A frozen yogurt shop offers a rewards system for frequent customers. The graph below represents how much a rewards customer pays based on the number of ounces of frozen yogurt purchased.

A graph titled Customer Rewards. The horizontal axis shows ounces of yogurt purchased, numbered 2 to 22, and the vertical axis shows Total Spent (dollars) numbered 1 to 11. A line begins at 0, extends to 5 dollars spent at 10 to 12 ounces, and ends at 9 dollars spent at 20 ounces.

Which statement describes the total amount a rewards customer pays for 10 ounces and 12 ounces of yogurt?

Yes..............................

The value of constant  variation is √16.

A mathematical constant is a significant integer that has a steady value and is specified by a precise definition.

relationship between two variables in mathematics that may be represented by an equation where the product of their products equals a constant

Inverse variation is y = k. 1/x

given y = √18

x = √2

So, √8 = k. 1/√2

So, the value of k = √16

We can conclude that the value of constant variation is √16

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Answer:

w = 0.9

Step-by-step explanation:

What I did is I subtracted 2.7 from 3.7 bc it was the least number and that gave me 1 so that left me with 0.43 = w - 0.47. Then I added 0.47 to 0.43 and that gives me 0.9 which would be the answer

If you don't understand how I got it I can try to explain a little better, but hopefully, you understand:)

The equation of the line perpendicular to the given line and that passes through the point is x + 3y = 6

From the question, we are to determine the equation of the line that is perpendicular to the given equation.

A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.

That is,

If m₁ is the slope of one of the lines

and m₂ is the slope of the other line

Then,

m₁ = -1/m₂

First, we will determine the slope of the given line

The equation of the given line is

y = 3x - 9

Compare the equation to the general form of the equation of a straight line

y = mx + b

Where m is the slope

and b is the y-intercept

By comparison,

m = 3

∴ The slope of the given line is 3

Thus,

The slope of the line that is perpendicular to this line is -1/3

Now,

To determine the equation this line,

We have that the line passes through the point (3, 1)

Using the point-slope form of the equation of a straight line,

y - y₁ = m(x - x₁)

m = -1/3

x₁ = 3

y₁ = 1

Putting the parameters into the equation,

y - 1 = -1/3(x - 3)

Expressing the equation in standard form

3(y -1) = -1(x - 3)

3y - 3 = -x + 3

3y + x = 3 + 3

x + 3y = 6

Hence, the equation of the line perpendicular to the given line and that passes through the point is x + 3y = 6

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Step-by-step explanation:

GOOD RIGHT?

Answer:

A function is a mathematical relation that maps a value in a set of input numbers to a value in a set of output numbers. Some functions can map multiple values in one set to one value in the other set.

Step-by-step explanation:

The side length of the square in centimeters is 13 centimeters

The area of a shape is the amount of space on the shape

The equation of the area of the square is given as

p² = 169

The area of a square is the product of its length

This means that we simply take the square root of both sides of the equation to determine the side length

Next, we take the square root of both sides of the equation

So, we have

√p² = √169

Evaluate the square roots

So, we have

p = 13

Hence, the side length of the square in centimeters is 13 centimeters

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The value of [tex]f^{-1}(x)[/tex] is [tex]\frac{x}{\sqrt[3]{2} }[/tex]  when f(x) = 16  is [tex]x=2^\frac{11}{3}[/tex] .

We have given a function [tex]f(x)=x\sqrt[3]{2}[/tex].        ....(1)

 Let y = f(x)

         [tex]y=x\sqrt[3]{2} \\\\x=\frac{y}{\sqrt[3]{2} }[/tex]                         ......(2)

Swap the values of x and y, then the inverse is then

         [tex]y=\frac{x}{\sqrt[3]{2} }[/tex]

        [tex]f^{-1}(x)=y[/tex]                             ...(3)

Comparing equation (2) and (3) , we get

      [tex]f^{-1}(x)=\frac{x}{\sqrt[3]{2} }[/tex]

It is given that f(x) = 16 on comparing it with equation (1) , we get

              [tex]x\sqrt[3]{2}=16\\x=\frac{2^4}{2^\frac{1}{3} } \\x=2^{4-\frac{1}{3} }\\x=2^\frac{11}{3}[/tex]

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The addition of the fractions means that the value when combined is 1.

It should be noted that based on the information given, we simply have to add the fractions that are given and this will be:

= 1/2 + 1/3 + 1/6

= 3/6 + 2/6 + 1/6

= 6/6

= 1

Therefore, the addition of the fractions means that the value when combined is 1.

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The answer is x = [tex]\frac{1}{25}[/tex].

5√x + 7 = 8

⇒ 5√x = 8 - 7

⇒ 5√x = 1

⇒ √x = [tex]\frac{1}{5}[/tex]

Squaring both sides, we get,

⇒ x = [tex]\frac{1}{25}[/tex]

Answer) x = [tex]\frac{1}{25}[/tex]

         An extraneous solution refers to the roots of the transformed equation. This root is not the root of the original equation, as the original equation has been transformed to create another equation from which the answer has been found. The original equation has been excluded from the domain of the function.

         In the given equation, I have tried to take the equation in the value of x, and hence, after squaring the value, the root has been found.

         Since the square root function is used, we get a single value for the variable x.

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The scale of the drawing is 1 inch represents 300 feet .

A scale drawing is a smaller image of a larger diagram or object in terms of dimensions. The scale drawing is usually reduced at a constant dimension.

In order to determine the scale of the drawing, divide the base of the actual Federal triangle by the base of the drawing.

Scale of the drawing = original dimensions / dimensions of the scale drawing

3000 / 10 = 300

1 inch represents 300 feet

1 inch : 300 feet

The scale of a drawing is usually written in this format - one a colon (:), the result of the division of the original dimension and the dimension of the scale.

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The equivalent expression of (64x^2/3)^-1/3 is 1/(4x^1/9)

Expressions are mathematical statements that are represented by variables, coefficients and operators

Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.

This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals

The expression is given as

(64x^2/3)^-1/3

Evaluate the product of the exponents

So, we have

(64x^2/3)^-1/3 = 64^-1/3 * x^(2/3*-1/3)

Evaluate the product of the exponents

So, we have

(64x^2/3)^-1/3 = 64^-1/3 * x^-1/9

Evaluate the exponent

So, we have

(64x^2/3)^-1/3 = 1/4 * x^-1/9

Evaluate the product

So, we have

(64x^2/3)^-1/3 = 1/4x^-1/9

Rewrite as

(64x^2/3)^-1/3 = 1/(4x^1/9)

Hence, the equivalent expression of (64x^2/3)^-1/3 is 1/(4x^1/9)

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Answer:

-5, 1/2, -0.45, -0.05 would be the solution

We need to know about the difference between relation and function to solve this problem. Options 1 and 3 are functions but 2 and 4 are just relation not functions.

A relation is a relationship between two or more sets of values. A function is an expression that defines the relationship between two variables. The main difference between a relation and a function is that a relation can have multiple output for a single input but a function only has single output for a single input. Every function is a relation but every relation is not a function. In this question x is the input variable and y is the output variable,for option (1) all the input values have single output values, for option (2) the value x=0 has two different output values so this relation is not a function, for option (3) all input values have single output values, so it is a function and for option (4) the input value x=2 has two different output values so it is not a function.

Therefore we found out that options (1) and (3) are functions and the rest are just relations.

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Answer:

its simply a, and c

Step-by-step explanation:

yiippeeeeee

The number of girls and boys in the senior class is 240 and 150 respectively.

let

1/3x + 1/2y = 205

1/2x + y = 370

From (2)

y = 370 - 1/2x

1/3x + 1/2y = 205

1/3x + 1/2(370 - 1/2x) = 205

1/3x + 185 - 1/4x = 205

1/3x - 1/4x = 205 - 185

(4x-3x) / 12 = 20

x/12 = 20

x = 20 × 12

x = 240

1/2x + y = 370

1/2(240) + y = 370

120 + y = 370

y = 370 - 120

y = 150

Therefore, the number of girls and boys in the senior class is 240 and 150 respectively.

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The linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top.

Option (c) is correct.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

The given inequality is

y< - 2/5x + 2

According to given question we have

The  inequality is

y< - 2/5x + 2

To solve the inequation by putting the value of

At x=0

y< - 2/5x + 2

y<-2/5*0+2

y<2

The points are (0,2).

At x= 5

y< - 2/5x + 2

y<-2/5*5+2

y<-2+2

y<0

The points are (5,0).

At x= -5

y< - 2/5x + 2

y<-2/5*-5+2

y<2+2

y<4

The points are (-5,4).

Therefore, the linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top.

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Answer: The linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top.

Option (c) is correct.

What is inequality?

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

The given inequality is

y< - 2/5x + 2

According to given question we have

The inequality is

y< - 2/5x + 2

To solve the inequation by putting the value of

At x=0

y< - 2/5x + 2

y<-2/5*0+2

y<2

The points are (0,2).

At x= 5

y< - 2/5x + 2

y<-2/5*5+2

y<-2+2

y<0

The points are (5,0).

At x= -5

y< - 2/5x + 2

y<-2/5*-5+2

y<2+2

y<4

The points are (-5,4).

Therefore, the linear function on a coordinate plane passes through (minus 5, 4), (0, 2), and (5, 0) to form a blue shaded portion at the top.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The radicands have at least one prime-factor that is not in common.

Answer (y2 -y1) / (x2 - x1)

hope this helps

Answer:

(y2 -y1) / (x2 - x1)

Step-by-step explanation:

Use that formula. The answer should be -3/0 which doesn't make sense. Are you sure you have your x values correct? Since in that case, it would be a straight line and the equation for that would be x = 6 since it is a straight line up with no y-intercept.

The Subject formula for r= 3t/ ( t- 1)

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

t= r/r-3

Now, writing the above equation for r

tr - 3t = r

tr - r= 3t

r( t - 1)= 3t

r= 3t/ ( t- 1)

Hence, the Subject formula for r= 3t/ ( t- 1)

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 +4}{2}~~~ ,~~~ \cfrac{ 3 +6}{2} \right) \implies \left(\cfrac{ 5 }{2}~~~ ,~~~ \cfrac{ 9 }{2} \right)\implies \left(2\frac{1}{2}~~,~~4\frac{1}{2} \right)[/tex]

The equation that justifies [tex]7^{\frac{1}{3} } = \sqrt[3]{7}[/tex] is [tex](7^{\frac{1}{3} } )^{3} = 7^{\frac{1}{3} .3} = 7[/tex]

The equation is as follows;

[tex]7^{\frac{1}{3} } = \sqrt[3]{7}[/tex]

using laws of indices, the equation can be simplified.

[tex]a^{1 / b} = \sqrt[b]{a}[/tex]

Therefore,

[tex]7^{\frac{1}{3} } = \sqrt[3]{7}[/tex]   are the same.

Hence, it means the equation that justifies [tex]7^{\frac{1}{3} } = \sqrt[3]{7}[/tex] is as follows:

[tex](7^{\frac{1}{3} } )^{3} = 7^{\frac{1}{3} .3} = 7[/tex]

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Answer:

It has 2 angles right and acute

The vehicle travels 55 miles per hour, so for each hour "t" we will travel 55 miles.

[tex]d(t) = 55t[/tex]

Each 20 miles take 1 gallon, so for each gallon of fuel, we can travel 20 miles

[tex]d(g) = 20g[/tex]

In each hour we travel 55 miles, and each 20 miles require 1 gallon of fuel.

So,

[tex]55t = 20g \\ g = \frac{55}{20} t \\ g = 2.75t[/tex]

or you could set both d(t)=d(g) since they both are distance traveled.

[tex]g = 2.75(6) = 16.5 \: gallons[/tex]

[tex]d(6) = 55(6) = 330 \: miles \: \\ or \: \\ d(16.5) = 20(16.5) = 330 \: miles[/tex]

Answer:

4.6

Step-by-step explanation:

1. Multiply the whole number by the denominator

4 x 5 = 20

2. Add the result of step 1 to the numerator

20 + 3 = 23

3. Divide the result of step 2 by the denominator

23 ÷ 5 = 4.6

Answer:

I am pretty sure it is y^14/z^14

Answer

y^14 / z^14 (Option 3)

Step-by-step explanation:

The z^-4 adds to the z^3, making z^7

The y^-2 adds to the y^5 making y^7

The negative square flips the equation and essentially doubles it. leaving the Y on the numerator and Z on the denominator, doubling the 7 into 14

Random variables can be either discrete or continuous.

Sample spaces need not consist of numbers.  In statistics, we are most often interested in numerical outcomes such as the "count" of an occurrence.  We call X a random variable because its values vary when the phenomenon is repeated.  We use capital letters near the end of the alphabet like X or Y.

A random variable is a variable whose value is a numerical outcome of a random phenomenon.  When a random variable describes a random phenomenon the sample space S just lists the possible values of the random variable.  There are two ways of assigning probabilities to the values of a random variable that will dominate our application of probability as we study statistical inference.

Random variables can be either discrete or continuous.  A discrete random variable X has a "countable number of possible values.  The probability distribution of X lists the values and their probabilities in table form.  The probabilities must satisfy two requirements:

1)  every probability pi is a number between 0 and 1

2) p1 + p2 +,,,+pk = 1.

The probability of any event is found by adding the probabilities pi of the particular values xi that makes up the event.

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Answer:

2,129

5 times 2129 = 10645

Step-by-step explanation:

Hope it helps! =D