Answer with Step-by-step explanation:
We are given that
[tex]f(x)=-sin x[/tex]
[tex][0,\infty][/tex]]
Average value of the function is given gy
[tex]f_{avg}=\frac{1}{b-a}\int_{a}^{b}f(x)dx=\frac{1}{\pi-0}\int_{0}^{\pi}-sinx dx[/tex]
[tex]f_{avg}=\frac{1}{\pi}[cosx]^{\pi}_{0}[/tex]
Using the formula
[tex]\int sin xdx=-cos x[/tex]
[tex]f_{avg}=\frac{1}{\pi}(cos\pi-cos0)[/tex]
[tex]f_{avg}=\frac{1}{\pi}(-1-1)=-\frac{2}{\pi}[/tex]
[tex]f(x)=f_{avg}[/tex]
[tex]-sinx=-\frac{2}{\pi}[/tex]
[tex]sinx=\frac{2}{\pi}[/tex]
[tex]x=sin^{-1}(\frac{2}{\pi})=0.69radian[/tex]
The average value of the function is [tex]-\frac{2}{\pi}[/tex].
Average value :The average value of the function is given as,
[tex]Average=\frac{1}{\pi} \int\limits^\pi_0 {f(x)} \, dx[/tex]
Given function is, [tex]f(x)=-sinx[/tex]
Substitute values in above relation.
[tex]Average=\frac{1}{\pi} \int\limits^\pi_0 {-sinx} \, dx\\\\Average=\frac{1}{\pi} (cosx)^{\pi} _{0}\\\\Average=\frac{1}{\pi}(cos\pi - cos 0)\\\\Average=\frac{1}{\pi}(-1-1)\\\\Average=-\frac{2}{\pi}[/tex]
The values of x in the interval for which the function equals its average value is,
[tex]-sinx=-\frac{2}{\pi}\\ \\x=sin^{-1} (\frac{2}{\pi} )=39.56[/tex]
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Find the diameter of the circle with the given circumference use 3.14 C=18
store sold combined totalof 412 biology and math books in a week. the number of biology textbooks sold was three times the number of math books sold. how many textbooks of each type were sold?
Step-by-step explanation:
Total books sold = 412
So if there are 103 maths books then biology books should be three times = 103 × 3 = 309
So when we add 103 + 309 = 412
It means the number of biology books is 309 and maths book is 103
The image of the lemon is at point I. What is the size of the image compared to the size of the lemon?
same size...hope this helps :)))))
Evaluate: 955-105 x 4 +118
Answer: −420x+1073
Step-by-step explanation:
Let's simplify step-by-step.
955−105x(4)+118=955+−420x+118
Combine Like Terms:
=955+−420x+118=(−420x)+(955+118)=−420x+1073
Answer: =−420x+1073
I did it on my calculator and it got 653. The calculator is never wrong.
Which operation is performed in the derivation of the quadratic formula moving from Step 6 to Step 7? subtracting StartFraction b Over 2 a EndFraction from both sides of the equation squaring both sides of the equation taking the square root of both sides of the equation taking the square root of the discriminant
Answer: C. Taking the square root of both sides of the equation.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
i got it right
Order the decimals from least to greatest 7.508,5.2161,7.5,7.58
Answer:
5.2161,7.5,7.508,7.58
Step-by-step explanation:
Answer:
5.2161; 7.5; 7.508; 7.58
Step-by-step explanation:
-First you will look at the first digit of each number given, obviously 5 is the smallest so it will go first
-Then you will check the following number after the first digit to see which one is smaller of the "7" values. In this case, they all have the number "5" has their second value, so we move on to the third digit.
-Since "7.5" does not have a third digit, it will be the smallest of the number "7" values.
-We then have a remaining of two values, 7.508 and 7.58. Still looking at the third numbers of each of the two, we see "0" and "8," and obviously 0 is smaller than 8, so 7.508 is smaller than 7.58
The length of the rectangle is 4 less than twice the width . The perimeter is 28 . Find the length and width .
Answer:
Length=8 and width=6
Step-by-step explanation:
The length of the rectangle is 4 less than twice the width, let l stand for length and w for width: l=2w-4
The perimeter is equal to 28 and the formula for the perimeter of a rectangle is 2l+2w: 28=2l+2w
Substitute l into the equation:
28=2(2w-4)+2w
28=4w-8+2w
28=6w-8
36=6w
w=6
Find for l:
l=2w-4
l=2(6)-4
l=12-4
l=8
Solve the division problem. Round answer to the nearest hundredth.
9.2.15 2.0 6 3
Answer:
6
Step-by-step explanation:
If the mean GPA among students is 3.25 with a standard deviation of 1.75, and we select a random sample of 300 people, at what value for the sample mean would be greater than exactly 95% of possible sample means?
To find the sample mean greater than 95% of possible sample means for a population mean of 3.25 and standard deviation of 1.75 with a sample size of 300, apply the Central Limit Theorem to calculate the standard error and use the 95th percentile z-score to compute the desired sample mean.
Explanation:To find the sample mean that is greater than exactly 95% of possible sample means given a population mean (μ) of 3.25 and a standard deviation (σ) of 1.75 for a sample size (n) of 300, we use the concept of a z-score in conjunction with the Central Limit Theorem.
The Central Limit Theorem states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough. Since we have a large sample size of 300, we can assume normality. The formula for the standard error of the mean (SEM) is given by σ divided by the square root of n, SEM = σ / √n. In this case, SEM would be 1.75 / √300.
To find the specific sample mean that would exceed 95% of the sample means, we need to find the z-score that corresponds to the 95th percentile, which is typically around 1.645 for a one-tailed test (since we're looking for means greater than a value). We then multiply this z-score by the SEM and add it to the population mean. The calculation is as follows:
Calculate SEM: SEM = 1.75 / √300 Find the z-score corresponding to the 95th percentile: z ≈ 1.645 Calculate the sample mean: sample mean = μ + (z * SEM)
By carrying out these calculations, we will obtain the sample mean that is greater than 95% of possible sample means.
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The sample mean that would be greater than exactly 95% of possible sample means is approximately 3.4164.
Given that the population mean [tex](\(\mu\))[/tex] is 3.25 and the population standard deviation [tex](\(\sigma\))[/tex] is 1.75, we can use the z-score formula to find the sample mean [tex](\(\bar{x}\))[/tex] that corresponds to the 95th percentile:
[tex]\[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \][/tex]
We know that for a standard normal distribution, the z-score that corresponds to the 95th percentile is approximately 1.645 (since we want the value that is greater than exactly 95%, we use the one-tailed z-score). We can rearrange the formula to solve for [tex]\(\bar{x}\)[/tex]:
[tex]\[ \bar{x} = \mu + (z \times \frac{\sigma}{\sqrt{n}}) \][/tex]
Now we plug in the values:
[tex]\[ \bar{x} = 3.25 + (1.645 \times \frac{1.75}{\sqrt{300}}) \] \[ \bar{x} = 3.25 + (1.645 \times \frac{1.75}{\sqrt{300}}) \] \[ \bar{x} = 3.25 + (1.645 \times \frac{1.75}{17.3205080756888}) \] \[ \bar{x} = 3.25 + (1.645 \times 0.1010101010101) \] \[ \bar{x} = 3.25 + 0.16641664166417 \] \[ \bar{x} = 3.4164166416642 \][/tex]
Greg Evaluated has And found that he was spending $50 more per month on Utilities that he has budgeted. He can transfer money from other categories To increase his utility budget to $125 per month. If his total monthly income is $2400 To the nearest percent, what Percent of his monthly income will be budgeted for utilities?
Answer:
22%
Step-by-step explanation:
Answer:
5%
Step-by-step explanation:
There are two ways to solve this
a fast way: 125/2400 which equals approx 0.05208
when you convert this to a percentage it is about 5%
another way is take 2400 has 100% and 125 as x%
so
125/2400 = x/100
cross multiply so
2400x = 12500
then
x= 12500/2400 which simplifies to about
5.208. since this was out of 100 from the start you don't need to convert it to percentage form
A clothing business finds there is a linear relationship between the number of shirts, Q ,it can sell and the price, P , it can charge per shirt. In particular, historical data shows that 4000 shirts can be sold at a price of $ 133 , while 27000 shirts can be sold at a price of $ 41 . Give a linear equation in the form P = a Q + b that gives the price P they can charge for Q shirts. (This is called a demand function.)
Answer:
P = -0.004Q + 149
Step-by-step explanation:
The general form of the linear equation is:
[tex]P=aQ+b[/tex]
The slope of the equation (a) can be found by using the two given points (4,000; $133) and (27,000; $41)
[tex]a = \frac{\$41-\$133}{27,000-4,000}\\a=-0.004[/tex]
Applying the point (4,000; $133) to the equation below yields in the linear equation for Price as a function of the number of shirts:
[tex]P-P_0=a(Q-Q_0)\\P-133=-0.004(Q-4,000)\\P = -0.004Q+149[/tex]
The linear equation is:
P = -0.004Q + 149
Please hurry i don't have much time left!
If this rectangle is dilated using a scale factor of One-half through point B, what is the result?
Answer:
Check below
Step-by-step explanation:
That's too bad you haven't attached a rectangle.
Here's an example, with the data you've typed in.
1) When we dilate a rectangle we either grows it or shrink it through a scale factor.
Check the first picture below.
The New Dilated Rectangle A'B'C'D' will follow its coordinates, when the Center of Dilation is at its origin(Middle):
[tex]D_{A'B'C'D'}=\frac{1}{2}(x,y)[/tex]
2) But In this question, B is the center of Dilation. So, Since B is the Dilation Point B=B' . And More importantly:
[tex]\bar{AB}=\frac{1}{2}\bar{A'B'}\\\bar{CD}=\frac{1}{2}\bar{C'D'}\\\bar{AC}=\frac{1}{2}\bar{A'C'}\\\bar{CD}=\frac{1}{2}\bar{C'D'}\\[/tex]
3) So check the pictures below for a better understanding.
Answer:
Pretty sure its B
Find the equation of a quadratic function from its graph|
Answer:
U shape
Step-by-step explanation: look for a U shape and youll have chosen a quadratic function but find the vertex and put them into the format then find the slope
Much like sound bytes of news stories, statistical studies are often reduced to one- or two- sentence stat-bytes. For the following stat-byte, discuss what crucial information is missing and what more you would want to know before acting on the study. A cable network reports on a survey of America's top restaurants that found that "only nine restaurants achieved a rare 29 out of a possible 30 rating and none of those restaurants are in the Big Apple." Which of the following are crucial information that you would want to know before acting on the study? Select all that apply.
A. The goal of the study
B. How the quality of restaurants was measured
C. The variable of interest
D. Who the respondents in the survey were
E. How the respondents were selected
To make informed decisions based on a statistical study about restaurants, it's critical to understand the goal of the study, how the quality was measured, what the variable of interest was, who the respondents were and how they were selected.
Explanation:The crucial information that would need to know before acting on the study mentioned in the question includes all of the options provided and more. Let's discuss each option in detail:
A. The goal of the study. This would provide context and help to determine why these specific variables were chosen and measured. Without a clear goal, interpreting findings can be difficult.
B. How the quality of restaurants was measured. It's important to understand how the '29 out of 30' rating was developed - what specific factors led to this score. If the rating system or measurement techniques are flawed, the results could possibly be inaccurate.
C. The variable of interest. It would be necessary to understand what variable is being measured. Is it the food quality, service, ambiance, or some other factor of a restaurant's operation?
D. Who the respondents in the survey were. The demographic and social details of the respondents are also vital. If all respondents are from a certain group (for example, high-income people), results may not be representative for the general public.
E. How the respondents were selected. This would throw light on the methodology and the degree to which the findings can be generalized to the larger population.
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Suppose that on a true/false exam you have no idea at all about the answers to three questions. You choose answers randomly and therefore have a 50–50 chance of being correct on any one question. Let CCW indicate that you were correct on the first two questions and wrong on the third, let WCW indicate that you were wrong on the first and third questions and correct on the second, and so forth. a. List the elements in the sample space whose outcomes are all possible sequences of correct and incorrect responses on your part. b. Write each of the following events as a set and find its probability: (i) The event that exactly one answer is correct. (ii) The event that at least two answers are correct. (iii) The event that no answer is correct.
Answer:
a.
[tex]\text{Sample Space} = \{ CCC,CCW,CWW,WWW,WWC,WCC,WCW,CWC \}[/tex]
b.
(i) 1/2
(ii) 2/3
(iii) 1/6
Step-by-step explanation:
a.
The sample space is the list of all possibilities.
[tex]\text{Sample Space} = \{ CCC,CCW,CWW,WWW,WWC,WCC,WCW,CWC \}[/tex]
b.
(i)
If exactly one answer is correct the favorable outcomes are
CWW , WCW , WWC.
And the probability would be 3/6 = 1/2.
(ii)
If at least two answers are correct then the favorable outcomes are
CCC,CCW,WCC,CWC
and the probability is 4/6 = 2/3.
(iii)
If no answer is correct, the favorable outcomes are
WWW
and the probability is 1/6.
The Shady Farm Milk Company can process milk at a fixed rate of 7500 gallons/hour. The company’s clients request 100,000 gallons of milk over the course of one day. This demand is spread out uniformly from 8 a.m. to 6 p.m. The company starts producing at 8 a.m. and continues to work until all of the demand has been satisfied. At noon, how many gallons of milk are in the queue to be processed?
At noon, the Shady Farm Milk Company has 10,000 gallons of milk in the queue to be processed given the demand and the processing rate.
Explanation:The Shady Farm Milk Company can process 7500 gallons of milk per hour. Given that the company operates from 8 a.m. to 6 p.m., this is a total of 10 hours of operation in a day. Therefore, in 10 hours, the company can process 7500 × 10 = 75,000 gallons of milk.
However, the demand for milk is 100,000 gallons over the course of the day. Therefore, by noon, the company has been operating for 4 hours, meaning they can process 7500 × 4 = 30,000 gallons.
The demand over the same 4 hours period (from 8 a.m. to noon) is calculated by dividing the total demand over the entire course of the day (which is evenly spread) by the number of operating hours. Thus: 100,000 / 10 = 10,000 gallons/hour.
Consequently, the demand from 8 a.m. to noon is: 10,000 × 4 = 40,000 gallons. So, the amount of milk in the queue at noon would be the demand minus what the company has processed at that time.
Hence: 40,000 (demand from 8 a.m. to noon) - 30,000 (processed milk from 8 a.m. to noon) = 10,000 gallons. Therefore, at noon, the company has 10,000 gallons of milk in the queue to be processed.
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At noon, there are 20,000 gallons of milk in the queue to be processed.
To find out how many gallons of milk are in the queue to be processed at noon, we first need to calculate how many gallons of milk have been processed by noon.
The company can process milk at a fixed rate of 7500 gallons per hour. From 8 a.m. to noon, there are 4 hours.
Total gallons processed by noon = Rate of processing Time
[tex]\[ = 7500 \, \text{gallons/hour} \times 4 \, \text{hours} = 30000 \, \text{gallons} \][/tex]
Now, we need to find out how many gallons of milk are still in demand by noon. The total demand over the course of the day is 100,000 gallons, and it is spread out uniformly from 8 a.m. to 6 p.m.
This means that by noon, half of the day has passed.
So, the total demand by noon = Total demand / 2
[tex]\[ = \frac{100000}{2} = 50000 \, \text{gallons} \][/tex]
Now, to find out how many gallons are in the queue to be processed at noon, we subtract the gallons already processed from the total demand:
Gallons in the queue at noon = Total demand by noon - Gallons processed by noon
[tex]\[ = 50000 \, \text{gallons} - 30000 \, \text{gallons} = 20000 \, \text{gallons} \][/tex]
So, at noon, there are 20,000 gallons of milk in the queue to be processed.
If a calcium carbonate supplement is ordered at a dose of 600 mg daily, and the available form is 400 mg tablets, how many tablets do you give?
Answer:
500 tablets is what you give
Final answer:
To provide a daily dose of 600 mg of calcium carbonate with 400 mg tablets, we need to administer 2 tablets because the calculation of 600 mg divided by 400 mg per tablet equals 1.5, and we round up to the next whole tablet.
Explanation:
If a calcium carbonate supplement is ordered at a dose of 600 mg daily, and the available form is 400 mg tablets, we need to determine how many tablets to administer. To calculate this, we divide the total daily dose required by the dosage available per tablet. Therefore, 600 mg / 400 mg/tablet equals 1.5 tablets. Since we cannot give half a tablet, we round up to the next whole tablet, as it is important not to under-dose a medication.
We get:
600 mg / 400 mg per tablet = 1.5 tablets
Thus, we need to administer 2 tablets to achieve the required daily dose of 600 mg.
How can you best describe a stop sign using
polygons?
The sign has 8 sides, so it is an octagon
It appears to be
because the sides and
angles appear to be congruent.
STOP
Dene
Answer:
The answer to the last one is regular
Step-by-step explanation:
A polygon is a planar figure defined by a finite number of straight-line segments. The polygon that best describes a stop sign is a regular polygon.
What is a polygon?A polygon is a planar figure defined by a finite number of straight-line segments that are joined to form a closed polygonal chain in geometry. A polygon can be defined as a bounded planar region, a bounding circuit, or both.
The polygon that best describes a stop sign is a regular octagon because a stop sign has 8 sides and the length of each side is the same, therefore, the polygon will be a regular polygon.
Thus, the polygon that best describes a stop sign is a regular polygon.
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The radius of the large sphere is times longer than the radius of the small sphere.
How many times the volume of the large sphere is the volume of the small sphere?
A-1/27
B-1/18
C-1/9
D-1/3
Answer:
1/3
Step-by-step explanation:
You can try it I keep getting 3 so maybe that’s the answer
1/3, because 18.6 / 3 = 6.2
True or False: The mean and the average are the same number/
Answer:
true
Step-by-step explanation:
Isabella's car used 3 gallons of gas to drive 48 miles. At what rate does her car use gas in gallons per mile?
Answer:
0.0625 gallons per mile
Step-by-step explanation:
Find two positive numbers such that the ratio of the two numbers is 7 to 3 and the product of the two numbers is 525.
Answer:
35 and 15
Step-by-step explanation:
Process of elimination:
Try 105 and 5 - 105 is way too much and 5 is way too little. We know that they are between 5 and 105.
Try 50 and 10.5 - This is closer, but 50 is still too much and 10.5 is too little. We now know that the two numbers are between 10.5 and 50
Try 30 and 17.5 - This is very close, but now 30 is not enough and 17.5 is too much. We now know that the smaller number is between 10.5 and 17.5 as well as the larger number is between 30 and 50.
Try 40 and 13.125 - This is also very close, but 40 is too much and 13.125 is too little. We now know that the lower number is between 13.125 and 17.5 as well as the larger number is between 30 and 40.
Try 35 and 15 - Success: 35 and 5 make the simplified ratio of 7:3! They also are products of 525!
Final answer:
The two positive numbers with a ratio of 7 to 3 and a product of 525 are found to be 35 and 15, by assigning a constant to the numbers, forming and solving a quadratic equation to find the value of the constant, and then using it to find the two numbers.
Explanation:
To find two positive numbers where their ratio is 7 to 3, and their product is 525, we can assign values x and y to the numbers such that x/y = 7/3, and x*y = 525. We can solve these equations simultaneously to find the values of x and y.
Step-by-step solution:
Let the two numbers be 7k and 3k, where k is a constant. This ensures that the ratio 7 to 3 is preserved.Since the product of the two numbers is 525, we have that 7k * 3k = 525.Combining like terms, we get 21k^2 = 525.Dividing both sides by 21 gives k^2 = 25.Taking the square root of both sides, we find that k = 5.Substitute k = 5 back into 7k and 3k to find the two numbers: 7*5 = 35 and 3*5 = 15.Therefore, the two numbers are 35 and 15.
Given the following equation:
4(x + 2) = 20
Use the two methods you have learned to eliminate the parentheses and create a new equation that can be solved using inverse operations.
One method is to use the distributive property.
Using this method, the equivalent equation is .
Another method is to use the reciprocal.
Using this method, the equivalent equation is .
Answer: useing the distributive property the method is 4x+8=20
using the reciprocal the method is x+2=5
Step-by-step explanation:
Answer:
Using this method, the equivalent equation is 4x+8=20.
Another method is to use the reciprocal.
Using this method, the equivalent equation is x+2=5.
Step-by-step explanation:
IT IS CORRECT
The line graph contains an error. Study the graph carefully and use complete sentences to describe the error.
Answer:
The scale doesn't start at 0. One could argue the maximum value should be 7, but this is a formatting choice.
Step-by-step explanation:
Answer:
The scale doesn't start at 0. One could argue the maximum value should be 7, but this is a formatting choice.
Step-by-step explanation:
The common fruit fly Drosophila melanogaster is the most studied organism in genetic research because it is small, easy to grow, and reproduces rapidly. The length of the thorax (where the wings and legs attach) in a population of male fruit flies is approximately Normal with mean 0.800 millimeters (mm) and standard deviation 0.078 mm. Draw a Normal curve on which this mean and standard deviation are correctly located. (Hint: Draw an unlabeled Normal curve, locate one, two and three standard deviations away from the mean, then add number labels on the horizontal axis.)
Answer:
The Normal curve with the mean and standard deviations is shown below.
Step-by-step explanation:
According to the Empirical Rule in a normal distribution with mean µ and standard-deviation σ, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be broken into three parts:
68% data falls within 1 standard deviation of the mean. That is P (µ - σ ≤ X ≤ µ + σ) = 0.68. 95% data falls within 2 standard deviations of the mean. That is P (µ - 2σ ≤ X ≤ µ + 2σ) = 0.95. 99.7% data falls within 3 standard deviations of the mean. That is P (µ - 3σ ≤ X ≤ µ + 3σ) = 0.997.The length of the thorax in a population of male fruit flies is approximately Normal.
The mean is, µ = 0.800 mm and the standard deviation is, σ = 0.078 mm.
Then:
68% data falls within 1 standard deviation of the mean. That is P (µ - σ ≤ X ≤ µ + σ) = P (0.722 ≤ X ≤ 0.878) = 0.68.95% data falls within 2 standard deviations of the mean. That is P (µ - 2σ ≤ X ≤ µ + 2σ) = P (0.644 ≤ X ≤ 0.956) = 0.95.99.7% data falls within 3 standard deviations of the mean. That is P (µ - 3σ ≤ X ≤ µ + 3σ) = P (0.566 ≤ X ≤ 1.034) = 0.997.The Normal curve with the mean and standard deviations is shown below.
1. Solve for x.
Need help in math
Answer:
21 maybe?
Step-by-step explanation:
if those numbers represent lengths and those lines are the same size, x is 21
change the decimal number 3.5 into a mixed number
Answer: [tex]3\frac{1}{2}[/tex]
Multiply
[tex]3.5/1*10/10=35/10[/tex]
Divide each side by 5
[tex]35/10[/tex] ÷ [tex]5/5=7/2[/tex]
[tex]7/2=3\frac{1}{2}[/tex]
Answer:
[tex] \frac{3.5}{1} \frac{ \times }{ \times } \frac{10}{10} = \frac{35}{10} \\ \frac{35}{10} \frac{ \div }{ \div } \frac{5}{5} \\ = \frac{7}{2} = 3 \frac{1}{2} [/tex]
hope this helps you...
Use the normal distribution to find a confidence interval for a proportion p given the relevant sample results. Give the best point estimate for p, the margin of error, and the confidence interval. Assume the results come from a random sample. A 99% confidence interval for p given that p-hat = 0.34 and n= 500. Point estimate ___________ (2 decimal places) Margin of error __________ (3 decimal places) The 99% confidence interval is ________ to _______ (3 decimal places)
Answer:
(a) The point estimate for the population proportion p is 0.34.
(b) The margin of error for the 99% confidence interval of population proportion p is 0.055.
(c) The 99% confidence interval of population proportion p is (0.285, 0.395).
Step-by-step explanation:
A point estimate of a parameter (population) is a distinct value used for the estimation the parameter (population). For instance, the sample mean [tex]\bar x[/tex] is a point estimate of the population mean μ.
Similarly, the the point estimate of the population proportion of a characteristic, p is the sample proportion [tex]\hat p[/tex].
The (1 - α)% confidence interval for the population proportion p is:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided is:
[tex]\hat p=0.34\\n=500\\(1-\alpha)\%=99\%[/tex]
(a)
Compute the point estimate for the population proportion p as follows:
Point estimate of p = [tex]\hat p[/tex] = 0.34
Thus, the point estimate for the population proportion p is 0.34.
(b)
The critical value of z for 99% confidence level is:
[tex]z={\alpha/2}=z_{0.01/2}=z_{0.005}=2.58[/tex]
*Use a z-table for the value.
Compute the margin of error for the 99% confidence interval of population proportion p as follows:
[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]=2.58\sqrt{\frac{0.34(1-0.34)}{500}}[/tex]
[tex]=2.58\times 0.0212\\=0.055[/tex]
Thus, the margin of error for the 99% confidence interval of population proportion p is 0.055.
(c)
Compute the 99% confidence interval of population proportion p as follows:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]CI=\hat p\pm MOE[/tex]
[tex]=0.34\pm 0.055\\=(0.285, 0.395)[/tex]
Thus, the 99% confidence interval of population proportion p is (0.285, 0.395).
The point estimate for p is 0.34. The margin of error, calculated using a z-score of 2.576, is 0.034. The 99% confidence interval is from 0.306 to 0.374.
Explanation:This question is about calculating a confidence interval for a proportion using the normal distribution. The best point estimate for p is the sample proportion, p-hat, which is 0.34.
For a 99% confidence interval, we use a z-score of 2.576, which corresponds to the 99% confidence level in a standard normal distribution. The formula for the margin of error (E) is: E = Z * sqrt[(p-hat(1 - p-hat))/n]. Substituting into the formula, E = 2.576 * sqrt[(0.34(1 - 0.34))/500] = 0.034.
The 99% confidence interval for p is calculated by subtracting and adding the margin of error from the point estimate: (p-hat - E, p-hat + E). The 99% confidence interval is (0.34 - 0.034, 0.34 + 0.034) = (0.306, 0.374).
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For the 405 highway that car pass through a checkpoint, assume the speeds are normally distributed such that μ= 61 miles per hour and δ=4 miles per hour. Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.
Answer:
[tex]Z = 1[/tex]
Step-by-step explanation:
Z - score
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 = 61, \sigma = 4[/tex]
Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.
This is Z when X = 65. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{65 - 61}{4}[/tex]
[tex]Z = 1[/tex]
a circle with circumference 18 had an arc with 120 central angle. what is the length of the arc
Answer:
c
Step-by-step explanation:
a circle with circumference 18 had an arc with 120 central angle. what is the length of the arc
To find the length of a 120-degree arc in a circle with an 18-unit circumference, we apply the fraction of a full circle the angle represents to the total circumference, resulting in an arc length of 6 units.
To determine the length of an arc with a 120-degree central angle in a circle with an 18-unit circumference, we use the relationship between the angle and the circumference of the circle. By knowing that the circumference corresponds to 360 degrees, we can calculate the length of the arc for any given angle by finding what fraction of 360 degrees the angle represents and applying that fraction to the total circumference.
The formula to use is: Arc length (s) = (Angle in degrees/360) * Circumference of the circle. For an angle of 120 degrees, this becomes: s = (120/360) * 18. Doing the math, we find that s = (1/3) * 18, which simplifies to s = 6. Therefore, the length of the arc is 6 units.