.
-Dhruva;)
What is the formula for the volume of a hemisphere?
Answers
Answer:
The formula to find the volume of a hemisphere is 2TTr3 / 3, where pi is 3.14, and the radius is half of the diameter.
Step-by-step explanation:
Answer:
hiii, the answer would be
b. 2/3 pi 3
hope this helps :)
Step-by-step explanation:
i just did the assignment
Shameel has a flight to catch on Monday morning. His father will give him a ride to the airport. If it rains, the traffic will be bad and the probability that he will miss his flight is 0.06. If it doesn't rain, the probability that he will miss his flight is 0.01. The probability that it will rain on Monday is 0.19. Suppose that Shameel misses his flight. What is the probability that it was raining
Answers
Answer:
The probability that it was raining on Monday given that Shameel misses his flight is 0.5846.
Step-by-step explanation:
The Bayes' theorem states that the conditional probability of an event E[tex]_{i}[/tex], of the sample space S = {E₁, E₂, E₃,...Eₙ}, given that another event A has already occurred is given by the formula:
[tex]P(E_{i}|A)=\frac{P(A|E_{i})P(E_{i})}{\sum\limits^{n}_{i=1} {P(A|E_{i})P(E_{i})}}[/tex]
Denote the events as follows:
X = it will rain on Monday
Y = Shameel misses his flight.
The information provided is:
[tex]P(X) = 0.19\\P(Y|X)=0.06\\P(Y|X^{c})=0.01[/tex]
Compute the probability that it will not rain on Monday as follows:
[tex]P(X^{c})=1-P(X)\\\\=1-0.19\\\\=0.81[/tex]
Compute the probability that it was raining on Monday given that Shameel misses his flight as follows:
Use the Bayes' theorem:
[tex]P(X|Y)=\frac{P(Y|X)P(X)}{P(Y|X)P(X)+P(Y|X^{c})P(X^{c})}[/tex]
[tex]=\frac{(0.06\times 0.19)}{(0.06\times 0.19)+(0.01\times 0.81)}\\\\=\frac{0.0114}{0.0114+0.0081}\\\\=\frac{0.0114}{0.0195}\\\\=0.58462\\\\\approx 0.5846[/tex]
Thus, the probability that it was raining on Monday given that Shameel misses his flight is 0.5846.
Final answer:
The probability that it was raining given Shameel misses his flight is approximately 58.46%, calculated using Bayes' theorem with the given probabilities of rain and missing the flight under different weather conditions.
Explanation:
The student is asking about conditional probability related to Shameel missing his flight given that it is raining. We need to use Bayes' theorem to solve this problem. The equation for Bayes' theorem, in this case, is:
P(Rain|Miss) = (P(Miss|Rain) × P(Rain)) / (P(Miss|Rain) × P(Rain) + P(Miss|Not Rain) × P(Not Rain))
Let's plug in the values given:
P(Miss|Rain) = probability that Shameel misses his flight given it is raining = 0.06
P(Rain) = probability that it will rain = 0.19
P(Miss|Not Rain) = probability that Shameel misses his flight given it is not raining = 0.01
P(Not Rain) = probability that it does not rain = 1 - P(Rain) = 1 - 0.19 = 0.81
Substitute all the values into the equation:
P(Rain|Miss) = (0.06 × 0.19) / (0.06 × 0.19 + 0.01 × 0.81)
After calculating:
P(Rain|Miss) = 0.0114 / (0.0114 + 0.0081)
P(Rain|Miss) = 0.0114 / 0.0195 ≈ 0.5846 or 58.46%
So, if Shameel misses his flight, the probability that it was raining is approximately 58.46%.
What is the hourly compensation per worker for a company with a unit labor cost of 0.9 and an hourly output per worker of $32.50? round your answer if necessary to the nearest whole number
Answers
Given Information:
Unit labor cost = 0.9
Hourly output per worker = $32.50
Required Information:
Hourly compensation per worker = ?
Answer:
Hourly compensation per worker = $36
Step-by-step explanation:
The unit labor cost is given by
[tex]U = \frac{O}{W}[/tex]
Where W is the hourly compensation per worker, O is the hourly output per worker and U is the unit labor cost.
Re-arranging for the hourly compensation yields,
[tex]U = \frac{O}{W}\\\\W =\frac{O}{U}\\ \\[/tex]
Now substitute the given values
[tex]W =\frac{32.50}{0.9}\\\\W = 36.11\\\\W = \$ 36[/tex]
Therefore, the hourly compensation per worker is $36.
Bonus:
Unit labor cost is the amount incurred with regard to labor expenses to produce one unit of a product. Calculating the unit labor cost helps in analyzing other aspects of the business such as product pricing, profit margin, sales etc.
Choose the function whose graph is given below.
-6
5
-3
4
5
-2.
-3
.4
O A. y= tan x
Answers
i need to see it
Jayden’s lunch at the diner cost $17. He leaves a 18% tip for the server. How much money did Jayden leave the server for a tip?
Answers
Answer:
The tip is $3.06
Step-by-step explanation:
To find the tip, take the amount of the bill and multiply by 18%
17 * 18%
17 * .18
3.06
The tip is $3.06