In the past, 21% of all homes with a stay-at-home parent, the father is the stay-at-home parent. An independent research firm has been charged with conducting a sample survey to obtain more current information. (a) What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.09? Use a 95% confidence level. (Round your answer up to the nearest whole number.)

Answers

Answer 1

Answer:

Answer:

A sample size of 79 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{(\pi(1-\pi))/(n)}$

In which

z is the zscore that has a pvalue of $1 - (\alpha)/(2)$ .

For this problem, we have that:

$\pi = 0.21$

The margin of error is:

$M = z\sqrt{(\pi(1-\pi))/(n)}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - (0.05)/(2) = 0.975$ , so $Z = 1.96$ .

What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.09?

A sample size of n is needed.

n is found when M = 0.09. So

$M = z\sqrt{(\pi(1-\pi))/(n)}$

$0.09 = 1.96\sqrt{(0.21*0.79)/(n)}$

$0.09√(n) = 1.96√(0.21*0.79)$

$√(n) = (1.96√(0.21*0.79))/(0.09)$

$(√(n))^(2) = ((1.96√(0.21*0.79))/(0.09))^(2)$

$n = 78.68$

Rounding up to the nearest whole number.

A sample size of 79 is needed.

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What is the value of x in the equation 8+4 = 2(x-1)?
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11/2
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Answers

Answer:

x = 7

Step-by-step explanation:

I hope this helps!

Can anyone help me wit this!!

Answers

Answer:

See attachment for table values
y₁ = y₂ for x = 6

Step-by-step explanation:

In each case, put the x-value in the formula and do the arithmetic. If you're allowed, you can save some time and effort by realizing that the solution (x) will have to be an even number.

y₁ is an integer value for all integer values of x. y₂ is an integer value for even values of x only. y₁ and y₂ will both be integers (and possibly equal) only when x is even.

For example, for x = 6, we have

... y₁ = 3·6 - 8 = 18 -8 = 10

... y₂ = 0.5·6 +7 = 3 +7 = 10

That is, for x = 6, both columns of the table have the same number (10). That is, y₁ = y₂ for x = 6. The solution to the equation

... y₁ = y₂

... x = 6.

A flywheel is attached to a crankshaft by 12 bolts, numbered 1 through 12. Each bolt is checked to determine whether it is torqued correctly. Let A be the event that all the bolts are torqued correctly, let B be the event that the #3 bolt is not torqued correctly, let C be the event that exactly one bolt is not torqued correctly, and let D be the event that bolts #5 and #8 are torqued correctly. State whether each of the following pairs of events is mutually exclusive.a. A and Bb. B and Dc. C and Dd. B and C

Answers

Answer:

Mutually exclusive

Not Mutually exclusive

Step-by-step explanation:

From the question we are told that

The number of bolt is n = 12

The event that all the bolt are torqued correctly is A

The event that the 3rd bolt is not torqued correctly is B

The event that exactly one bolt is not torqued correctly is C

The event that the $4^(th)$ and $8^(th)$ are torqued correctly is D

Generally for an event to be mutually exclusive it means that both event can not occur at the same time

Considering a

The A and B are mutually exclusive because they can not occur at the same time

Considering b

The event B and D are not mutually exclusive because they can occur at the same time

Considering c

Event C and D are not mutually exclusive because they can occur at the same time

Considering d

Event B and C are not mutually exclusive because they can occur at the same time

Final answer:

Event pairs A and B, and B and C are mutually exclusive. Event pairs B and D and C and D are not mutually exclusive.

Explanation:

In order to determine whether two events are mutually exclusive, we need to check if they can both occur at the same time. If the occurrence of one event necessarily means that the other event cannot occur, then the events are mutually exclusive. Let's analyze each pair of events:

a. A and B: These events are mutually exclusive because if all the bolts are torqued correctly (event A), then it is not possible for the #3 bolt to be not torqued correctly (event B) at the same time.

b. B and D: These events are not mutually exclusive because it is possible for the #3 bolt to be not torqued correctly (event B) while the bolts #5 and #8 are torqued correctly (event D).

c. C and D: These events are not mutually exclusive because it is possible for exactly one bolt to not be torqued correctly (event C) while the bolts #5 and #8 are torqued correctly (event D).

d. B and C: These events are mutually exclusive because if exactly one bolt is not torqued correctly (event C), then it is not possible for the #3 bolt to be not torqued correctly (event B) at the same time.

Learn more about Mutually exclusive events here:

brainly.com/question/31910317

#SPJ3

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Answers

Answers:

9/2

5/1

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9/2
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The sum of two consecutive integers is -39. List the two numbers from smallest to greatest

Answers

Answer:

-20, -19

Step-by-step explanation:

The average of the two numbers is -39/2 = -19.5. The smaller number is 0.5 less than this, -20, and the larger number is 0.5 more than -19.5, so is -19.

_____

Comment on the problem and solution

I find that working consecutive integer problems is often simplified by working with the average value of those integers:

the average of two consecutive odd integers is the even integer between them
the average of two consecutive even integers is the odd integer between them
the average of an odd number of integers of the same type (consecutive, consecutive odd, consecutive even) is the middle one
The average of an even number of consecutive integers is the "half" number between the middle two (as in this problem).

I need help on a question but im kinda in a rush

Answers

12√3

1) To find out the Lateral Area of this pyramid we need to calculate the area of those three equilateral triangles.

$\begin{gathered} Lateral_(Area)=3(s^2\frac{\sqrt[]{3}}{4})=3(16\frac{\sqrt[]{3}}{4}) \n L=3\cdot4\sqrt[]{3} \n L=12\sqrt[]{3} \end{gathered}$

2) Hence, the Lateral Area of that pyramid is 12√3 u²

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