If 6 people in the United States each eat the average amount of popcorn for 5 years, how many quarts of popcorn will they eat.

r/5 - 6 = -1

add 6 to both sides

r/5 = 5

multiply both sides by 5

r = 5 *5 = 25

r = 25

Answer:100,000,000 tons

word form: one hundred million tons

Step-by-step explanation:

The given function 3xy = 27 is not a linear function.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

A linear function is defined as when the function has the highest degree of expression is 1, such as y = mx + c.

here,
Given function,
3xy = 27,

Simplifying the function,
3xy = 27
xy = 27/3
y = 9/x

Since, from the definition of the function, the given function is 9 reciprocal of x and is said to be a reciprocal function.

Thus, the given function 3xy = 27 is not a linear function.

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Answer:

B. [tex]\text{cos}(52^{\circ})[/tex].

Step-by-step explanation:

We have been given a right triangle. We are asked to complete our given statement.

[tex]\text{sin}(38^{\circ})[/tex] equals ___.

We will use identity [tex]\text{sin}(x)=\text{cos}(90-x)[/tex] to solve our given problem.

[tex]\text{sin}(38^{\circ})=\text{cos}(90^{\circ}-38^{\circ})[/tex]

[tex]\text{sin}(38^{\circ})=\text{cos}(52^{\circ})[/tex]

Therefore, [tex]\text{sin}(38^{\circ})[/tex] equals [tex]\text{cos}(52^{\circ})[/tex].

Answer:

11x^3 - 2x^2 + 3x + 11

Step-by-step explanation:

we need to find the sum of 4x^3 + 2x^2 - 4x + 3 and 7x^3 -4x^2 + 7x + 8

To find the sum we add both the polynomials

4x^3 + 2x^2 - 4x + 3 + 7x^3 -4x^2 + 7x + 8

To add the polynomials we combine like terms

4x^3 + 7x^3 = 11x^3

2x^2 - 4x^2 = -2x^2

-4x+7x= 3x

3+8 = 11

So final expression is 11x^3 -2x^2 +3x+11

Answer:

Deductive reasoning

Step-by-step explanation:

Given : John concludes that, since (x-5) is a factor of the polynomial [tex]x^2-25[/tex], if he performed the long division [tex](x^2-25)\div (x-5)[/tex], the remainder would be zero.  

To find : This is an example of ___________ reasoning [tex]x^2-25[/tex]?

Solution :

The above situation make conclusion when we know the fact that (x-5)

is the factor as the factor of polynomial divide it completely.

Therefore, This is the example of deductive reasoning.

Deductive reasoning is the process by which a person makes conclusions based on previously known facts.

The values of sine, cosine, and tangent for angle θ, where (1, -1) is on its terminal side, are sin(θ) = -1, cos(θ) = 1, and tan(θ) = -1, knowing that the point lies in the fourth quadrant.

To find the values of the sine, cosine, and tangent of an angle θ where the point (1, -1) is on its terminal side, we first recognize that this point lies in the fourth quadrant of the coordinate system. In this quadrant, cosine is positive, and sine and tangent are negative.

The point (1, -1) gives us the x and y coordinates on the Cartesian plane, which correspond to the lengths of the adjacent side and the opposite side of the right-angle triangle formed by the radius (hypotenuse) from the origin to the point, and the axes. Assuming we're dealing with a unit circle (which has a radius of 1), we can directly use the coordinates (1, -1) to find the cosine and sine:

Hence, for angle θ, cos(θ) is 1, sin(θ) is -1, and tan(θ) is -1.

As per linear equation, the value of Mayam's benefits is $12250.

A linear equation is an equation where there are one or multiple variables. However, the highest power of any variable is one.

Given, Maryam earns a salary of $35,000 a year.

Her benefits are equal in value to 35 percent of her salary.

Therefore, the value of Mayam's benefits is

[tex]=[/tex] $[tex]\frac{(35000)(35)}{100}[/tex]

[tex]=[/tex] $12250

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when m = 5:

2k = 5+3

2k = 8

k = 8/2

k=4

when m = 7

2k = 7+3

2k =10

k = 10/2

k = 5

when m = 9

2k = 9+3

2k = 12

k = 12/2

k = 6

k = {4,5,6}

The relationship between variance and standard deviation is simply:

s = standard deviation

s^2 = variance

s = sqrt (s^2)

Therefore calculating for s:

s = sqrt (144)

s = 12

So we get the standard deviation is simply 12 scores.

I believe that aside from the bar graph, the line graph would actually best suits to convey this information. Because just like the bar graph, we can actually see the peaks of the grades. And through the peaks, we can easily compare the grades one by one.

Answer:

line graph

The height of the tree will be 45 feet.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

A tree is standing next to a 40-foot-high building. the tree has an 18-foot shadow, while the building has a 16-foot shadow.

Let x be the height of a tree. Then we have

x / 18 = 40 / 16

x = 45 feet

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Answer: Yes

Step-by-step explanation: This table does represent a function. A function is where each input has exactly one output. Since none of the x-values repeat, this would represent a function.