The area of a hexagon is 42 square centimeters. If all the dimensions of the hexagon are multiplied by 3, what will be
the area of the new figure?

Final answer:

To construct a 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important, calculate the sample proportions for women and men, calculate the standard error, calculate the margin of error, and calculate the lower and upper bounds of the confidence interval.

Explanation:

To construct a 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important, we can use the formula for calculating the confidence interval for a difference in proportions.

The resulting 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important would be interpreted as follows: We are 95% confident that the true difference in proportions lies between the lower and upper bounds calculated above. This means that there is a high likelihood that women place a higher value on job security compared to men, but there is still some uncertainty due to sampling variability.

We are 95% confident that the difference in the proportion of working women and men who consider job security very or extremely important is between -0.0043 and 0.0595. This indicates there is no statistically significant difference between the proportions at the 95% confidence level.

To construct a 95% confidence interval for the difference in the proportion of working women and men who consider job security very or extremely important, we will follow these steps:

1. Determine the sample proportions:

  For women:

 [tex]\[ \hat{p}_1 = \frac{702}{798} = 0.8797 \][/tex]

  For men:

 [tex]\[ \hat{p}_2 = \frac{802}{940} = 0.8521 \][/tex]

2. Calculate the difference in sample proportions:

[tex]\[ \hat{p}_1 - \hat{p}_2 = 0.8797 - 0.8521 = 0.0276 \][/tex]

3. Calculate the standard error (SE) for the difference in proportions:

  [tex]\[ SE = \sqrt{\frac{\hat{p}_1 (1 - \hat{p}_1)}{n_1} + \frac{\hat{p}_2 (1 - \hat{p}_2)}{n_2}} \][/tex]

  Plugging in the values:

  [tex]\[ SE = \sqrt{\frac{0.8797 (1 - 0.8797)}{798} + \frac{0.8521 (1 - 0.8521)}{940}} \][/tex]

 [tex]\[ SE = \sqrt{\frac{0.1059}{798} + \frac{0.1260}{940}} \][/tex]

  [tex]\[ SE = \sqrt{0.0001327 + 0.0001340} \][/tex]

  [tex]\[ SE = \sqrt{0.0002667} = 0.0163 \][/tex]

4. Determine the critical value (z*) for a 95% confidence interval:

  The critical value for a 95% confidence interval (using a standard normal distribution) is approximately 1.96.

5. Calculate the margin of error (ME):

 [tex]\[ ME = z^* \cdot SE = 1.96 \cdot 0.0163 = 0.0319 \][/tex]

6. Construct the confidence interval:

 [tex]\[ \text{Lower limit} = (\hat{p}_1 - \hat{p}_2) - ME = 0.0276 - 0.0319 = -0.0043 \][/tex]

 [tex]\[ \text{Upper limit} = (\hat{p}_1 - \hat{p}_2) + ME = 0.0276 + 0.0319 = 0.0595 \][/tex]

  So, the 95% confidence interval for the difference in the proportion of all working women and men who consider job security very or extremely important is:

 [tex]\[ -0.0043 \text{ to } 0.0595 \][/tex]

Interpretation:

We are 95% confident that the true difference in the proportion of all working women and men who consider job security very or extremely important is between -0.0043 and 0.0595. This interval includes 0, which suggests that there is no statistically significant difference between the proportions of women and men who value job security at the 95% confidence level.

Answer:

i predict the 150 will have defects

Step-by-step explanation:

you do 280 divided by 4 which gives you 70

then 10,500 divided by 70 which gives you

There is a probability that 150 total autos will have defects if 10,500 vehicles are inspected this month.

A chance that something might exist, happen, or be true: the state or fact of being possible.

Given, A worker at an automobile assembly plant checks new cars for defects. Of the first 280 cars he checks, 4 have defects.

Out of 280 cars defected = 4

out of 10500 cars defected = (4* 10500) / 280

out of 10500 cars defected = 150

therefore, If 10,500 cars will be checked this month there is a possibility of getting a total number of cars that will have defects of 150.

Learn more about possibilities here:

https://brainly.com/question/27741413

#SPJ2

Answer:

Point Q is 6 units from Point R.

Point R is 7 units from Point T.

Point T is 3 units from Point S.

The area of polygon QRSU is 42 square units.

Please mark my answer brainliest so I can move up to the next rank.

Step-by-step explanation:

Answer:

y = x/2 + 2

Step-by-step explanation:

y = 2x - 4

swap y and x

x = 2y - 4

x + 4 = 2y

x/2 + 2 = y

Answer:

d(x) = 1/2x + 2  or  d(x) = (x + 4)/2

Step-by-step explanation:

y = 2x - 4

y + 4 = 2x

(y + 4)/2 = x

y = (x + 4)/2  or  y = 1/2x + 2

The length of the diagonal of the rectangular cardboard Hermina cut

is 10√5''.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given, Hermina cut a 10" by 20" piece of cardboard down the diagonal.

So, The diagonal can be thought of as the hypotenuse of a right-angle triangle with a base 20'' and a height of 10''.

Therefore,

Hypotenuse² = Base² + Height².

Hypotenuse² = 20² + 10².

Hypotenuse² = 400 + 100.

Hypotenuse² = 500.

Hypotenuse = √(500).

Hypotenuse = 10√5''.

So, The length of the diagonal is 10√5''.

learn more about Pythagoras' theorem here :

https://brainly.com/question/21926466

#SPJ5

The length of the cut (c) is 5 times the square root of 20 inches, which is approximately 22.36 inches when rounded to two decimal places.

When Hermina cuts a 10" by 20" piece of cardboard down the diagonal, she essentially creates two right triangles. The diagonal of a rectangle splits it into two congruent right triangles. This diagonal acts as the hypotenuse of each right triangle.

In a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse (c) if we know the lengths of the other two sides (a and b).

The Pythagorean theorem states: c^2 = a^2 + b^2, where c is the length of the hypotenuse.

In this case, one side (a) is 10 inches long, and the other side (b) is 20 inches long. Plugging these values into the formula:

c^2 = 10^2 + 20^2

c^2 = 100 + 400

c^2 = 500

Now, to find c, we take the square root of both sides to isolate c:

c = √500

To simplify the square root:

c = √(25 * 20)

c = 5√20

In summary, Hermina's diagonal cut creates two right triangles, and the length of the cut (c) can be found using the Pythagorean theorem. The calculated length is approximately 22.36 inches.

For more such questions on length.

https://brainly.com/question/28322552

#SPJ3

Answer:

The surface area of the sphere is about [tex]97,264.64 yd^{2}[/tex]

Step-by-step explanation:

Answer:

76,415.04

Step-by-step explanation:

Answer:

Into 1/3 pieces

Step-by-step explanation:

1/3 + 1/3 + 1/3 = 1 the whole pizza pie, yum

Answer:

Hello there the Correct answer is Jane should cut 2 equal pieces, as a diameter of a pizza.

Hope it helps!

From ItsNobody

Answer:

is it 54?

Explanation:

there are about 54 squares which could also be called units

Answer:

A

Step-by-step explanation:

i did the questions already

Answer:

B

Step-by-step explanation:

Answer:

C. 540

Step-by-step explanation:

A=2(wl+hl+hw)

Answer:2

Step-by-step explanation:

Answer:

Each postcard cost $0.7.

Step-by-step explanation:

In this problem we have two variables, the price of the postcard and the price of the stamp, since the price for the pain is known. We also have the total cost of the purchase that is $14.1. So we can create an equation as shown:

12*postcards + 12*stamps + pen = 14.1

This represents the total amount spent by Claudia, but we know that each pen costs $1.5, therefore:

12*postcards + 12*stamps + 1.5 = 14.1

12*postcards + 12*stamps = 14.1 - 1.5

12*postcards + 12*stamps = 12.6

We also know that the postcards cost twice as much as the stamps, so we have:

postcards = 2*stamps

Using this info we can solve for stams as shown below:

12*(2*stamps) + 12*stamps = 12.6

24*stamps + 12*stamps = 12.6

36*stamps = 12.6

stamps = 12.6/36

stamps = 0.35

postcards = 2*stamps = 2*0.35 = 0.7

Each postcard cost $0.7.

Answer:

the cost of a post card is $0.7

Step-by-step explanation:

Given

Number of postcard = 12

Number of stamp = 12

Number of pen = 1

Cost of a pen = $1.5

Required

Cost of each postcard..

Let P represent postcards, S represent stamps,Sp represented Pen.

Since there's a total of 12 postcard and 12 staffs, we have:

12P + 12S + 1.50 = $14.10

From the question, we have that the postcards cost twice as much as the stamps.

So, P = 2S.

Substitute 2S for P

12 * 2S+ 12S + 1.5 = 14.10

24S + 12S + 1.5. = 14.10

36S + 1.5 = 14.10

Collect like terms

36S = 14.10 - 1.5

36S = 12.6

Divide through by 36

S = 0.35

Recall that P = 2S.

So, p = 2 * 0.35

P = 0.7

Hence, the cost of a post card is $0.7

Answer:

20 (Assuming even distribution of letters)

Step-by-step explanation:

There are 26 letters in the alphabet.

Vowels consist of 5 of these letters.

The percentage of total letters that are vowels is:

[tex]\frac{5}{26} *100= 19.231[/tex] (3dp)

As we have total 105 letters, and we know the percentage of vowels to letters - we can work out how many of these letters we expect to be vowels by finding a percentage of the total number.

19% of 105 is:

[tex]105*0.19=19.95[/tex]

Which is approximately equal to 20

Answer:.

Step-by-step explanation: Answer:

1. 0 and 1

2. about 0.6

3. 2 and 3

4. about 2.2

For the graph the solution of the system, X+2y=5, -x+3y=6

1. The integer  values of x in between -6 and 5 are (-5, -4, -3, -2, -1, 0, 1, 2, 3, 4)

2.  The x-value to the nearest tenth is 1

3.  The integer  values of y in between 0 and 3 are (1, 2)

4.  The y-value to the nearest tenth is 2

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Given that,

system of lines , X+2y=5, -x+3y=6

by plotting graph of it,

we get following conclusions,

Point of intersection is (0.6, 2.2)

1. both the lines are intersecting x axis at (-6, 0) & (5, 0)

So, integers will be  (-5, -4, -3, -2, -1, 0, 1, 2, 3, 4)

2. The coordinate of x is, 0.6

The x-value to the nearest tenth is 1

3. both the lines are intersecting y axis at (0, 2) & (0, 2.5)

So, integers will be  ( 0, 1, 2)

4. The coordinate of y is, 2.2

The y-value to the nearest tenth is 2

To know more about line check:

https://brainly.com/question/17188072

#SPJ5

Answer:

2/3 x 2/3 x 2/3 x 2/3 = 16/81

Then show decimal form = 0.19753086...

Step-by-step explanation:

Answer:

Length of each side 3/2 or 1.5 square units

Step-by-step explanation:

(4^2 − 12x + 9)

=(2x-3)(2x-3)

2x-3=0

2x=3

x=3/2

The length of each side of the square by factoring in the area expression completely is 3/2.

We have given that,

The area of a square is (4x^2 − 12x + 9) square units.

We have to determine the,

Determine the length of each side of the square by factoring in the area expression completely.

Length of each side 3/2 or 1.5 square units

(4^2 − 12x + 9)

=(2x-3)(2x-3)

2x-3=0

2x=3

x=3/2

The length of each side of the square by factoring in the area expression completely is 3/2.

To learn more about the area of the square visit:

https://brainly.com/question/11444061

#SPJ5

Answer:

262.96 Dollars is for interest

271.91 Dollars is the monthly charged price monthly with the interest included

3262.96 Dollars is the total cost with APR

Divide the yearly payout by the amount in the bank:

40,000 / 2,500,000 = 0.016

Multiply by 100 to get the percentage:

0.016 x 100 = 1.6%

The answer is D. 1.6%

The insurance company expects an interest rate of 1.6% to provide the yearly payment of $40,000, calculated by dividing the annual payment by the principal amount deposited.

The student's question asks to calculate the interest rate expected by Bette's insurance company in order to provide a yearly payment of $40,000 to her family, given that the company needs to deposit $2,500,000 into a bank account.

To find the interest rate, we can use the formula for simple interest: Interest = Principal times Rate times Time. Since we are looking for the rate and are given the annual interest (the yearly payment) and the principal (the amount deposited), we can rearrange the formula to solve for the rate: Rate = Interest / Principal / Time. Here, Interest is $40,000, Principal is $2,500,000, and Time is 1 year.

Plugging in the values gives us: Rate = $40,000 / $2,500,000 / 1 = 0.016 or 1.6%. Therefore, the expected interest rate is 1.6%, which corresponds to option D.

1. T1: Translate ABCDE.

2. R1: Rotate the translated polygon.

3. S1: Scale the rotated polygon.

4. F1: Reflect the scaled polygon if needed.

To determine a series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E', you can break down the process into individual steps. Here, I'll describe each transformation step:

1. Translation:

  Translate polygon ABCDE to align its center of mass with the center of mass of polygon A'B'C'D'E'. This ensures that the polygons are roughly in the same position. Let's denote this transformation as "T1."

2. Rotation:

  Rotate the translated polygon so that one of its sides aligns with a side of polygon A'B'C'D'E'. You can use the center of mass as the pivot point for rotation. Denote this transformation as "R1."

3. Scaling:

  Scale the rotated polygon proportionally to match the size of polygon A'B'C'D'E'. This will make sure that the two polygons have the same size. Denote this transformation as "S1."

4. Reflection:

  Reflect the scaled polygon if needed to match the orientation of polygon A'B'C'D'E'. This step may not always be necessary, depending on the orientation of the two polygons. Denote this transformation as "F1" (for reflection).

So, the series of transformations can be written as follows:

1. T1: Translate ABCDE.

2. R1: Rotate the translated polygon.

3. S1: Scale the rotated polygon.

4. F1: Reflect the scaled polygon if needed.

These transformations will map polygon ABCDE onto polygon A'B'C'D'E' while preserving their size and shape.

Learn more about polygon here:

https://brainly.com/question/29425329

#SPJ3

Answer:

4/25 would be the answer as;

-1/2 + 1/3 = -0.16666666666

Step-by-step explanation:

‑1/2+(3/4•4/9) =

-1/2 + (1/3) = -4/25

-0.16

However true answer is  16666666666/100000000000. = 0.1666666666

The rule is when fractions reoccur, we show closest and -4/25 is closer than -1/6

Answer:

Area of the rectangle = [tex]35\,\,units^2[/tex]

Step-by-step explanation:

Area of the Rectangle= Product of the two Unequal sides

Finding the two unequal sides of the rectangle using the distance formula:

For the coordinates:

A(2,3)  B(9,3)  C(9,-2)  D(2,-2)

Using Distance formula:

AB=

            [tex]=\sqrt{(9-2)^2+(3-3)^2} \\\\=\sqrt{7^2+0} \\\\=\sqrt{49}\\\\ =7\,\,units[/tex]

Similarly, BC= 5 units

Area of the rectangle is:

                                 [tex]=7\times 5\\\\=35\,\,units^2[/tex]

Answer:

The answer is definitely 35

Answer:

The distance is 5.

Step-by-step explanation:

As you want distance, the best approach is to subtract.

My advice when you're dealing with a number line, and a negative and a positive number, is to subtract the negative from the positive, so that you get a positive distance.

Therefore:

[tex]2 - ( - 3) = 2 + 3 = 5[/tex]

Answer:

They look like they are 90° angles

Step-by-step explanation:

(What are the options?)

Answer:

Goodness, hard question... I believe it is, uh 4?

2+2=4

for eg: if u buy 2 pencils and 2 erasers then,you have total 4 stationery items

hope it will help you

Answer:

30 [tex]ft^2[/tex]

Step-by-step explanation:

To find the area of a triangle, you must use the formula:

[tex]\frac{1}{2} bh[/tex]

The "[tex]b[/tex]," is the base (12), and the "[tex]h[/tex]," is the height (5).

Plug in the numbers accordingly:

[tex]\frac{1}{2} (12)(5)[/tex]

[tex]\frac{1}{2} (60)[/tex]

30

Ok, first let's find how much a nickle is worth, a nickle is worth $0.05.

0.05 x 27 = $1.35

0.05 x 32 = $1.60

0.05 x 39 = $1.95

0.05 x 47 ≠ $2.45 (It's equal to $2.35)

I hope this helps!

Step-by-step explanation:

Step 1:  Find f(2)

[tex]f(p) = 3p - 2[/tex]

[tex]f(2) = 3(2) - 2[/tex]

[tex]f(2) = 6 - 2[/tex]

[tex]f(2) = 4[/tex]

Answer:  Option C, 4

Answer:

C. 4

Step-by-step explanation:

f(p) = 3p - 2

Is a function with:

Input: p

Output: 3p - 2

p = 2

f(2) = 3(2) - 2 = 6 - 2 = 4

Answer: -42+6i

Step-by-step explanation:

1. Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd(a+b)(c+d)=ac+ad+bc+bd.

−18−18i+24i−24

2. Collect like terms.

(−18−24)+(−18i+24i)

3. Simplify.

−42+6i