Mathematics College

## Answers

**Answer 1**

**Answer:**

$26

**Step-by-step explanation:**

65 x 60% = 39

65 - 39 = 26

## Related Questions

Show how you can make a ten to find the sum of 6+5

### Answers

By** rewritting **the 6 as 5 + 1 we will get:

1 + 5 + 5 = 1 + (5 + 5) = 11

**How to make a ten to simplify the sum?**

One trick we do a lot when we do **additions **os making tens (or hundreds, thousands, etc... depending on the case).

This means that we play with the **numbers **in such a way that we can make tens, in this case we have the **sum**:

6 + 5

We can rewrite this as:

6 + 5 = 1 + 5 + 5

Using the **associative property** we rewrite:

1 + 5 + 5 = 1 + (5 + 5)

1 + (5 + 5) = 1 + 10 = 11

The **sum **is equal to 11.

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a 20$ bill, two $10 three $5 and four $1 are placed in a bag, if a bill is chosen at random what is the expected value for the amount choses

### Answers

The** expected value f**or the amount chosen from the bag is $5.90

**How to get the expected value?**

We have

one $20 bill.two $10 bills.three $5 billsfour $1 bills.

So in **total**, we have 1 + 2 + 3 +4 = 10 bills.

The **expected value** will be then given by the sum of the products between the value of each bill and the number of bills of that type, divided by the total number of bills.

EV = (1*$20 + 2*$10 + 3*$5 + 4*$1)/10 = $5.9

The **expected value** is $5.9

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What is the equation of the line that passes through (-3,-1) and has a slope of 2/5? Put your answer in slope intercept form 1. Y=2/5x+1/52. Y=2/5x-1/53. Y= -2/5x-1/5

### Answers

We are asked to determine the equation of a line that passes through the point (-3, -1) and has a slope 2/5. To do that we will use the point-slope form of a line equation:

[tex]y-y_0=m(x-x_0)[/tex]

Where:

[tex]\begin{gathered} (x_0,y_0)=\text{ point on the line} \\ m=\text{ slope} \end{gathered}[/tex]

Now, we plug in the values:

[tex]y-(-1)=\frac{2}{5}(x-(-3))[/tex]

Simplifying we get:

[tex]y+1=\frac{2}{5}(x+3)[/tex]

Now, we apply the distributive law:

[tex]y+1=\frac{2}{5}x+\frac{6}{5}[/tex]

Now, we subtract 1 from both sides:

[tex]\begin{gathered} y=\frac{2}{5}x+\frac{6}{5}-1 \\ \\ y=\frac{2}{5}x+\frac{1}{5} \end{gathered}[/tex]

and thus we get the equation of the line.

solve for x if the equation is[tex]3 \sqrt{x + a - z = b} [/tex]

### Answers

EXPLANATION

Given the expression:

[tex]b=\sqrt[3]{x+a-z}[/tex]

Applying the cubic power to both sides:

[tex]b^3=(\sqrt[3]{x+a-z})^3[/tex]

Simplifying the cubic root with the cubic power:

[tex]b^3=x+a-z[/tex]

Subtracting -a to both sides:

[tex]b^3-a=x+a-a-z_{}[/tex]

Adding z to both sides:

[tex]b^3-a\text{ +z = x + a - a -z + z}[/tex]

Simplifying terms:

[tex]b^3-a+z=x[/tex]

Switching sides:

[tex]x=b^3-a+z[/tex]

The line y=kx+4 goes through the point (2,-2)

K=-3

Sketch the graph of the line (need ASAP!)

### Answers

The **graph **of the **linear equation:**

y = -3x + 4

Can be seen in the image at the end.

**How to sketch a graph of the line?**

Here we know that the **equation **for the **line **is:

y = k*x + 4

We know that this line goes through the point (2, -2), then we can replace these values in the above **line** so we get the value of k.

-2 = k*2 + 4

With this, we can find the value of k.

-2 - 4 = k*2

-6 = k*2

-6/2 = k = -3

Then the line is:

y = -3*x + 4

If we evaluate in x = 0, we get:

y = -3*0 + 4 = 4

So, at this point we know that the line passes through points (0, 4) and (2, -2), so to **graph the line**, we just need to graph these two points and draw a **line **that connects them, like in the example below.

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The Life time in hours of a certain aircraft has the normal distribution with mean 80, Standard devation 16. What is the probability that the aircraft Will last 100 hours

### Answers

1.25 is the **probability** that the aircraft Will last 100 hours.

What is probability?

The area of mathematics described as **probability** concerns with numerical representations of the likelihood that an event will occur or that an assertion is correct. An event's probability is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 represents certainty.

Given Data

**Mean** = 80

**Standard** **deviation** = 16

P( x < 100)

P( x < 100) = P( Z< [tex]\frac{x- mean}{standard deviation}[/tex])

P(x<100 ) = P( Z < [tex]\frac{100-80}{16}[/tex])

P(x< 100) = P(Z< [tex]\frac{20}{16}[/tex])

P(x < 100) = 1.25

1.25 is the **probability** that the aircraft Will last 100 hours.

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15 POINT AND BRANLIEST

A 15-gallon gas tank. If you can drive 330 miles on a full tank of gas, what is the unit rate of miles per gallon he gets?

### Answers

The **unit rate **he can drive in mile per gallon is 22 miles per gallon.

How to find unit rate?

**Unit rate** can be defined as the ratio between two measurements with the second term as 1.

In other words, a **unit rate** describes the ratio of two different units for the quantity of one.

Therefore, the **unit rate** in miles per gallon can be calculated as follows:

Hence,

**unit rate** = number of miles / number of gallons

number of miles = 330 miles

number of gallons = 15 gallons

**unit rate** = 330 / 15

Therefore,

**unit rate** = 22 miles per gallon

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As long as you follow through with a plan to save $2000 a year, at the end of each year, in your account that earns 4% interest how much would you have after 25 years future value?

### Answers

We have to use the simple interest formula.

[tex]A=P(1+rt)[/tex]

Where P = 2,000, r = 0.04, t = 25. Let's solve for A

[tex]\begin{gathered} A=2,000(1+0.04\cdot25)=2\cdot2,000 \\ A=4,000 \end{gathered}[/tex]Therefore, you will have $4,000 in 25 years.

a₁ = 4; a = (a)²-3 (n ≥2) list the first five terms

### Answers

The** first five terms **of the given sequence are **4, 1, 6, 13, 22**

We can solve this problem by following a few steps.

The formula to find the next four terms is**, a = (n)²- 3, (n ≥2)** as per the question.

Where n is the sequence of the number ( n = 2, 3, 4, 5, 6, etc. )

So, for the 2nd term A₂ = 2² - 3 = 4 - 3 = 1 [As** n = 2** for the second term ]

Similarly, for the 3rd term A₃ = 3² - 3 = 9 - 3 = 6 [ As** n = 3 **for the third term ] ,

for the 4th term A₄ = 4² - 3 = 16 - 3 = 13 [ As** n = 4 **for the second term ] ,

for the 5th term A₂ = 5² - 3 = 25 - 3 = 22 [As **n = 5 **for the second term ]

Now, we can conclude that **the first five terms** of the given sequence are **4, 1, 6, 13, 22**

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The **correct question** is :

a₁ = 4; a = (n)²-3 (n ≥2) list the first five terms

Solve the quadratic equation using the method indicated. See attached photo. Thanks in advance!

### Answers

The quadratic formula is given by th following formula:

[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

where a, b and c are the coefficients of the quadratic equation. In this case, you have:

**a = 6**

**b = 9**

**c = -22**

replace the previous values into the quadratic formula and simplify:

[tex]\begin{gathered} x=\frac{-9\pm\sqrt[]{(9)^2-4(6)(-22)}}{2(6)} \\ x=\frac{-9\pm\sqrt[]{609}}{12} \\ x_1\approx1.31 \\ x_2\approx-2.81 \end{gathered}[/tex]

**Hence, the solutions for the given equation are 1.31 and -2.81**

Given P(A) = 0.2, P(B) = 0.31 and P(AB) = 0.152, find the value of

P(AUB), rounding to the nearest thousandth, if necessary.

### Answers

**Probability - **The **value** of P(AUB) = 0.557

**What is Probability ?**

The area of** mathematics **known as **probability **deals with **numerical representations** of the likelihood that an event will occur or that a **statement** is true. An event's **probability **is a number between 0 and 1, where, roughly speaking, 0 **denotes** the event's **impossibility** and 1 **denotes **certainty.

Given,

P(A) = 0.2,

P(B) = 0.31 and

P(A/B) = 0.152,

Since, we know that

P(A⋃B) = P(A)+P(B)-P(A⋂B)

So, we have to find P(A⋂B)

We know that,

P(A/B) = P(A⋂B)/P(B)

Putting the **values** we get,

0.152 = P(A⋂B) / 0.31

P(A⋂B) = 0.152 x 0.31

P(A⋂B) = 0.047

Now, lets find the** value** of P(A⋃B)

P(A⋃B) = P(A)+P(B)-P(A⋂B)

Putting the **values** we get,

P(A⋃B) = 0.2 + 0.31 + 0.047

P(A⋃B) = 0.557

Hence the **value** of P(A⋃B) = **0.557**

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When using the standard algorithm to find the product 5,917x29, the first step is multiplying 9 ones by 7 ones. Explain why you regroup before the next step

### Answers

When using the standard **algorithm** to find the product 5,917x29, the first step is multiplying 9 ones by 7 ones, it's important to regroup in order to correctly **multiply** the values.

How to illustrate the information?

Using partial **products** or multiplying in parts is how the conventional method does multiplication. A word that also signifies multiplication is "product," so keep that in mind. Any two numbers, regardless of how tiny or how large, can be **multiplied** using this standard technique.

The top number is **multiplied** by the bottom number, one **digit** at a time, working your way from right to left, using this procedure.

In this case, it should be noted that the **value **of 5,917 × 29 is 171593.

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Based on this data what is the probability that the next car will not be white why

### Answers

The **probability **of the next car not being a white car is 0.92

What is probability?

The **probability **of an event is the chance or the likelihood that the event would occur.

Note that the chance or the **likelihood **is represented as a numerical value

How to determine the probability?

The complete question is added as an attachment

From the attached question, we have the following parameters

P(White Vehicle) = 0.25

P(Car) = 0.36

P(White Car) = 0.08

Using the **complement rule **of **probability**, we have the following equation

P(White Car) + P(Not White Car) = 1

Substitute the known values in the above equation

So, we have the following equation

0.08 + P(Not White Car) = 1

Subtract 0.08 from both sides of the equation

So, we have

P(Not White Car) = 1 - 0.08

Evaluate the difference

P(Not White Car) = 0.92

Hence, the **probability **that the next car will not be a white car is 0.92

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Simplify

Y exponent -5/ y exponent -4

### Answers

**Answer:**

"Simplify" is an instruction to rewrite the expression with as few symbols as possible. 5y-4 and 5/y4 have the same number of symbols.

A possible alternative direction might have been to rewrite without the negative exponent.

**Answer:**

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

**Step-by-step explanation:**

using the rule of exponents

• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

given

[tex]\frac{y^{-5} }{y^{-4} }[/tex]

= [tex]y^{(-5-(-4))}[/tex]

= [tex]y^{(-5+4)}[/tex]

= [tex]y^{-1}[/tex]

= [tex]\frac{1}{y}[/tex]

Each of the four shapes represents a positive whole number. The sum of the shapes in

each row and column is displayed at the end of each row and column. Using this

information, determine the numerical value of each shape.

### Answers

The **numerical value** of each of the four given shapes filled in the rows and columns are;

**pentagon** shape = 8star shapes = 6**spiral** shapes = 3rectangle shape = 5

How to find numerical value of each shape.

let

pentagon shape = AStar shape = BSpiral shape = Crectangle shape = D

Row 1: There are 2 stars, one **pentagon** and one spiral shape.

A + 2B + C = 23 .....(equation 1)

Row 2: There are 2 **spiral shapes** and 2 rectangle shape.

2C + 2D = 16 ......( equation 2)

Row 3: There are 1 star, one pentagon and 2 **rectangle** shape.

A + B + 2D = 24 ....(equation 3)

Row 4: There are 3 spiral shapes and one star shape.

B + 3C = 15 ....(equation 4)

Column 1:

2C + A + D = 19 ....(equation 5)

Column 2:

2B + C + D = 20 .....(equation 6)

From equation 4;

B = 15 - 3C

From equation 2:

D = 8 - C

**Substitute** B = 15 - 3C into equation 1;

A + 2B + C = 23

A + 2(15 - 3C) + C = 23

A + 30 - 6C + C = 23

A = 5C - 7

**Substituting** D = 8 - C and A = 5C - 7 into equation 5;

2C + A + D = 19

2C + (5C - 7) + 8 - C = 19

6C + 1 = 19

6C = 18

C = 3

**Substitute** 3 for C in

A = 5C - 7

A = 5(3) - 7

A = 8

**Substitute** 3 for C in

B = 15 - 3C

B = 15 - 3(3)

B = 6

**Substitute** 3 for C in

D = 8 - C

D = 8 - 3

D = 5

Therefore, there are 8 **pentagon** shape, 6 star shapes, 3 **spiral** shapes and 5 rectangle shape.

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A high school band raises $6, 764 to buy instruments

and uniforms for its members. Half the money is spent

on new instruments. They buy 38 new uniforms with

the remaining money.

### Answers

**Answer:**

$89 dollars per uniform

**Step-by-step explanation:**

Total amount of money raised= $6,764.

Money spent on new instruments= $6,764÷1/2 = $3382

The number of new uniforms bought with the remaining money= 38.

How much was spent on one= $3,382÷38 = $89

A company borrows $68,000 for 8 years at a simple interest rate of 15.5%. Find the interest paid on the loan and the total amount paid.

### Answers

The** interest paid** on the loan and the** total amount paid** are $84,320 and $152,320 respectively.

It is given in the question that:-

**Money borrowed** by the company (Principal) = $68,000

**Time period** for which the money is borrowed = 8 years

Simple Interest rate = 15.5 %

We have to find the interest paid on the loan and the total amount paid.

We know that,

**Simple interest** = (Principal * Interest * Rate)/100

Hence, we can write,

Simple interest = (68000 * 15.5 * 8)/100 = $84,320

Also, we know that,

Amount = Principal + Interest

Hence, we can write

Amount = 68,000 + 84,320 = $152,320

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Assume that when you take a bath, you fill a tub to the haltway point. The tub measures 5 feet by 2 feet by 2.7 feet. When you take a shower, you

use a shower head with

flow rate of 2.03 gallons per minute, and you typically spend 9 minutes in the shower. There are 7.5 gallons in one cubic

foot. Complete parts (a) through (c) below.

a. Do you use more water taking a shower or taking a bath? Select the correct choice below

and fill in the answer box to complete your choice.

(Round to one decimal place as needed.)

O A. Shower; you use

more cubic feet of water than taking a bath.

• B. Bath; you use

more cubic feet of water than you do taking a shower.

### Answers

The person is therefore using **more** water for bathing than for showering, according to the conclusion.

Half of the tub's total water is consumed while taking a bath.

Water used divided by **volume **equals

[tex]\frac{volume}{2}[/tex]

= [tex]\frac{(5)(3)(2.8)}{2}[/tex]

=[tex]\frac{42}{2}[/tex]

=21 cubic feet.

The following will provide the total **amount **of water utilized while having a shower:

Total water Equals **rate** ×time

= 1.52 × 12

= 18.24 gallons.

So, if there are 7.5 gallons in a cubic foot, the amount of water in cubic feet will be amount

=[tex]\frac{18.24}{7.5}[/tex]

=2.432 cubic feet.

The person is therefore using more water for bathing than for showering, according to the conclusion.

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You purchase 5 tickets to a football game from TicketMaster. In addition to the cost per ticket, the agency charges a convenience charge of $2.50 per ticket. You also choose to pay for rush delivery, which costs $15. The total cost of your order is $352.50. What is the price per ticket before the convenience charge?

### Answers

The **price** per ticket, excluding the** convenience charge**, is $65.

How to solve for the privce per ticket

the rush delivery is given as $15.

The total cost of the tickets is said to be put at $352.50

Then the value that we would have for the the 5 tickets wpould be 352.50 - 15 = $337.50.

There is the c**onvenience charg**e of $2.50 per ticket. This charge is excluded from the convenience charge that is to be paid.

Hence you would have to make the payment of

337.50 - 5*2.50

= 325.

Next we are to solve for the price of the ticket whioch is independent of the **convenience charge**

= 325 / 5

= $65

Hence the price per ticket is given as 65 dollars

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Answer to exercise 1 please

### Answers

Using an **exponential function** and a differential equation, the** constant k **for the situation is given by:

k = 0.03.

What is an exponential function?

An **increasing **exponential function is modeled according to the following rule:

[tex]A(t) = A(0)e^{kt}[/tex]

In which:

**A(0) **is the initial amount of the function.**k **is the exponential growth rate of the function, as a decimal.

This exponential function is the solution to the following **differential equation**:

A'(t) = kA(t)

One example of application of these functions is for **continuous compounding,** in which the value of an investment of P(0) after t years is given by:

[tex]P(t) = P(0)e^{kt}[/tex]

For the continuous compounding situation in this problem, the **interest rate is of 3%**, hence k = 0.03, which is the desired **parameter**.

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n

Find the value of x that makes m ||

(180 − x)°

m

An

to

W

### Answers

**Answer:**

The value of x will be 90°

The height of a wave in California varies directlywith the seconds that pass by. At 4 seconds,the wave is 6 feet high. Find the constant ofvariation.Weight varies directly with arit

### Answers

The **constant variation **of hight(y) to seconds(x) is 3y/2x.

**What is the constant variation?**The quantity that connects two variables that are directly or inversely proportional to one another is known as the **constant of variation. **By dividing the** y-coordinate** by the **x-coordinate**, we can find k when given any point because it is constant (the same for every point). For instance, the constant of variation is k = = 3 if y varies directly as x and y = 6 when x = 2.

So, let the second be 'x' and the height is 'y'.

At 4 seconds the wavelength is 6 ft high.

Constant variation:

y/x = 6/4 = 3/23y/2x

So,

x = 4, x = 8, x = 12y = 6, y = 12, x = 18

Therefore, the **constant variation **of hight(y) to seconds(x) is 3y/2x.

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Joanne deposits $4,300 into a l-year CD at a rate of 2.3%, compounded daily.a. What is her ending balance after the year, to the nearest cent?b. How much interest does she earn, to the nearest cent?c. What is her annual percentage yield to the nearest hundredth of a

### Answers

Joanne deposits $4,300 into a l-year CD at a rate of 2.3%, compounded daily.

a. What is her ending balance after the year, to the nearest cent?

b. How much interest does she earn, to the nearest cent?

c. What is her annual percentage yield to the nearest hundredth

Remember that

The compound interest formula is equal to

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=$4,300

t=1 year

r=2.3%=2.3/100=0.023

n=365

Part a

Find out the value of A

substitute the given values in the formula

[tex]A=4,300(1+\frac{0.023}{365})^{365\cdot1}[/tex]

A=$4,400.04

Part b

I=A-P

I=4,400.04-4,300

I=$100.04

Part c

we have

4,300 -----> represent 100%

so

Applying proportion

Find out how much percentage is 4,400.04

100/4,300=x/4,400.04

x=(100/4,300)*4,400.04

x=102.33%

therefore

102.33-100=**2.33%**

Please help, Pre-Algebra super easy math question

### Answers

**Answer:**

-16

**Step-by-step explanation:**

b) -x²; x = -4

-(-4)²

-(16)

-16

I hope this helps!

**Answer: -16**

**Step-by-step explanation:**

simplify (-2)(-3)(6) 20 points plus brainliest if right

### Answers

**Answer:**

36

**Step-by-step explanation:**

-2(-3)(6)

6(6)

36

**Answer:**

**-8/2 / 6/-3 -8/2 x -3/6 24/12= 2**

**Step-by-step explanation:**

1/16x+1/320y-29=0 rewrite the equation as a function of x

### Answers

The equation as a **function** of x is y = 9280 -20x

What is equation ?

**Equations** are logical assertions in mathematics that have two **algebraic expressions** on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all **mathematical equations**. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an **equation** if there is no "equal to" **sign** in the statement. It shall be taken into account as an expression.

The equation is =[tex]\frac{1}{16}x + \frac{1}{320}y - 29= 0[/tex]

Now rearranging the **function** we write

[tex]\frac{y}{320}= 29 -\frac{x}{16}[/tex]

y = 9280 -20x

The equation as a function of x is y = 9280 -20x

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3. a) Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. The actual

was 4.1 ft. What is John's percent decrease on his measurement?

measurement

### Answers

Jack's **percentage decrease** on his measurement of painting by **18%**.

**What is meant by percentage change?**

Measures of **percent change **include percent increase and percent decease, which indicate how much an element of a variable changes in terms of intensity, size, extent, or value.

Given that,

Jack's measurement for his room = 5 ft (taking this as old value)

Actual measurement for Jack's room = 4.1 ft (taking this as new value)

Using formula for Percent change = [tex]\frac{new - old}{old}[/tex] × 100% = [tex]\frac{4.1 - 5}{5}[/tex] × 100%

= [tex]\frac{-0.9}{5}[/tex] × 100% = -0.18 × 100%

= -18%

Here, minus sign represents the decrease in percentage.

Hence, Jack's** percentage decrease** on his measurement of painting by **18%**.

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**Correct question will be :**

Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. But the actual measured painting is 4.1 ft. What is Jack's percent decrease on his measurement of the painting?

The vertices of triangle FGH are F(-5,1,) G(-2,4), and H(-1,2) the vertices of triangle F’G’H are F’(-5,-1) G(-2,-4) H (-1-2)Identify the transformation of triangle FGH to triangle F’G’H A. A translation across the x-axis B. A reflection across the x-axis C. A dilation D. A rotation

### Answers

The transformation of △FGH to △F’G’H is (B) the** reflection across the x-axis.**

**What do we mean by reflection across the x-axis?**The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the **additive inverse. **Point (x, y) is reflected across the x-axis as (x, -y).A **graph **will appear to be inverted or on the other side of an axis, such as the x-axis, when it is reflected along that axis.If you look closer, you'll notice that it's **symmetrical**, meaning that each point is equally spaced from the axis of reflection and the axis of its reflection.As a result, if you reflect a **point **(x, y) along the x-axis, its x abscissa will remain the same but its y ordinates will negate. So (x,y) becomes (x, -y)

So, the difference between the vertices of triangle FGH and F’G’H is the y-coordinates of the F’G’H triangle are inverse of the y-**coordinates **of the FGH triangle.

And as we know that in **reflection **across x-axis the x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse.

Therefore, the transformation of △FGH to △F’G’H is (B) the** reflection across the x-axis.**

Know more about **reflection across the x-axis **here:

**https://brainly.com/question/11453535**

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Find the value of x

### Answers

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Ventana High School has found that some offerings on the lunch menu aremuch more popular than others. The following table displays students'favorite lunch choices:1875923PizzaTacosSubSandwichesChineseComboPlate98What is the estimated population proportion of students who prefer tacos?A. 0.12B. 0.32C. 0.16D. 0.06

### Answers

**Answer:**

**C. 0.16**

**Explanation:**

In the table there are 59 students that prefer tacos and there are 367 students in total because

187 + 59 + 23 + 98 = 367

Then, the estimated population proportion of students that prefer tacos is calculated as

P = 59/367 = 0.16

Therefore, the answer is

C. 0.16