Graph y = 6X

This is all we have along with a graph that we have to move the line.

The required equation of the trigonometric graph is y = 2cos[(π/8)(x-2)-2] which represents the cosine function.

The cosine function has a range of values between -1 and 1, and it is a periodic function that repeats every 2π radians or 360 degrees.

The graph of the cosine function is a wave-like curve that oscillates between -1 and 1, with a period of 2π radians or 360 degrees.

As we can see, the function's behavior repeats itself. In terms of the form of the function, we may select any interval of length 2π and the following interval of length 2π will be equal to the previous one.

Here, y = 2cos[(π/8)(x-2)-2]

Thus, the equation of the trigonometric graph is y = 2cos[(π/8)(x-2)-2] which represents the cosine function.

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The probability that the mean of a sample of 78 computers would differ from the population mean by less than 0.4 months is:

P (μ-0.4 <x<μ +0.4) = P (-0.39<x<0.39) = 0.3035

By simply dividing the favourable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favourable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Moreover, the proportion of positive outcomes cannot be negative.

Here we have,

μ = 83,0 = 9, n = 78

Since sample size is large so we can assume normal distribution using CLT.

The z-score for x= μ-0.4 is

z=(μ-0.4-μ)/o/√n

=-0.4/9/√78

= -0.39

The z-score for x= μ +0.4 is

z=(μ+0.4-μ)/σ/√n

= 0.4/9/√78

= 0.39

The probability that the mean of a sample of 78 computers would differ from the population mean by less than 0.4 months is:

P (μ-0.4 <x<μ +0.4) = P (-0.39<x<0.39) = 0.3035.

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Answer:

Roughly 10.30

Step-by-step explanation:

Use Pythagorean theorem:
[tex]c^2 = a^2 + b^2[/tex]

Where [tex]c[/tex] is your hypotenuse

So:

[tex]c^2 = (9)^2 + (5)^2[/tex]

[tex]c= \sqrt{106}[/tex]

[tex]c[/tex] ≈ [tex]10.30[/tex]

Answer:10.3

Step-by-step explanation:

John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. $75 = $15p + A

What is the total of the cost?

Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.

Let the number of people on John's family plan be represented by p.

According to the problem, the family plan cost is $68, and there is an additional cost of $15 for each person on the plan. Therefore, the total cost C of the plan with p people is:

C = $68 + $15p

We know that John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. Therefore, we can write:

$143 = C + A

where A represents any additional charges.

Substituting C into this equation, we get:

$143 = ($68 + $15p) + A

Simplifying, we can write:

$75 = $15p + A

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The total surface area of the building block is therefore (4×l×w) + (2×(b×h)/2), which is equal to (2×l×w) + bh.

Surface area is the total exposed area of a three-dimensional object, including the object's base area and lateral area. It is the area of the surface or outer boundary of an object and is measured in units squared such as square meters or square centimeters. Surface area is an important concept in mathematics, physics, and engineering, as it is used to calculate the amount of material needed to construct an object.

The total surface area of the building block can be found by adding the area of the six faces of the block together. To calculate the surface area of the block, we first need to find the area of each face. The six faces of the building block are four rectangular faces and two triangular faces. The area of each rectangular face can be found using the formula A=l×w, where l is the length and w is the width. The area of each triangular face can be found using the formula A=(b×h)/2, where b is the base and h is the height.

By adding the area of each face together, the total surface area of the building block can be found. The total surface area is equal to the sum of the four rectangular faces plus the two triangular faces. The total surface area of the building block is therefore (4×l×w) + (2×(b×h)/2), which is equal to (2×l×w) + bh.

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The normal distribution is N(151, 7), the z-score for verbal and quantitative reasoning are 1.29 and 0.52 respectively.

(a) The shorthand for the normal distribution of the Verbal Reasoning section is N(151, 7), where 151 is the mean score and 7 is the standard deviation. The shorthand for the normal distribution of the Quantitative Reasoning section is N(153, 7.67), where 153 is the mean score and 7.67 is the standard deviation.

(b) Sophia’s Z-score on the Verbal Reasoning section is (160-151)/7 = 1.29. Her Z-score on the Quantitative Reasoning section is (157-153)/7.67 = 0.52.

(c) The Z-scores represent how many standard deviations above or below the mean Sophia’s scores are. A Z-score of 1.29 on the Verbal Reasoning section means Sophia’s score is 1.29 standard deviations above the mean score of all test takers. A Z-score of 0.52 on the Quantitative Reasoning section means Sophia’s score is 0.52 standard deviations above the mean score of all test takers.

(d) Sophia did better on the Verbal Reasoning section because her Z-score is higher for that section.

(e) To find the percentile scores, we use the standard normal distribution table. Sophia’s percentile score on the Verbal Reasoning section is the percentage of test takers who scored lower than her. Using the Z-score of 1.29 and the table, we find that her percentile score is approximately 90.7%. Her percentile score on the Quantitative Reasoning section is the percentage of test takers who scored lower than her. Using the Z-score of 0.52 and the table, we find that her percentile score is approximately 69.4%.

(f) To find the percentage of test takers who did better than Sophia on each section, we can use the standard normal distribution table again. For the Verbal Reasoning section, we need to find the area to the right of Sophia’s Z-score of 1.29. Using the table, we find that this area is approximately 9.3%. Therefore, approximately 9.3% of test takers did better than Sophia on the Verbal Reasoning section. For the Quantitative Reasoning section, we need to find the area to the right of Sophia’s Z-score of 0.52. Using the table, we find that this area is approximately 30.4%. Therefore, approximately 30.4% of test takers did better than Sophia on the Quantitative Reasoning section.

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None of the statements (1) to (6) are true about the equation [tex]x^2-6x+2=0[/tex].

Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd polynomial formula in a variable. a 0. It has at least 1 solution since it is a 2nd polynomial equation, which is guaranteed by the algebraic theorem. The solution might be simple or difficult.

None of the statements (1) to (6) are true about the equation. [tex]x^2-6x+2=0[/tex].

Reason why:

(1) The coefficient of the [tex]x^2[/tex] term is positive, so the graph of the quadratic equation is a parabola that opens upward. Therefore, it does not have a minimum value, but instead has a minimum point.

(2) The coordinates of the minimum point can be found using the formula x = -b/2a, which gives x = 6/2 = 3. Substituting x = 3 into the equation gives y = 2, so the minimum point is (3, 2).

(3) The point (7,-3) is not on the graph of the equation.

(4) The solutions to the equation are given by the quadratic formula x = [tex][6\± \sqrt{(6^2 - 4(1)(2))]}/2 = [6\± \sqrt{(28)]}/2 = 3\± \sqrt{7}[/tex]. So, statement (4) is partially correct, but the value of -3 is incorrect.

(5) Statement (5) is correct, as the solutions to the equation are x = [tex]3\±\sqrt7}[/tex].

(6) The graph of the quadratic equation has a minimum value, not a maximum value.

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Complete question is: Which of the following statements are true about the equation below?

x^2-6x+2=0

( 1 ) The graph of the quadratic equation has a minimum value.

( 2 ) The extreme value is at the point (3,-7).

( 3 ) The extreme value is at the point (7,-3).

( 4 ) The solutions are x = -3 + or - the square root of 7 .

( 5 ) The solutions arex = 3 + or - the square root of 7.

( 6 ) The graph of the quadratic equation has a maximum value.

Answer:

Number 2 and number 1

Step-by-step explanation:

youre all good

Answer:

Step-by-step explanation: It is a function. Because one input goes to exact one output.

Answer:

7 minutes

Step-by-step explanation:

It is 7 minutes because the bank it the top straight line and it elapses for 7 minutes

Answer: 48

Step-by-step explanation: 9p p=4 9*4=36 +18 = 48

The total number of cards sold for Mother's Day is 290 cards.

What is the proportions?

Proportion is a mathematical concept that expresses the equality of two ratios. Two ratios are said to be proportional if they have the same relative size or relationship.

Let x be the total number of cards sold for Mother's Day. We know that one salesman sold 29 cards, which is 10% of the total number of cards sold. Using this information, we can set up the following proportion:

(10/100) * x = 29

Simplifying, we get:

x = 290

Hence, the total number of cards sold for Mother's Day is 290 cards.

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The triangles are classified as:

4. Acute 5. Obtuse 6. Obtuse 7. Acute 8. Obtuse 9. Acute 10. Obtuse

To classify a triangle as right, obtuse, or acute, we need to apply the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

If the square of the hypotenuse is greater than the sum of the squares of the other two sides, then the triangle is obtuse. If the square of the hypotenuse is less than the sum of the squares of the other two sides, then the triangle is acute.

4. To check if this is a right triangle, we need to find if 9² is equal to 4² + 6², which is not true, so the triangle is acute.

5. To check if this is a right triangle, we need to find if 16² is equal to 10² + 12², which is not true, so the triangle is obtuse.

6. To check if this is a right triangle, we need to find if (8√6)² is equal to 8² + 16², which is not true, so the triangle is obtuse.

7. To check if this is a right triangle, we need to find if 29² is equal to 20² + 21², which is true, so the triangle is acute.

8. To check if this is a right triangle, we need to find if √73² is equal to 3² + 8², which is not true, so the triangle is obtuse.

9. To check if this is a right triangle, we need to find if 12² is equal to 8² + 10², which is true, so the triangle is acute.

10. To check if this is a right triangle, we need to find if (3√34)² is equal to 9² + 15², which is not true, so the triangle is obtuse.

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There are 5 methods to determine which player has less pieces, 5! ways probability to arrange the Xs, and 4! ways to order the Os, for a total of 5 x 5 x 4! = 28,800 possible games.

Calculating the chance that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all possible outcomes when a certain event occurs.

Case 1: There are 5 Xs and 4 Os on the board, and there is a one-point difference in the number of Xs and Os. In this situation, starting with the player who has less pieces on the board, we must alternately put the Xs and Os in the squares. There are 5 methods to determine which player has less pieces, 5! ways to arrange the Xs, and 4! ways to order the Os, for a total of 5 x 5 x 4! = 28,800 possible games.

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Answer:its a

Step-by-step explanation:you did it wrong

The length of the hypotenuse is approximately 6.7.

What is the Pythagorean theorem and how is it used to find the hypotenuse of a right triangle?

The Pythagorean theorem is a fundamental relationship in Euclidean geometry that relates the lengths of the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, the Pythagorean theorem can be expressed as:

[tex]c^2 = a^2+ b^2[/tex]

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Finding the missing length :

In the given problem, we are given the lengths of two sides of a right triangle, which are 3 and 6. We can use these values to find the length of the hypotenuse using the Pythagorean theorem:

[tex]h^2 = 3^2+ 6^2[/tex]

[tex]h^2 = 9 + 36[/tex]

[tex]h^2 = 45[/tex]

Taking the square root of both sides gives:

[tex]h = \sqrt{45}[/tex]

Using a calculator, we can simplify this to:

[tex]h \approx 6.7[/tex] (rounded to the nearest tenth)

Therefore, the value of the hypotenuse of the right triangle with sides 3 and 6 is approximately 6.7.

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The exponential growth equation is P ( t ) = 332 ( 1.0059 )^t , where t is the number of years and P ( t ) is the population after 2020

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the initial population be represented as x₀

Now , the value of x₀ = 332 million

And , the exponential growth rate r = 0.59 %

where the population of the U.S. at time/ years after 2020 is of the form equation P( t ) = aekt

On simplifying , we get

The population of the U.S. at a time P ( t ) = 332 ( 1 + 0.59% )^t

Now , the value of P ( t ) is

The population of the U.S. at a time P ( t ) = 332 ( 1 + 0.0059 )^t

The population of the U.S. at a time P ( t ) = 332 ( 1.0059 )^t

where the growth factor k = 1.0059

Hence , the exponential growth equation is P ( t ) = 332 ( 1.0059 )^t

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Marginal cost refers to the additional cost of producing one more unit of a product or service.

Marginal cost is the cost of producing one additional unit of a good or service.

In math, marginal cost refers to the additional cost of producing one more unit of a product or service. It is calculated by taking the change in total cost divided by the change in quantity produced.

Marginal cost is an important concept in economics and is used to determine the optimal level of production to maximize profits.

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The third side of the triangle is 8  

Pythagoras' theorem is a fundamental principle in geometry that describes the relationship between the sides of a right triangle.

It states that: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Here we have

A right-angled triangle

From the figure

The sides of the triangle are 7 and √15  

As we know from Pythagoras' theorem

=> Hypotenuse² = side² + side²    

Substitute the above values in the condition

=> Hypotenuse² = (7)² + (√15)²    

=> Hypotenuse² = 49 + 15

=> Hypotenuse² = 64

=> Hypotenuse = 8  

Therefore,

The third side of the triangle is 8  

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Complete Question is given picture

The measure of ∠M and ∠N = 76

An isosceles triangle is a triangle that has two sides of equal length and two equal angles opposite those sides.

Given:- ∠NLM = 28°

The given triangle is an isosceles triangle as sides LM and LN are equal.

Therefore ,∠LMN and ∠LNM will be equal.

Let us assume ∠M as x

Therefore,

∠LMN = ∠LNM = x

Sum of all angles of a triangle =180°

Therefore,

∠NLM + ∠LNM + ∠LMN = 180°

28 + x + x = 180

28 + 2x = 180

2x = 180 – 28

2x = 152

x = 152/2

x = 76

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Answer:

Step-by-step explanation:

0.003125

Answer:0.003125

When dividing by a bigger number to turn it to a decimals with 0s because it will always help and also use the simple way of division writing it down ex. 3.1 I 992 and put it in as many times as possible

One example of a quantity in the life sciences that is modeled by a function of time is the population size of a species.

This can be modeled using a differential equation, where the rate of change of the population size is proportional to the current population size.

If we knew the values of the derivative of this function (i.e., the first derivative), we would be able to make inferences about the growth or decline of the population.

A positive derivative value would indicate that the population is growing, while a negative derivative value would indicate that the population is declining. The magnitude of the derivative would also give us information about the rate of growth or decline of the population. If the derivative is large, the population is changing quickly, while a small derivative indicates slower change.

If we had information about the second derivative of the function (i.e., the rate of change of the derivative), we would be able to make further inferences about the behavior of the population.

A positive second derivative value would indicate that the population is accelerating in its growth, while a negative second derivative value would indicate that the population is decelerating in its growth. This information could be useful in predicting future trends in population size and in making decisions about conservation efforts or resource management.

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The response to the given question would be that As a result, we have demonstrated that ABCD's opposing sides are parallel, proving that ABCD is a parallelogram.

A simple quadrilateral with two sets of parallel sides is known as a parallelogram in Euclidean geometry. Both sets of opposite sides are parallel and equal in a particular type of quadrilateral known as a parallelogram.

We must demonstrate that the opposing sides of ABCD's parallelogram are parallel.

CBA = DAB (Alternate interior angles)

Alternative interior angles (ABD = BAC; ADC = CBD) (Alternate interior angles)

DCA = ACD (Alternate interior angles)

Considering that AD = BC, we also have:

A + B Equals A + C. (Also on both sides)

AD = BC

Think about the two pairs of sides that are diagonally opposed: AB and CD and AD and BC.

We have these for AB and CD:

Interior angles of a quadrilateral: DAB + ABD + BCD + CDA = 180°; CBA + BAC + ADC + DCA = 180°. (Substituting corresponding angles)

We may insert them in and simplify to get: since DAB = CBA and ABD = BAC.

BCD = ADC

As a result of having the same transversal CD and equal alternative interior angles, AD and BC are also parallel. As a result, we have demonstrated that ABCD's opposing sides are parallel, proving that ABCD is a parallelogram.

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The lateral limits of the function g(x) at x = 4 are given as follows:

[tex]\lim_{x \rightarrow 4^-} g(x) = -4, \lim_{x \rightarrow 4^+} g(x) = 2[/tex]

To obtain lateral limits, we need to take the limit of a function as it approaches a point from the left-hand side and the right-hand side separately.

If the two limits are equal, then this is the limit of the function, while if the lateral limits are different, then the limit of the function does not exist for the value of x.

On a coordinate plane, a curve starts at closed circle (4, negative 4), curves up to (3, negative 3), and curves down to (negative 1, negative 8), and then curves up through (negative 3, 4), hence the lateral limit to the left of x = 4, where x is less than 4, is given as follows:

[tex]\lim_{x \rightarrow 4^-} g(x) = -4[/tex]

A curve starts at open circle (4, 2) and curves up through (8, 5), hence the lateral limit to the right of x = 4, where x is greater than 4, is given as follows:

[tex]\lim_{x \rightarrow 4^+} g(x) = 2[/tex]

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The analysis of the distances and angles viewed by Felix are presented as follows;

2. The angle formed is a right angle

3. Please find the drawing of the scenario created with MS Word

4. The distance obtained using Pythagorean Theorem is about 438.53 miles

5. The distance the person travels is about 437.86 miles

6. The central angle Felix is viewing from his altitude is about 6.34°

The Pythagorean Theorem states that the square of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the legs of the right triangle.

2. The angle formed by a tangent to a spherical surface, such as the Earth's approximately spherical surface and the radius of the sphere is a right angle.

Therefore;

3. The possible elevation of Felix above the Earth's surface, obtained from a similar question is; 24.214 miles

Therefore;

The legs of the right triangle are the radius of the Earth and the distance from Felix's to the point on the horizon.

The hypotenuse sum of Felix's altitude and the radius of the Earth

Please find attached the drawing of the scenario created with MS Word

4. Pythagorean Theorem indicates that the distance from Felix to the image on the horizon, d, can be obtained as follows;

d = √((3,959 + 24.214)² - 3,959²) ≈ 438.53

The distance from Felix to the image on the horizon is about 438.53 miles

5. The distance the person has to travel can be found as follows;

The surface of the Earth is assumed to be flat

The distance to the horizon from Felix is about 438.53 miles

The distance, l, the person on the ground has to travel is therefore;

l = √(438.53² - 24.214²) ≈ 437.86

6. The central angle, θ, of the Earth that Felix is viewing, with an arc length of 437.86 miles can be found using the formula for finding the arc length of a sector of a circle as follows;

θ/360 × 2 × π × 3,959 ≈ 437.86

θ ≈ 437.86 × 360/(3,959 × 2 × π) ≈ 6.34°

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By answering the above question, we may state that Therefore, all possible values of x that satisfy the inequality [tex]x^3[/tex] - 8 ≥ 1 are x ≥ 2.08.

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Hence, inequity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and inequality are not the same. Use the not equal symbol most frequently when two values are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two sides until just the variables are left, many straightforward inequalities may be solved. Nonetheless, a variety of factors support inequality: Both sides' negative values are split or added. Exchange the left and the right.

[tex]x^3[/tex] - 8 ≥ 1

[tex]x^3[/tex] ≥ 9

Taking the cube root of both sides, we get:

x ≥ ∛9

Since ∛9 ≈ 2.08, the solution to the inequality is:

x ≥ 2.08

Therefore, all possible values of x that satisfy the inequality [tex]x^3[/tex] - 8 ≥ 1 are x ≥ 2.08.

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In order to create a 28-pound blend that he can sell for $1.45 per pound, the grocer should combine approximately 17.73 pounds of the less costly coffee and 10.27 pounds of the more expensive coffee.

Let's designate the quantity of the less expensive coffee X and the more expensive coffee Y. Since we are aware that the grocer wishes to combine 28 pounds altogether, we can write:

x + y = 28

The total profit from selling the mixture would be: 28($1.45) = $40.60 because we also know that he intends to sell it for $1.45 per pound.

The costs and quantities of the two varieties of coffee can be used to create a new equation.

0.9x + 2.4y = $40.60

With two variables in each equation, we now have two equations that we can solve by substitution or elimination. Use of substitution

28 + y = x - 0.9x + 2.4y = 40.60

0.9x + 2.4(28 - x) = $40.60

0.9x + 67.2 - 2.4x = $40.60\s-1.5x = -$26.60\sx = 17.73

We can apply the first equation to determine y now that we know x: x + y = 28.

17.73 + y = 28 \sy = 10.27

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These figures have curved surfaces, not flat faces. A cylinder is similar to a prism, but its two bases are circles, not polygons. Also, the sides of a cylinder are curved, not flat. A cone has one circular base and a vertex that is not on the base.

When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.

The cost of apples when the number of apples bought is n can be found using the function:

    C(n) = 0.9n

What is a function?

A mathematical statement or rule that establishes the link between an independent variable and a dependent variable is called a function. Relationships called functions provide an output for each input. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Often, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.

Assuming the question is the one given below.

Given a function C which gives the cost of buying the n apples in dollars.

The first expression given is:

1) C(5) = 4.50

The input of the function is 5 and the output is 4.50.

This means that when the number of apples is 5 the total cost is $4.50.

Let us assume the general equation of the function as below:

C(n) = kn

When n = 5

C(5) = 5k = 4.50

k = 4.50/5 = 0.9

Hence the function is C(n) = 0.9n

2) We found the function as C(n) = 0.9n

 C(2) means the cost when the number of apples is 2.

C(2) = 0.9 * 2 = $1.8

Therefore the cost of apples when the number of apples bought is n can be found using the function:

    C(n) = 0.9n

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