Mathematics College

## Answers

**Answer 1**

**Bode plots** depict the frequency response, or the magnitude and phase changes as a function of frequency. This is accomplished using two semi-log scale plots. Using** MATLAB**, plot Bode diagrams of G1(s) and G2(s) given below.

(a) The** first function** is:

G1(s) = (1 + s)/(1 + 2s)

**MATLAB Code:**

%G1(s)

n1 = [1 1] %coefficients of numerator

d1 = [2 1] %coefficients of denominator

sys1 = f(n1,d1) %the transfer function

bode(sys1) %bode plot

grid on

**Command Window:**

>> Untitled

n1 = 1 1

d1 = 2 1

sys1 = (1 + s)/(1 + 2s)

Continuous-time transfer function.

(b) The second function is:

G(s) = (1 - s)/(1 - 2s)

**MATLAB Code:**

%G2(s)

n2 = [-1 1] %coefficients of numerator

d2 = [2 1] %coefficients of denominator

sys2 = f(n2, d2) %the transfer function

bode(sys2) %bode plot

grid on

**Command Window:**

>> Untitled

n2 = -1 1

d2 = 2 1

sys2 = (1 - s)/(1 - 2s)

Continuous-time transfer function.

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The complete question is:

Using MATLAB, plot Bode diagrams of G1(s) and G2(s) given below:

G1(s) = (1 + s)/(1 + 2s)

G2(s) = (1 - s)/(1 - 2s)

Note that the second transfer function is a non-minimum phase system; meaning it has a zero on the right-half plane. Note how the phase plot is affected.

## Related Questions

EASY POINTS!

Two runners are training for their next competitions. Each runner is able to run a certain

distance in proportion to the time. The table on the left displays the distance Runner A

can run in relation to the time. Meanwhile, the graph on the right displays the distance

Runner B can run in relation to time.

What are the unit rates for the two runners? Which runner can run faster?

### Answers

The **unit rate** for the **speed **of Runner A and B is 12 and 15 ft / sec respectively, where Rubber B is **faster**.

What is unit rate?

A **unit rate **means a rate for one of something.

Given that, Two runners are training for their next competitions. Each runner is able to run a certain **distance **in **proportion **to the time. The **table **displays the **distance **Runner A can run in relation to the time. Meanwhile, the **graph **on the right displays the **distance **Runner B can run in relation to time. We need to find the **unit rates** for both runners,

Runner A =

**Unit rate = distance / time**

= 54 / 4.5

= 12 ft / sec

Therefore, **unit rate** for the **speed **of Runner A is 12 ft / sec

Runner B =

According to graph, the Runner B can run 75 ft in seconds

**Unit rate = distance / time**

= 75 / 5

= 15 ft / sec

Therefore, **unit rate** for the **speed **of Runner B is 15 ft / sec

Since, the **speed **of Runner B is greater than Runner A therefore, Rubber B is **faster**.

Hence, the **unit rate** for the **speed **of Runner A and B is 12 and 15 ft / sec respectively, where Rubber B is **faster**.

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A cylindrical soup can has a radius of 1.5 inches and holds 11.25π cubic

inches of soup. What is the height of the can to the nearest tenth?

### Answers

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1.5\\ V=11.25\pi \end{cases}\implies 11.25\pi =\pi (1.5)^2 h \\\\\\ \cfrac{11.25\pi }{\pi (1.5)^2}=h\implies 5=h[/tex]

C. How much car can you afford to finance a new car if your proposed monthly payment is $240, for 60 months (5 years), with a credit score between 601-660?

Finance amount: __________________________________

Estimated percentage rate: ____________________

Amount of interest you will pay for the loan: _____________________________

### Answers

**Finance amount: **The amount you can finance for a new car with a monthly payment of $240, for 60 months (5 years), depends on several factors, including the loan interest rate, the down payment, and the **value of the car.**

**Estimated percentage rate:** The interest rate for a new car loan with a credit score between 601-660 typically range**s from 5% to 10%**.

**Amount of interest you will pay for the loan**: The amount of interest you will pay for the loan can be calculated by multiplying the loan amount by the interest rate and the number of months.

How to calculate the total interest?

For example, if you** finance $20,000 at a 7% interest rate** for 60 months, the total interest paid over the life of the **loan would be $3,140.**

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Zachary purchased a computer for $1,600 on a payment plan. Four months after he purchased the computer, his balance was $1,160. Five months after he purchased the computer, his balance was $1,050. What is an equation that models the balance y after x months?

### Answers

**Answer:**

y = -110x + 1,600

**Step-by-step explanation:**

Zachary purchased a computer for $1,600 on a payment plan. Four months after he purchased the computer, his balance was $1,160. Five months after he purchased the computer, his balance was $1,050. What is an equation that models the balance y after x months?

1,160 - 1,050 = $110 change from month 5 to 4

Double check if the rate of decrease is steady over time:

1,600 - ($110 * 4 months) = 1,160

1,600 - ($110 * 5 months) = 1,050

This means, Zachary is paying $110 per month for his computer.

SO:

remaining payment plan balance = initial balance - 110 per month

This can be modeled by the algebraic equation:

y = 1,600 - 110x

rearrange right side:

**y = -110x + 1,600 **

**Answer:**

[tex]y=-110x+1600[/tex]

**Step-by-step explanation:**

Given information:

Purchase price = $1,600Balance = $1,160 after 4 months.Balance = $1,050 after 5 months.

Define the variables:

Let x be the number of months.Let y be the balance of the payment plan (in dollars).

Therefore:

x = 0, y = 1600x = 4, y = 1160x = 5, y = 1050

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Determine if the equation is **linear **by calculating the slope between each pair of (x, y) points:

[tex]\implies \text{Slope}\;(m)=\dfrac{1050-1160}{5-4}=-110[/tex]

[tex]\implies \text{Slope}\;(m)=\dfrac{1160-1600}{4-0}=-110[/tex]

As the slope is the same, the equation is **linear**.

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

As the initial purchase price of the computer was $1,600, the **y-intercept **is **1600**. We have already calculated the slope. Therefore, substitute the found slope and y-intercept into the **slope-intercept formula** to create an **equation **that models the balance y after x months:

[tex]y=-110x+1600[/tex]

Find the volume of the figure. Express answers in terms of pi, then round to the nearest whole number.

### Answers

pleaseee i really need help with this

here is the picture

### Answers

I think these are the answers, I didn’t write out the full questions just the first part

4 divided by 2 left square brackets 2 plus 2 right square brackets equals?

### Answers

The given **expression** "4 divided by 2 left square brackets 2 plus 2 right square **brackets** equals" gives the solution one divided by 2.

How to solve expressions?

4 **divided** by 2 left square brackets 2 plus 2 right square brackets equals?

4 ÷ 2(2 + 2)

based on the concept of **PEMDAS**

P = parenthesis

E = Exponent

M = Multiplication

D = Division

A = Addition

S = **Subtraction**

= 4 ÷ 2(4)

= 4 ÷ 8

= 4/8

= 1/2

Therefore, the correct answer is 1/2(one divided by two

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What number should go in the space?

Multiplying by 0.65 is the same as decreasing by _____%.

### Answers

**Answer:**** **35%

**Explanation:**** **

**1**** ****-**** ****0****.****6****5**** ****=**** ****0****.****3****5**

**0****.****3****5**** ****in ****percentage ****is ****3****5****%**

30 pts! Which could be the function of the following graph?

### Answers

**Answer:**

It might be "C"

**Step-by-step explanation:**

A company believes it has a 40% chance of being successful on bidding a contract that yields a net profit of $30,000. Assume it costs $5,000 in consultant fees to prepare the bid. What is the expected gain or loss for the company if it decides to bid on the contract?

### Answers

**Answer:**

Joe mum so gaeee

**Step-by-step explanation:**

your answer is 1000

Find an ordered pair (x,y) that is a solution to the equation

### Answers

**Answer:**

(3, -11)

**Step-by-step explanation:**

Rearranging the equation becomes a slope-intercept form:

[tex]y = 2 - 3x[/tex]

where **m = slope of equation **= [tex]-3[/tex]

and **c = intercept = **[tex]2[/tex]

Substitute any value of **x** into the above slope-intercept equation to determine it's corresponding **y** value. Together these **x **and **y **values** **will form an **ordered pair**.

*For example:*

Take **x = 3** and substitute in the above mentioned equation:

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

** **[tex]= 2 - 9[/tex]

**y = **[tex]-11[/tex]

∴ An ordered pair that is a solution to the equation: (**3**, **-11**)

The researcher who conducted the study discovered that the number of hours spent studying reported by the student represented by P was recorded incorreetly. The corrected data point for this student is represented by the letter Q in the scatterplot below. Explain how the least squares regression line for the corrected data (in this part) would differ from the least squares regression line for the original data

### Answers

The least squares regression line for the corrected data would be shifted upwards compared to the original **data**, indicating that increasing the amount of time spent studying would likely have a greater impact on a student's **grades**.

The least squares regression line for the corrected **data** would be shifted upwards compared to the least squares regression line for the original data, since the corrected data point has a higher value than the original data point. This shift in the regression line would indicate that, in general, increasing the amount of time spent studying would have a greater impact on the student's **grades** than the original data indicated.

The least squares **regression** line for the corrected data would be shifted upwards compared to the original data, indicating that increasing the amount of time spent **studying** would likely have a greater impact on a student's grades.

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Airline travelers should be ready to be more flexible as airlines once again cancel thousands of flights this summer. The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines (seattlepi.com, July 10, 2008). Suppose the hotline is staffed for 16 hours a day. a. Calculate the average number of calls in a one-hour interval; 30-minute interval; 15-minute interval. (Round your answers to 2 decimal places.) Interval Average Number of Calls 60-minute 30-minute 15-minute b. What is the probability of exactly 6 calls in a 15-minute interval? (Round your intermediate calculations and final answer to 4 decimal places.) Probability c. What is the probability of no calls in a 15-minute interval? (Round your intermediate calculations and final answer to 4 decimal places.) Probability d. What is the probability of at least two calls in a 15-minute interval? (Round your intermediate calculations and final answer to 4 decimal places.) Probability

### Answers

The Coalition for Airline Passengers Rights, Health, and Safety **averages** 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.

To calculate the average number of calls in different** time intervals** and the probability of different events related to these calls.

Part 1:

a. 60-minute interval average number of calls: 400/16 = 25 calls

30-minute interval average number of calls: 25/2 = 12.5 calls

15-minute interval average number of calls: 12.5/2 = 6.25 calls

Part 2:

b. To find the **probability **of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:

P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686

c. To find the probability of no calls in a 15-minute interval, we can use the Poisson **distribution formula**. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:

P(0 calls) = e^-6.25 = 0.0047

d. To find the probability of at least two calls in a 15-minute interval, we can use the **cumulative distribution function** of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:

P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906

Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.

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A phone company charges each customer a monthly fee of $11.25. In addition, it charges $0.05 per minute for in-state calls and $0.13 per minute for out-of-

state calls. What is the total monthly charge for a customer who made 300 minutes of in-state calls and 50 minutes of out-of-state calls?

### Answers

The monthly charge is $11.25. 300x0.05=$15. 50x0.13=$6.50. So 11.25+15+6.50=$32.75

The subtotal for Abdiel's takeout order is $21.50. What will Abdiel's total be if he uses a coupon for 10% off the subtotal and leaves a 20% tip before the discount? (2 points)

$22.15

$27.95

$23.22

$23.65

### Answers

**Answer: To calculate the total, we need to first calculate the discount and then the tip.**

**First, calculate the discount: $21.50 x 10% = $2.15**

**Then, subtract the discount from the subtotal: $21.50 - $2.15 = $19.35**

**Next, calculate the tip: $19.35 x 20% = $3.87**

**Finally, add the tip to the subtotal after the discount to find the total: $19.35 + $3.87 = $23.22**

**Therefore, Abdiel's total would be $23.22 if he uses a coupon for 10% off the subtotal and leaves a 20% tip before the discount.**

**Step-by-step explanation:**

The perimeter of a rectangle is 60 cm. Its width measures

16 cm. What is its length?

Let x= the length of the rectangle. Choose the equation that represents this

problem.

O A. 2x-32=60

O B. 2x+16=60

O C. 2x+32=60

O D. x+16=60

### Answers

O D. x+16=60

The answer

Vertex angles. Please help me

### Answers

For the given **triangle **the value of z = 1, y = 6, and x = 4.75.

What is geometry?

One of the earliest areas of **mathematics **is geometry, along with **arithmetic**. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of **objects**.

The value of x,y, and z will be calculated by the **property **states that the ratio of the **median **line passing from the centroid of the triangle is divided into the **ratio **of 1: 2.

The value of x,

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

2 ( 2x - 6 ) = 7

4x - 12 = 7

4x = 19

x = 19 / 4

The value of y,

3 / y = 1 / 2

y = 3 x 2

y = 6

The value of z,

2z / 4 = 1 / 2

4z = 4

z = 1

Therefore, the values are z = 1, y = 6, and x = 4.75.

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refers to the consistency of measures, whereas refers to the truthfulness of a measurement.

### Answers

Reliability refers to the consistency of **measures**, whereas validity refers to the truthfulness of a measurement.

What do we mean by measure?

The size, capacity, or amount of something determined by measurement. Use equal amounts of ingredients. Something used for measurement (such as a ruler or cup).A unit used to measure. A foot is a **measure** of length.

What is statistics in mathematics?

Statistics is a science concerned with developing and studying methods for **measure**, collecting, analyzing, interpreting, and presenting empirical data.

Significance of statistics:

Statistics is the branch of mathematics for collecting, analyzing and interpreting data. Statistics can be used to predict the future, determine the likelihood of certain events occurring, and answer research questions.

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Jack Roper is a college student. He pays $17,000 per year in tuition and books, $600 per month in rent, $400 per month for food, and $125 per month for on-campus parking. He gave up a job that pays $45,000 per year to attend college. Given this, the implicit cost of his education equals

### Answers

The **implicit cost** of Jack's education is **$77,000, **which is the amount of **foregone **income he gave up in order to attend college.

The **implicit **cost of Jack's education refers to the **opportunity **cost or the foregone income he gave up in order to attend college. It is a measure of the value of the next best **alternative **that he had to sacrifice.

First, let's find the total cost of tuition and books. Jack pays $17,000 per year, so the total cost will be 17,000 * 4 = $68,000 over 4 years of college.

Next, let's find the total cost of **rent **and food. Jack pays $600 per month for rent and $400 per month for food, so the total cost will be 600 + 400 = $1,000 per month. Over 4 years of college, this comes to 1,000 * 12 * 4 = $48,000.

Finally, Jack also pays $125 per month for on-campus parking, so the **total **cost will be 125 * 12 * 4 = $6,000.

Putting it all together, we can write the **equation **for the implicit cost of Jack's education as follows:

Implicit Cost = **Foregone **Income - Total Cost of Tuition, Rent, Food and Parking

Implicit Cost = 45,000 - (68,000 + 48,000 + 6,000)

Implicit Cost = 45,000 - 122,000

**Implicit Cost** = -77,000

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Wellington Elementary School bought a printer one year ago for $3,100. Today, the value of the printer has decreased to $2,170 and is expected to continue decreasing each year.

Write an exponential equation in the form y=a(b)x that can model the value of the printer, y, x years after purchase.

Use whole numbers, decimals, or simplified fractions for the values of a and b

### Answers

The value of **variables **are,

⇒ a = 3100

⇒ b = 0.7

**What is exponential decay?**

An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.

The exponential decay function:

Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.

Given that;

**Wellington Elementary **School bought a printer one year ago for $3,100.

And, Today, the value of the printer has decreased to $2,170 and is expected to continue decreasing each year.

Now, An equation in the required **exponential form,**

A = A₀(1 - r)ˣ

Substituting the values,

A = 3100(1-r)ˣ.

To find the r:

2170 = 3100(1-r)

r = 0.3

So, The **equation **is,

Aₙ = 3100(1-0.3)ˣ.

y = 3100(0.7)ˣ.

Therefore, The value of **variables **are,

⇒ a = 3100

⇒ b = 0.7

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claire has a points card for a movie theater. she receives 75 rewards points just for signing up. she earns 13.5 points for each visit to the movie theater. she needs at least 210 points for a free movie ticket. use the drop-down menu below to write an inequality representing vv, the number of visits she needs to make in order to get a free movie ticket.

### Answers

**Using **the drop-down menu **below **to write an **inequality **is V ≥ 10. The number of **visits **she needs to make in order to get a free movie ticket is 10.

We have,

75 rewards points just for **signing **up.

**earns **13.5 points for each visit to the movie theater

she needs at least 210 points for a **free **movie ticket

To write the **inequality **representing v is,

75 + 13.5v ≥ 210

13.5v ≥ 210 - 75

13.5 v ≥ 135

v ≥ 10

**Therefore**, by solving **inequality **the number of visits she needs to make in order to get a **free **movie ticket is 10.

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x divided by 12; x =2/3

### Answers

**Step-by-step explanation:**

x÷12

2/3/12

2×12/3

24/3

8

Consider a set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3. Calculate the z-score given that x = 79.8. Round your answer to two decimal places.

### Answers

For a set of data in which the** sample mean** is 83.3 and the sample standard deviation is 6.3 the **z-score** given that x = 79.8 would be -0.555

We know that the **formula **for calculating a **z-score** is :

z = (x - μ) / σ

where z is the **standard z - score**

x is the **observed value**

μ is the **mean **of the sample

σis the **standard deviation** of the sample

here, set of **data **in which the **sample mean** is 83.3 and the **sample standard deviation** is 6.3

i.e., μ = 83.3, σ = 6.3

We calculate the z-score for x = 79.8

Using above **formula**,

z = (x - μ) / σ

z = (79.8 - 83.3) / (6.3)

z = (-3.5) / (6.3)

z = -0.555

Therefore, the** z-score **is: -0.555

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Bridget has 13 gallons of gasoline to use for her lawnmowing business. She uses gasoline in the lawnmower at a consistent rate. Let X represent the number of lines mode and Y represent the amount of gasoline remaining. Look at the graph of the function construct the function for this scenario.

### Answers

The** linear function** that models this scenario is given as follows:

y = -0.25x + 13.

How to define the linear function?

The **slope-intercept **definition of a linear function is given as follows:

y = mx + b.

In which:

The slope m represents the rate of change.The intercept b represents the initial amount.

Bridget has 13 gallons of gasoline to use for her lawnmowing business, hence the** intercept b **is given as follows:

b = 13.

From the graph, when x increases by 20, y decays by 5, hence the **slope m** is given as follows:

m = -5/20

m = -0.25.

Hence the **function **is given as follows:

y = -0.25x + 13.

Missing Information

The problem is given by the image presented at the end of the answer.

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what is the estimate square root of 63

### Answers

The square root is between 7 and 8

Convert the angle 3 radians to degrees, rounding to the nearest 10th.

### Answers

**Answer: 172.0 degrees**

**Step-by-step explanation:**

In 180 degrees, there are [tex]\pi[/tex] radians. That means each radian is equal to:

[tex]\frac{180}{\pi }[/tex]

= 57.3248408

Then we simply multiply that by 3 to get:

3 * 57.3248408

= 171.974522

Rounded to the nearest tenth is 172.0

**Answer:**

172

**Step-by-step explanation**

180 degrees is equal to one pi.

That means each radian is equal to:= 57.3248408

Then multiply that number by 3

Written out is: 3 x 57.3248408= 171.97452

When rounded to the nearest tenth is 172.0

You have a total of 25 coins, all nickels and quarters. The total value is

$3.85. Write and solve a system of equations to find the number of

nickels n and the number of quarters q that you have. Can you solve it

### Answers

**Answer: Yes, I can solve this problem using a system of equations. Let n be the number of nickels and q be the number of quarters. Then we can write two equations:**

**The total number of coins is 25: n + q = 25.**

**The total value is $3.85: 0.05n + 0.25q = 3.85**

**We can solve this system of equations using substitution or elimination. Let's use substitution:**

**From equation (2), we can solve for n: n = (3.85 - 0.25q)/0.05.**

**Substitute this expression for n into equation (1): (3.85 - 0.25q)/0.05 + q = 25.**

**Multiply both sides by 0.05 to clear the denominators: 3.85 - 0.25q + 0.05q = 25 * 0.05.**

**Simplify the left side: 3.85 = 1.25q.**

**Divide both sides by 1.25 to solve for q: q = 3.08**

**Substitute this value for q into equation (1) or the expression for n from step (1) to find n: n = 25 - q = 25 - 3.08 = 21.92**

**Since n and q represent the number of coins, we round them down to the nearest whole number. So, there are 21 nickels and 3 quarters.**

**Step-by-step explanation:**

Kerys is trying to expand the binomial using the binomial theorem expression, . What value(s) should she substitute for k? Why?Kerys is trying to expand the binomial using the binomial theorem expression, . What value(s) should she substitute for k? Why?

### Answers

Kerys should **substitute **the values of k from 0 to 4 (inclusive) in the **binomial** theorem** expression** to expand the binomial (2x + y)⁴.

What is the Binomial Theorem?

The **binomial** theorem states the principle for expanding the** algebraic expression** (x + y)ⁿ and describes it as the total of the** phrases** involving the unique **exponents** of the x and y variables. Each word in a binomial expansion has a **coefficient,** which is a numerical **value**.

here, we have,

The** binomial** theorem states that the expansion of the **binomial** (x+y)^n is given by the** formula:**

(x+y)n = ∑nk=0nCk xn-kyk = ∑nk=0nCk xkyn-k

The variable n** represents **the power to which the **binomial **is raised, in this case n = 4.

The** variable **k is the exponent of the second term in the **binomial** (b), in this case y.

So, with k = 0, the term will be aⁿ = (2x)⁴, with k = 1, the term will be

a^(n-1) *b = (2x)³y , and so on.

Therefore, he should substitute the** values **of k from 0 to 4 (inclusive) in the binomial **theorem** expression to expand the** binomial** (2x + y)⁴.

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The Chess Club president brought donuts to the club meeting each week. As the club grew, more donuts were needed so that each member could have a donut. The table below shows the ratios of boxed donuts to the cost. Donuts 2 4 5 C Cost A B 38.00 45.60 Determine which table has the correct values for A, B, and C. Donuts 2 4 5 7 Cost 15.80 30.40 38.00 45.60 Donuts 2 4 5 6 Cost 15.20 27.60 38.00 45.60 Donuts 2 4 5 6 Cost 15.20 30.40 38.00 45.60 Donuts 2 4 5 7 Cost 15.80 31.60 38.00 45.60

### Answers

Using** proportional** relationships, it is found that:

1. A = 15.8, B = 5, C = 63.2.

2. A table with a rate of 0.82 **represents** the data.

3. Candidate B received 54 votes.

What is a direct proportional relationship?

A direct **proportional** relationship is a function in which the output variable is given by the** multiplication **of the input variable and the constant of **proportionality** k, also called unit rate, as follows:

y = kx

here, we have,

For item 1, the **constant **is given as follows:

k = 31.6/4 = 7.9.

Hence the equation is:

y = 7.9x.

Then the** value **of A is found as follows:

A = 7.9(2)

= 15.8.

The **value** of B is found as follows:

7.9B = 39.5

B = 39.5/7.9

B = 5.

The **value** of C is:

C = 7.9(8) = 63.2.

For item 2, the rate is given as **follows:**

k = 35/42.5 = 0.82.

Hence a table with a rate of 0.82 **represents** the data.

For item 3, we have that the relation is:

B = kA.

Hence the** constant **is:

k = 18/15

k = 1.2.

Then the** number** of votes received by Candidate B is:

B = 1.2 x 45 = 54 votes.

More can be learned about **proportional **relationships at brainly.com/question/10424180

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If f ( x ) = x 2 + 2 x − 3 and g ( x ) = x 2 − 9 , find ( f g ) ( 4 ) and ( f + g ) ( 4 ) . ( f g ) ( 4 ) is , and ( f + g ) ( 4 ) is .

(Photo)

Pls help…

### Answers

**Answer:**

3

28

**Step-by-step explanation:**

The expression (f/g) (4) is equal to f(4) / g(4).

f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21

g(4) = 4^2 - 9 = 16 - 9 = 7

So, (f/g) (4) = 21 / 7 =** 3.**

The expression (f + g) (4) is equal to f(4) + g(4).

f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21

g(4) = 4^2 - 9 = 16 - 9 = 7

So, (f + g) (4) = 21 + 7 = **28.**