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1 year ago

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Provide an appropriate response.The mean annual income for adult women in one city is $28,520 and the standard deviation of thei

ncomes is $5,190. The distribution of incomes is skewed to the right. For samples of size 30, whichof the following statements best describes the sampling distribution of the mean?

1 answer:

8090 [49]1 year ago

7 0

Recall the Central Limit Theorem.

The Central Limit Theorem says that no matter what the distribution of the population is, as long as the sample is “large,” meaning of size 30 or more, the sample mean is approximately normally distributed.

If the population is already normal, then any sample size will produce a normal sampling distribution.

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Identify the polygon with vertices A(5,0), B(2,4), C(−2,1), and D(1,−3), and then find the perimeter and area of the polygon. HE

inn [45]

Answer:

Part 1) The polygon is a square

Part 2) The perimeter is equal to $20\ units$

Part 3) The area is equal to $25\ units^{2}$

Step-by-step explanation:

we have

$A(5,0), B(2,4), C(-2,1),D(1,-3)$

Plot the points

see the attached figure

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance AB

$A(5,0),B(2,4)$

substitute in the formula

$d=\sqrt{(4-0)^{2}+(2-5)^{2}}$

$d=\sqrt{(4)^{2}+(-3)^{2}}$

$d=\sqrt{25}$

$AB=5\ units$

Find the distance BC

$B(2,4), C(-2,1)$

substitute in the formula

$d=\sqrt{(1-4)^{2}+(-2-2)^{2}}$

$d=\sqrt{(-3)^{2}+(-4)^{2}}$

$d=\sqrt{25}$

$BC=5\ units$

Find the distance CD

$C(-2,1),D(1,-3)$

substitute in the formula

$d=\sqrt{(-3-1)^{2}+(1+2)^{2}}$

$d=\sqrt{(-4)^{2}+(3)^{2}}$

$d=\sqrt{25}$

$CD=5\ units$

Find the distance AD

$A(5,0),D(1,-3)$

substitute in the formula

$d=\sqrt{(-3-0)^{2}+(1-5)^{2}}$

$d=\sqrt{(-3)^{2}+(-4)^{2}}$

$d=\sqrt{25}$

$AD=5\ units$

we have that

AB=BC=CD=AD

Find the distance BD (diagonal)

$B(2,4),D(1,-3)$

substitute in the formula

$d=\sqrt{(-3-4)^{2}+(1-2)^{2}}$

$d=\sqrt{(-7)^{2}+(-1)^{2}}$

$BD=\sqrt{50}\ units$

<em>Verify if the polygon is a square</em>

If the triangle BDA is a right triangle, then the polygon is a square

Applying the Pythagoras theorem

$BD^{2}=AD^{2}+AB^{2}$

substitute

$(\sqrt{50})^{2}=5^{2}+5^{2}$

$50=50$ -----> is true

so

The triangle BDA is a right triangle

therefore

The polygon is a square

<em>Find the Area of the polygon</em>

The area of a square is equal to

$A=b^{2}$

we have

$b=5\ units$

$A=5^{2}=25\ units^{2}$

<em>Find the perimeter of the polygon</em>

The perimeter of a square is equal to

$P=4b$

we have

$b=5\ units$

$P=4(5)=20\ units$

6 0

3 years ago

Frans filing cabinet is 6 feet tall 1 1/3 feet wide and 3 feet deep. She plans to paint all sides except the bottom of the cabin

GalinKa [24]

I think the answer shouls be 80. But its not given in the options.

3 0

3 years ago

Read 2 more answers

The circumference of a circle is 15 m. Find the area. Use 3.14 for pie

zloy xaker [14]

Answer: Its 94.2

Step-by-step explanation:all you do to get the area is double 15 meaning 15 times 2 equal 30 times 3.14 equal 94.2 *that's crazy your in high school*

7 0

3 years ago

Read 2 more answers

Charity sold 110 cookies for $0.75 each. Her cost to make each cookie was $0.20 plus $20 for boxes. How much profit will charity

Ad libitum [116K]

The anwser is $40.50

8 0

3 years ago

Alex and his friend Kim made a one-gallon pitcher of lemonade because it was so hot. They drank 5 glasses that each help 2 cups

natulia [17]

we know that

4 cups of lemonade = 1 quart

1 gallon of lemonade = 4 quarts

1 gallon of lemonade = 16 cups

Step 1

<u> find the amount of lemonade that's left expressed in cups</u>

5 glasses * 2 cups = 10 cups

16 cups - 10 cups = 6 cups.

There are 6 cups of lemonade left.

Step 2

<u> find the amount of lemonade that's left expressed in quarts: </u>

4 cups = 1 quart.

(6 cups divided by 4 cups will equal the quarts.)

6/4=1.5

6 cups = 1.5 quarts.

There are 1.5 quarts of lemonade left.

Step 3

<u> find the amount of lemonade that's left expressed in gallons </u>

4 quarts = 1 gallon.

(1.5 quarts divided by 4 quarts will equal the gallon)

1.5/4=0.375

1.5 quarts = 0.375 gallon.

There is 0.375 gallon left of lemonade.

6 0

3 years ago