2 - [7+5 - (-4)]<br> show work too, please

The countries of Europe report that 46% of the labor force is female. The United Nations wonders if the percentage of females in

Anestetic [448]

Answer:

a) Point estimate p=0.43.

b) The 95% confidence interval for the population proportion of female workers in US is (0.388, 0.473).

c) This confidence interval tells us that, with 95% confidence, the true proportion of females in the U.S. labor force is within 0.388 and 0.473.

d) We can conclude that females do not make up a majority of the US labor force, because we can claim, with 95% confidence, that the true proportion of female workers is under 0.473, which is below 0.5 (or 50%).

Step-by-step explanation:

a) A point estimate can be calculated using the sample results and dividing the amount of female workers in the sample by the sample size:

$p=X/n=226/525=0.43$

b) We have to calculate a 95% confidence interval for the proportion.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.43*0.57}{525}}\\\\\\ \sigma_p=\sqrt{0.000467}=0.022$

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.96 \cdot 0.022=0.042$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.4305-0.042=0.388\\\\UL=p+z \cdot \sigma_p = 0.4305+0.042=0.473$

The 95% confidence interval for the population proportion of female workers in US is (0.388, 0.473).

c) This confidence interval tells us that, with 95% confidence, the true proportion of females in the U.S. labor force is within 0.388 and 0.473.

d) We can conclude that females do not make up a majority of the US labor force, because we can claim, with 95% confidence, that the true proportion of female workers is under 0.473, which is below the 50%.

If the confidence interval have included the value 0.5, we could not be sure (with 95% confidence) that female workers do not represent de majority, as there would be possibility that the true proportion is 0.5.

3 0

4 years ago

Emily says she can prove the Pythagorean Theorem using the following diagram. She explains that she can divide the squares on th

irinina [24]

Answer: Yes, It is

Step-by-step explanation:

Demonstrating the Pythagorean Theorem

When you think of each side of a right triangle as also being a side of a square that's attached to the triangle. The area of a square is any given side multiplied by itself. (For example, b x b = b^2).

In order to show that a^2 + b^2 = c^2,

follow these steps:

Get a right triangle on grid paper that you can print. You'll also need scissors, and a ruler.

Cut out the triangle.

Make three squares with sides that are equal to each side of the triangle. Begin with side

a. Measure the length of side a. On the blank piece of grid paper,

- draw a square with sides that are the same length as side a.

- Label this square a2.

- Repeat these steps to create squares for sides b and c. (If you don't have a ruler, just use the triangle as a guide; trace the length of one side, and then draw three more sides of the same length to make a square.)

Cut out the squares. Place each square next to the corresponding sides of the triangle.

Now show that a2 + b2 = c2. Place the squares made from sides a and b on top of square c. You will have to cut one of the squares to get a perfect fit.

Area of Whole Square

The total area of a big square, where each side having a length of a+b, is:

A = (a+b)(a+b)

Area of The Pieces

By adding up the areas of all the smaller pieces:

First, the smaller (tilted) square has an area of:c^2

Each of the four triangles has an area of: ab^2

So all four of them together is: 4ab^2 = 2ab

Adding up the tilted square and the 4 triangles gives: A = c^2 + 2ab

Both Areas Must Be Equal

The area of the large square is equal to the area of the tilted square and the 4 triangles. This can be written as:

(a+b)(a+b) = c^2 + 2ab

By rearrange this, we shall see if we can get the pythagoras theorem:

Start with:(a+b)(a+b) = c^2 + 2ab

Expand (a+b)(a+b): ag2 + 2ab + b^2 = c^2 + 2ab

Subtract "2ab" from both sides: a^2 + b^2 = c^2

Therefore, it's been proven that, a^2 + b^2 = C^2

5 0

3 years ago

PLEASE HELP BUT REALLY Find the value of x. Write your answer in simplest radical form, if necessary.

SCORPION-xisa [38]

Answer: x = √141

Step-by-step explanation: 22² + x² = 25² -> 484 + x² = 625

625 - 484 = 141

x² = 141

x = √141

7 0

3 years ago

the coordinates of point t are (0, 6) the midpoint of line st is (2, 5) what are the coordinates of point s

tankabanditka [31]

The coordinates of S would be (4, 4)

In order to find this, we need to know that the value of midpoint (M) points will always be the average of S and T's points. This is because it is the midpoint. Therefore we can use the following formula.

Value of x

(S + T)/2 = M

(S + 0)/2 = 2

S + 0 = 4

S = 4

Then we can do the same for the y values

Value of y

(S + T)/2 = M

(S + 6)/2 = 5

S + 6 = 10

S = 4

7 0

4 years ago

A ball is thrown from an initial height of 7 feet with an initial upward velocity of 30ft/s . The ball's height h (in feet) afte

exis [7]

This is a parabola. 20 ft represents the height of the ball. Height is represented by the letter h. Thus you need to plug 20 into the equation for h and solve for t.

4 0

3 years ago

2 - [7+5 - (-4)] show work too, please