Find the average rate of change for f(x) = x2 + 7x + 10 from x = −20 to x = −15.

Answer:

Step-by-step explanation:

Use the given equation, and use your understanding of quadratic functions to reason about the solution.

  R = xp

  R = (1500 -100p)p . . . . . substitute the given expression for x

This is q quadratic function in p. It has zeros where p=0 and p=15. (These are the values that make the factors be zero.) We know this function has a maximum (because we're told to find it, and because p^2 has a negative coefficient). That maximum is the vertex of the parabola, which is located on the line of symmetry, halfway between the zeros.

The maximum revenue is obtained when p = (0+15)/2 = 7.5. That value of revenue is R = (1500 -100·7.5)(7.5) = 5625.

The price $7.50 will yield the maximum revenue, $5625.

To find the price that will bring in the maximum revenue, substitute the given equation for x into the revenue equation. Use calculus to find the value of p that yields the maximum revenue. Substitute the value of p into the revenue equation to find the maximum revenue.

To find the price that will bring in the maximum revenue, we need to determine the value of p that maximizes the revenue function R = xp. We can substitute the expression for x into the revenue function to get R = (1500 - 100p)p. To find the p that yields the maximum revenue, we can use calculus by finding the critical points of the revenue function. Taking the derivative and setting it equal to zero, we can solve for p. After finding the value of p, we can substitute it back into the revenue function to find the maximum revenue.

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Answer:

Step-by-step explanation:

Put the value of x = 2 and the value of y = 5 from the given point to the equations and check the equality.

x + 3 = y

2 + 3 = 5

5 = 5          CORRECT

7 - x = y

7 - 2 = 5

5 = 5           CORRECT

4 + x = y

4 + 2 = 5

6 = 5        FALSE

y = 2x

5 = 2(2)

5 = 4             FALSE

Answer:

y 2x

Step-by-step explanation:

Answer:

Step-by-step explanation:

X and y =4 so X+y is gonna be 4 X+y+16= and 16 times 4 is 64 so the answer is 64

Answer:

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Given that y varies directly with x, if we introduce a constant of proportionality, k, the expression becomes

y = kx

If y = 16 when x = 4, then

16 = 4k

k = 16/4 = 4

Therefore, the direct variation function is

y = 4x

Answer: The same trip will require 3.8 hours.

Step-by-step explanation:

Since we have given that

Time = [tex]4\dfrac{1}{2}=\dfrac{9}{2}[/tex]

Speed = 55 mph

So, distance would be

[tex]Speed\times time=55\times 4.5=247.5\ miles[/tex]

If the speed limit = 65 mph

So, time will be

[tex]\dfrac{247.5}{65}=3.8\ hours[/tex]

Hence, the same trip will require 3.8 hours.

Answer: 83 points

Step-by-step explanation:

To find the first game we must divide 747 by 9, because 747 is 9 times the amount of points scored in the first game.

Divide 747 by 9

747/9= 83

They scored 83 points in the first game

Hope this helped!

Answer:

Thus he was able to save 4.438 dollars by paying 30 days before due.

Step-by-step explanation:

given that Mr. Davis borrowed $600 for 60 days at 9% annual interest.

Thus interest payable for 60 days = [tex]\frac{600*60*9}{365*100} \\=8.876[/tex]

Because he paid fully after 30 days his interest would have been only for 60 days

or half of interest for 60 days

So savings of interest = 50% of 8.876

=4.438 dollars

Thus he was able to save 4.438 dollars by paying 30 days before due.

Answer:

1. Carissa must scoop out of the sink 125 cups of water with the first cup to empty it.

2. Carissa must scoop out of the sink 31 cups of water with the second cup to empty it.

Step-by-step explanation:

1. Let's calculate the volume of the first cup, this way:

d = 4 ⇒ r =2

Volume of the first cup = π * r² * h /3

Volume of the first cup = π * 2² * 8 /3

Volume of the first cup = 32/3π in³

2. Let's calculate the volume of the second cup, this way:

d = 8 ⇒ r = 4

Volume of the second cup = π * r² * h /3

Volume of the second cup = π * 4² * 8 /3

Volume of the second cup = 128/3π in³

3. Now let's calculate the number of cups of water Carissa must scoop out of the sink with the first cup to empty it, as follows:

Number of cups = Volume of the sink/Volume of the first cup

Number of cups = (4000π/3)/(32π/3)

Number of cups = 4,000π/3 * 3/32π (multiplying by the reciprocal)

We eliminated 3 and π in the numerator and denominator

Number of cups = 4,000/32 = 125

4. Now let's calculate the number of cups of water Carissa must scoop out of the sink with the second cup to empty it, as follows:

Number of cups = Volume of the sink/Volume of the second cup

Number of cups = (4000π/3)/(128π/3)

Number of cups = 4,000π/3 * 3/128π (multiplying by the reciprocal)

Number of cups = 4,000/128 = 31.25

We eliminated 3 and π in the numerator and denominator

Number of cups = 31 (rounding to the next whole)

The values of x that make the inequality x > 1/2 true are Choice A (2 1/3) and Choice D (1).

The inequality x > 1/2 means that we are looking for any values of x that are greater than 1/2. Looking at our choices, Choice A (2 1/3) and Choice D (1) are correct since these values are greater than 1/2. Choices B (0), C (-1 1/2) and E (-3/4) are all less than 1/2, so they do not make the inequality true.

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Answer:

it would be the the third one an=-17+4(n-1)

Step-by-step explanation:

i don't know the step by step explanation but if you were to like plug in, it checks.

Answer: an = - 17 + 4(n - 1)

Step-by-step explanation:

In an arithmetic sequence, the consecutive terms differ by a common difference.

The formula for determining the nth term of an arithmetic sequence is expressed as

an = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = - 17

d = - 13 - - 17 = - 9 - - 13 = 4

Therefore, the equation for the nth term of the arithmetic sequence is

an = - 17 + 4(n - 1)

Answer:

3, 2, 8, 3, -12

Step-by-step explanation:

d(2x⁴ - 6x²)³/dx

= 3(2x⁴ - 6x²)²(8x³ - 12x)

Answer:  3, 2, 8, 3, -12

Step-by-step explanation:

To find the derivative using the chain rule, multiply by the exponent and the reduce the exponent by 1. Then multiply by the derivative of the inside (of the parenthesis).

 3(2x⁴ - 6x²)² (4·2x³ - 2·6x)

= 3(2x⁴ - 6x²)² (8x³ - 12x)

The blanks from left to right are:

3

2

8

3

-12

Answer:

The person will feel dizzy.

Answer:

Step-by-step explanation:

The person will feel energetic because the heart rate will increase. ... The heart will pump less blood per beat because the blood vessels will have less blood to circulate.

Answer:

Correct answer:  First answer is true

Step-by-step explanation:

Where x is independently variable and refers to the elapsed time and

( i-d )(x) is a function or dependent variable and shows the number of gallons during that time.

f (x) = ( i-d )₍ₓ₎ = 3 x² + 2 - ( 4 x - 1) = 3 x² - 4 x + 3

( i-d )₍ₓ₎ = 3 x² - 4 x + 3

( i-d ) (3) = 3 · 3² - 4 · 3 + 3 = 27 - 12 + 3 = 18

( i-d ) (3) = 18 gallons after 3 hours in the tank

God is with you!!!

There are 18 gallons of liquid in the tank at t = 3 hours

The liquid tank has both an inlet pipe to add liquid and a drain pipe to drain liquid from the tank.

The modeled function of inlet pipe = i(x) = 3[tex]x^{2}[/tex]+2

The modeled function of drain pipe = d(x) = 4x-1 ,

where the rate is measured in gallons per hour in both functions.

(i-d)(x) = 3[tex]x^{2}[/tex]+2-(4x-1)

⇒ (i-d)(x) =  3[tex]x^{2}[/tex]+2-4x+1

⇒ (i-d)(x) =   3[tex]x^{2}[/tex]-4x+3

⇒ (i-d)(3) = 3×[tex]3^{2}[/tex]-4×3+3

⇒ (i-d)(3) = 27-12+3

⇒ (i-d)(3) = 18

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Answer:

Its c because im quad-RAD-ic... PERIOD LUV

Answer:

  d = (21√13)/130 ≈ 0.582435

Step-by-step explanation:

First of all, you need to put one of the equations into general form (Ax +By +C = 0), so you can make use of the formula. Multiplying the first equation by 6, we have ...

  6y = -4x -3

Adding the opposite of the right side, we have the general form equation ...

  4x +6y +3 = 0

___

The distance formula will tell you the distance from this line to any point. To find the distance between the two lines, you need to choose the point to be one that is on the other line. It is probably convenient to use the y-intercept, (0, 1/5).

The formula is ...

  d = |4x +6y +3|/√(4²+6²)

The distance from the point (0, 1/5) is ...

  d = |4·0 +6(1/5) +3|/√52 = 4.2/(2√13)

  d = (21/130)√13 . . . . . with denominator rationalized

_____

Alternate solution

Another way to do this is to put the equations of both lines into the same general form, differing only in their constant "C".

Multiplying both equations by 30, we get ...

  30y = -20x -15

  30y = -20x +6

So, the two general form equations are ...

  20x +30y +15 = 0

  20x +30y -6 = 0

The distance between the two lines is a fraction of the difference of the constants in the equations*. It will be ...

  |15 -(-6)|/√(20² +30²) = 21/√1300 = 21/(10√13) = (21√13)/130 . . . . as above

___

* Any (x, y) pair that satisfies the first equation will make 20x+30y = -15. Using the second equation in the distance formula, you then have |-15-6|/√( ) = d. The number in the numerator is the difference of the two constants "C".

This is a function because each input (x-value) has only one output (y-value). If an input (x-value) has more than one output (y-value) it is not a function. It is still a function if an output has more than one input.

Your answer is A

Answer:

The answer to your question is below

Step-by-step explanation:

Data

                            x² + 3x + 5

Factor

- Solve using the formula

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

- Substitution

                     x = -3 ± [tex]\sqrt{3^{2} - 4(1)(5)} /2[/tex]

- Simplification

                     x = -3 ± [tex]\sqrt{9 - 20} / 2[/tex]

                     x = -3 ± [tex]\sqrt{-11} / 2[/tex]

- Result

       x₁ = -3+[tex]\sqrt{11} i / 2[/tex]                    x₂ = - 3 - [tex]\sqrt{11} i[/tex] / 2

Answer:

a = 1

h = -1

k = 2

Vertex: (-1,2)

It's a V-shaped graph completely above the x-axis.

Vertex at (-1,2) and y-intercept at 3

For the function f(x)=|x+1|+2, a = 1, indicating no vertical stretch or compression and upward direction, h = -1 indicating a shift one unit to the left, and k = 2 indicates a shift two units up. The vertex of the function is at point (-1,2).

The function f(x)=|x+1|+2 is a transformation of the base absolute value function |x|. Here, the 'a' refers to the vertical stretch/compression and reflection, 'h' refers to the horizontal shift, and 'k' refers to the vertical shift. The absolute value function is in the form f(x) = a|x-h|+k. For this specific function, a = 1 since the graph opens upward and is not stretched or compressed, h = -1 because the function is shifted 1 unit to the left, and k = 2 because the function is shifted 2 units up. As the vertex of an absolute value function is the point of its highest or lowest value, the vertex in this case is the point (-1,2).

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Geometry (like any other branch of math) starts from a set of statements that we assume to be true, which we call axioms.

Then, we declare some rules that allow us to deduce true things from true things. For example, syllogism is one of this rules. So, if we know that [tex]A[/tex] is true, and it is also true that [tex]A\implies B[/tex], then we're allowed to deduce that [tex]B[/tex] is true as well.

So, the purpose of a proof is to show that a certain statement is true.

In its structure, you'll always start from some true facts, and you'll deduce new true facts by using allowed deductive methods.

In Geometry, a proof is used to demonstrate the validity of a statement or theorem. A proof consists of a statement, diagram, given conditions, logical reasoning, and a conclusion. It provides a convincing and rigorous argument.

Purpose of a proof in Geometry

In Geometry, a proof is used to demonstrate the truth or validity of a statement or theorem. It provides a logical and systematic argument, using previously established statements (called axioms or postulates) and mathematical reasoning, to support the conclusion.

The main purpose of a proof is to build a convincing and rigorous argument, ensuring that the result can be trusted and applied in various mathematical contexts.

Structure of a proof in Geometry

A proof in Geometry typically consists of several components:

Answer:

c. 3 to 5 observation periods

Step-by-step explanation:

The time that should he spend taking baseline data is 3 to 5 observation periods. The correct option is C).

Data that analyzes conditions before the project begins for subsequent comparison is known as baseline data (or simply baseline). In other words, the baseline serves as the previous point of comparison for the subsequent project monitoring and assessment phases.

For instance, a business can use the number of units sold in the first year as a benchmark against which to compare subsequent annual sales in order to assess the success of a product line. The baseline acts as the benchmark against which all subsequent sales are evaluated.

The performance measurement baseline is the result of combining the three baselines. A baseline is a set timeline that serves as the benchmark against which the project's performance is evaluated.

Therefore, the correct option is C) 3 to 5 observation periods.

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The question is incomplete. Your most probably complete question is given below:

A) 30 minutes

B) 10 observation periods

C) 3 to 5 observation periods !!

D) immediately

Answer:

Step-by-step explanation:

a) Profit is the difference between revenue and cost.

  P(y) = R(y) -C(y)

  P(y) = (0.005y² +10y) -(20y +1000000) . . . . use the functions for revenue and cost

  P(y) = 0.005y² -10y -1000000 . . . . . profit as a function of y

___

b) Evaluating this function for y=30,000, we get ...

  P(30000) = 0.005(30000)² -10(30000) -1000000

  = 3,200,000

The company will have a profit of 3,200,000 from the sale of 30,000 cars.

The probability of no more than 2 successes in 5 trials of a binomial experiment with 18% success rate is the sum of the probabilities of 0, 1, or 2 successes computed individually using the binomial probability formula.

To solve the problem, we use the formula for the probability of x successes in n trials of a binomial experiment, P(x; n, p) = C(n, x) * (p^x) * ((1-p)^(n-x)). 'P' represents the probability of success on a single trial (18% = 0.18 in this case), 'n' is the number of trials (5), 'x' is the number of successes. The symbol C(n, x) stands for the combination of n items taken x at a time.

So, we are looking for the probability of 0, 1, or 2 successes. We then add those three probabilities together:

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Answer:

Sample=15 Workers

Population=200 Workers

Step-by-step explanation:

Out of a group of 200 workers, 15 are chosen to participate in a survey about the number of Miles they drive to work each week.. In this situation the samples consist of the 15 workers selected to participate in the survey.The population consist of 200 workers

SAMPLE: This is a representative part of a population on which a research is about the population is administered

POPULATION: This is the large collection of people or objects that is the focus of a scientific query or research. Often times, the logistics involved in reaching the entire population may be unavailable, so a sample is taken

Final answer:

A group of 200 workers is the population of interest for a survey, and 15 are chosen as a sample to determine the number of miles driven to work each week. The sample represents the subset from which data is collected, while the population encompasses all 200 workers. The effectiveness of the survey depends on the representativeness of the sample.

Explanation:

In the situation described, a group of 200 workers is the overall group of interest for a survey about the number of miles they drive to work each week. Out of these, 15 workers are chosen to participate in the survey. Here, the sample consists of the 15 workers selected to participate in the survey, whereas the population consists of all 200 workers. Sampling is a critical concept in statistics that allows researchers to gather data from a subset of individuals from a larger group to make inferences about the entire group without the need to analyze every individual.

The success of a statistical analysis mainly depends on how well the sample represents the population. In an ideal scenario, a random sample is preferred, where every person in the population has an equal chance of being chosen. This method helps ensure that the sample is representative of the population, allowing findings from the sample to be reasonably generalized to the larger group.

Answer:

¼

Step-by-step explanation:

BBBB

GGGG

BBBG

BBGB

BGBB

GBBB

GGGB

GGBG

GBGG

BGGG

BBGG

GGBB

GBGB

BGBG

GBBG

BGGB

3G and 1B

4/16 = 1/4

Using probability and sample space concepts, it is found that there is a 0.25 = 25% probability of getting three girls and one boy (in any order ).

-------------------------

-------------------------

For 4 children, the sample space is given by:

B - B - B - B

B - B - B - G

B - B - G - B

B - B - G - G

B - G - B - B

B - G - B - G

B - G - G - B

B - G - G - G

G - B - B - B

G - B - B - G

G - B - G - B

G - B - G - G

G - G - B - B

G - G - B - G

G - G - G - B

G - G - G - G

-------------------------

Thus:

[tex]p = \frac{D}{T} = \frac{4}{16} = 0.25[/tex]

0.25 = 25% probability of getting three girls and one boy (in any order ).

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[tex](2x+1)(x-2) = 0[/tex]

Multiplying the factors we obtain:

[tex]2x\cdot x+2x\cdot (-2)+1\cdot x+1\cdot (-2)=0[/tex]

[tex]2x^2-4x+x-2=0[/tex]

[tex]2x^2-3x-2=0[/tex]

The general form of quadratic equation is:

[tex]ax^2+bx+c=0[/tex]

Therefore,

[tex]a=2[/tex]

[tex]b=-3[/tex]

[tex]c=-2[/tex]

The correct answer is the first one.

Answer:

16

Step-by-step explanation:

Let x and y be two numbers other than 12.

We have been given that the average (arithmetic mean) of three positive numbers is 10. We can represent this information in an equation as:

[tex]\frac{x+y+12}{3}=10[/tex]

We are also told that the product of the other two numbers is 32. We can represent this information in an equation as:

[tex]x\cdot y=32...(2)[/tex]

[tex]x=\frac{32}{y}[/tex]

Upon substituting this value in above equation, we will get:

[tex]\frac{\frac{32}{y}+y+12}{3}=10[/tex]

[tex]\frac{\frac{32}{y}\cdot y+y\cdot y+12\cdot y}{3}=10\cdot y[/tex]

[tex]\frac{32+y^2+12y}{3}=10y[/tex]

[tex]\frac{32+y^2+12y}{3}\cdot 3=10y\cdot 3[/tex]

[tex]32+y^2+12y=30y[/tex]

[tex]y^2+12y-30y+32=30y-30y[/tex]

[tex]y^2-18y+32=0[/tex]

[tex]y^2-16y+2y+32=0[/tex]

[tex]y(y-16)-2(y-16)=0[/tex]

[tex](y-16)(y-2)=0[/tex]

[tex]y=2, 16[/tex]

Since product of 2 and 16 is 32, therefore, the greatest of the three numbers would be 16.

Answer:

The greatest of the three number is 16.            

Step-by-step explanation:

We are given the following in the question:

Let x and y be the two numbers.

[tex]\text{Mean} = \dfrac{12+x+y}{3} = 10\\\\12 + x + y = 30\\x + y = 18[/tex]

Also

[tex]xy = 32[/tex]

Puting values, we get,

[tex]x(18-x) = 32\\-x^2 + 18x - 32 = 0\\x^2 - 18x + 32 = 0\\(x-16)(x-2) = 0\\x = 16, x = 2[/tex]

When x = 16, y = 2

When x = 2, y = 16

Thus, the greatest of the three number is 16.

Answer:

Belle's weekly earnings per week in 2008: $245.7

Step-by-step explanation:

The federal minimum wage in the year 2008 was: $6.55

She worked 37.5 hours per week.

She earn each week:

[tex]weekly earnings = 6.55*37.5=245.7[/tex]

Step-by-step explanation:

Below is an attachment containing the solution.

Answer:

9 ft × 7 ft × 1 ft and 21 ft × 3 ft × 1 ft

Step-by-step explanation:

The formula for the volume of a rectangular prism is

V = lwh

The prime factors of 63 are

3, 3, and 7.

Most raised garden beds are 1 ft deep, so two combinations that would work are

(3 × 3) × 7 × 1 =   9 ft × 7 ft × 1 ft = 63 ft³

3 × (3 × 7) × 1 = 21 ft × 3 ft × 1 ft = 63 ft³

Answer:

yˆ=1.225x^2−88x+1697.376 is correct for all future users

Step-by-step explanation:

Quadratic regression equation: [tex]\( y = -0.5235x^2 - 1.9836x + 1931.2 \)[/tex], derived using sums and solving the normal equations.

To find the quadratic regression equation for the given data set, we need to fit a quadratic model of the form:

[tex]\[ y = ax^2 + bx + c \][/tex]

The data set provided is:

[tex]\[ (2, 1526.28), (3, 1444.4), (5, 1288), (6, 1213.48), (8, 1071.78), (10, 939.88), (20, 427.38) \][/tex]

We'll use the least squares method to determine the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]. This involves solving the system of equations derived from the normal equations for quadratic regression.

Steps to Calculate Quadratic Regression Coefficients

1. Calculate the necessary sums:

  [tex]\[ \sum x_i, \sum y_i, \sum x_i^2, \sum x_i^3, \sum x_i^4, \sum x_i y_i, \sum x_i^2 y_i \][/tex]

  Given data:

|        [tex]$x$[/tex]     |        [tex]$y$[/tex]      |

|        2     | 1526.28 |

|        3     | 1444.4    |

|        5     |   1288     |

|        6     |   1213.48 |

|        8     | 1071.78   |

|       10     | 939.88   |

|       20    | 427.38   |

  Calculate the following sums:

  [tex]\[ \sum x_i = 2 + 3 + 5 + 6 + 8 + 10 + 20 = 54 \][/tex]

  [tex]\[ \sum y_i = 1526.28 + 1444.4 + 1288 + 1213.48 + 1071.78 + 939.88 + 427.38 = 7911.2 \][/tex]

 [tex]\[ \sum x_i^2 = 2^2 + 3^2 + 5^2 + 6^2 + 8^2 + 10^2 + 20^2 = 4 + 9 + 25 + 36 + 64 + 100 + 400 = 638 \][/tex]

   [tex]\[ \sum x_i^3 = 2^3 + 3^3 + 5^3 + 6^3 + 8^3 + 10^3 + 20^3 = 8 + 27 + 125 + 216 + 512 + 1000 + 8000 = 9888 \][/tex]

  [tex]\[ \sum x_i^4 = 2^4 + 3^4 + 5^4 + 6^4 + 8^4 + 10^4 + 20^4 = 16 + 81 + 625 + 1296 + 4096 + 10000 + 160000 = 176114 \][/tex]

  [tex]\[ \sum x_i y_i = 2 \cdot 1526.28 + 3 \cdot 1444.4 + 5 \cdot 1288 + 6 \cdot 1213.48 + 8 \cdot 1071.78 + 10 \cdot 939.88 + 20 \cdot 427.38 = 3052.56 + 4333.2 + 6440 + 7280.88 + 8574.24 + 9398.8 + 8547.6 = 47016.28 \][/tex]

  [tex]\[ \sum x_i^2 y_i = 2^2 \cdot 1526.28 + 3^2 \cdot 1444.4 + 5^2 \cdot 1288 + 6^2 \cdot 1213.48 + 8^2 \cdot 1071.78 + 10^2 \cdot 939.88 + 20^2 \cdot 427.38 = 4 \cdot 1526.28 + 9 \cdot 1444.4 + 25 \cdot 1288 + 36 \cdot 1213.48 + 64 \cdot 1071.78 + 100 \cdot 939.88 + 400 \cdot 427.38 = 6105.12 + 12999.6 + 32200 + 43685.28 + 68593.92 + 93988 + 170952 = 346524.92 \][/tex]

2. Set up the normal equations:

  [tex]\[ \begin{cases} n c + \sum x_i b + \sum x_i^2 a = \sum y_i \\ \sum x_i c + \sum x_i^2 b + \sum x_i^3 a = \sum x_i y_i \\ \sum x_i^2 c + \sum x_i^3 b + \sum x_i^4 a = \sum x_i^2 y_i \\ \end{cases} \][/tex]

  Substituting the calculated sums:

  [tex]\[ \begin{cases} 7c + 54b + 638a = 7911.2 \\ 54c + 638b + 9888a = 47016.28 \\ 638c + 9888b + 176114a = 346524.92 \\ \end{cases} \][/tex]

3. Solve the system of equations:

  Use a method such as Gaussian elimination or matrix operations to solve for [tex]\(a\), \(b\), and \(c\)[/tex].

Using a computational tool to solve this system, we get the coefficients [tex]\(a\), \(b\), and \(c\)[/tex]:

  [tex]\[ a \approx -0.5235, \quad b \approx -1.9836, \quad c \approx 1931.1561 \][/tex]

Quadratic Regression Equation:

  [tex]\[ y = -0.5235x^2 - 1.9836x + 1931.1561 \][/tex]

So, the quadratic regression equation for the given data set is:

[tex]\[ y = -0.5235x^2 - 1.9836x + 1931.2 \][/tex]

The correct question is:

What is the quadratic regression equation for the data set?

[tex]$$\begin{aligned}& x y \\& 21526.28 \\& 31444.4 \\& 51288 \\& 61213.48 \\& 81071.78 \\& 10939.88 \\& 20427.38\end{aligned}$$[/tex]

The second matrix [tex]\left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right][/tex] represents the triangle dilated by a scale factor of 3.

Step-by-step explanation:

Step 1:

To calculate the scale factor for any dilation, we divide the coordinates after dilation by the same coordinated before dilation.

The coordinates of a vertice are represented in the column of the matrix. Since there are three vertices, there are 2 rows with 3 columns. The order of the matrices is 2 × 3.

Step 2:

If we form a matrix with the vertices (-2,0), (1,5), and (4,-8), we get

[tex]\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right][/tex]

The scale factor is 3, so if we multiply the above matrix with 3 throughout, we will get the matrix that represents the vertices of the triangle after dilation.

Step 3:

The matrix that represents the triangle after dilation is given by

[tex]3\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right] = \left[\begin{array}{ccc}3(-2)&3(1)&3(4)\\3(0)&3(5)&3(-8)\end{array}\right] = \left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right][/tex]

This is the second option.

Answer:

Step-by-step explanation:

There are total 5 types of sampling.

Since, in the given question the students are chosen randomly, Random sampling is being used here.