Last year, nine employees of an electronics company retired. Their ages at retirement are listed below in years. Find the mean retirement age.56 65 62 53 68 58 65 52 56

Answer:

a) 95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.

b) Margin of error  = 0.0270.

Step-by-step explanation:

a)

[tex]\hat{p}[/tex] = point estimate of p [tex]= 268/1020 =0.2627[/tex]

[tex]\hat{q}= 1 - 0.2627 = 0.7373[/tex]

[tex]SE = \sqrt{\hat{p}\hat{q}/n}\\\\=\sqrt{0.2627\times 0.7373/1020}=0.0138\\\alpha = 0.05[/tex]

From Table, critical values of [tex]Z= \pm1.96[/tex] ,

Lower limit

                  [tex]= \hat{p} - Z SE\\ = 0.2627 - (1.96 X 0.0138) \\ = 0.2627 - 0.0276 \\ = 0.236[/tex]

upper limit = 0.2627 + 0.0276

                 = 0.2903

Correct option:

95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.

b) Margin of error =Z SE

                              = 1.96 X 0.0141

                              = 0.0270.

Answer:

[tex]y=-3x+3[/tex]

Step-by-step explanation:

We start by finding the slope of the line, which is given by the formula:

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

The points (x1, y1) and (x2, y2) are represented by the pairs given: (-2, 9) and (1, 0). WE can substitute this in and simplify.

[tex]m=\frac{0-9}{1-(-2)} =\frac{-9}{1+2} =\frac{-9}{3} =-3[/tex]

Using the point-slope formula, [tex]y-y_{1} =m(x-x_{1} )[/tex], we can find the equation. We can substitute the point (-2, 9) for (x1, y1):

[tex]y-9=-3(x+2)\\y-9=-3x-6\\y=-3x+3[/tex]

Answer:

Step-by-step explanation:

y is the remote exterior angle. The remote exterior angle has the strange property that it is equal to the two remote interior angle. The two remote interior angles are the two, neither of which is the supplement of the exterior angle

So y = x/2 + x/2 which are marked as being opposite equal angles.

1/2 x + 1/2 x = x

y by substitution is = x /2 + x/2

y = x

Answer:

54.3°

Step-by-step explanation:

sinθ=opposite/hypotenuse

sinθ=26/32

sinθ=0.8125

θ=54.3°

9514 1404 393

Explanation:

Divide the figure into areas for which you have a surface area formula. Use the appropriate formula for each area, then add up the results.

Formulas are available for surface areas of a cone, cylinder, sphere, pyramid, rectangular prism, and for plane shapes that are circles, ellipses, triangles, rectangles, trapezoids, and regular polygons.

Most of the figures for which you are asked to find the area will decompose to some subset of these shapes. Take care to identify the relevant dimensions of each of the constituent parts of the area, and to make sure that all parts are accounted for. Do not allow your parts of the area to overlap, unless you intend to account for that overlap by subtracting the area that is counted more than once.

Also, use your common sense. A semicircle will have half the area of a circle, for example.

In some cases, it may be expedient to compute the area of a larger figure than the one you have, then subtract the part of that area that is missing from your figure.

Answer:

A. 115°

Step-by-step explanation:

180° - 65° = 115°

Answer:

Step-by-step explanation:

For independent events,

P(AB)=P(A)orP(B)

= P(A)uP(B)

=P(A)×P(B)

= 0.55×0.72

P(AB)=0.396

Answer:555

Step-by-step explanation:

Answer:

545

Step-by-step explanation:

you are just adding one

544+1=

Answer:

1) (2, 1)

2) (2, -2)

3) (-1, -1)

4) (-5, -5)

Answer:

1. Pairs A(2, 5), B(6, 5), and C(6, 1)

missing coordinate is (2,1)

2. Pairs A(2, 3), B(7, 3), and C(7, -2)

missing coordinate is (2,-2)

3. Pairs A(-5, -1), B(1, -1), and C(1, -5)

missing coordinate is (-5,-5)

4. Pairs A(-1, 4), B(7, 4), and C(7, -1)

missing coordinate is (-1,-1)

Hope this is correct!! Have a nice day!!<3

Answer:C=10

Step-by-step explanation:

Follow along with the picture below

The formula for this type of problem is a^2+b^2=c^2

We know that 6=a and 8=b so we fill in the formula and square them

we then add the two values we got which get us to 100=c^2

we want to get rid of that square with we square root bothe sides and get c and the square root of 100 is 10.

So C=10

Answer:

Step-by-step explanation:

Answer:

The width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.

Step-by-step explanation:

Given that a rectangular garden covers 80 square yards, and the length is 7 yd longer than the width, to find the length and width of the rectangle the following calculation must be performed, knowing that the area of a rectangle arises from multiplying its width by its length:

X x (X + 7) = 80

5 x 12 = 60

6 x 13 = 78

8 x 14 = 112

6.1 x 13.1 = 79.91

6,105 x 13,105 = 80

Therefore, the width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.

Given:

The two polygons are similar.

To find:

The value of [tex]a,\ b,\ m\angle C,\ m\angle D[/tex].

Solution:

We know that the corresponding side of similar figures are proportional. So,

[tex]\dfrac{5}{4}=\dfrac{5.39}{a}[/tex]

[tex]1.25=\dfrac{5.39}{a}[/tex]

[tex]a=\dfrac{5.39}{1.25}[/tex]

[tex]a=4.312[/tex]

Similarly,

[tex]\dfrac{5}{4}=\dfrac{5.83}{b}[/tex]

[tex]1.25=\dfrac{5.83}{b}[/tex]

[tex]b=\dfrac{5.83}{1.25}[/tex]

[tex]b=4.664[/tex]

We know that the corresponding angles of similar figures are congruent and their measures are equal. So,

[tex]m\angle C=99.2^\circ[/tex]

[tex]m\angle D=149^\circ[/tex]

Therefore, [tex]a=4.312\text{ units},\ b=4.664\text{ units},\ m\angle C=99.2^\circ,\ m\angle D=149^\circ[/tex].

A. 4/7 Answer:

B. 60/7 or (8 and 4/7)

Step-by-step explanation:

A. 4 divided by 7 is the same as 4/7

B. 4/7 • 15/1= 60/7

Answer:

Surface area add together all 6 sides = 24+36+108=168m^2

Volume L x W x D = 2 x 6 x 9 = 108 m ^3

Step-by-step explanation:

2 x 6 = 12

12 x 2 = 24 base and top

2 x 9 = 18

2 x 18 = 36 identical pair sides

6 x 9 = 54

2 x 54 = 108 identical pair sides

Surface area add together all 6 sides = 24+36+108=168m^2

Volume L x W x D = 2 x 6 x 9 = 108 m ^3

Answer:

x = (-1 ± √21) / 2

The first choice

Step-by-step explanation:

x² = 5 - x

Put in standard form

x² + x - 5 = 0

Use quadratic equation

x = ( -b ± √( b² - 4ac) ) / (2a)

Plug in a = 1, b = 1 , c = -5

x = (-1 ± √( 1² - 4*1*(-5)) ) / 2

evaluate

x = (-1 ± √21) / 2

Answer:

41, 43 and 82

Step-by-step explanation:

hope it may help you

Answer:

Step-by-step explanation:

A = P(1+r/n)^ nt

A = 2000(1+.04/2)^(5*2)

A = [tex]2000(1.02)^{10}[/tex] = $2437.99

Answer:

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Step-by-step explanation:

To solve this question, we need to use the binomial and the normal probability distributions.

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.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Probability the president will have an IQ of at least 107.5

IQs of adults in a certain country are normally distributed with mean 100 and SD 15, which means that [tex]\mu = 100, \sigma = 15[/tex]

This probability is 1 subtracted by the p-value of Z when X = 107.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{107.5 - 100}{15}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915.

1 - 0.6915 = 0.3085

0.3085 probability that the president will have an IQ of at least 107.5.

Probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

First, we find the probability of a single person having an IQ of at least 130, which is 1 subtracted by the p-value of Z when X = 130. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{130 - 100}{15}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

Now, we find the probability of at least one person, from a set of 2, having an IQ of at least 130, which is found using the binomial distribution, with p = 0.0228 and n = 2, and we want:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.9772)^{2}.(0.0228)^{0} = 0.9549[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 0.0451[/tex]

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?

0.3085 probability that the president will have an IQ of at least 107.5.

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Independent events, so we multiply the probabilities.

0.3082*0.0451 = 0.0139

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Answer:

The maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200 is 19.

Step-by-step explanation:

Since Greg is installing a tile floor in a room that is 10 feet long by 15 feet wide, and he will use 1-foot square tiles, and he has two different types of tile: plain and hand-painted, and plain tiles cost $ 0.79 per tile, while hand-painted tiles cost $ 5.00 per tile, to determine what is the maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200, the following calculation must be performed:

10 x 15 = 150

150 x 0.79 + 0 x 5 = 118.5

130 x 0.79 + 20 x 5 = 202.7

131 x 0.79 + 19 x 5 = 198.49

Therefore, the maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200 is 19.

Answer:

The student is comparing the different heart rates due to the temperature. The independent variable is the Temperature and the dependent variable is the beats of the heart from the larva.

Answer: you can buy 6apples for$1

Step-by-step explanation: you divide 36 by 6 and get 6 so it’s 6apples.

Answer:

5000

Step-by-step explanation:

but this depends upon how much room each person needs

Answer:

Project A :

NPV : $703,888.64

IRR : 44.882%

Project B:

NPV : $5,241.26

IRR : 49.662%

Project B is more profitable

Step-by-step explanation:

The NPV gives the difference between the present value of cash inflow and cash outflow over a certain period of time.

The Internal rate of return is the discount rate which makes the NPV of an investment 0. It is used to estimate the potential return on an investment. Investments with higher IRR are said to be better than those with lower IRR value.

Using the net present value, (NPV) Calculator, the NPV for project A is : $703,888.64

The IRR of project A is : 44.882%

The NPV for Project B is : $5,241.26

The Internal rate of return (IRR) : 49.662%

From the Internal rate of return value obtained, we can conclude that, project B is more profitable as it has a higher IRR than project A.

Answer:

since her score was -12 from being perfect

if she had scored 12 more points her score would have been perfect .

that is difference between her score and the perfect score o each quiz was 12

Answer:

3/36 or 8.333

Step-by-step explanation:

the way you get it is write all the possibilities and that how you get 3/36

9514 1404 393

Answer:

  448

Step-by-step explanation:

(4 pt/da)×(7 da/wk)×(16 oz/pt) = 448 oz/wk

That would be 448 fluid ounces per week.