please look at the attachment

The distributive property of multiplication justifies that 3(x-2) is equivalent to 3x-6.

When a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then the two products added together to produce the same result as multiplying the first number by the sum. When you multiply a value by a sum, the distributive property of multiplication over addition is used. For instance, suppose you want to multiply 5 by the sum of 10 + 3. When we have similar terms, we usually add the numbers and then multiply by 5. However, the property states that you must first multiply each addend by 5.

Here,

3(x-2) is equivalent to 3x-6 due to the distributive property of multiplication.

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The estimated cost of tuition in 2018 using this linear function model is $726,430

What is the linear function?

A linear function is a mathematical function that describes a straight line. The general form of a linear function is:

y = f(x) = mx + b

To estimate the cost of tuition in 2018 using a linear function model, we can use the two given data points to find the slope and y-intercept of the line.

First, we can find the slope of the line by using the formula:

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) is the data point for 2002 and (x2, y2) is the data point for 2012.

Substituting the values, we get:

m = (8,240 - 4,790) / (2012 - 2002) = 3,450 / 10 = 345

Next, we can use one of the data points and the slope to find the y-intercept of the line. Let's use the data point for 2002:

y = mx + b

4,790 = 345 * 2002 + b

b = 4,790 - 345 * 2002 = -1,015,290

So, the equation of the line is y = 345x - 1,015,290

To estimate the cost of tuition in 2018, we can substitute x = 2018 into the equation:

y = 345(2018) - 1,015,290 = 726,430

Hence, the estimated cost of tuition in 2018 using this linear function model is $726,430

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Answer:

Step-by-step explanation:

212+105

We make this the equation because it says he charges 105 and he owes 212, so 212+105=317

Frank owes: $317

The equation in the simplest form that represents the perimeter of the bookend in centimeters is 11 [tex]\frac{1}{2}[/tex] m - 11 = 58 and the value of m is 6.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Part A :

Perimeter of a closed figure is the sum of the lengths of it's boundary.

Given the lengths of the sides of the bookend as,

5m - 14, 2m - 7, 3/2 m + 2 and 3m + 8.

Perimeter is given as 58 centimeters.

(5m - 14) + (2m - 7) + (3/2 m + 2) + (3m + 8) = 58

(5m + 2m + 3/2 m + 3m) + (-14 - 7 + 2 + 8) = 58

23/2 m - 11 = 58

11 [tex]\frac{1}{2}[/tex] m - 11 = 58

Part B :

We have,

11 [tex]\frac{1}{2}[/tex] m - 11 = 58

11 [tex]\frac{1}{2}[/tex] m = 58 + 11

11 [tex]\frac{1}{2}[/tex] m = 69

23/2 m = 69

m = 6

Hence the required equation is 11 [tex]\frac{1}{2}[/tex] m - 11 = 58 and the value of m is 6.

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If the triangles ABC and DEF are similar, then the measurement of line segment DE = 108.72 units.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

It is given that triangle ABC is similar to triangle DEF.

It can be seen in the image that ΔDEF is a dilated version of ΔABC.

In ΔABC the measurement of side AB = 23 units

In ΔABC the measurement of side BC = 11 units

In ΔDEF the measurement of side EF = 52 units

In ΔDEF the measurement of side DE = x units

Apply the formula for indirect measurement to find the measurement of side DE.

AB/DE = BC/EF

Substitute the values in the equation -

23/x = 11/52

23 × 52 = 11x

x = (23 × 52)/11

x = 1196/11

x = 108.72

Therefore, the measurement of DE is 108.72 units.

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Answer:

-1

Step-by-step explanation:

top: -20/(-4) = 5

bottom: -49+44 = -5

5/(-5) =-1

Answer: 189 degrees

Step-by-step explanation:

Since 17x + 2 = 16x + 9, we can solve for x:

17x + 2 = 16x + 9

Subtract 16x from both sides:

x + 2 = 9

Subtract 2 from both sides:

x = 11

The angle indicated in bold is 17x + 2, so we just substitute 11 into x and get 17 * 11 + 2, = 187 + 2 = 189 degrees :>

Answer:

answer is no

Step-by-step explanation:

Xavier is not getting better mileage with his new car.

it is given that

distance traveled by Xavier's new car in 20.28 gallons = 472miles

the mileage can be calculated using the formula = (distance traveled)/( gallons of fuel used).

So, the mileage of the new car = 472/20 = 23.06 miles per gallon, and the mileage of Xavier's former car = 20.28 miles per gallon.

From the above data, we can see that the mileage of the former car is greater than the new car.

Therefore, Xavier is not getting better mileage with his new car.

The given question is incomplete, the complete question is

Xavier's new car uses 25 gallons for 472  miles, His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas mileage in his new car?

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The probability that the company will make less than $2m is 0.8 and b) the probability that the company will make less than $1m or at least $2m is 0.7

Here we are given respective probabilities of the revenue a company could make in a year.

a) Here we need to find the probability that it makes a revenue less than $ 2 million

This means that we need t find the probability that it makes revenue

less than $1M + greater than $1 M but less than $2M

= P(A₁) + P(A₂)

= 0.5 + 0.3

= 0.8

b)

The probability that the company will make less than $1M or at least $2M is

P(A₁ U A₃)

= P(A₁) + P(A₃) - P(A₁ ∩ A₃)

Since A₁ and A₃ are clearly mutually exclusive events, P(A₁ ∩ A₃) will be 0.

Hence we get

P(A₁ U A₃) = 0.5 + 0.2

= 0.7

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Complete Question

Assume the following in regard to a company’s annual revenue:

A₁ : Revenue < $1M; P(A₁) = 0.5

A₂ : Revenue > $1M but < $2M; P(A₂) = 0.3

A₃ : Revenue > $2M; P(A₃) = 0.2

a)What is the probability that the company will make less than $2M?

b)What is the probability that the company will make less than $1M or at least $2M

Answer:

yes

Step-by-step explanation:

A proportional relation has an equation of the form

y = kx,

where k is a real number.

y = 2.2x is an equation of the form y = kx with k = 2.2, so y = 2.2x is proportional.

Answer: yes

The length of line segment AB is 8 cm in the above-mentioned diagram.

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Answer:

Step-by-step explanation:

we know the slope and we have a point , so

y = 7x + b

sub in the point ...

-8 = 7(-1) + b

-8 + 7 = b

b = -1

y = 7x - 1

The diagonal is equal to the sum of the square roots of the width and height.[tex]\sqrt{}[/tex]14[tex]n^{2}[/tex]

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Answer:

..........................

The probability that both bulbs fail the test is 1/9. This is because out of the twelve lights, three of them have already failed the test, leaving nine lights that passed.  

This is because out of the 12 lights tested, 3 have already failed and there is a 1 in 4 chance that the two bulbs selected at random will be the same two failed bulbs.

Since the bulbs are selected at random with replacement, the probability that both bulbs fail the test is 1/9, or 11.11%.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

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The fire station should be located at the midpoint (a/2) of the road to minimize the expected distance from the fire.

The total distance cost will be infinite if we start at one point on a given line at an infinite distance. However, as we move this point toward the given points, the total distance cost begins to decrease. After a while, it then increases once more, reaching infinite at the other infinite end of the line. Therefore, the distance cost curve resembles a U-curve, and its bottom value must be determined.

The fire station should be located at the midpoint (a/2) of the road (0,a) to minimize the expected distance from the fire.

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The required total cost of the two shirts after 6.5% of the tax is given as 2.13s.

Now, According to the question:

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Benita buys 2 shirts for the same price, s.

The sales tax rate is 6. 5%.

Write an expression to represent the total cost of the shirts.

1 way, paid the cost of 2 shirts jointly

The total cost of the two shirts becomes,

Total cost = 2[ s + 0.065s]

Total cost = 2.13s

2nd way, paid the cost of two shirts individually,

total cost = s + 0.065s + s + 0.065s

              = 2.13s

Thus, the required total cost of the two shirts after 6.5% of the tax is given as 2.13s.

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Answer:

18 miles

Step-by-step explanation:

m = # of miles

$4.60 + ($0.50/mi)m = $13.60

($0.50/mi)m = $13.60 - $4.60 = $9.00

m = ($9.00) / ($0.50/mi) = 18 miles

Answer:

Category A 0.75

Category B 0.25

Hope it helps !!

The axis of symmetry of the graphed function is:

x = -2

Here we want to find the axis of symmetry of the graphed function, which is a quadratic one.

The axis of symmetry is a line of the form:

x = a

Where a is a real number

Such that it divides the graph of the function in two equal parts.

Notice that the parabola is perfectly divided by the line x = -2, so that is the axis of symmetry of the graphed function.

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Answer:

Step-by-step explanation:

Move each point up by 3 points. you should have the same shape moved up on the graph. then move each point to the right by 6 squares. This should be your final square D''E''G''F''

The difference between the volume of the sphere and an approximation using a left sum with 16 intervals is 17.51 mm.

The term called volume in math is known as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Here we know that the sphere has a radius of 2 mm.

Then the volume of the sphere is calculated by using the formula,

=> V = 4/3πr³

Here we know that the value of r = 2.

Then the volume is calculated as,

=> V = 4/3 x π x 2³

When we simplify this one then we get,

=> V = 10.67π = 33.51

Here we need to find the difference between the volume of the sphere and an approximation using a left sum with 16 intervals is

=> 33.51 - 16

=> 17.51

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The inequalities that are equivalent are 3x+6≤8+ 2x and 12-3x ≤18

Inequalities are simply defined as relations that makes a non-equal comparison between two mathematical expressions, equations or numbers.

It is mostly used to compare two numbers or expressions based on the magnitude on the number line.

Inequality signs in mathematic include;

Given the inequalities;

3x + 6 ≤ 8 + 2x

collect like terms

3x - 2x≤ 8 - 6

subtract like terms

x ≤ 2

12-3x ≤18

collect like terms

3x≤ 18 - 12

3x ≤ 6

Divide both sides by 3

x ≤ 2

Hence, the inequalities are 3x+6≤8+ 2x and 12-3x ≤18

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The change represents growth and percentage rate of increase is 95.8%.

The exponential function y = 880(1.958)^x is a function that models growth.

The base of the exponential function, 1.958, is greater than 1. This means that the function is increasing with respect to x, which is the independent variable.

For every unit increase in x, the function increases by a factor of 1.958. This is evident from the fact that 1.958 is raised to the power of x.

The percentage rate of increase is calculated by taking the difference between the base of the exponential function and 1, and then multiplying that difference by 100%.

In this case, the base of the exponential function is 1.958, so the percentage rate of increase is

(1.958- 1)*100 = 95.8%.

This means that for every unit increase in x, the value of y increases by 95.8% of its previous value.

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The longer crosspiece needs to be about 18 inches long.

To find the length of the longer crosspiece, you need to use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse).

Let's call the length of the longer crosspiece x. Then, we have two right triangles:

x^2 = (37-24)^2 + (13)^2

x^2 = 13^2 + 13^2

Solving for x:

x = sqrt(13^2 + 13^2) = sqrt(2 * 13^2) = 13 * sqrt(2) = 18.03 inches

So, the longer crosspiece needs to be about 18 inches long.

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Answer:

Check image :D

Step-by-step explanation:

The image is the answer. I hope this helps you out :D

If the engine with 12 gallon fuel tank uses fuel at a constant rate of 0.6 gallons per hour , then the equation to find number hours the engine has been running is "12 - 0.6x = 9.3"  .

the total capacity of the tank is = 12 gallon ;

the constant use rate of engine is = 0.6 gallons per hour ;

the amount of fuel left in the tank is = 9.3 gallons ;

let the number of hours the engine is running is = x hours  ;

the above situation can be represented as ⇒ 12 - 0.6x = 9.3 ;

⇒ 12 - 0.6x = 9.3  ;

⇒ 12 - 9.3 = 0.6x  ;

⇒ 0.6x = 2.7  ;

⇒  x = 2.7/0.6  ;

⇒ x = 4.5 hours

Therefore , the engine has been running for 4.5 hours .

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The ratio of the number of empty tables to the total number of tables is 13:21

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, 8 of the tables at Joy's Italian Restaurant are full, and the other 13 tables are empty, we are asked to find the ratio of the number of empty tables to the total number of tables,

Number of empty table = 13

Total number of tables = 13 + 8 = 21

Ratio of the number of empty tables to the total number of tables = 13 / 21

Hence, the ratio of the number of empty tables to the total number of tables is 13:21

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