If h(x) =(fog)(x) and h(x) = 3(x+2)^2, find one possibility for f(x) and g(x)​

Answers

Answer 1

[tex]f(x)=3x^2 \\ \\ g(x)=x+2[/tex]

Explanation:

In this case we have the composition of two function called [tex]f(x)[/tex] and [tex]g(x)[/tex] that results in another function [tex]h(x)[/tex]. So:

[tex]h(x) =(f\circ g)(x)[/tex]

Another way to write this function is:

[tex]h(x)=f(g(x)) \\ \\ So \ g(x) \ becomes \ the \ domain \ of \ f[/tex]

One possibility for [tex]f(x)[/tex] and [tex]g(x)[/tex] is:

[tex]f(x)=3x^2 \\ \\ g(x)=x+2[/tex]

Because [tex]h(x)=f(g(x))[/tex] is:

[tex]h(x)=3(x+2)^2[/tex]

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Related Questions

The point P has coordinates (-4,1). In which quadrant does point P lie?

Answers

Answer: quadrant 2

Step-by-step explanation:

u first go to the left side because your x axis is a negative than u go up one positive and u are on quadrant 2

Omar made $299 for 13 hours of work.
At the same rate, how many hours would he have to work to make $253?

Answers

Answer:

The answer is (11 hours)

Step-by-step explanation:

I first divided 299 by 13 hours to find the rate.

I got the dividend of 23.

All you do now is add $23 per hour.

Once you add 11 hours of this rate. You'll get the sum of $253.

Solving for the amount of hours by cross multiplication

money/hours=money/hours

$299/13hours=$253/x hours

[tex]\frac{299}{13} =\frac{253}{x} \\\\23=\frac{253}{x} \\\\23x=253\\\\x=253/23\\\\x=11[/tex]

Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! I also hope you had a great Superbowl Weekend! :-)

- Cutiepatutie ☺❀❤

Erica ate 5/8 of a sandwich. Sven ate 2/5 of a sandwich. Micah ate 3/4 of a sandwich. Gabe ate 6/12 of a sandwich. Who ate the most of his sandwich?

Answers

The answer is that Micah ate more of a sandwich because he is 1/4 from eating the whole thing.

Answer:

Micah ate the most of their sandwich.

Step-by-step explanation:

If you convert all of the fractions into a percentage,

Erica ate 62.5% of a sandwich

Sven ate 40% of a sandwich

Micah ate 75% of a sandwich

Gabe ate 50% of a sandwich

Micah ate the most of their sandwich.





Find the area of the hexagon.
A) 36 in2
B) 52 in2
C) 78 in2
D) 144 in2

Answers

Answer: C) 78 in2

Step-by-step explanation:

The polygon is divided into two trapezoids with equal measurements.

Area of a trapezoid:

1

2

(b1 + b2)h

Since the area of the hexagon equals the area of two trapezoids with equal measurements, do not multiply by 1/2.

(b1 + b2)h

(10 + 16)3

26(3)

78 in2

Answer:

Answer: C) 78 in2

Step-by-step explanation:

chevy have some yarn that he wants to use to make hats and scarves. each hat uses 0.2 kilograms of yarn and each scarf uses 0.1 kilograms of yarn. chevy wants to make a total of 15 items. let h be the number of hats chevy makes and s be number of scarves he makes.

Answers

Answer:

[tex]The\ following\ system\ of\ equations\ gives\ number\ of\ hats\ and\ scarves\\\\h+s=15\\\\0.2h+0.1s=k\\\\Where\ k\ is\ total\ yarn\ in\ kg.\\\\If\ k=2\ kg\\\\h=5\ hats,\ s=10\ scarves[/tex]

Step-by-step explanation:

[tex]Number\ of\ hats=h\\\\Number\ of\ scarves=s[/tex]

Total Number of items:

[tex]Total\ items=15\\\\Total\ number\ of\ items=Number\ of\ hats+Number\ of\ scarves\\\\Total\ Number\ of\ items=h+s\\\\h+s=15.......................................eq(1)[/tex]

Total yarn used:

[tex]Yarn\ used\ in\ 1\ hat=0.2\ kg\\\\Yarn\ used\ in 1\ scarf=0.1\ kg\\\\Yarn\ used\ in\ hats=Yarn\ used\ in\ 1\ hat\times Number\ of\ hats\\\\Yarn\ used\ in\ hats=0.2\times h=0.2h\\\\Yarn\ used\ in\ scarves=Yarn\ used\ in\ 1\ scarf\times Number\ of\ scarves\\\\Yarn\ used\ in\ hats=0.1\times s=0.1s\\\\Total\ yarn\ used=0.2h+0.1s\\\\If\ total\ yarn=k\ kg\\\\Solution\ of\ following\ system\ of\ equations\ gives\ number\ of\ hats\ and\ scarves\\\\h+s=15\\\\0.2h+0.1s=k[/tex]

[tex]if\ k=2\\\\h+s=15...............eq(2)\\\\0.2h+0.1s=2.......eq(3)\\\\eq(2)-0.2\times eq(3)\\\\0.1s=1\\\\s=10\\\\From\ eq(2)\\\\h=15-s\\\\h=5\ hats[/tex]

36 divided by 6a I’m confused plz help

Answers

Answer: 6

Step-by-step explanation:

what is the sum of the distances of R to Q and P to Q?

Answers

The sum of the distances of R to Q and P to Q is 9 units.

Solution:

Given points are P(–3, 6), Q(3, 6) and R(3, 3).

Distance between two points formula:

   [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance from R to Q:

Here [tex]x_1=3, y_1=3, x_2=3, y_2=6[/tex]

Substitute these in the given formula, we get

Distance = [tex]\sqrt{(3-3)^2+(6-3)^2}[/tex]  

               [tex]=\sqrt{0+9}[/tex]

               = 3 units

Distance from R to Q is 3 units.

Distance from P to Q:

Here [tex]x_1=-3, y_1=6, x_2=3, y_2=6[/tex]

Substitute these in the given formula, we get

Distance = [tex]\sqrt{(3-(-3))^2+(6-6)^2}[/tex]  

               [tex]=\sqrt{36+0}[/tex]

               = 6 units

Distance from P to Q is 6 units.

Sum of the distances = 3 + 6 = 9 units

Hence the sum of the distances of R to Q and P to Q is 9 units.

Use the figure. Identify a segment that intersects Ef.

Answers

Answer:

[tex]\overline{FG}[/tex]

Step-by-step explanation:

When two line segments intersects, then they have a common point.

From the diagram FG intersects EF

Also HG intersects EF

From the given options, the correct answer is [tex]\overline{FG}[/tex]

Therefore the first choice is correct

The function f(x) = 2x + 210 represents the number of calories burned when exercising, where x is the number of hours
spent exercising.
The function g(x) = 2x + 125 represents the calorie deficit that occurs when following a particular diet, where x is the
number of hours spent exercising.
What is (f + g)(2)? Explain.

A. 214 burned just exercise 2 hours
B. 214 burned exercise and
diet 2 hours
C. 343 burned dieting 2 hours
D. 343 burned exercise and diet 2 hours.

Answers

The true statement about (f + g)(2) is (D). 343 burned exercise and diet 2 hours.

The functions are given as:

f(x) = 2x+ 210

g(x) =2x + 125

Start by calculating (f + g)(x) using:

(f + g)(x) = f(x) + g(x)

So, we have:

[tex](f + g)(x) = 2x + 210 + 2x + 125[/tex]

This gives

[tex](f + g)(x) = 4x + 335[/tex]

When x = 2, we have:

[tex](f + g)(x) = 4*2 + 335[/tex]

[tex](f + g)(x) = 343[/tex]

This means that 343 calories were burned by exercising and dieting for 2 hours

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Simplify eighth root of y squared

Answers

Answer:

The simplified expression is y raised to the 2/8 power

Step-by-step explanation:

Let's recall that one of the properties of fractional exponents is:

x ^ a/b = ᵇ√x ᵃ

​​ therefore,

⁸√y² = y ^2/8

The simplified expression is y raised to the 2/8 power

​​

I’m so confused geometry

Answers

x=50 and y=10

because of vertical angles: 3y=x-20

and we also have 3y+5x-100=180 , if we simplify we get 3y=280-5x

we can combine the two equations and get x-20=280-5x and when we solve we get x=50 degrees

then we can plug that into the first equation and get 3y=30, and y=10 degrees

Answer:

x = 50°

y = 10°

Step-by-step explanation:

The vertical angles theorem states that angles across from each other must be equal.

This means that:

3y = x - 20°    or    x = 3y + 20°

5x - 100° = y + 140°

Start with the second equation

5x - 100° = y + 140°

Add 100° to both sides of the equation

5x = y + 240°

Now, substitute the value of x found at the beginning into this equation

5(3y + 20°) = y + 240°

Multiply

15y + 100° = y + 240°

Subtract 100° from both sides of the equation

15y = y + 140°

Subtract y from both sides of the equation

14y = 140°

y = 10°

x = 3y + 20 = 3(10) + 20 = 30 + 20 = 50°

Hope this helps :)

There will be 25 party guests. 8
pieces of pizza dough come in a
package. How many packages do
I need to buy? ​

Answers

First you need to know how much each guest will eat
well if you bought 3 packages that would be 24 pieces of pizza dough. and you still need one more piece, so 4 packages!

How do you solve 12x -2/3 = 83 1/3

Answers

Answer:

4

Step-by-step explanation:

<=> 12x = 83 1/3 + 2/3

<=> 12x = 84

<=> x = 84/12

<=> x = 4

X should be equaled to 9/4.

Please help. There is a file included.

Answers

Answer:

0

Step-by-step explanation:

8 + - 4 - 4

(goes in the 2nd box)

0

(goes in the last empty box)

I need help on this:(

Answers

Answer:

Not to sure if this is correct but I think it is 6: 1 : 18

pls msg me if you need explanation

claudia is 6 years older than bill. the sum of their ages is 120. How old is Claudia

Answers

Answer:

The answer is 66

Step-by-step explanation:

plz give brainliest

Answer:

Claudia is 63 years old

Step-by-step explanation:

Find two numbers that subtract to get 6, but add to get 120.

I used 57 and 63. If Claudia is 6 years older than Bill, then she would have to be 63.  

57 + 63 = 120

63  - 57 = 6

Use the formula for finding the surface area of a rectangular prism.
A=PH+2B
Solve for B
I will mark brainliest for the first to answer RIGHT
Thanks

Answers

The formula, when solved for B is, [tex]\frac{1}{2}(A-PH)[/tex].

Step-by-step explanation:

Given,

Formula used to find surface area of a rectangular prism

A = PH + 2B

Solving the formula for B;

Subtracting PH from both sides

[tex]A-PH=PH-PH+2B\\A-PH=2B\\2B=A-PH[/tex]

Dividing both sides by 2

[tex]\frac{2B}{2}=\frac{A-PH}{2}\\\\B=\frac{1}{2}(A-PH)[/tex]

The formula, when solved for B is, [tex]\frac{1}{2}(A-PH)[/tex].

Keywords: subtraction, division

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Final answer:

To solve for B in the formula A=PH+2B, subtract PH from A and then divide by 2, resulting in B = (A - PH) / 2.

Explanation:

The student is asking to solve for B from the surface area formula of a rectangular prism, given by A=PH+2B, where A is the surface area, P is the perimeter of the base, H is the height of the prism, and B is the area of the base.

To solve for B, we'll rearrange the formula as follows:

First, we subtract the term PH from both sides of the equation, which gives us A - PH = 2B.

Then, we divide both sides by 2 to isolate B, resulting in B = (A - PH) / 2.

This process reveals that the base area B can be found by taking the total surface area A, subtracting the product of the perimeter of the base and the height, and then dividing by 2.

Tobias is making scones. The recipe calls for 2/3 cup of flour to make 6 scones. What is the unit rate for cups of flour per scone​? For scones per cup of flour​? Use pencil and paper. Show or describe at least two ways to find the unit rate for scones per cup of flour.

Answers

Answer:

A. 1/9 cup of flour per scone.

B. 9 scones per cup of flour.

Step-by-step explanation:

We're given that Tobias uses 2/3 cup of flour makes 6 scones.

A. The unit rate of cup of flour per scone will be the cup of flour used to make a particular number of scones divided by that number of scones. Mathematically,

U. R. = (cup of flour)/(number of scones)

U. R. = (2/3)/6= 2/(3 *6)

U. R. = 2/18 = 1/9 or 0.11 scones per cup of flour.

B. (i) Method 1

Following the same method we used in (A) above, we need to divide the number of scones by the cup of flour used to make said number of scones. Mathematically,

U. R. = (number of scones)/(cup of flour)

U. R. = 6/(2/3) = (6 * 3)/2

U. R. = (6 * 3)/2 = 18/2

U. R. = 9 scones per cup of flour.

(ii) Method 2

Let the number of scones that can be made with 1 cup of flour(Unit rate for number of scones per cup of flour) be x. Then:

2/3 cup of flour = 6 scones

1 cup of flour = x scones

By cross multiplying and solving:

x = (6 * 1) / (2/3)

x = (6 * 3) / 2

x = 18/2 = 9 scones per cup of flour.

Does 5 go into 100 equally

Answers

yes, 5 goes into 100 exactly 20 times because 5 multiplied by 20 is 100

What is -4 divided by 2/5

Answers

The answer is -10

Step by step:
-4 / 2/5
-4/1 x 5/2
-20/2 simplifies to -10

Answer:

-10

Step-by-step explanation:

multiply by the reciprocal

-4÷5/2

reduce the numbers with greatest common factor 2

-2 x 5

multiply the numbers

-10

can someone please help? if can include working out​

Answers

Answer:

Step-by-step explanation:

a. 5 x (c) = -35

Divide each side by 5, which is equal to -6. Remember, two negatives make a positive and one negative and one positive makes a negative.

c. 16/(x) = -4

What times what is equal to a positive 16? To solve, multiply x on both sides of the equation to get 16 = -4x then divide -4 on both sides. You'll get the answer -4. 16/-4 = -4.

e. x/(-3)= -9

Like c, multiply both sides by the denominator, so -3. You'll get x by itself for an equation like x = -9 x -3. Then multiply, remember two negatives equal a positive, so x = 27. 27/-3 = -9.

g. -5000 x y = -10,000

Divide -5000 on both sides to get the equation y = -10,000/-5000. Then solve. y= 2. -5000 x 2 = -10,000.

i. 243/x = -81

Mutiply both sides of the equation by x, so x cancels out. You'll end up getting the equation 243= -81x. Then divide both sides of the equation by -81. Now that we have 1 positive and 1 negative we know our answer has to be negative. The equation should look like 243/-81 = x, which is equal to x=-3. Thus, the answer is 243/(-3)= -81.

k. -92 x y= 184

Divide both sides by -92 to get x by itself. Then you'll get the equation y= 184/-92. y= -2 so, -92 x -2 = 184.

clint has 6 apple muffins, 2 corn muffins, and 4 bran muffins what fraction of muffins are bran weite the fraction in simplest form​

Answers

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The fraction of bran muffins is expressed as bran muffins over total muffins.

Total muffins = 6 + 2 + 4 = 12 and bran muffins = 4, thus

fraction = [tex]\frac{4}{12}[/tex] ← divide ( cancel ) each value by 4 )

fraction = [tex]\frac{1}{3}[/tex] ← in simplest form

Answer:

1/3

Step-by-step explanation:

4 bran muffins out of 12 muffins in total.

4/12

4 ÷ 4 / 12 ÷ 4

1 / 3

Find the amount of air it would take to fill a basketball if the diameter of the ball is 12 inches

Answers

to find the volume of a sphere, use the formula 4/3*pi*radius cubed. the radius of this circle is 6 (half diameter) so use 4/3*pi*6 cubed, which is 4/3*pi*216. multiply by pi to get 678.58*4/3 is the volume. multiply by 4/3 to get about 904.78 inches cubed as the volume. so about 904.78 cubic inches of air.
Final answer:

In order to find the amount of air to fill a basketball with a diameter of 12 inches, convert the diameter to a radius and then to metric units. Then, use the formula for the volume of a sphere (4/3 * π * r³) to calculate the volume.

Explanation:

This is a problem relating to the volume of a sphere, based in Physics. Given the diameter of the ball (12 inches), we first convert this measure to the radius, which would be half of the diameter (6 inches). This can also be converted to the metric system for ease of calculation, where 1 inch equals roughly 2.54 cm, leading to 6 inches as approximately 15.24 cm.

To find the air required to fill up the ball, we apply the formula for the volume of a sphere (4/3)πr³. Plugging in the value of the radius we get, V = (4/3) * π * (15.24 cm)³. Solving this will get us the volume of air required to fill up the basketball.

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Which line is the graph of y = -2x + 2?

line a
line b
line c
line d

Answers

Answer:

The Answer is Line B

Step-by-step explanation:

the points that make up the graph is ( 0,2) and (1,0)

Answer:

Line B

Step-by-step explanation:

n(17+x)=34x-r solve for x

Answers

Answer:

[tex]x=\frac{-17n-r}{(n-34)}[/tex]

Step-by-step explanation:

 Given:                      

                          [tex]n(17+x)=34x-r[/tex]

                Taking the terms of x to one side.

                                [tex]17n+nx=34x-r\\[/tex]

                              [tex]nx-34x=-17n-r\\\\x(n-34)=-17n-r\\\\x=\frac{-17n-r}{(n-34)}[/tex]

The value of x is:

                                 [tex]x=\frac{-17n-r}{(n-34)}[/tex]

                   

The table shows the yearly earnings, in thousands of dollars, over a 10-year period for college graduates. Which statement is true about the distributions representing the yearly earnings?

a) The mean earnings of the self-employed are higher than the mean earnings of the wage earners.

b) The distribution of earnings for wage earners is more symmetric than the distribution of earnings for the self-employed.

c) The IQRs of the distributions are equal.

d) The standard deviations of the distributions are equal.

nvm its b :)

Answers

Answer:

Its B i just got it right

Step-by-step explanation:

The distribution of earnings for wage earners is more symmetric than the distribution of earnings for the self-employed.

What is IQR?

IQR stands for Interquartile Range, which is a measure of variability or spread in a set of data. It is calculated by finding the difference between the first quartile (Q1) and the third quartile (Q3) of a data set.

Without the table, it is difficult to provide a definitive answer. However, based on the information given, we can make some general observations:

a) It is possible that the mean earnings of the self-employed are higher than the mean earnings of the wage earners, but this cannot be determined from the information given.

b) It is also impossible to determine which distribution is more symmetric without further information.

c) The statement about the IQRs is also impossible to verify without more information.

d) It is unlikely that the standard deviations of the distributions are equal, as the earnings of self-employed individuals are typically more variable than those of wage earners. However, this also cannot be determined without more information.

Thus, the correct statement can be The distribution of earnings for wage earners is more symmetric than the distribution of earnings for the self-employed.

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what is y+7= -1/2 (x-6)​

Answers

Answer:

Step-by-step explanation:

y + 7 = -1/2(x - 6)

y + 7 = -0.5x +3

y = -0.5x - 4

Answer:

y=-1/2x-4

Step-by-step explanation:

first distribute the -1/2 into both terms in the parentheses. next solve for y by subtracting 7 from both sides. combine like terms

Which is the simplified form of r Superscript negative 7 Baseline + s Superscript negative 12?
StartFraction 1 Over r Superscript 7 Baseline s Superscript 12 EndFraction
Negative r Superscript 7 Baseline minus s Superscript 12
StartFraction r Superscript 7 Over s Superscript 12 EndFraction
StartFraction 1 Over r Superscript 7 Baseline EndFraction + StartFraction 1 Over s Superscript 12 EndFraction
Mark

Answers

Answer:

[tex] \frac{1}{ {r}^{7} } + \frac{1}{ {s}^{12} } [/tex]

Step-by-step explanation:

We want to simplify:

[tex] {r}^{ - 7} + {s}^{ - 12} [/tex]

Let us rewrite as positive index to get:

[tex]{r}^{ - 7} + {s}^{ - 12} = \frac{1}{ {r}^{7} } + \frac{1}{ {s}^{12} } [/tex]

We now find LCM to get:

[tex]{r}^{ - 7} + {s}^{ - 12} = \frac{ {r}^{7} + {s}^{12} }{ {r}^{7} {s}^{12} } [/tex]

Therefore the simplified form of the given expresion is:

[tex] \frac{ {r}^{7} + {s}^{12} }{ {r}^{7} {s}^{12} } [/tex]

But from the provide option, they only want us to rewrite as positive index without simplifying further

On a coordinate plane, is translated 3 units up and 3 units to the right to create Line p is drawn through P and and Line q is drawn through Q and Which statement about Lines p and q is true?

Lines p and q are parallel.

Lines p and q are perpendicular.

Lines p and q have the same x-intercept.

Lines p and q have the same y-intercept.

Answers

Answer:

Lines p and q are parallel

Step-by-step explanation:

1) Completing the question:

On a coordinate plane, is translated 3 units up and 3 units to the right to create ′′. Line p is drawn through and ’, and Line is drawn through and ’. Which statement about Lines and is true?

2)

If PQ (x, y) according to that rule then P'Q' (x+3, y+3). So let's plot to answer the question. Setting numbers for,x and y.

3) As you can see below, since we add 3 units to the right and 3 units up then no x-coordinate must be the same, no y-coordinate must remain the same. In addition, p and q won't have the same intercept, neither x nor y.

markdown $20 by [tex][/tex]7%

Answers

The final discounted price is $18.6

Step-by-step explanation:

In this problem we have to decrease the value of $20 by 7%.

First of all, we have to calculate the 7% of $20. We can do it as follows:

[tex]d=\frac{7}{100}\cdot 20 = 1.4[/tex]

This means that the 7% of $20 is 1.4$.

Now we want to decrease the original value by 7%, so we calculate the difference:

[tex]f=20 - d = 20-1.4=18.6[/tex]

So, the final discounted price is $18.6

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WILL GIVE BRAINLIEST You can draw a quadrilateral with no parallel lines and at least one right angle. True/ False Solve, graph, and give interval notation for the compound inequality:2x 4 > 6 AND 3(x + 2) 18 Read the excerpt from "Flowers for Algernon."That crazy TV kept up all night. How can I sleep with something yelling crazy things all night in my ears. And the nuttypictures. Wow. I don't know what it says when Im up so how am I going to know when Im sleeping.How does Charlie's opinion of the doctors' tests change from the beginning of the story?He used to think the tests were easy, now he thinks they are hard.He used to understand how the sts worked; now he doesn'tHe used to want to do well on the tests, now he is frustrated by them.He used to think the tests were meaningless now he knows they aren't Which factor had the greatest influence on the growth of ranching in Texas?The cattle breeds from Texas avoided carrying the deadly tick that killed otherbreeds.High demand for Texas cattle in the north offered the opportunity for largeprofits.Texas ranchers were welcomed in Missouri railroad towns where cattle wereshipped east.Texas cattle could be shipped around the world from ports on the Gulf ofMexico Which is an example of physical weathering?(1 point)acid rain breaking down compounds inrock statuesrock breaking apart when it falls from acliffoxygen interacting with minerals in rockbits of iron in rock rusting when exposedto oxygen and water in How does the setting and character development in a passage work together? PLEASE HELP ME FAST. WILL MARK AS BRAINLIEST IF GIVEN GOOD ANSWER The following data set is graphed on a coordinate plane: (10,45), (25,70), (46,105). If the y-intecept of the line of best fit is at 28.5 ,what would be the most reasonable slope of line: 1/3, 5/3, or -4/3? Show/explain how you know. The st. Lawrence is in the epicenter of..... a. THE GPD b. winter sports c. fishing d. trade between the US and canada this is how dora subtracts 73-26. 73-3=70. 70-?=50. ?-?=? fill in the blanks to solve The perimeter of a rhombus is 64 and one of its angles has measure 120. Find the lengths of the diagonals. Whenever dry nitrogen from a portable cylinder is used in service and installation practice, what item is of most importance in consideration of safety? PLEASE ANSWER!! I WILL GIVE BRANLIEST!!!A wealthy businessman is campaigning for state governor. During a debate he states, "I will use the leadership and financial skills I acquired as a successful businessman to restructure the state system, eliminating waste and inefficiency." Which of the following is it most important for voters to do in evaluating these statements? Review his record in business. Agree with his position on key issues. Analyze his lifestyle and spending. Examine his background and family. PLEASE HELP I NEED TO PASS THIS TEST!!! (first actual answer gets brainliest) Iliana rotated trapezoid WXYZ 180 about the origin.*graph below*What is the correct set of image points for trapezoid WXYZ? A segment is dilated, and the resulting segment is shorter than the original.Which of the following options could be the scale factor of the dilation?Select all that apply.3/8151/5 A landscaping company is putting small stones around a circular fish pond with a diameter of 5.5 yards. If each bag of stones fills a distance of 4 yards, how many bags do they need Question 3 (1 point)a nonconformity is a "hiatus" in time between rock layers. This is usually shown by uneven meeting point between 2 layers. Why does thisoccur?igneous intrusionweathering and erosion of the old layerlithification of a new layerheat and pressure on the old layer Increasing muscle mass and decreasing fat content in your body can increase ones use of energy. Why is this? When Alice spends the day with the babysitter, there is a 0.6 probability that she turns on the TV and watches a show. Her little sister Betty cannot turn the TV on by herself. But once the TV is on, Betty watches with probability 0.8. Tomorrow the girls spend the day with the babysitter.a) What is the probability that both Alice and Betty watch TV tomorrow?b) What is the probability that Betty watches TV tomorrow?c) What is the probability that only Alice watches TV tomorrow? What would happen of scientific knowledge was not debated and confirmed by scientist? The XO Group Inc. conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of a wedding is $29,858 (XO Group website, January 5, 2015). Assume that the cost of a wedding is normally distributed with a mean of $29,858 and a standard deviation of $5600.a. What is the probability that a wedding costs less than $20,000 (to 4 decimals)?b. What is the probability that a wedding costs between $20,000 and $30,000 (to 4 decimals)?c. For a wedding to be among the 5% most expensive, how much would it have to cost (to the nearest whole number)?