For each pair of triangles below, decide whether the triangles are similar and/or congruent. Justify each conclusion. Show all work.

Answer:

3 1/8 or 25/8

Step-by-step explanation

This is because you are trying to find how much longer milan took. So we subtract 3 1/4 - 1/8

To do this convert 3 1/4 to 3 2/8 -1/8

Answer:

  (x, y, z) = (-20, 10, -19)

Step-by-step explanation:

You want the values of x, y, and z given a rhombus with sides marked (-2x+6), (5y-4), (-2z+8), and 46.

The side lengths of a rhombus are all the same. This tells us ...

Each of these 2-step equations can be solved by subtracting the unwanted constant and dividing by the coefficient of the variable.

  x = (46 -6)/(-2) = -20

  y = (46 -(-4))/5 = 10

  z = (46 -8)/-2 = -19

The values of x, y, and z are -20, 10, and -19, respectively.

The area of the triangle is 13.5 square units

The area of a triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by:

A =  (1/2) [x₁(y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]

Where:

L: (x₁, y₁) = (-9,6)

M: (x₂, y₂) = (-5,7)

N: (x₃, y₃) = (-8,9)

A =  (1/2) [x₁ (y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]

A =  (1/2) [-9 (7 – 9) + (-5)(9 – 6) + (-8)(6 – 7)]

A = (1/2) [18 -15 + 24]

A = 13.5  square units

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The z score of 0.166 square units of the standard normal distribution is to leave z is -0.999.

It is clear that 0.166 square units of the standard normal distribution is to the left of z. This means that the area under the standard normal distribution curve to the left of z is 0.166.

Using a standard normal distribution table or calculator, we can find the z-score corresponding to this area. For example, using a calculator, we can use the inverse normal cumulative distribution function (also called the probit function) to find the z-score:

invNorm(0.166) ≈ -0.999

Therefore, the z-score corresponding to 0.166 square units of the standard normal distribution is to the left of z is approximately -0.999.

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From the given distribution we have: Option A. No, 13 would not be significantly high because the probability of 13 or more is 0.6478 which is not low.

A binomial distribution, which only has two possible outcomes for each trial: success or failure, is a probability distribution that specifies the number of successes in a set number of independent trials. The number of trials (n) and the likelihood that each trial will be successful are the two parameters that define the binomial distribution (p). Given the likelihood of success in each trial, the distribution provides the probabilities of receiving precisely 0, 1, 2,..., or n successes in n independent trials. The binomial distribution is frequently used to simulate situations where there are two possible outcomes and a set number of trials in a variety of disciplines, including statistics, economics, genetics, and engineering.

Given that, n = 24 and p = 0.31 for the given distribution.

Thus, the probability of 13 or more human resource professionals being at companies that rejected job candidates is:

P(X ≥ 13) = 1 - P(X < 13)

Now,  P(X < 13) = 0.3522.

Thus,

P(X ≥ 13) = 1 - 0.3522 = 0.6478

Hence, from the given distribution we have Option A. No, 13 would not be significantly high because the probability of 13 or more is 0.6478 which is not low.

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a. After 30 years, your account will be worth $131,433.84. b. Money total = $72,000

To solve these questions, we can utilize the compound interest formula:

a. We can use the following formula to calculate the amount in the account after 30 years:

A = $200 * (1 + 0.03/12)^(12*30) = $131,433.84

So, after 30 years, your account will be worth $131,433.84.

b. To calculate the total amount of money you will deposit into the account:

Money total = $200 * 12 * 30 = $72,000

So, over the course of 30 years, you will deposit a total of $72,000 into the account.

c. To calculate the total interest you will earn, do the following:

Interest total = $131,433.84 - $72,000 = $59,433.84

So, over the course of 30 years, you will receive a total of $59,433.84 in interest.

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Answer:

The new prism has 9 times the surface area of the original prism

Step-by-step explanation:

There are three ways in which you can answer this question.

The hard way:

The surface area of a rectangular prism is given by
A = 2(LW+ LH+ WH)
where L= length, W= width and H = height)

If we were to triple the sides we would get the new side measures as
3L, 3W, 3H

New surface area becomes:
A' = 2 (3L · 3W + 3L · 3H · 3W· 3H)

A' = 2(9LW + 9 LH + 9 WH)

Factoring out 9 from the brackets we get

A' = 2 · 9 (LW+ LH+ WH)

A'/A = 2 · 9 (LW+ LH+ WH) /2(LW+ LH+ WH)

The common term 2(LW+ LH+ WH) cancels out from numerator and denominator leaving 9 as the answer

A smarter and easy way of doing this

A cube is nothing but a rectangular prism with all sides equal. Let a be the length of a side of the cube

A cube has 6 sides. The surface area of each side = a x a = a²

So total surface area A = 6a²

If each side is tripled, each side becomes 3a.
New surface area A' = 6 (3a)² = 6 (9a²)

A'/A = 6 (9a²)/6(a²) = 9

An even easier way

Again we take a cube. But instead of using a variable, let's assign the side of the cube a length of 1 unit

Surface area A = 6 · 1² = 6

After tripling each side becomes 3 units long
New surface area A' = 6 · 3² = 6.9 = 54

A'/A = 54/6 = 9

Choose whichever method you feel comfortable with

Answer:

1.fraction=1/4

percentage is 0.25

likelihood=unlikely

2.fraction=5/16

percentage=0.3125

likelihood=unlikely

3.fraction=11/16

percentage=0.6875

likelihood=likely

also no need for brainliest instead I would like u to follow me

y-intercept - (0, 4)

slope - +2

Domain - input values

Range - output values

Is this graph increasing, decreasing, or both? - Increasing

x-intercept - (-2, 0)

Answer: Yes, the triangles are congruent.

Step-by-step explanation:

According to the Side-Angle-Side (SAS) congruence theorem, if two triangles have two pairs of corresponding sides that are congruent and the included angle between those sides is also congruent, then the triangles are congruent.

In this case, we know that four parts (angles and sides) of one triangle are congruent to the corresponding four parts of another triangle. This means that two pairs of corresponding sides are congruent (since corresponding sides are equal) and the included angles between those sides are also congruent (since corresponding angles are equal). Therefore, the triangles satisfy the conditions of the SAS congruence theorem and are congruent.

It's important to note that this applies only to two triangles with exactly the same four congruent parts. If there is even one part that is not congruent between the two triangles, they cannot be proven to be congruent just by these means alone.

Answer:

If you know that 4 parts (angles and sides) of one triangle are congruent to the corresponding 4 parts of another triangle, then the triangles are congruent by the Side-Angle-Side (SAS) Congruence Postulate. This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

The SAS postulate is one of five ways to prove that two triangles are congruent. The other four ways are Angle-Side-Angle (ASA), Side-Side-Side (SSS), Hypotenuse-Leg (HL), and Reflexive Property of Congruence.

As per the given equation the correct time, t, that it took for the ball to hit the ground is t = 3 seconds.

An equation is a mathematical statement that expresses the equality between two expressions. Equations typically include variables, which are symbols that represent unknown or varying quantities, and constants, which are known values.

An equation can be written in various forms, depending on the type of equation and the context in which it is used. Some common forms of equations include linear equations, quadratic equations, and polynomial equations.

For example, the equation x + 5 = 10 is a linear equation that has one variable, x. It can be solved by subtracting 5 from both sides of the equation to get x = 5.

A quadratic equation, such as x² + 2x + 1 = 0, has a variable raised to the second power. It can be solved using the quadratic formula or by factoring.

To solve the equation 0=−16t²+32t+48, Greg factored out a common factor of -16 from all three terms to get:

0 = -16(t² - 2t - 3)

Then, he factored the quadratic expression inside the parentheses as:

0 = -16(t - 3)(t + 1)

This gives us two solutions for t: t = 3 and t = -1.

However, we can discard the solution t = -1, since time cannot be negative in this context. Therefore, the correct time, t, that it took for the ball to hit the ground is t = 3 seconds.

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I can assist you in determining the r-coordinate of vertex K* following the reflection if you provide me the coordinates of vertex K in the original quadrilateral.

It is possible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical expression (such as addition, subtraction, multiplication or division, etc.) include numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and an arithmetic operation between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as does the variable m in the expression 4m + 5.

I can assist you in determining the r-coordinate of vertex K* following the reflection if you provide me the coordinates of vertex K in the original quadrilateral.

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The Distributive Property of multiplication indicates that the area of the rectangular deck is; Area = 5.5·x + 46.75 square meters

The Distributive Property of multiplication states that a × (b + c) = (a·b + a·c).

The increase in the length of the deck = x meters

The area of the deck 5.5·(x + 8.5)

The width of the deck = 5.5 meters

The length of the deck = (x + 8.5) meters

The expression that represents the area of the whole deck obtained using the Distributive Property is therefore;

Area = 5.5·(x + 8.5) = 5.5 × (x + 8.5)

Distributive Property indicates that we multiply each term in the expression within the bracket symbol by 5.5 as follows;

Area = 5.5 × x + 5.5 × 8.5 = 5.5·x + 46.75

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Step-by-step explanation:

The answer is:

- Control of significant inventory balances

This is because just-in-time processing is a system that emphasizes on producing goods or services at the exact time they are needed, without accumulating inventory. Therefore, it does not prioritize the control of significant inventory balances. The other options are benefits of just-in-time processing.

Answer:

f(10) = 110 , f(a) = a² + 10

Step-by-step explanation:

(a)

to evaluate f(10) , substitute x = 10 into f(x)

f(10) = 10² + 10 = 100 + 10 = 110

(b)

to evaluate f(a) , substitute x = a into f(x)

f(a) = a² + 10

On differentiating, the derivative of the functions at x = a, is

(i) f'(a) = 14/(a+9)²,

(ii) f'(a) = [tex]-\frac{1}{2(a+1)^{\frac{3}{2} } }[/tex].

Part (i) : To find the derivative of f(t) = (2t+4)/(t+9) at x = a, we can use the quotient rule:

The "quotient-rule" is defined as a formula which is used in finding  derivative of a function which is quotient of two other functions.

The formula is : (f/g)' = (f'g - g'f)/g²,

where f' , g' = derivatives of functions "f" and "g", respectively.

So, f'(t) = [(t+9)×(2) - (2t+4)×(1)] / (t+9)²,

Substituting t = a,

We get,

⇒ f'(a) = [(a+9)(2) - (2a+4)(1)] / (a+9)²,

⇒ f'(a) = (2a+18 - 2a-4) / (a+9)²,

⇒ f'(a) = 14/(a+9)²,

So, the derivative of f(t) at x = a is f'(a) = 14/(a+9)².

Part (ii) : To find the derivative of the function, f(x) = 1/√(x+1) at x = a, we use the chain rule:

The "Chain-Rule" is defined as a formula which is used in finding derivative of a "composite-function".

So, f'(x) = [tex]-\frac{1}{2(x+1)^{\frac{3}{2} } }[/tex] × (1)

Substituting x = a,

We get,

⇒ f'(a) =  [tex]-\frac{1}{2(a+1)^{\frac{3}{2} } }[/tex] ,

Therefore, the derivative of f(x) at x = a is f'(a) = [tex]-\frac{1}{2(a+1)^{\frac{3}{2} } }[/tex].

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The given question is incomplete, the complete question is

Find the derivative of the given functions at "x=a".

(i) f(t) = (2t+4)/(t+9),

(ii) f(x) = [tex]\frac{1}{\sqrt{x+1} }[/tex]  1/√(x+1)

The completion of the table, showing the total costs for the number of pictures taken at Picture Co. is as follows:

Picture Co.

Number of   Total Costs

 Pictures

      1                $15

     2                $22

     3                $29

     4                $36

     5                $43.

The total costs is computed using addition and multiplication operations.

Addition and multiplication operations are two of the four basic mathematical operations, including subtraction and division.

The charge for the first picture = $15

The charge per additional picture = $7

Picture Co.

Number of   Total Costs

 Pictures

      1                $15

     2                $22 ($15 + $7)

     3                $29 ($15 + $7 x 2)

     4                $36

     5                $43 ($15 +$7 x 4)

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Drag the numbers (22, 27, 29, 33, 41, and 43) to complete the table.

Picture Co.

Number of   Total Costs

 Pictures

      1                $15

     2                $

     3                $

     4                $36

     5                $

the final result of the double integral is `(4/3)*a. we have to Integrate the inner integral with respect to z.

what is inner integral ?

An inner integral is a mathematical term that refers to the integral function that is evaluated first in a double integral.

In the given question,

To solve this double integral, we will use the following steps:

Integrate the inner integral with respect to z.

Evaluate the result of the inner integral at  upper and lower limits of z.

Substitute the result of the inner integral into the outer integral and integrate with respect to y.

Evaluate the result of the outer integral at the upper and lower limits of y.

Simplify the expression.

Now, let's apply these steps to solve the given double integral:

Integrate the inner integral with respect to z:

∫(x²*z + y²*z + z³) dz = x²/2*z² + y²/2*z² + z^4/4 + C

where C is the constant of integration.

Evaluate the result of the inner integral at the upper and lower limits of z:

(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)

- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)

Substitute the result of the inner integral into the outer integral and integrate with respect to y:

markdown

∫[(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)

- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)] dy

Evaluate the result of the outer integral at the upper and lower limits of y:

= ∫[(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)] dy

from y = -sqrt(a²-x²) to y = sqrt(a²-x²)

= (2/3)*x²*(a²-x²)¹⁵ + (2/3)*(a²-x²)²⁵

- (2/3)*x²*(-a²+x²)¹⁵ + (2/3)*(-a²+x²)²⁵

Simplify the expression:

= (4/3)*a³ - (4/3)*a*x²

Therefore, the final result of the double integral is `(4/3)*a

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The limit of the given sum as n approaches infinity is 0.

We have the limit as n approaches infinity of the sum from i = 1 to n of 1/(n+i). We can rewrite this sum using the hint provided as:

[tex]\lim_{n \to \infty} \sum_{\substack{i=1}} ^{n}[/tex](1/ n + i) = [tex]\lim_{n \to \infty} \sum_{\substack{i=1}} ^{n}[/tex] (1/n) * (1 + i/n)

To find the limit, we need to take the limit of the Riemann sum as n approaches infinity. This is equivalent to taking the limit of the area of n rectangles under the curve y=1/x as n approaches infinity.

As n becomes very large, the width of each rectangle becomes very small, and the height of each rectangle approaches 1/n. Therefore, the area of each rectangle approaches zero.

We can then express the limit as an integral:

[tex]\lim_{n \to \infty} \sum_{\substack{i=1}} ^{n}[/tex](1/ n + i) =[tex]\lim_{n \to \infty} \sum_{\substack{i=1}} ^{n}[/tex] (1/n) * (1 + i/n) =[tex]\lim_{n \to \infty} \int ^1 _{1+1/n}[/tex] 1/x dx

Evaluating this integral gives:

[tex]\lim_{n \to \infty} \int ^1 _{1+1/n}[/tex] 1/x dx = [tex]\lim_{n \to \infty}[/tex] ln(1+1/n) = ln(1+0) = 0

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Answer:

please insert question

Step-by-step explanation:

The total number of sales after 8 weeks through which the given condition is satisfied is 4060 sales.

Explain the process through which sales is identified?

There are several mathematical formulas that can be used in sales to calculate different metrics such as profit, revenue, and discounts. Here are some examples:

Profit formula: Profit = Revenue - Cost

This formula is used to calculate the profit earned from the sale of a product or service. Revenue is the total amount of money generated from sales, and cost includes all the expenses associated with producing and selling the product.

Gross margin formula: Gross Margin = (Revenue - Cost of Goods Sold) / Revenue

This formula is used to calculate the gross margin percentage, which is the difference between revenue and the cost of goods sold, divided by revenue. This metric represents the percentage of revenue that is left over after accounting for the cost of producing the product.

Discount formula: Discount = List Price x Discount Rate

This formula is used to calculate the amount of discount applied to the list price of a product. The discount rate is expressed as a percentage, and is multiplied by the list price to determine the amount of the discount.

Markup formula: Markup = (Selling Price - Cost) / Cost

This formula is used to calculate the markup percentage, which is the difference between the selling price and the cost of producing the product, divided by the cost. This metric represents the percentage increase in price that is added to the cost to arrive at the selling price.

According to the given information:

Given, 350 sales in the first week and increases the number of sales by 45 each week.

Based on the given condition fromulate:

⇒ 8 x ( 2 x 350 + 45 x (8-1)) / 2

After solving the above relation we get,

⇒ 4 x (2x350 + 45 x 7)

⇒ 4 x (700 + 315)

⇒ 4 x 1015

⇒ 4060.

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Answer: Mean = 1.15       Median = 1

Step-by-step explanation: add all numbers up and then divide it by 4 which will give you the mean.

Median: 0.9 and 1.1 are the 2 middle numbers in which you will add together then divide by 2 to get the exact middle value which is 1 exactly.

If the recipe requires 3(1/2) pounds of flour for every (3/4) cups of sugar, then for 1 cup of sugar , Joseph should use 4.67 pounds of flour.

A "Proportion" is defined as a statement that two fractions are equal. It expresses the relationship between two quantities that are in the same ratio.

To solve the problem, we set up a proportion to relate the amount of flour to the amount of sugar:

We know that, recipe requires 3(1/2) pounds of flour for every (3/4) cups of sugar,

Which means,

⇒ (3.5 pounds of flour)/(0.75 cups of sugar) = (x pounds of flour)/(1 cup of sugar),

where x is = amount of flour needed for 1 cup of sugar.

We "cross-multiply" and simplify;

⇒ 3.5 × 1 = 0.75 × "x" pounds of flour,

⇒ 3.5/0.75 = x,

⇒ x ≈ 4.67 pounds of flour,

Therefore, Joseph should use 4.67 pounds of flour for 1 cup of sugar.

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We need to show that if we choose right triangle with the interior angle θ, the ratios of the sides will be the same as shown in below figure.

The mathematical subject of trigonometry is the study of the connections between the angles and sides of triangles. It entails investigating trigonometric functions like sine, cosine, and tangent, which examine the relationship between a triangle's sides' lengths and its angles.

Let's consider a right triangle with acute angles α and β, as shown below:

To relate the sides of this triangle, we can use the Pythagorean theorem:

a² + b² = c²

Now, let's define the six trigonometric functions in terms of the sides of the triangle:

Sin(θ) = a/c

Cos(θ) = b/c

tan(θ) = a/b

csc(θ) = c/a

sec(θ) = c/b

cot(θ) = b/a

We want to show that these functions are well-defined, i.e., they do not depend on the particular triangle we choose. To do this, we need to show that if we choose another right triangle with the same interior angle θ, the ratios of the sides will be the same.

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To make m the subject of the formula in the equation E = mgh + 1 / 4mv² is m = E / mgh + 1 / 4mv²

The equation E = mgh + 1 / 4mv².

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

A variable is a number represented with a letter in an equation. m is the variable to make the subject of the formula.

Therefore,

E = mgh + 1 / 4mv²

factorise the equation on the right side

E = m(gh + 1 / 4v²)

Divide both sides of the equation by mgh + 1 / 4mv²

Hence,

m = E / mgh + 1 / 4mv²

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The absolute value function can be written as:

f(x) = |x - a| + b

where a is the x-coordinate of the vertex and b is the y-coordinate of the vertex.

To find the equation of the absolute value function that passes through the points (-3, 9), (-1, 1), and (2, 5), we need to find the vertex and the value of b.

The vertex of an absolute value function that opens upwards is the point where the absolute value function changes direction. This occurs at the point where the argument of the absolute value function equals zero. In this case, the argument of the absolute value function is x - a, so we need to find a such that:

-3 - a = 0 or a = -3

-1 - a = 0 or a = -1

2 - a = 0 or a = 2

So the vertex of the absolute value function is at (-1, b), where b is the y-coordinate of the vertex. To find the value of b, we can substitute one of the points into the equation of the absolute value function:

f(-3) = |(-3) - (-1)| + b = 2 + b = 9

f(-1) = |(-1) - (-1)| + b = b = 1

f(2) = |2 - (-1)| + b = 3 + b = 5

Solving these equations, we get:

b = 7/2

So the equation of the absolute value function that passes through the points (-3, 9), (-1, 1), and (2, 5) is:

f(x) = |x + 1| + 7/2

The graph of f is translated 3 units up and 6 units to the left from the graph of g(x) = 4|x + 5| - 3.

The probability that the lead singer's voice will be fine at the following Saturday gig is 23.6%

The probability that the lead singer's voice is in good condition on any particular Saturday is 1 - 0.07 = 0.93.

Since the lead singer's voice has been fine at all 19 Saturday shows this year, the probability of this happening is:

P(voice good at all 19 Saturday gigs) = 0.9319 = 0.236

This suggests that the lead singer's voice has a 23.6% chance of being fine at the following Saturday gig, presuming the probability of her voice being fine is independent of Saturday to Saturday.

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It should spend $252,857 on each type of advertising to minimize the cost.

What is linear program?

Linear programming is a mathematical method used to optimize a linear objective function, subject to linear constraints. It is a technique used in operations research, management science, and engineering to allocate resources efficiently. The goal of linear programming is to find the optimal solution that maximizes or minimizes the objective function while satisfying all the constraints.

To solve the problem, we need to use linear programming.

Let x be the number of dollars spent on radio advertising

y be the number of dollars spent on newspaper advertising

We want to minimize the cost, which is given by:

C = x + y

We also have the following constraints:

x/70 + y/100 ≥ 177,000 (we need to reach at least 177,000 people in the Gen X market)

x/50 + y/20 ≥ 200,000 (we need to reach at least 200,000 people in the millennials market)

We can rewrite the constraints as:

7x/10 + y/100 ≥ 177,000

2x/5 + y/20 ≥ 200,000

Multiplying both sides of the first constraint by 100, and both sides of the second constraint by 20, we get:

70x + y ≥ 17,700,000

4x + y ≥ 4,000,000

Now we can plot the feasible region defined by these two constraints:

70x + y ≥ 17,700,000

4x + y ≥ 4,000,000

y ≥ 0

x ≥ 0

This region is bounded by the x-axis, the y-axis, the line 70x + y = 17,700,000, and the line 4x + y = 4,000,000. It looks like this:

|\

| \

y | \

| \

| \

| \

|------\

x

The optimal solution will be at one of the vertices of this region. We can find these vertices by solving the system of equations formed by the two constraint lines and the two axes:

70x + y = 17,700,000

4x + y = 4,000,000

x = 0

y = 0

The solutions are (0, 4,000,000),(57,000, 17,190,000), (252,857.14, 0), (0, 0)

The first and last solutions correspond to spending all the budget on newspaper or radio advertising, respectively. These solutions are not optimal, because they don't reach the required number of people in either market.

The second solution corresponds to spending approximately $57,000 on radio advertising and approximately $17,190,000 on newspaper advertising. This solution reaches 199,300 people in the Gen X market and 200,400 people in the millennials market, which is slightly more than the required number in both markets. However, this solution is not optimal, because it is not on one of the vertices of the feasible region.

The third solution corresponds to spending approximately $252,857 on radio advertising and $0 on newspaper advertising. This solution reaches exactly 177,000 people in the Gen X market and 200,000 people in the millennials market, which is the required number in both markets. This solution is also on one of the vertices of the feasible region, so it is optimal.

Therefore, the hardware store should spend approximately $252,857 on radio advertising and $0 on newspaper advertising to reach the required number of people in both markets and minimize the cost.

Learn more about linear program here,

https://brainly.com/question/14309521

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