At a research facility that designs rocket engines, researchers know that some engines fail to ignite as a result of fuel system error. From a random sample of 40 engines of one design, 14 failed to ignite as a result of fuel system error. From a random sample of 30 engines of a second design, 9 failed to ignite as a result of fuel system error. The researchers want to estimate the difference in the proportion of engine failures for the two designs. Which of the following is the most appropriate method to create the estimate?
a. A one-sample z-interval for a sample proportion
b. A one-sample z-interval for a population proportion
c. A two-sample z-interval for a population proportion
d. A two-sample z-interval for a difference in sample proportions
e. A two-sample z-interval for a difference in population proportions

Answers

Answer 1

Answer:

d) A two-sample z-interval for a difference in sample proportions

Step-by-step explanation:

Explanation:-

Given data a random sample of 40 engines of one design, 14 failed to ignite as a result of fuel system error.

First sample proportion    [tex]p_{1} = \frac{14}{40} = 0.35[/tex]

Given data random sample of 30 engines of a second design, 9 failed to ignite as a result of fuel system error.

second sample proportion   [tex]p_{2} = \frac{9}{30} = 0.30[/tex]

Null hypothesis: H₀: Assume that there is no significant between the two designs

H₀: p₁ = p₂

Alternative Hypothesis: H₁:

H₁: p₁ ≠ p₂

The test statistic

                          [tex]Z = \frac{p_{1}-p_{2} }{\sqrt{p q(\frac{1}{n_{1} } + \frac{1}{n_{2} } } )}[/tex]

where [tex]p = \frac{n_{1} p_{1}+n_{2} p_{2} }{n_{1} +n_{2} }[/tex]

          q =1-p

Answer 2

Answer:

E

Step-by-step explanation:

A two-sample z-interval for a difference in population proportions


Related Questions

A corporation is considering a new issue of convertible bonds, mandagemnt belives that the offer terns will be founf attractiv by 20% of all its current stockholders, suppoer that the belif is correct, a random sample of 130 stockholderss is taken.

a. What is the standard error of the sample proportion who find this offer attractive?
b. What is the probability that the sample proportion is more than 0.15?
c. What is the probability that the sample proportion is between 0.18 and 0.22?
d. Suppose that a sample of 500 current stockholders had been taken. Without doing the calculations, state whether the probabilities in parts (b) and (c) would have been higher, lower, or the same as those found.

Answers

Answer:

a. What is the standard error of the sample proportion who find this offer attractive? =  0.0351

b. What is the probability that the sample proportion is more than 0.15? = 0.9222

c. What is the probability that the sample proportion is between 0.18 and 0.22? =  0.4314

Step-by-step explanation:

see attachment for explanation

Answer:

Step-by-step explanation:

Given that,

p = 0.20

1 - p = 1 - 0.20 = 0.80

n = 130

\mu\hat p = p = 0.20

A) \sigma \hat p =  \sqrt[p( 1 - p ) / n] = \sqrt [(0.20 * 0.80 ) / 130] = 0.0351

B) P( \hat p > 0.15) = 1 - P( \hat p < 0.15)

= 1 - P(( \hat p - \mu \hat p ) / \sigma \hat p < (0.15 - 0.20) / 0.0351 )

= 1 - P(z < -1.42)

Using z table

= 1 - 0.0778

= 0.9222

C) P(0.18 < \hat p < 0.22)

= P[(0.18 - 0.20) / 0.0351 < ( \hat p - \mu \hat p ) / \sigma \hat p < (0.22 - 0.20) / 0.0351]

= P(-0.57 < z < 0.57)

= P(z < 0.57) - P(z < -0.57)

Using z table,    

= 0.7157 - 0.2843

= 0.4314

Solve for x: 3x + 3 = -2x + 13

Please add step by step! I am here to understand, not just for answers.
Please and thank you!!​

Answers

Answer:

x=2

Step-by-step explanation:

To solve, we need to isolate the variable (x)

To do this, we must get all the variables to one side of the equation, and all the numbers to the other

3x+3= -2x+13

Add 2x to both sides to "reverse" the subtraction

5x+3=13

Subtract 3 from both sides to "reverse" the addition

5x=10

Divide both sides by 5 to "reverse" the multiplication

x=2

how many cups are equal to 34 pint

Answers

34 (US) pints is equal to 64 (US) cups

Explanation: _ Pints x2 = cups
Example: 44 pints = 88 cups

By using multiplication, there are 68 cups is equal to 34 pints.

Given that,

Change the number 34 pint into cups.

Used the concept of measurement unit,

A measurement unit is a standard quality used to express a physical quantity. Also, it refers to the comparison between the unknown quantity with the known quantity.

Since we know that;

1 pint = 2 cups

Hence, we get;

34 pint = 34 x 2 cups

= 68 cups

Therefore, the number of cups in 34 pints is 68.

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solve the system equations -x-y=0 and 6x-5y=66 by combining the equations

Answers

Answer:

x,y(6.-6)

Step-by-step explanation:

{x=-y

6(-y)-5y=66

-6-5y=66

11y=66

y=6

-x-y=0

x=-y;

x=-6

Suppose that 73.2% of all adults with type 2 diabetes also suffer from hypertension. After developing a new drug to treat type 2 diabetes, a team of researchers at a pharmaceutical company wanted to know if their drug had any impact on the incidence of hypertension for diabetics who took their drug. The researchers selected a random sample of 1000 participants who had been taking their drug as part of a recent large-scale clinical trial and found that 718 suffered from h The researchers want to use a one-sample z-test for a population have hypertension while taking their new drug, p, is different from the proportion of all type 2 diabetics who have hypertension. They decide to use a significance level of a 0.01. to see if the proportion of type 2 diabetics who Determine if the requirements for a one-sample z-test for a proportion been met. If the requirements have not been met leave the rest of the questions blank. O The requirements have not been met because there are two samples: the type 2 diabetics with hypertension who are not taking the drug and the ones who are taking the drug O The requirements have been met because the sample was appropriately selected, the variable of interest is categorical with two possible outcomes, and the sampling distribution is approximately normal. O The requirements have not been met because the population standard deviation is unknown. O The requirements have been met because the sample was appropriately selected, the variable of interest is categorical with two possible outcomes, and the sample size is at least 30.

Answers

Using the normal approximation to the binomial, it is found that the correct option is:

The requirements have been met because the sample was appropriately selected, the variable of interest is categorical with two possible outcomes, and the sampling distribution is approximately normal.

The binomial distribution, which is the probability of exactly x successes on n repeated trials, with p probability of success on each trial(each trial either is a success or it is a failure), can be approximated to the normal if in a sample, there are at least 10 successes and at least 10 failures.

In this problem:

Random sample of 1000, hence, appropriately selected.For each person, there are two possible outcomes, either they suffered from hypertension, or they did not, hence, the variable is categorical.718 have hypertension, 282 have not, at least 10 of each, hence, the sampling distribution is approximately normal.

Thus, the correct option is:

The requirements have been met because the sample was appropriately selected, the variable of interest is categorical with two possible outcomes, and the sampling distribution is approximately normal.

A similar problem is given at https://brainly.com/question/24261244

Jim bought a new bicycle for $129. If the sales tax is 8%, how much did Jim pay in sales tax? What was the total cost?

Answers

Answer:

$10.32 is the sales tax.

$139.32 is the total price.

Step-by-step explanation:

Sales tax is 8% of the original price.

First, change the percentage into a decimal, by moving the decimal point to the left two place values: 8% = 0.08

Next, multiply 129 with 0.08:

129 x 0.08 = 10.32

$10.32 is the sales tax.

Then, add 10.32 to the original price:

10.32 + 129 = 139.32

$139.32 is the total price.

14) World Wide Insurance Company found that 53% of the residents of a city had homeowner’s insurance (H) with the company. Of these clients, 27% also had automobile insurance (A) with the company. If a resident is selected at random, find the probabil- ity that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company.

Answers

Answer:

The probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company is 14% (P=0.1431).

Step-by-step explanation:

The probability of having homeowner’s insurance (H) with the company is P(H)=0.53.

The probability that, given that the resident has homeowner insurance with the company, also had a automobile insurance is P(A|H)=0.27.

We have to calculate P(A&H): probability of having automovile and homeowner:

[tex]P(A\&H)=P(H)*P(A|H)=0.53*0.27=0.1431[/tex]

Answer:

The probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company is 0.143 OR 14.3%.

Step-by-step explanation:

We are given that:

53% of the residents had homeowner's insurance i.e. P(H) = 0.53

Of these people, 27% also had automobile insurance i.e. they had automobile insurance given that they had homeowner's insurance. So, P(A|H) = 0.27.

We need to find out the probability that the resident has both homeowner's and automobile insurance i.e. P(A and H) or P(A∩H). To compute P(A∩H) we will use the conditional probability formula:a

P(A|B) = P(A∩B)/P(B)

Here we have:

P(A|H) = P(A∩H)/P(H)

P(A∩H) = P(A|H) * P(H)

            = 0.27 * 0.53

P(A∩H) = 0.143

The probability that the resident has both homeowner’s and automobile insurance with World Wide Insurance Company is 0.143 OR 14.3%.

What is the answer of 7/8 x 1/2 equals

Answers

Answer:

[tex]\frac{7}{16}[/tex]

Step-by-step explanation:

[tex]\frac{7}{8}[/tex]×[tex]\frac{1}{2}[/tex]

Multiply straight forward:

So 7 and 1. 8 and 2.

7x1=7

8x2=16

[tex]\frac{7}{16}[/tex]

An "x-bar" control chart is developed for recording the mean value of a quality characteristic by use of a sample size of three. The control chart has control limits (LCL and UCL) of 1.000 and 1.020 pounds, respectively. If a new sample of three items has weights of 1.023, 0.999, and 1.025 pounds, what can we say about the lot (batch) it came from?

Answers

Answer:

0.0879 or 8.79 % is the process capability of the batch and the batch doesn't meet the control limits.

Step-by-step explanation:

mean of three readings=(1.023+0.999+1.025)/3= 1.0157

standard deviation=√((1.023-1.0157)² + (0.999-1.0157)²+ (1.025-1.0157)²)/3)

                             = 0.0163

Process Capability= min((USL-mean)/3SD, (Mean-LSL)/3SD)

(USL-mean)/3SD= (1.02-1.0157)/(3×0.0163)= 0.0879

(Mean-LSL)/3SD)= (1.0157-1.00)/(3×0.0163)= 0.321

Process capability=(0.0879,0.321)

0.0879 or 8.79 % is the process capability

Final answer:

The x-bar control chart and other statistical tools are used to assess whether product weights are within acceptable limits, thereby determining if quality standards are met and if equipment recalibration might be necessary.

Explanation:

The question involves evaluating if a batch of products (in this case, potentially cereal boxes, soda servings, lifting weights, apples, or lettuce) meets certain quality control standards, specifically relevant to the weights and measurements being within predefined control limits or tolerances. Using an x-bar control chart and statistical methods like hypothesis testing or calculating percent uncertainty, quality control specialists can determine whether a product's quality characteristic, such as weight, is within acceptable ranges, thereby assessing if equipment recalibration is needed or if a batch complies with quality standards.

For instance, if a new sample of items has weights that fall outside of the established control limits on the x-bar control chart, it would suggest that there may be an issue with the process control, indicating potential problems with the lot from which the sample was taken.

Concerning the exercises provided: In the case of the cereal boxes with a standard deviation higher than the acceptable limit, it suggests that recalibration might be needed. For the Class A apples, a hypothesis test at the specified significance levels would help determine compliance with weight tolerance. Calculating the percent uncertainty of a bag's weight informs us about the relative size of the uncertainty in measurements.

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Write parametric equations of the line 9x + y = -1
a. X= 1, y = -9z+ 9
b. X= 1, y =--9
C. X= t_y= 9- 1
d. X= 1, y=-97- 1

Answers

The question is faulty written. I'll solve it assuming values for one variable and provide the answer to guide the student in their own question

Answer:

x=t

y=-1-9t

Step-by-step explanation:

Parametric Equations

Given an explicit relation between variables x and y, we can find expression for both of them in term of a third parameter t, such as

x=f(t)

y=g(t)

provided the main relation holds.

we have the equation

9x+y=-1

There are infinitely many forms to find parametric expressions for the variables, let's assume

x=t

Solving the equation for y

y=-1-9x=-1-9t

Thus the parametric equations are

x=t

y=-1-9t

Ms. Burke invested $23,000 in two accounts, one yielding 4% interest and the other yielding 10%. If she received a total of $1,280 in interest at the end of the year, how much did she invest in each account?

Answers

Answer:

$17,000 at 4%$6,000 at 10%

Step-by-step explanation:

Let x represent the amount invested at 10%. Then 23000-x is the amount invested at 4%, and the total interest is ...

  0.10x +0.04(23000-x) = 1280

  0.06x = 360 . . . . . subtract 920, simplify

  x = 6000 . . . . . . . . divide by the coefficient of x

Ms Burke invested $6000 at 10% and $17000 at 4%.

Do flashcards help students retain the Chinese Language? Six randomly selected students are given a pretest, asked to study a set of flashcards once a day for a week and then given post test for their Chinese Language class. Is there evidence that flashcards can improve scores? Their data is below. What is the test statistic?(pretest – posttest)

Answers

Answer:

-1.64

Explanation:

Multiple Choice Answers that were not provided in the question:

a. 0.103 .

b. None of the above.

c. -4.16

d. -1.45

e. 2.86

f .-1.64

The provided data is as below:

             Student 1  Student 2  Student 3  Student 4  Student 5  Student 6

Pre- test    80              76              76              50             48              67

Post- test   75              86              87              60            48               68

Further Explanation:

                    Student 1  Student 2  Student 3  Student 4  Student 5  Student 6

Pre- test             80              76              76              50             48              67

Post- test            75              86              87              60            48               68

Pretest-Postest   5               -10              -11              -10            0                 -1

Calculating the mean of the difference (Pretest-postest) we get d bar = -4.5

Calculating the standard deviation  of the difference  (Pretest-postest) we get sd= 6.716.

Since sample score is under 30 and population standard deviation is unknown, we will use a tscore to find the standardized test statistic

t = dbar/(sd/√n) = -4.5/(6.716√6) = -1.642 ≈ -1.64

The test statistic is -1.64.

About 8 million tons of plastic waste enters the world’s oceans every year. Write a y = mx equation to show this

Answers

Answer: [tex]y=8x[/tex]

Step-by-step explanation:

For this exercise it is important to remember that the equation of a line that passes through the origin (this is located at the point [tex](0,0)[/tex]), has the following form:

[tex]y=mx[/tex]

Where "m" is the slope of the line.

In this case, according to the information given in the exercise, you know that 8 million tons of plastic waste enters the world’s oceans every year, apprdoximately.

Then, let the independent variable "x" represents the number of years.

 Analizing the data given, you can identify that the slope of that line is the following:

[tex]m=8[/tex]

So, knowing the value of "m", you can subsitute them into the equation  [tex]y=mx[/tex], in order to get the equation that shows that situation.

This is:

[tex]y=8x[/tex]

The supervisor of a production line wants to check if the average time to assemble an electronic component is different from 14 minutes. Assume that the population of assembly time is normally distributed with a standard deviation of 3.4 minutes. The supervisor times the assembly of 14 components, and finds that the average time for completion is 11.6 minutes. How would you calculate the p-value for the hypothesis test

Answers

Answer:

The p-value for the hypothesis test is 0.0042.

Step-by-step explanation:

We are given that the supervisor of a production line wants to check if the average time to assemble an electronic component is different from 14 minutes.

Assume that the population of assembly time is normally distributed with a standard deviation of 3.4 minutes. The supervisor times the assembly of 14 components, and finds that the average time for completion is 11.6 minutes.

Let [tex]\mu[/tex] = average time to assemble an electronic component.

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 14 minutes  {means that the average time to assemble an electronic component is equal to 14 minutes}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 14 minutes   {means that the average time to assemble an electronic component is different from 14 minutes}

The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;

                        T.S.  = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample average time for completion = 11.6 minutes

             [tex]\sigma[/tex] = population standard deviation = 3.4 minutes

             n = sample of components = 14

So, test statistics  =  [tex]\frac{11.6-14}{\frac{3.4}{\sqrt{14} } }[/tex]  

                               =  -2.64

Now, P-value of the hypothesis test is given by the following formula;

         P-value = P(Z < -2.64) = 1 - P(Z [tex]\leq[/tex] 2.64)

                                              = 1 - 0.99585 = 0.0042

Hence, the p-value for the hypothesis test is 0.0042.

The p-value for the hypothesis test is approximately 0.0082

To calculate the p-value for the hypothesis test, follow these steps:

1. State the null and alternative hypotheses:
  - Null hypothesis (\(H_0\)): The average assembly time is 14 minutes. \( \mu = 14 \)
  - Alternative hypothesis (\(H_1\)): The average assembly time is different from 14 minutes. \( \mu \ne 14 \)

2. Determine the test statistic:
  Since the population standard deviation (\(\sigma\)) is known, use the \( z \)-test for the mean. The test statistic is calculated using the formula:
[tex]\[ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \][/tex]
  where:
  - \(\bar{x}\) is the sample mean,
  - \(\mu\) is the population mean under the null hypothesis,
  - \(\sigma\) is the population standard deviation,
  - \(n\) is the sample size.

  Given:
  [tex]\(\bar{x} = 11.6\) minutes,\\ \(\mu = 14\) minutes,\\ \(\sigma = 3.4\) minutes,\\ \(n = 14\).[/tex]

  Plug these values into the formula:
  [tex]\[ z = \frac{11.6 - 14}{3.4 / \sqrt{14}} \][/tex]

3. Calculate the value of the test statistic:
  [tex]\[ z = \frac{11.6 - 14}{3.4 / \sqrt{14}} = \frac{-2.4}{3.4 / \sqrt{14}} \approx \frac{-2.4}{0.9087} \approx -2.64 \][/tex]

4. Find the p-value:
  The p-value for a two-tailed test is calculated by finding the probability that the test statistic is at least as extreme as the observed value, under the null hypothesis.

  [tex]\[ p\text{-value} = 2 \times P(Z \leq z) \][/tex]

  Since we have a \( z \)-score of -2.64, we look up the cumulative probability for \( Z = -2.64 \) in the standard normal distribution table or use a calculator to find:
  [tex]\[ P(Z \leq -2.64) \approx 0.0041 \][/tex]

  Therefore:
  [tex]\[ p\text{-value} = 2 \times 0.0041 = 0.0082 \][/tex]

5. Interpret the results:
  Compare the p-value to the significance level (\(\alpha\)) to make a decision. Typically, \(\alpha\) is set at 0.05. If the p-value is less than \(\alpha\), we reject the null hypothesis.

  In this case:
  [tex]\[ p\text{-value} = 0.0082 \][/tex]

  Since \(0.0082 < 0.05\), we reject the null hypothesis. There is significant evidence to suggest that the average assembly time is different from 14 minutes.

So, the p-value for the hypothesis test is approximately 0.0082.

Two married couples have purchased theater tickets and are seated in a row consisting of just 4 seats. If they take their seats in a completely random order, what is the probability that at least one of the wives ends up sitting next to her husband? Hint: Use probability of a complement event. That is, P(A) = 1 − P(A′), where A′ is the complement of an event A.

Answers

Answer:

The answer is 0.75.

Step-by-step explanation:

To use probability of a complement event, we need to find the situation where none of the couples are sitting next to each other which can happen either two husbands are sitting in the seats 2 and 3 or two wives are sitting in the seats 2 and 3. Also in the first scenario, the wives would need to be sitting at the opposite ends to their husbands and vice versa for the second scenario.

So there are in total 4 scenarios where no couple is sitting next to each other.

There are a total of 16 different ways that they can be seated so the probability of compelement is 16 - 4 = 12, which is 3/4 of the total, meaning that the probability of at least one of the wives sittting next to her husband is 0.75 or 75%.

I hope this answer helps.

Riddle me this. A New Hotel containing 100 rooms. Tom was Hired to paint the numbers from 1-100 on the doors. How many times will Tom have to paint the number 8?

I beat Desi Velasquez

Answers

Answer:

20 times

Step-by-step explanation:

8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 98

1     2    3   4   5   6      7   8     9   10  11    12   13   14   15   16  17 18 19 20

From1-100, the numbers that contain eight include;
8
18
28
38
48
58
68
78
80
81
82
83
84
85
86
87
88
89
98
So, tom would have to paint the number "8", 19 times.

6.6.1. Rao (page 368, 1973) considers a problem in the estimation of linkages in genetics. McLachlan and Krishnan (1997) also discuss this problem and we present their model. For our purposes, it can be described as a multinomial model with the four categories C1, C2, C3 , and C4 . For a sample of size n, let X = (X1, X2, X3 , X4 )′ denote the observed frequencies of the four categories. Hence, n = +4 i=1 Xi. The probability model is

Answers

Answer:

Step-by-step explanation:

find attached the solution

Find the volume of a cone with a diameter of 40cm and a height of 40 cm.

Answers

Answer:

[tex]v = \pi {r}^{2} \frac{h}{3} \\ \: \: \: \: = \pi \times 20 \frac{40}{3} \\ \: \: \: \: = 16755.16 {cm}^{3} [/tex]

hope this helps you

From the Balance Sheet and Income Statement Information below, calculate the following ratios:
[a.] Return on Sales
[b.] Current Ratio
[c.] Inventory Turnover – If there are no beginning inventory or ending inventory figures, then use the Merchandise Inventory figure.

ABC INC. Income Statement Year Ended December 31, 2018
Net Sales Revenue $20,941
Cost of Goods Sold 7,055
Gross Profit 13,886
Operating Expenses 7,065
Operating Income 6,821
Interest Expense 210
Income Before Taxes 6,611
Income Tax Expense 2,563
Net Income $4,048

ABC INC. Balance Sheet December 31, 2018 Assets
Current Assets
Cash $2,450
Accounts Receivable 1,813
Merchandise Inventory 1,324
Prepaid Expenses 1,709
Total Current Assets 7,296
Long-Term Assets 18,500
Total Assets $25,796

Liabilities
Current Liabilities $7,320
Long-Term Liabilities 4,798
Total Liabilities 12,028

Stockholders’ Equity
Common Stock 6,568
Retained Earnings 7,200
Total Stockholders’ Equity 13,768
Total Liabilities & Stockholders’ Equity $25,796

1. NOTES: 1- Round up
2- Your responses should be in the following formats

a. XX% b. x.xx c. x.xx

Answers

Answer:

a)   32.57%

b)   0.9967

c)   5.3285 times.

Step-by-step explanation:

a. Return on sales is a simple ratio that is calculated by dividing the operating profit/income  by the net sales revenue.

-Given net sales revenue is $20,941 and the operating income is $6,821:

[tex]Return \ on \ sales(ROS)=\frac{Operating \ Income}{Net \ Sales \ Revenue}\\\\=\frac{6821}{20941}\\\\=0.3257\\\\=32.57\%[/tex]

Hence, the return on sales is 32.57%

b. Current ratio is a simple ratio that compares the current assets to the current liabilities.

-Given that current assets=$7,296 and current liabilities=$7,320, the current ratio is calculated as below:

[tex]Current \ Ratio=\frac{Current \ Assets}{Current \ Liabilities}\\\\=\frac{7296}{7320}\\\\=0.9967[/tex]

Hence, the current ratio is 0.9967

c. Inventory turnover is a measure of the frequency with which a company's goods is used or sold and subsequently restocked in given period.

-It's calculated by dividing the cost of goods sold by the average invenory as below:

[tex]Inventory \ Turnover=\frac{Cost \ of \ goods \ sold}{mean \ Invenory}\\\\\\=\frac{7055}{1324}\\\\=5.3285\ times[/tex]

Hence, the inventory turnover is 5.3285 times.

Final answer:

The calculated ratios for ABC Inc. are: Return on Sales of 19.3%, a Current Ratio of 0.997, and an Inventory Turnover of 5.33.

Explanation:

To calculate the ratios requested, we'll be using the financial data from ABC Inc.'s income statement and balance sheet.

[a.] Return on SalesThe Return on Sales (ROS) is calculated by dividing the Net Income by the Net Sales Revenue. Here it's $4,048 / $20,941 = 0.193 or 19.3%.[b.] Current RatioThe Current Ratio represents a company's ability to repay its short-term liabilities with its short-term assets. It's calculated by dividing Total Current Assets by Total Current Liabilities: $7,296 / $7,320 = 0.997.[c.] Inventory TurnoverSince we don't have beginning inventory or ending inventory figures, we use the Merchandise Inventory of $1,324 in our calculation. Inventory Turnover is Cost of Goods Sold divided by Merchandise Inventory: $7,055 / $1,324 = 5.33.

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Find the cubic unit make sure to put cubic units after your answer

Answers

Answer:

24 cubic units

Step-by-step explanation:

4 times 2 times 3 equals 24

Paul plays a video game that is scored by round . In about 500 rounds his career average is 20 points per round with a standard deviation of 5 points per round . Suppose we take random samples of past 3 rounds and calculate the mean number of points scored in each sample . What is the mean and sd of sampling distribibution

Answers

Answer:

The mean of the sampling distribution is 20 and the standard deviation is 2.89.

Step-by-step explanation:

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.

Population:

Mean 20, standard deviation of 5.

Sampling distribution:

3 rounds

Mean = 20

[tex]s = \frac{5}{\sqrt{3}} = 2.89[/tex]

The mean of the sampling distribution is 20 and the standard deviation is 2.89.

Final answer:

The mean of Paul's sampling distribution is 20 points per round, and the standard deviation is approximately 2.89 points per round, calculated using the formula for the standard error of the mean.

Explanation:

The scenario involves a sampling distribution of the mean scores over random samples of 3 rounds from Paul's video game scores. To calculate the mean and standard deviation (sd) of the sampling distribution, we use the following formulas:

The mean of the sampling distribution (μX) is equal to the population mean (μ), which is 20 points per round.The standard deviation of the sampling distribution (σX), also known as the standard error, is equal to the population standard deviation (σ) divided by the square root of the sample size (n), so σX = σ/√n. In this case, it would be 5/√3, approximately 2.89 points per round.

Therefore, the mean of the sampling distribution is 20, and the standard deviation is approximately 2.89.

If f(-3) = -8, then f(x)= 3x +

Answers

Answer:

f(x)= 3x + 1

Step-by-step explanation:

Let's set the unknown variable as b, since it's a linear equation.

Using the point given (-3, -8), we can find b by plugging in the known numbers and solving.

-8 = -3 (3) + b

-8 = -9 + b

b = 1

If you want, you can check it by forming the complete equation and plugging in -3.

f(x)= 3x + 1

f(-3) = -9 + 1

f(-3) = -8 = -8

I hope this helped!

Csc^2 u -cos u sec u=cot^2 u

Answers

Step-by-step explanation:

csc²u − cos u sec u

csc²u − 1

cot²u

A circle has a radius of square root 98 units and is centered at (5.9, 6.7). Write the equation of this circle. Please help!

Answers

Given:

Given that the radius of the circle is √98 units.

The circle is centered at the point (5.9, 6.7)

We need to determine the equation of the circle.

Equation of the circle:

The general form of the equation of the circle is given by

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where (h,k) is the center and r is the radius of the circle.

Substituting the center point (h,k) = (5.9, 6.7) and r = √98, we get;

[tex](x-5.9)^2+(y-6.7)^2=(\sqrt{98})^2[/tex]

Simplifying, we get;

[tex](x-5.9)^2+(y-6.7)^2=98[/tex]

Thus, the equation of the circle is [tex](x-5.9)^2+(y-6.7)^2=98[/tex]

the equation of the circle with radius square root of 98 centered at (5.9, 6.7) is: [tex](x - 5.9)^2 + (y - 6.7)^2 = 98[/tex]

We know that the equation of circle is given by the formula:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

here h and k are the x and y coordinates of the center of circle and r is the radius. It is given to us that:

Radius = √98 units

Center at (5.9, 6.7)

Putting values into the equation we get:

[tex](x - 5.9)^2 + (y - 6.7)^2 = (\sqrt{98})^2\\\\ (x - 5.9)^2 + (y - 6.7)^2 = 98[/tex]

Therefore, the equation of the circle with radius square root of 98 centered at (5.9, 6.7) is: [tex](x - 5.9)^2 + (y - 6.7)^2 = 98[/tex]

You wish to test the following claim ( H a ) at a significance level of α = 0.01 . H o : μ = 60.8 H a : μ ≠ 60.8 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 8 with mean M = 66.9 and a standard deviation of S D = 10.7 . What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = -.1228 Incorrect The p-value is... less than (or equal to) α greater than α Correct This p-value leads to a decision to... reject the null accept the null fail to reject the null Incorrect

Answers

Answer:

Step-by-step explanation:

This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 60.8

For the alternative hypothesis,

µ ≠ 60.8

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 8,

Degrees of freedom, df = n - 1 = 8 - 1 = 7

t = (x - µ)/(s/√n)

Where

x = sample mean = 66.9

µ = population mean = 60.8

s = samples standard deviation = 10.7

t = (66.9 - 60.8)/(10.7/√8) = 1.61

We would determine the p value using the t test calculator. It becomes

p = 0.076

Since alpha, 0.01 < than the p value, 0.076, then we would fail to reject the null hypothesis. Therefore, At a 1 % level of significance, the sample data showed that there is no significant evidence that μ ≠ 60.8

Therefore, this p-value leads to a decision to accept the null hypothesis

A rectangular prism has a volume of 120 square feet a height of 15 feet and a width of 4 feet find the length

Answers

Volume = length x width x height

120 = 15 x 4 x length

Simplify:

120 = 60 x length

Divide both sides by 60:

Length = 2 feet

Formula for the volume of a rectangular prism: V = length x width x height

120 = l x 4 x 15

120 = l x 60

l = 2

The length of the rectangular prism is 2 feet.

Hope this helps!! :)

A product with an annual demand of 1000 units has Co = $25.50 and Ch = $8. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with μ=25 and σ=5. a.What is the recommended order quantity? b. What are the recorder point and safety stock if the firm desires at most a 2% probability of stockout on any given order cycle? c. If a manager sets the reorder point at 30, what is the probability of a stockout on any given order cycle? How many times would you expect a stockout during the year if the reorder point were used?

Answers

Answer:

a) Recommended order quantity = 79.84 = 80

b) recorder point = 35

Safety stock = 10

Safety stock cost = $0/year

ci) P(stock out/cycle) = 0.1587

cii) Number of stock outs/ year = 2

Step-by-step explanation:

The pictures attached show a clear explanation of all the processes.

Final answer:

To determine the recommended order quantity, use the EOQ formula. The reorder point and safety stock can be calculated using the normal distribution. If the reorder point is set at 30, the probability of a stockout and the expected number of stockouts can be calculated.

Explanation:

To determine the recommended order quantity, we need to consider the economic order quantity (EOQ) model. The EOQ formula is given by:

EOQ = √((2 * D * Co) / Ch)

Where:

D is the annual demand (1000 units)

Co is the ordering cost per order ($25.50)

Ch is the holding cost per unit ($8)

Plugging in the values, we get:

EOQ = √((2 * 1000 * 25.50) / 8) = 79.79 (rounded to 2 decimal places)

Therefore, the recommended order quantity is 80 units.

To calculate the reorder point, we need to consider the lead-time demand. Since the lead-time demand follows a normal probability distribution with μ=25 and σ=5, we can use the normal distribution to find the reorder point.

To calculate the recorder point and safety stock for a desired probability of stockout of 2%, we need to find the Z value corresponding to the desired probability. We can use the Z-score table or a calculator to find the Z value. For a 2% probability of stockout, the Z value is approximately -2.05 (rounded to 2 decimal places).

The reorder point is given by:

Reorder Point = μ + (Z * σ)

Where:

μ is the mean of the lead-time demand (25 units)

Z is the Z value (-2.05)

σ is the standard deviation of the lead-time demand (5 units)

Plugging in the values, we get:

Reorder Point = 25 + (-2.05 * 5) = 14.75 (rounded to 2 decimal places)

The safety stock is given by:

Safety Stock = Z * σ

Plugging in the values, we get:

Safety Stock = -2.05 * 5 = -10.25 (rounded to 2 decimal places)

Therefore, the recorder point is approximately 15 units (rounded to the nearest whole unit) and the safety stock is approximately 10 units (rounded to the nearest whole unit).

If the manager sets the reorder point at 30 units, we can use the normal distribution to find the probability of a stockout. The probability of a stockout can be calculated using the Z-score formula.

The Z value is calculated using the formula:

Z = (Reorder Point - μ) / σ

Where:

Reorder Point is the given reorder point (30 units)

μ is the mean of the lead-time demand (25 units)

σ is the standard deviation of the lead-time demand (5 units)

Plugging in the values, we get:

Z = (30 - 25) / 5 = 1 (rounded to 1 decimal place)

Looking up the Z value in the Z-score table, we find that the corresponding probability is approximately 0.8413. Therefore, the probability of a stockout on any given order cycle is approximately 0.1587 or 15.87% (rounded to 2 decimal places).

The number of times you would expect a stockout during the year can be estimated using the formula:

Number of Stockouts = (Annual Demand / EOQ) * (1 - Probability of Stockout)

Plugging in the values, we get:

Number of Stockouts = (1000 / 80) * (1 - 0.1587) = 10.69 (rounded to 2 decimal places)

Therefore, you would expect a stockout approximately 11 times during the year (rounded to the nearest whole number).

A manufacturer of brand A jeans has daily production costs of Upper C equals 0.3 x squared minus 114 x plus 11 comma 405​, where C is the total cost​ (in dollars) and x is the number of jeans produced. How many jeans should be produced each day in order to minimize​ costs? What is the minimum daily​ cost?

Answers

Answer:

190 Jeans

Step-by-step explanation:

The daily production cost of the jeans manufacturer is given as:

[tex]C=0.3x^2-114x+11405[/tex]

To determine the number of Jeans,x that should be produced daily to minimize cost, C. We take the derivative of C and solve for its critical points.

[tex]C'=0.6x-114\\$When C'=0\\0.6x-114=0\\0.6x=114\\x=190[/tex]

Therefore, to minimize daily cost, 190 Jeans is the number of jeans that should be produced daily.

What is the simplification if (x+2)(x+7)

Answers

Answer: 6969 or its 69

Convert 30°to radians. Leave answer as a reduced fraction in terms of π.

a: pi/3
b: pi/6
c: pi/4
d:pi/2

Answers

Answer: B

Step-by-step explanation:

[tex]30(\frac{\pi}{180})=\frac{\pi}{6}[/tex]

30 degree to radian= 0.523598776. b: pi/6 is your answer
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