On a map, 1/2 inch represents 4/5 mile. What distance on the map represents 1 mile?

Value of f(g(3)) is -22.

Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given

f(x) = 4x – 2

g(x) = -2x + 1

Value of f(g(3))

g(x) = -2x + 1

g(3) = -2(3) + 1

g(3) = -6 + 1

g(3) = -5

f(g(3)) = f(-5)

f(x) = 4x – 2

f(-5) = 4(-5) - 2

f(g(3)) = -20 -2

f(g(3)) = -22

Hence, value of f(g(3)) is -22.

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Answer and explanation;

If we choose two whole numbers; 8 and 10

We want to divide certain numbers by 8 and 10 to get 9 remainder 5.

In this case; 77 divided by 8 is equal to 9 rem 5

and 95 divided by 10 is equal to 9 rem 5

To justify which is greater, we use decimal division;

= 77 divided by 8 we get 9.625 ( 77 ÷ 8 = 9.625)

and

= 95 divided by 10 is equal to 9.5 (95 ÷10 = 9.5)

Therefore; the first case is greater since 9.625 is greater than 9.5

That is; 9 rem 5 got after dividing 77 by 8 is greater than 9 rem 5 got after dividing 95 by 10.

The number of teams Ms.Morris can make would be 5-students groups.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given that there are 25 students in Ms.Morris's class. She wants to divide the class into 3,4,or 5 equal teams with all students on a team.

If Ms. Morris wants to divide all the students in 3, 4 or 5 equal teams, then apply a division to know the number of students per group.

If she makes 3-students groups, it would be;

25/3

If she considers 4-students groups, then it would be;

25/4

Thus, it can be seen that she cannot divide a students in parts to have equal groups.

Therefore, she has to make 5-students groups,

25/5 = 5

This means that she can make groups of 5 students each, and she would have equal groups.

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In  order to raise $100, Bo should charge $5 for each game. In mathematics, "at least one" refers to one or more.

He provided the least amount of money of any donor, whether in size, quantity, degree, etc. lowest in importance, standing, or consideration. noun. The smallest possible quantity, degree, or other attribute.

In mathematics, "at least one" refers to one or more. It is frequently employed when existence can be proved but there is no way to know how many possible solutions there are.

Given ,

Let x represent the lowest price per video game.

The number of games available is 23.

Selling video games will need to raise $100 as the minimum amount.

The necessary inequality follows:

total number of games need minimum sum

i.e.[tex]23x\geq 100[/tex]

23 divided by both sides gives us

[tex]x\geq 4.24782608696[/tex]≈5

So, in order to raise $100, Bo should charge $5 for each game.

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The cost of 8 cups of lemonade would be $14.40

Price of lemonade :

price per cup:

for 3 cups:

for 4 cups:

for 5 cups:

for 6 cups:

for 7 cups:

for 8 cups:

Therefore , the cost of 8 cups of lemonade is $14.40

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Answer:

The overall change is -250 feet. 50 times 5 is 250 feet, and the mountain climber descended. Therefore, the change is -250 feet in elevation.

Step-by-step explanation:

Answer:

the overall changes is -250 its descended 50×5=250

Step-by-step explanation:

Final answer:

Carlos can divide his 24-inch string into 3 equal parts by solving the equation 3x = 24, which gives each part a length of 8 inches.

Explanation:

Carlos has a string that is 24 inches long and wants to divide it into 3 equal parts. To find how long each part will be, we can represent the unknown length of each part by the variable ? (which we will replace with x for the equation). The equation we can write for this scenario is 3x = 24.

To solve for x, we divide both sides of the equation by 3:

So, each part of the string will be 8 inches long.

It will not have any possible solutions

Step-by-step explanation:

this would actually have some solutions because

y=3.5x−3.5

Step: Substitute 3.5x−3.5 for y in y=−3.5x+3.5:

y=−3.5x+3.5

3.5x−3.5=−3.5x+3.5

3.5x−3.5+3.5x=−3.5x+3.5+3.5x(Add 3.5x to both sides)

7x−3.5=3.5

7x−3.5+3.5=3.5+3.5(Add 3.5 to both sides)

7x=7

7x

7

=

7

7

(Divide both sides by 7)

x=1

Step: Substitute 1 for x in y=3.5x−3.5:

y=3.5x−3.5

y=(3.5)(1)−3.5

y=0(Simplify both sides of the equation)

x=1 and y=0

The expression that will represent Cindy’s bill is 0.95(1.09m + 2.79n). Hence, the correct option is D. 0.95(1.09m + 2.79n).

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

It is given that store sells 12-packs of ballpoint pens for $1.09 each.

The store also sells composition books for $2.79 each.

Cindy buys 'm' packs of ballpoint pens and 'n' composition books.

So, the equation for this becomes

1.09m + 2.79n

Cindy gets a 5% discount, so she has to pay 95% of the regular price.

Then the expression that will represent Cindy’s bill,

0.95(1.09m + 2.79n)

Hence, the correct option is D. 0.95(1.09m + 2.79n).

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Answer: 3.4875

Step-by-step explanation:

Here, According to the question,

Total amount is $23.25

[tex]100\% = 23.25[/tex]

⇒[tex]1\% = \frac{23.25}{100}[/tex]

⇒[tex]1\%= \frac{0.95}{8}[/tex]

⇒ [tex]15\%= 15\times \frac{0.95}{8}[/tex] ( By multiplying 15 on both sides)

⇒ [tex]15\%= \frac{14.25}{8}[/tex]

⇒  [tex]15\%= 3.4875 [/tex]

Thus, 15% of $23.25 is $3.4875

To find the equivalent number of calories per serving based on that a can of juice contains 175 calories for 2.5 servings, divide 175 by 2.5 to get 70 calories per serving. Any amount other than 70 calories per serving would not be equivalent.

The question is asking to find an equivalent number of calories per serving based on the information that a can of juice contains 175 calories per 2.5 servings. To calculate the calories per serving, we divide the total number of calories by the number of servings, so:

Calories per serving = Total calories ÷ Number of servings = 175 calories ÷ 2.5 servings = 70 calories per serving.

Now, let's say we have several options that represent the number of calories per serving:

From this list, every option except for the first one (70 calories per serving) is not an equivalent number of calories per serving as our calculated 70 calories per serving.

Answer:

Step-by-step explanation:use the greatest common factor of 28 and 68 would give you 4

Using a linear function, it is found that the value is: y = 32.

A linear function has the following format:

[tex]y = mx + b[/tex]

In which:

In this problem, when [tex]x = 0, y = 0[/tex], and thus, the y-intercept is [tex]b = 0[/tex].

Then

[tex]y = mx[/tex]

She also plots the point (14, 448), which means that when [tex]x = 14, y = 448[/tex], and this is used to find m.

[tex]14m = 448[/tex]

[tex]m = \frac{448}{14}[/tex]

[tex]m = 32[/tex]

Hence, the linear function is:

[tex]y = 32x[/tex]

Then, when x = 1, the point is (1,y), and:

[tex]y = 32(1) = 32[/tex]

The y-value is y = 32.

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The volume of a sphere can be calculated using the formula V = (4/3)πr³, where π can be approximated as 3.14 for simpler calculations. Volume is proportional to the cube of the radius, so if the radius changes significantly, the volume adjusts correspondingly by the cube of the factor of change.

To calculate the volume of a sphere using the value 3.14 for pi, you can apply the formula V = (4/3)πr³. If the radius of the sphere is 'r', you would plug in the value of 'r' into this formula. Next, you would multiply the result by 4/3 and then by 3.14 in place of π to get the volume. It's important to note that the volume of the sphere increases proportionally to the cube of the radius, meaning if the radius changes by a factor of 10, the volume changes by a factor of 10³ or 1000.