what was the mistake that was made?

The dimensions of the enclosure that is most economical to construct will be 3 feet and 86.67 feet.

For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.

The maximum and minimum value of the function is at f'(x) = 0.

A wall is to be worked to encase a rectangular area of 260 square feet. The wall along three sides is to be made of material that costs 3 bucks for every foot, and the material for the fourth side costs 15 bucks for each foot.

LW = 260

L = 260 / W

Then the minimum cost is given as,

y = 3L + 3W + 3L + 15W

y = 18W + 6L

y = 18W + 6(260 / W)

y = 18W + 1560 / W

Differentiate with respect to W and put it zero, then we have

y' = 0

18 - 1560/W² = 0

W² = 1560 / 18

W = 86.67 feet

Then the length is given as,

L = 260 / 86.67

L = 3 feet

The dimensions of the enclosure that is most economical to construct will be 3 feet and 86.67 feet.

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Using the t-distribution, it is found that the null hypothesis is rejected for a, b, c

Item a:

We have a right-tailed test, as it is being tested if the mean is more than a value.

The p-value is found using a t-distribution calculator, with 11 - 1 = 10 df and t = 1.91, hence it is of 0.0426.

The p-value is of 0.0426, which is less than 0.05, thus the null hypothesis is rejected.

Item b:

We have a left-tailed test, as it is being tested if the mean is less than a value.

The p-value is found using a t-distribution calculator, with 17 - 1 = 16 df and t = -3.45, hence it is of 0.0016.

The p-value is of 0.0016, which is less than 0.05, thus the null hypothesis is rejected.

Item c:

We have a two-tailed test, as it is being tested if the mean is different than a value.

The p-value is found using a t-distribution calculator, with 7 - 1 = 6 df and t = 0.83, hence it is of 0.4383.

The p-value is of 0.4383, which is more than 0.05, thus the null hypothesis is not rejected.

Item d:

We have a right-tailed test, as it is being tested if the mean is more than a value.

The p-value is found using a t-distribution calculator, with 28 - 1 = 27 df and t = 1.91, hence it is of 0.0195.

The p-value is of 0.0195, which is less than 0.05, thus the null hypothesis is rejected.

Therefore, in an independent random sample is selected from an approximately normal population with an unknown standard deviation. Using the t-distribution, it is found that the null hypothesis is rejected for a, b, c

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To compare two fractions, we need to find a common denominator and then compare the fractions using the numerators. In this case, we can find a common denominator by finding the least common multiple (LCM) of 7 and 8. The LCM of 7 and 8 is 56.

We can then rewrite both fractions using a denominator of 56:

-9/7 = -36/28

-11/8 = -44/28

Now we can compare the fractions using their numerators:

-36/28 < -44/28

Therefore, -9/7 is less than -11/8.

The Latin word "nomen" (which also appears in words like "nominate" and "nomenclature"), which meaning "name," is the root of the word "denominator." And that is essentially what the denominator of a fraction does: it "names" or specifies the kind of fraction that is specified by the numerator (the top part).

The numerator of a fraction, which determines how many parts are being taken into account, is equal to the number of equal parts that make up the total. You can think of a fraction as being composed of p parts, which is the numerator of an item, and q equal parts, which is the denominator.

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Answer:

40

Step-by-step explanation:

let x = # of Qs on the test

0.85x = 34

x = 34/0.85 = 40

Answer:

write your question in a proper way

Tamia will need 166 feet of fabric

Given that:

Tamia wants each curtain to be 24 inches long

At the fabric store, fabric is sold by the foot

Tamia's curtain company wants to make 83 curtains

1 curtain = 24 inches

83 curtains = 24×83 = 1992 inches

To convert inches to feet multiply by 1/12:

1992 inches =  1992 × 1/12 feet = 166 feet

Thus, she will need 166 feet

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The polygon shown in the figure is trapezoid and the value if x is  .

What is trapezoid?

A trapezoid may be a polygonal shape that has just one try of parallel sides. These parallel sides also are referred to as parallel bases of trapezoid. the opposite 2 sides of trapezoids area unit non-parallel and referred to as legs of trapezoids

Main body:

by using the property of trapezoid ,

1/2(sum of both bases) = mid-line passing through trapezoid

according to question:

x = 1/2(x-8+2x-12)

x = 1/2(3x -20)

2x = 3x - 20

x = 20

Hence value of x is 20.

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The Z-value posted in part(c) for a confidence level of 74% is 1.150

The Confidence level in statistics denotes the likelihood that an estimate of the location of a statistical parameter (such as an arithmetic mean) in a sample survey will also hold true for the population.

Confidence levels must be determined before conducting a survey since they affect the poll's margin of error and necessary coverage. 90, 95, and 99% confidence intervals are widely employed in surveys.

A calculated statistic that was based on a sample would also be true for the entire population, within the established confidence level, with a 95% likelihood, if the confidence level were set at 95%.

Every confidence level has different z-value

In the question, We have to write the Z-value of 74% which is 1.15

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No, least-squares fitting of a regression line doesn't only applies when there is one dependent variable and one independent variable.

A least-squares regression line, which minimizes the vertical distance between the data points and the regression line, is the line that best fits a linear relationship between two variables when the data indicates such a relationship.

The most used modeling technique is without a doubt linear least squares regression. It is what most people mean when they claim they fitted a model to their data using "regression," "linear regression," or "least squares."

The independent variable in a cause-and-effect relationship is the cause, while the dependent variable is the effect. A technique for predicting the value of a dependent variable Y based on the value of an independent variable X is known as least squares linear regression. That's why least-squares fitting of a regression line doesn't only applies when there is one dependent variable and one independent variable.

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Jane must therefore deposit her savings in the four rivers bank.

Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.

As per the data provided in the question,

Rate, r = 12%

After five years, the total amount, if Jane had saved at Mystic Bank,if Jane had saved at Mystic Bank would be:

[tex]A = P(1+\frac{r}{100} )^n[/tex]

For compounded quarterly,

n = 5 × 4

n = 20

A = 40000(1 + 12/(4 × 100))²⁰

A = 72244.44     (i)

If Jane placed her savings with the Four Rivers, then,

A = 40000(1 + 14/(2 × 100))¹⁰

A = 40000 × 1.9671

A = 78686.054  (ii)

Therefore, it is evident that case (ii) is higher than case (i). Jane must therefore deposit her savings in the four rivers bank.

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Answer: No, i dont think so.

Step-by-step explanation:

AC = BC is not listed as given.

There are two points, 4 units from the origin and 2 units from the line x = -1.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given point is at a distance of 4 units from origin,

that is √x² + y² = 4

x² + y²= 16 is the equation of the locus of the point.

The given point is also 2 units from the line x =-1

that is √(x+1)² + y² = 2

(x+1)² + y²= 4 is the equation of the locus of the point.

Subtracting the second given equation from the first one,

we get x² - (x+1)² = 12

simplifying, x = 11/2

So the common coordinate point for these 2 points which is 11/2.

Substituting this value to the first equation,

(11/2)²+ y² = 16

Simplifying, y = ±(i√57)/2.

There are 2 points whose coordinates are;

( i√57/2 , 11/2 ) and ( -i√57/2 , 11/2 ).

Therefore there are two points, 4 units from the origin and 2 units from the line x = -1.

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The number of items 125 they will sell if the price per item is $3.50. They will sell 125 items if the price is $3.50.

In the given question, a manufacturing company finds that they can sell 275 items at $2.50 per item and 350 items at $2.00 per item.

If the relationship between the number of items sold i and the price per item p is a linear one then we have to find a formula that gives x in terms of p, x =

Now we have to use the formula to find the number of items they will sell if the price per item is $3.50. They will sell items if the price is $3.50.

Let’s find the slope using

m = {y(2)-y(1)}/{x(2)-x(1),

where

x(1) = 2.5      y(1)=275

x(2) = 2         y(2)=350

m = (350-275)/(2-2.5)

m = 75/(-0.5)

m = -150 is the slope

Point slope form to find the equation:

y - y1 = m(x-x1)

y - 275 = -150(x - 2.5)

y - 275 = -150x + 375

y = -150x + 275 + 375

y = -150x + 650,

But they want to have x = items sold and p = the price

So we have to write the equation where x is in terms of p

x = -150p + 650:

then use the formula to find the number of items they will sell if the price per item is $3.00.

x = -150(3.5) + 650

x = -525 + 650

x = 125 items sold when the price is $3.5

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The approximate distance from the playground to the road along the other path is 1.3 miles.

A town park has two paths leading to the playground. One path is 2 miles from the road and the other path makes a right angle with the road. The two paths intersect at an angle of  50 degrees.

The approximate distance from the playground to the road along the other path can be calculated as follows;

using trigonometric ratios,

cos 50° = adjacent / hypotenuse

let

x =  distance from the playground to the road along the other path

Hence,

cos 50 = x / 2

cross multiply

x = 2 cos 50°

x = 2 × 0.64278760968

x = 1.28557521937

x = 1.3 miles.

Therefore,

distance form play ground to the road = 1.3 miles.

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When she did all three activities on Tuesday, the number of days that Gina will do all three activities again on the same day is in 48 days.

The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, denoted by lcm in arithmetic and number theory, is the smallest positive integer that is divisible by both a and b.

LCM is an abbreviation for "Least Common Multiple." The smallest multiple that two or more numbers have in common is defined as the least common multiple.

Since Gina runs every 8 days, cycles every 16 days, and jogs every 24 days. This will be:

Multiples of 8 = 8, 16, 24, 32, 40, 48

Multiples of 16 = 16, 32, 48

Multiples of 24 = 24, 48

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There are 364 positive variables and 5984 non - negative integers.

An integer is zero (0), a positive integer (1, 2, 3, etc.), or a negative integer with a minus sign (-1, -2, -3, etc.). [1] A negative number is the additive reciprocal of the corresponding positive number. [2] In mathematics languages, sets of integers are often represented by a bold Z or blackboard bold . The integers form the smallest group and smallest ring containing the natural numbers. In algebraic number theory, integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, (rational) integers are algebraic integers that are also rational numbers.

Let us take each xi = a₁+1

x₁+x₂+x₃+x₄ = 35

∴a₁+a₂+a₃+a₄ = 31 ,where each ai is non-negative.

Now using the stars and bars method the answer is -

([tex]\left \{ {{31 + 4 - 1} \atop {4 - 1}} \right.[/tex]  = [tex]\left \{ {{34} \atop {3}} \right.[/tex]}

               = [tex]\frac{34!}{3! * (34 - 3)!}[/tex]

               = 5984

A particular solution of this equation corresponds to the placement of 3 addition signs in the 14 spaces between successive ones in a row of 15 ones.

Since, a particular solution of the equation corresponds to the placement of k−1 addition signs in the n−1 spaces between successive ones in a row of n ones, the number of solutions of the equation x₁ + x₂ + x₃ +⋯+xₐ=n in the positive integers is

[tex]\left \{ {{n - 1} \atop {k - 1}} \right.[/tex]}

For instance, placing an addition sign in the fourth, seventh, and twelfth spaces gives

                         1111+111+11111+111

which corresponds to the solution x₁ = 4, x₂ = 3, x₃ = 5, x₄ = 3.

Hence, the number of such solutions is the number of ways we can select which three of the 14 spaces between successive ones in a row of 15 ones will be filled with addition signs, which is

                                    [tex]\left \{ {{14} \atop {3}} \right.[/tex]}

                             = [tex]\frac{14!}{3! * (14 - 3)!}[/tex]

                             = 364

Therefore, there are 364 positive variables and 5984 non - negative integers.

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Missing part of the equation is 6.0 × [tex]10^{-8}[/tex] [tex]m^{3}[/tex].

It is given that students sets up the equation (0.060 [tex]cm^{3}[/tex])(_) = (_) [tex]m^{3}[/tex].

i.e. we have units of [tex]cm^{3}[/tex] and wants units of [tex]m^{3}[/tex] .

We know that 100 cm = 1 meter

i.e. 100cm/1 meter

⇒  [tex](100cm/1 meter)^{3}[/tex] = 1 × [tex]10^{6} cm^{3}/m^{3}[/tex]

⇒1/(1 × [tex]10^{6} cm^{3}/ m^{3}[/tex]) = (1 × [tex]10^{-6} m^{3}/cm^{3}[/tex])

We can use this new conversation factor to convert volume from [tex]cm^{3}[/tex] to [tex]m^{3}[/tex].

(0.060 [tex]cm^{3}[/tex])(1 × [tex]10^{-6} m^{3}/cm^{3}[/tex]) = (_) [tex]m^{3}[/tex]

(0.060 [tex]cm^{3}[/tex])(1 × [tex]10^{6} cm^{3}/m^{3}[/tex]) = 6.0 × [tex]10^{-8} m^{3}[/tex].

This is the required equation.

If we want to convert measurement,

to convert a smaller unit to a larger init, divide it by the number of smaller units which are needed to make larger unit. To convert from a larger unit to a smaller one, multiply. To convert from a smaller unit to a larger one, divide.

A conversation factor is a number used to change one set of units to another, by multiplying or dividing.

Given question is incomplete.

a student sets up the following equation to convert a measurement. (the stands for a number the student is going to calculate.) fill in the missing part of this equation  (0.060 [tex]cm^{3}[/tex])(_) = (_) [tex]m^{3}[/tex].

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The sum of money that will amount to 5,200 in 6 years at the same rate at which #1706 amounts to #3412 in 20 years is 4000.

The rate of simple interest for changing 1706 to 3412 in 20 years is this:

S.I = PRT/100

Since the principal amount doubled, we can call this a 100% increase.

Thus the rate in 20 years

= 100/20

=5%

Since the rate for the principal amount is 5%, we can apply the same in the second sentence which gives us:

5% × 6

= 30%

5200 = 130%X

X = 520,000/130

= 4,000

So, the sum of money that will amount to #5200 in 6 years at the same rate of interest (simple) as the initial figures is 4000.

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Answer:

b

Step-by-step explanation:

did the math?

8 is the best estimate of [tex]8\frac{1}{8}[/tex].

In simple words, the ratio of the two numbers is called a fraction.

Mixed fraction is a form of a fraction which is defined as the ones having a fraction and a whole number.

For example, 2 (1/3) is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Step 1: Multiply the denominator with the whole number,

i.e. Multiply 8 with 8 in the given example, 8(1/8).

                                            8× 8  =64

Step 2: Add the numerator of the Fraction to the result in step 1. i.e.,             Add                                      1+ 64=65.

Step 3: Keep the Denominator same i.e. 8.

Step 4: The Improper fraction obtained is: 65/8.

Given number can be denoted as 8+[tex]\frac{1}{8}[/tex] = 8+0.15 = 8.15

So the number is nearest to 8 itself.

i.e. 8 is the best estimate.

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A person who watches 14 hours of TV can do 21.1 sit-ups.

The regression equation is used to predict or estimate the value of the response (or dependant) variables based on an understanding of the explanatory (or predictor) variables.

A regression equation has the following general form:

y = ax + b

Here,

y = dependent variable

x = independent variable

a = intercept

b = slope

The regression equation showing the relationship between the number of sit-ups a person can accomplish (y) and the number of hours of TV viewed each day (x) is:

y = -1.284x + 39.108

Compute the number of sit-ups a person who watches 14 hours of TV can do as follows:

y = -1.284(14) + 39.108

y = -17.976 + 39.108

y = 21.132 ≈ 21.1

Thus, a person who watches 14 hours of TV can do 21.1 sit-ups.

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We want to see for which one of the given functions, the inverse derivate evaluated in x = 20 is equal to 1/5.

The correct option is B:  f(x) = x^3 + 5x + 20

What is inverse derivative?

The inverse function rule in calculus is a formula that converts the derivative of the inverse of a bijective and differentiable function, f, into the derivative of f.

Remember that two functions f(x) and g(x) are inverses if:

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

And for the inverse derivate of a function, we have the rule:

[tex]\frac{d}{dx}[f^{-1} (f(x))]=\frac{1}{{f^'}(x)}[/tex]

So first we need to find for what value of x each function is equal to 20, and then we need to see if the derivate of the function evaluated in that same value of x is equal to 5.

For example, for the first option we have:

A: f(x) = x + 5

We find the x-value such that the function is equal to 20.

f(15) = 15 + 5 = 20

We derivate the function.

f'(x) = 1

We evaluate the function in the x-value we got above.

f'(15) = 1

This is not the correct option, as this is not 5.

Now we need to do that for all the given options.

The only correct option will be the second one:

B: f(x) = x^3 + 5x + 20

First we find the x-value such that this is equal to 20

f(0) = 0^3 + 5*0 + 20 = 20

Then the x-value is x = 0.

Now we find the derivate of f(x).

f'(x) = 3*x^2 + 5

Now we evaluate that in the x-value we got before:

f'(0) = 3*0^2 + 5 = 5

As wanted, this is equal to 5.

Then we have:

[tex]\frac{d}{dx}[f^{-1} (f(0))]=\frac{1}{{f^'}(0)}[/tex]

[tex]\frac{d}{dx} [f^{-1} (20)]=\frac{1}{5}[/tex]

As wanted.

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The statement that characterizes the outcome of the game is option d;

All of the above are correct.

Given,

The statements;-

a. Both Firm A and Firm B have a dominant strategy to advertise.

b. There is a Nash equilibrium when both firms advertise.

c. Although both firms collectively would earn higher profits by maintaining the agreement not to advertise, self-interest will cause each firm to break the agreement.

d. All of the above are correct

We have to find the correct statement that characterize the outcome of this game.

Here,

All the statement will characterize the outcome of this game. So correct answer is option d, All of the above are correct

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The valid conclusion is  A. We can be 90% confident that the mean amount of money spent at sporting events last year by all the students at this university is between $217 and $677.

The confidence interval used by the student researcher refers to the probability that the university's population parameter (average amount that students spent on sporting events last year) will fall between $217 and $677 for 90% of the time.

Thus, the interval measurement gives the researcher some degree of certainty that the calculated sample mean falls within the population mean most of the time.

Hence ,we can be 90% confident that the mean amount of money spent at sporting events last year by all the students at this university is between $217 and $677.

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5.8525 grams out of 25 grams of xenon will be left after 11 days.

The amount of time needed for an isotope's radioactivity to decrease to 50% of its initial value.

The given data is

T1/2=5.25 days.

No=25g

T=11 days

We'll have to find the disintegration constant first.

The formula for finding it is

T½ = In2 / λ

T½ = half-life

λ = disintegration constant

λ = In2 / T½

λ = 0.693 / 5.25

λ = 0.132

In(N / No) = -λt

where,

N = final mass of the radioactive sample

No = initial mass of the sample

λ = disintegration constant

t = time for the radioactive decay

In(N/No) = -λt

N / No = e^-λt

N = No(e^-λt)

N = 25 × e^-(0.132 × 11)

N=5.8525 g.

Therefore 5.8525 grams of Xe-133 will be left after 11 days.

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Gracie shay must add $11,873 to buy that new hammer with its initial investment.

Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.

As per the given information in the question,

The price of hammer =$28,000

The annual rate of interest = 6%

Total number of years = 5

Principal investment = $12,000

The equation for annual compound interest, with the principal amount included, is :

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

Substitute all the values from above in the equation,

A = 12,000(1+0.06/2)⁽²⁾⁽⁵⁾

A = 12,000 × 1.03¹⁰

A = $16127

After five years, Gracie won't be able to be the hammer and will have to pay more money:

28000 - 16127 = $11,873.

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The original amount of the loan is $23,000.

What is the simple interest?

Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

The formula of simple interest is I = PRT.

I =  interest

P = Principal

R = rate of interest

T = time

Given that the rate of interest is 6.5%. Thus R = 6.5% = 0.065

The interest that she paid after 1 year is $149.50.

Thus I = $149.50 and T = 1

Putting R = 0.065, I = $149.50, and T = 1 in I = PRT

149.50 = P × 0.065 × 1

Divide both sides by 0.065

P = 23000

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Answer: Translation T = (x + 8, y + 4)

Step-by-step explanation:

The x coordinate moved to the right by 8 and the y coordinate moved up by 4.

After solving the given equations the value obtained for x and y will be equal to 2 and 14 respectively.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

The given equations are:

y = 9x - 4 and,

y = -2x + 18

Equate both equations,

9x - 4 = -2x + 18

9x + 2x = 18 + 4

11x = 22

x = 2

Substitute x = 2 in the first equation,

y = 9x - 4

y = 9(2) - 4

y = 14

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The option that would be an appropriate procedure for this experiment is option A) The doctor needs to randomly assign 15 patients to the new medication and 15 to the original medication to even out the variability between the patients.

Random assignment is seen as a method of assigning participants from your sample to various groups in experimental research by using randomization. By using this technique, each sample member has a known or equal chance of being assigned to either the control group or the experimental group.

Note that with the goal of making the groups equal at the start of the study, random assignment is a method used in experiments to divide participants into multiple study groups that include those who share similar traits.

Therefore, in regards to the work of the doctor in the above case, any observed differences in the two groups' cholesterol levels would most likely be brought on by the new medication because the subjects' variability would be evenly distributed between the two groups. Hence option A is correct.

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The values of the expression (1)  (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7

The given parameters that will help us to calculate the values are

r(x) = x+5

s(x) = 4x +2

(1)  r*s(x) will be

(x+5)(4x+2)

Opening the brackets we have

4x²+2x+20x+10

= 4x²+22x+10

(2) (r-5)(x)

Putting the values of r and s

(x+5)- (4x+2)

Open the brackets to have

x+5-4x-2

Collecting like terms to get

-3x+3

(3) (r+s)(x)

By substitution we have

x+5+4x+2

⇒5x +7

In conclusion the values of the expressions are (1)  (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7

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