Find the area of the shaded region.

The option D "Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent." describes the correct method. So the option D is correct.

The substitution method is a method of solving a system of linear equations by expressing one variable in terms of the other and then substituting the expression into the other equation. This method can be used when the system of equations consists of two linear equations with two unknowns.

The elimination method is a technique used to solve systems of linear equations. It involves transforming the given system into an equivalent system of equations in which the coefficients of one of the variables are the same in each equation, and then eliminating that variable by addition or subtraction. So the option D is correct.

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Which describes the correct method?

A. Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent.

B. Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.

C. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent.

D. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.

The complex zeros of the given polynomial function f(x) = x^4 + 170x^2 + 169 are [-i\sqrt{2}, i\sqrt{2}, -1, 1].

To find the complex zeros of the given polynomial function f(x) = x^4 + 170x^2 + 169, we can start by noting that this polynomial is a perfect square of a binomial. Specifically, we have:

f(x) = (x^2 + 13)^2

Therefore, the zeros of f(x) are the values of x that satisfy f(x) = 0. In other words, we need to solve the equation:

(x^2 + 13)^2 = 0

Taking the square root of both sides, we get:

x^2 + 13 = 0

Solving for x, we get:

x = ±i√13

However, we need to find the complex zeros of f(x), which are the roots of the equation f(x) = 0. Since f(x) = (x^2 + 13)^2, the zeros of f(x) are exactly the same as the zeros of x^2 + 13, namely ±i√13.

But this is not the end of the story. Since x^2 + 13 has only two distinct roots, namely ±i√13, each of these roots must occur with multiplicity 2 in f(x). This means that f(x) has a repeated root at each of the values ±i√13.

Finally, we note that x^2 + 13 can be factored as:

x^2 + 13 = (x + i√13)(x - i√13)

Therefore, we can write f(x) as:

f(x) = (x^2 + 13)^2 = (x + i√13)^2(x - i√13)^2

This gives us the factored form of f(x), and we can see that it has four roots, namely -i√13, i√13, -i√13, and i√13, which can be simplified to -i√2, i√2, -1, and 1.

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The trinomials that have (3x+2) as a factor are [tex]x^{2} 6x^2+19x+10, 6x^2-x-2\sqrt{x} \\\\[/tex]  , [tex]6x^2+7x-3, 6x^2-5x-6 and 12x^2-x-6.[/tex]

A trinomial is a polynomial with three terms. Each trinomial can be written in the form ax^2+bx+c, where a, b and c are constants, and x is a variable. If a trinomial has (3x+2) as a factor, then it can be written in the form (3x+2)(ax+b). By multiplying out this expression, we can obtain the trinomial ax^2+bx+c.

To find the trinomials that have (3x+2) as a factor, we need to solve the equation ax^2+bx+c = (3x+2)(ax+b). This can be done by equating coefficients of the same powers of x. For example, equating the coefficients of x^2 gives us the equation a = 3a. Since a cannot equal both 3a and 0, we must have a = 0. Similarly, equating the coefficients of x gives us the equation b = 3b+2a, so b = -2a. Finally, equating the constants gives us the equation c = 3b+2a, so c = 2a.

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To simplify 3(w+11) /6w, we can first simplify the numerator by distributing the 3:

3(w+11) = 3w + 33

Now we have:

(3w + 33) / 6w

We can further simplify by factoring out a 3 from the numerator:

3(w + 11) = 3 * 1(w + 11)

So we have:

(3 * 1(w + 11)) / 6w

The 3's cancel out, leaving:

(w + 11) / 2w

Therefore, the fully simplified expression is (w + 11) / 2w.

The value of h is 1.89. The solution involves setting up and solving an equation involving the probabilities of selecting a red or white present.

Santa Claus has a total of 3h+11 red presents and h+5 white presents in his stocking. If Ethan selects a present at random from the stocking, the probability of obtaining a red present is given as 19/26. Using this information, we can form an equation (3h+11)/(4h+16) = 19/26 and solve for h. Cross-multiplying and simplifying, we get 494h = 936, which leads to h = 1.89. Therefore, the value of h that satisfies the given conditions is approximately 1.89.

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Complete question:

Santa Claus has 3h+11 red presents and h+5 white presents in his stocking. Ethan selects a present at random from the stocking. Given that the probability that he obtains a red present is 19/26, find the value of h. ​

The statement that is true about the boxplot is option (E) I, III, and IV

I. It is a left skewed distribution which has outliers.

True. The boxplot is skewed to the left, as the median line is closer to the bottom whisker than to the top whisker. Additionally, there are circles (outliers) on the left-hand side of the plot.

II. It is a symmetrical distribution which has outliers.

False. The plot is not symmetrical because the median line is not in the middle of the box.

III. The interquartile range is less than 1.

True. The box covers the range from the first quartile (Q1) to the third quartile (Q3), and the length of the box is less than 1.

IV. Approximately 75% of the observations have a GPA of less than 3.

True. The top of the box represents the 75th percentile, which is approximately 3.

Therefore, the correct option is (E) I, III, and IV

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The given question is incomplete, the complete question is:

Which statement is true about the boxplot below?

I. It is a left skewed distribution which has outliers.

II. It is a symmetrical distribution which has outliers.

III. The interquartile range is less than 1.

IV. Approximately 75% of the observations have a GPA of less than 3.

(A) I only

(B) II only

(C) II and III

(D) III and IV only

(E) I, III, and IV

1, 3, -4

Second-degree functions are known as quadratics.

Quadratic Functions

Quadratic functions are second-degree. This means that the highest exponent of any term is 2. When graphed, quadratic functions form parabolas, which look like U-shape.

To find the a, b, and c values of a quadratic, the function must be set equal to zero and in standard form. Remember that standard form is when the terms are written in descending order of degree (exponent). This equation given is already set equal to zero and in standard form.

Standard Form

When in standard form, quadratics are written like ax^2+bx+c. The coefficients go in alphabetic order.

This means that for the given equation: a = 1, b = 3, c = -4. These values can be used in different ways, mainly the quadratic equation.

Answer:

Let's call the number of hours before 8 P.M. that Meghan babysat "x", and the number of hours after 8 P.M. "y". We can set up two equations based on the information given:

5x + 8y = 26 (this is the total amount she earned)

x + y = total number of hours she babysat

We can solve for one of the variables in terms of the other and substitute it into the first equation:

y = total number of hours - x

5x + 8(total number of hours - x) = 26

5x + 8total number of hours - 8x = 26

3x = 26 - 8total number of hours

x = (26 - 8total number of hours)/3

Now we can try different values for the total number of hours she babysat to see if we get a whole number for x:

If she babysat for 1 hour, x = (26 - 8)/3 = 6, which is not a whole number.

If she babysat for 2 hours, x = (26 - 16)/3 = 3, which is a whole number.

If she babysat for 3 hours, x = (26 - 24)/3 = 0.67, which is not a whole number.

So we know she babysat for 2 hours before 8 P.M. and 1 hour after 8 P.M.:

5(2) + 8(1) = 18

2 + 1 = 3 total hours babysat

Therefore, Meghan babysat between 6 P.M. and 9 P.M.

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

The median will be the average of the 2 middle numbers

so it is:

(x + x + 2)/2 and this equal 53,

(2x + 2)/2 = 53

x + 1 = 53

x = 52.

So, the list is

45, 47, 50, 52, 54, 60, 62, 63

Mean = (45 + 47+ 50+ 52 +54+ 60+ 62+ 63)/ 8

          = 54.125

There is no Mode.

The polynomial function is V(x) = (30-2x)(20-2x)x and the volume of the pan is 864 cm^3.

The polynomial function

To find the volume of the pan, we first need to determine the dimensions of the base and height.

If we cut equal squares with sides of length x from the corners of a 30 cm by 20 cm piece of aluminum, then

Thus, the volume of the pan can be expressed as:

V(x) = (30-2x)(20-2x)x

The volume

Using the remainder theorem, we have

V(6) = (30 - 2 * 6)(20 - 2 * 6) * 6

Evaluate

V(6) = 864

Thus, when x = 6, the volume of the pan is:

V(6) = 864 cm^3.

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Answer:

Step-by-step explanation:

56+ 66 = 122

12-16 = -4

80 + 42 + 32 = 154

36 - 46 = -10

96 - 86 - 42 = -32

74 - 92- 84 = -102

(In case you need the total answer of everything added up the answer is : 128 )

A group of penguins swam 4/5 mile in 1/3 hour, [tex]\frac{4*3}{5}=\frac{12}{5}[/tex]  miles did the penguins swim in one hour.

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

We frequently employ these fundamental mathematical operations in our daily lives: +, -,, and. We employ mathematical operations for every situation when we must determine the annual budget or distribute things equitably to a lot of people.

[tex]\frac{4}{5}[/tex] miles swim in [tex]\frac{1}{3}[/tex] hour

swim in one hour = [tex]\frac{4*3}{5}=\frac{12}{5}[/tex] mile

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Answer:

The answer is D

Step-by-step explanation:

The value 8 is the common difference of the given sequence.

A sequence is a list of objects where repeats are allowed and the order is important. It includes members, much like a set. The length of the sequence is measured by the total number of elements.

Given the sequence below

12, 20, 28, 36...

The nth term of an arithmetic sequence is given as Tn = a + (n-1)d

The common difference is the difference between the preceding and the succeeding term.

First term = 12

Second term = 20

Common difference = 20 -12 = 28 - 20

Common difference = 8

Hence the common difference of the sequence is 8

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The experimental probability that the next customer will want mustard on their hot dog is 2/3.

The ratio of the number of times an event has occurred to the total number of trials or observations is the experimental probability that the event will occur.

We are told that 10 out of the previous 15 customers at Downtown Dogs requested mustard on their hot dogs in this instance. Hence, the following is the experimental likelihood that a client will request mustard on their hot dog:

Number of consumers who requested mustard divided by the total number of customers is the experimental probability.

10/15 is the experimental probability.

By dividing the numerator and denominator of the fraction by 5, we may simplify it to:

2/3 is the experimental probability.

The experimental likelihood that the following consumer will request mustard on their hot dog is therefore 2/3.

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Therefore , the solution of the given problem of probability comes out to be a random result will be produced with a success probability equal to the specified success rate of 0.702.

Finding the likelihood that a claim is true or that a specific event will occur is the primary objective of the branch of mathematics known as parameter estimation. Any number between range 0 but rather 1, where 1 is usually used to symbolise certainty and 0 is typically used to represent possibility, may be utilized to represent chance. A probability diagram shows the chance that a specific event will occur. .

Here,

Here is a potential Python method for modelling the subsequent pass:

Python: import the random package.

import arbitrary

0.702 is the desired performance rate:

makefile

success rate for copying is 0.702

The random.random() function can be used to produce a random integer between 0 and 1:

random.random rand num ()

Simulate the pass being caught if the random number is less than or equivalent to the success rate. If not, pretend that the throw was not caught:

python

output if rand num = success rate ("The pass is caught.")

if not: output ("The pass is not caught.")

Every time this process is executed, a random result will be produced with a success probability equal to the specified success rate of 0.702.

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Answer:

5

Step-by-step explanation:

First, we can add the whole numbers together.

1 + 3 = 4

Next, we know that the denominators (base/bottom of fraction) of the fractions are the same, meaning we simply add the numerators (top of fraction).

1/3 + 2/3 = 3/3

3/3 is equal to 1.

Now, we add the 4 from above to this 1 to get our answer, 5.

Feel free to comment down if this doesn't make sense, and I can explain it in a different way.

Hence the product of the slope of RT and SU is -1, so the lines are perpendicular

RS=ST, Hence RS, and ST are congruent to each other, which is why it is a rhombus.

A particular type of rhombus is a parallelogram. In a rhombus, the opposing sides and angles are parallel and equal. The diagonals of a rhombus meet at right angles to form its shape, and it also has equal-length sides on each side. Another name for the rhombus is a diamond or rhombus. The plural of a rhombus is a rhombus or rhombuses.

Quadrilateral RSTU has vertices at T(1,11), S(9,12), T(13,5) and U(2,-2).

The slope RT is k[tex]=-\frac{1}{2}[/tex] and the slope SU is [tex]l=2[/tex]

[tex]kl=-1\\\\RS=\sqrt{8^2+1}=\sqrt65\\and ST=\sqrt(65)\\\\[/tex]

RS=ST ,

hence RS is congurent to ST

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the perimeter of the figure is approximately 48.56 cm.

The perimeter of a shape in geometry refers to its whole boundaries. The lengths of a shape's edges and sides are added to find its perimeter.

from the question:

The lengths of all the figure's sides must be added up in order to determine their perimeter.

The rectangle has two sides that are 10 cm long and two that are 8 cm long, making its perimeter:

P_rect = 2(10 cm) + 2(8 cm) = 36 cm

Since it shares a side with the rectangle, the quarter circle has a radius of 8 cm and an arc length that is one-fourth of the circle's diameter, which is:

L_circle = (1/4)(2πr) = (1/4)(2π)(8 cm) = 4π cm

Therefore, the perimeter of the figure is:

P = P_rect + L_circle = 36 cm + 4π cm ≈ 48.56 cm

The figure's perimeter, when rounded to two decimal places, is roughly 48.56 cm.

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The required form of a(x + b)² + c to rewrite the given expression y = 3x² − 4x + 2 is given by y = 3(x - (2/3))² + 4/3.

Expression is equal to,

y = 3x² − 4x + 2

Required form to express 'y' is equal to,

a(x + b)² + c

Complete the square by adding and subtracting the square of half the coefficient of the x-term we get,

y = 3x² - 4x + 2

⇒ y = 3(x² - (4/3)x) + 2

⇒ y = 3(x² - 2(2/3)x) + 2

⇒ y = 3(x² - (4/3)x + (2/3)² - (2/3)²) + 2

⇒ y = 3(x - (2/3))² - 3(2/3)² + 2

Simplify the constant terms we have,

⇒ y = 3(x - (2/3))² - 2/3 + 2

⇒ y = 3(x - (2/3))² + 4/3

Therefore, the expression y = 3x² − 4x + 2  written in the form a(x + b)² + c is equal to y = 3(x - (2/3))² + 4/3.

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The above question is incomplete, the complete question is :

Let the expression y = 3x² − 4x + 2. Write expression y in the form

a(x + b)² + c.

Answer: To prove the relationship between segments AB and CD, we need to determine if they are parallel, perpendicular, or neither.

First, let's find the slope of line AB:

y − 9 = −4(x + 1)

y − 9 = −4x − 4

y = −4x + 5

So the slope of line AB is -4.

Now let's find the slope of line CD:

y − 6 = one fourth(x − 3)

y − 6 = (1/4)x − (3/4)

y = (1/4)x + (21/4)

So the slope of line CD is 1/4.

Since the slopes of the two lines are not equal and not negative reciprocals, they are neither parallel nor perpendicular. Therefore, we cannot determine the relationship between segments AB and CD based on the given information.

Step-by-step explanation:

The angles are classified as follows

angle 1 angle of elevation

angle 2 angle of depression

angle 3 angle of elevation

angle 4 angle of depression

The angle of elevation is the angle between the horizontal plane and the line of sight or upward direction to an object or point that is above the observer. It is usually measured from the observer's eye to the object or point of interest, and is expressed in degrees or radians.

The angle of elevation is commonly used in trigonometry to solve problems involving right triangles and heights of objects.

The angle of depression is the angle between the horizontal plane and the line of sight or downward direction to an object or point that is below the observer. It is measured from the observer's eye to the object or point of interest, and is also expressed in degrees or radians.

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The original price of the car is 85,000. b. The car loses 3,400 in value per year. c. The car will totally depreciate after 25 years. This is because 85,000 divided by 3,400 equals 25.

Value in math is the result of a mathematical operation or equation. It is a number or quantity assigned to a mathematical expression. Value can also refer to the worth of an object or activity, such as the value of a specific type of currency or the value of a certain action. Value can refer to the magnitude of a number or a quantity relative to other numbers or quantities, such as the value of a particular number on a scale.

a.  The original price of the car can be calculated by setting x=0 in the equation, which gives 85,000. This means that the original price of the car is 85,000.

b. The value of the car decreases by 3,400 per year. This is calculated by looking at the coefficient of x in the equation, which is −3,400. This means that for every year that passes, the value of the car decreases by 3,400.

c. The car will take 25 years to totally depreciate. This is calculated by setting the equation equal to 0 and solving for x. The equation 0 = −3,400x + 85,000 can be rearranged to x = 25. This means that the car will take 25 years to totally depreciate.

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(a) The probability that at least half the patients are under 15 years old is  0.01562.

(b)  The probability that from 2 to 5 patients are 65 years old or older is, 0.92179.

(c) The probability that from 2 to 5 patients are 45 years old or older is, 0.9216.
(d) The probability that all the patients are under 25 years of age is  0.00065.

(e) The probability that all the patients are 15 years old or older is 0.16777.

(a) We can model this situation as a binomial distribution with 8 trials, where success is a visitor age being under 15 years old and the probability of success is unknown.

To find the probability that at least half the patients are under 15 years old, we can use the binomial cumulative distribution function.

Assume that the probability of success (visitor age under 15) is 0.5,

The probability of at least half of the patients being under 15 is,

⇒ P(X ≥ 4) = 1 - P(X < 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))

                   = 1 - (0.03125 + 0.21875 + 0.42188 + 0.3125)

                    = 0.01562

Therefore,

The probability that at least half the patients are under 15 years old is  0.01562.

(b) To find the probability that from 2 to 5 patients are 65 years old or older,

First find the probability of each individual case and then add them up. The probability of success (visitor age being 65 or older) on a single trial is unknown.

Assume it is 0.2. Then,

⇒ P(X = 2) = 0.29376 P(X = 3)

                 = 0.32496 P(X = 4)

                 = 0.21499 P(X = 5)

                 = 0.08808

Therefore, the probability that from 2 to 5 patients are 65 years old or older is,

⇒ P(2 ≤ X ≤ 5) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

                           = 0.29376 + 0.32496 + 0.21499 + 0.08808

                           = 0.92179

(c) To find the probability that from 2 to 5 patients are 45 years old or older,

We need to use a different probability of success for each individual case, depending on the age of the patients scheduled for the day.

Assume that the probability of success (visitor age being 45 or older) is 0.6. Then,

⇒ P(X = 2) = 0.2304 P(X = 3)

                 = 0.3456 P(X = 4)

                 = 0.2592 P(X = 5)

                 = 0.0864

Therefore, the probability that from 2 to 5 patients are 45 years old or older is,

⇒ P(2 ≤ X ≤ 5)  = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

                            = 0.2304 + 0.3456 + 0.2592 + 0.0864

                            = 0.9216

(d) To find the probability that all the patients are under 25 years of age, we can assume that the probability of success (visitor age under 25) is unknown.

Assume it is 0.3. Then,

⇒ P(X = 8) = [tex]0.3^8[/tex]

                 = 0.00065

Therefore, the probability that all the patients are under 25 years of age 0.00065.

(e) To find the probability that all the patients are 15 years old or older, we can assume that the probability of success (visitor age being 15 or older) is unknown.

Assume it is 0.8. Then,

⇒ P(X = 8) = [tex]0.8^8[/tex]

                 = 0.16777

Therefore, the probability that all the patients are 15 years old or older is approximately 0.16777.

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The simplification of the following equations will be:[tex]4\sqrt{3}\ \ 6\sqrt{2}\ \ 20\sqrt{3}\ \ 5\sqrt{5}\ \ 50\sqrt{3}\ \ 24\sqrt{2}\ \ 20\sqrt{7}\ \ 6\sqrt{15}\ \ 40\ \ 21\sqrt{2}\ \ 10\sqrt{11907}[/tex].

Prime factorization is the process of transforming a number into a prime product. A prime number simply has the number itself and the number itself as its two components. The prime numbers, for instance, are 2, 3, 5, 7, 11, 13, and 19. Any integer can be expressed as the sum of prime integers thanks to prime factorization.

[tex]$\sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4 \sqrt{3}$[/tex]

[tex]$\sqrt{72} = \sqrt{36 \cdot 2} = \sqrt{36} \cdot \sqrt{2} = 6 \sqrt{2}$[/tex]

[tex]$\sqrt{1200} = \sqrt{400 \cdot 3} = \sqrt{400} \cdot \sqrt{3} = 20 \sqrt{3}$[/tex]

[tex]$\sqrt{125} = \sqrt{25 \cdot 5} = \sqrt{25} \cdot \sqrt{5} = 5 \sqrt{5}$[/tex]

[tex]$\sqrt{98}$[/tex] 98 already has the simplest root form, since it does not have a perfect square factor.

[tex]$\sqrt{7500} = \sqrt{25 \cdot 300} = \sqrt{25} \cdot \sqrt{300} = 5 \sqrt{300} = 5 \sqrt{100 \cdot 3} = 5 \cdot 10 \sqrt{3} = 50 \sqrt{3}$[/tex]

[tex]$6 \sqrt{32} = 6 \sqrt{16 \cdot 2} = 6 \sqrt{16} \cdot \sqrt{2} = 6 \cdot 4 \sqrt{2} = 24 \sqrt{2}$[/tex]

[tex]$10 \sqrt{28} = 10 \sqrt{4 \cdot 7} = 10 \sqrt{4} \cdot \sqrt{7} = 20 \sqrt{7}$[/tex]

[tex]$3 \sqrt{60} = 3 \sqrt{4 \cdot 15} = 3 \sqrt{4} \cdot \sqrt{15} = 6 \sqrt{15}$[/tex]

[tex]$5 \sqrt{64} = 5 \cdot 8 = 40$[/tex]

[tex]$7 \sqrt{18} = 7 \sqrt{9 \cdot 2} = 7 \sqrt{9} \cdot \sqrt{2} = 21 \sqrt{2}$[/tex]

[tex]$\sqrt{1190700} = \sqrt{100 \cdot 11907} = \sqrt{100} \cdot \sqrt{11907} = 10 \sqrt{11907}$[/tex]

So the above are the prime factors of the given equation. Among them, the square root is not exact. 

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Calvin's average score per game is 198.To find Calvin's average score per game, we need to divide the total points by the number of games played. Therefore, we can use the formula:

Average score per game = Total points / Number of games

Substituting the given values, we get:

Average score per game = 2,178 / 11

Simplifying the expression, we get:

Average score per game = 198

Therefore, Calvin's average score per game is 198. This means that over the course of 11 games, he scored an average of 198 points per game.

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The graph that shows the horizontal compression is graph A.

For a function f(x), we define a horizontal compression of scale factor k as :

g(x) =f(x*k)

In this case, the function f(x) is graphed at the top, and we want to identify the graph of f(4*x).

So we have a compression of scale factor k = 4.

This only changes the values in the horizontal axis, and the vertical axis remains unchanged, so option D and C can be discarded.

Now, B is a dilation and A is a compression, so the correct option is graph A.

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Answer:

im sure this isnt much help but i  used desmos and i  got the answer 0.5 w

Step-by-step explanation:

heres what i did on the calculator. i did what the screen shows it shows an adjacent(4) and the opposite(2) so therefor i  did the obvious evaluation and thought oppostie over adjacent which is tangent formula by the way. so then i  did tan(2/4) and got 0.008726867791 and then did what a video that i  watched to refresh myself on this topic. so the video said that after that your supposed to do tan-1(0.00872687791) and then i  got 0.5... not sure if that makes sense. i  typed alot so ill just link the video for you to watch.

https://youtu.be/Rbxb6DOjarI