We often use functions to model or represent situations and relationships. These
representations can be as equations, graphs, tables, or even verbal descriptions.
What does it mean to "represent" something? In what other situations have you heard
that term used, and how was its meaning in those situations similar to its usage in
algebra? please help

The frequency distribution of the data from 103 to 107 is 2, from 108 to 112 is 4 and from 113 to 117 is 2.

Frequency distribution in a data set is the no. of times a certain data of an interval of grouped data occurs.

Temperature(°F)                              Frequency

103 to 107                                                2

108 to 112                                                4

113 to 117                                                  2

The class width of a data set is represented by the two consecutive lower limits.

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The number of possible ways a person can order a two-course meal = 99

In this question, we have been given a restaurant offers 9 entrees and 11 desserts.

We need to find the number of possible combinations (ways) a person can order a two-course meal.

Here, the entrees = 9

and the desserts = 11

The entrees can be ordered in 9 ways

The desserts can be ordered in 11 ways.

a two-course meal = entrees * desserts

so,  the number of possible ways a person can order a two-course meal would be,

a two-course meal = 11 * 9

a two-course meal = 99

Therefore, in 99 ways a person can order a two-course meal.

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Answer:

153

Step-by-step explanation:

Use long division on a piece of paper I can't show photo sorry.

According to the given figure of triangle , f = 58 °

A linear pair of angles is formed when two lines intersect at a single point. The angles are said to be linear if they follow the point where the two lines intersect in a straight line.

The sum of the angles in a pair of linear equations is always 180°. These are also referred to as additional angles.

According to the given information

We are given that

a = 119°

Applying linear Pair of Angles

a + b = 180°

119° + b = 180°

b = 180° - 119°

b = 61 °

We know that

b = c = 61 °

According to Angle sum Property

b + c + f = 180°

61° + 61° + f = 180°

f = 180 - 61 -61

f = 58 °

According to the given figure of triangle , f = 58 °

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Answer: 2m-6+4m

Step-by-step explanation:

The percentage increase in the population of the chilrden since past year is 11.96%.

What is Percentage ?

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.

According to the question, the town's population of children increased from 376 to 421 during the past year.

So, the increase in the population of the children is-

Increase =421-376

Increase =45

Now, the percentage increase in population of the children per year is calculated as-

Percentage Increase [tex]$=\frac{\text { Increase }}{376} \times 100 \%$[/tex]

Percentage Increase [tex]$=\frac{45}{376} \times 100 \%$[/tex]

Percentage Increase [tex]$=0.1196 \times 100 \%$[/tex]

Percentage Increase [tex]$=11.96 \%$[/tex]

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Answer: A gym membership cost 3 dollars a month. There is an initial fee of $5. How many months would you need to be paying for the membership to have spent 20 dollars?

Step-by-step explanation:

3x+5=20

3x=15

x=5

5 Months

The correct integers are;

For first diver, the elevation = - 36 feet

For second diver , the elevation = - 44 feet

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

One diver is 36 feet below the surface.

And, The other diver is 44 feet below the surface.

Now,

Since, One diver is 36 feet below the surface.

And, The other diver is 44 feet below the surface.

Hence, The correct integers to represent the surface are;

For first diver, the elevation = - 36 feet

For second diver , the elevation = - 44 feet

Thus, The correct integers are;

For first diver, the elevation = - 36 feet

For second diver , the elevation = - 44 feet

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Answer: -8

Step-by-step explanation:

We see on the graph that there are two points located y=4. They are (7,4) ( -8,4).

So the other value other than 7 is -8!

Anserw:

Say the averge water a person uses a day is 90 gallons 30% of the water is used outside a day. So that would mean around 27 gallons.

hope that helps :)

Step-by-step explanation:

The percentage of students who live off campus and do not have a part-time job is 25.2%

The correct answer option is option C

Students who live off campus and gets a part-time job = Percentage of students who live off campus and gets a part-time job × Percentage of students who live off campus × 100

= 58% of 60% × 100

= 0.58 × 0.60 × 100

= 0.348 × 100

= 34.8%

percentage of students who live off campus and do not have a part-time job = Percentage of students who live off campus - Students who live off campus and gets a part-time job

= 60% - 34.8%

= 25.2%

Consequently, 25.2% of students live off campus and do not have a part-time job.

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Equation of line in slope-intercept form is 3y-2x= -1.

Hence, Equation of line in slope-intercept form is 3y-2x= -1.

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The monomial that we need to add to have a square of a difference is:

-2bc

Remember that the square of a difference is written as:

(a - b)^2 = a^2 - 2ab + b^2

Here we have the two  terms:

0.01*b^2 + ... + 100c^2

We can rewrite the known terms as:

0.01*b^2 = (0.1*b)^2

100*c^2 = (10c)^2

Then our expression becomes:

(0.1*b)^2 + ... + (10c)^2

And the missing term must be:

-2*(0.1b)*(10c) = -2bc

Then the complete expression is:

(0.1b)^2 - 2bc + (10c)^2 = (0.1b - 10c)^2

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Answer:

There was no data provided but due to simple research i have conducted the following data

Qualifiers are in bold, italics and underlined.

Step-by-step explanations:

Chio- 3 1/5

Kevin- 3.2

Ojas- 3 8/30

Sydney- 3 13/60

Qualifiers: Chico, Kevin

let me know if this is incorrect data

The solution set of the function based on the graph is (3, 1). Option D

We know that the solution set of a function would be obtained as the points where the graph cut the axes of the graph. The graph has to do with a system in which information is presented in the x, y coordinate system.

In this kind of system, the vertical axis is the y axis while the horizontal axis is the x axis, as such we would need to plot the data points of the graph and then try to obtain the points that would correspond to the solutions of the points on the graph.

We would now need to observe the graphs so as to be able to obtain the correct presentation of the data points that would serve as the solutions of the graph as we can see the function plotted completely here.

The line cut the y axis at y =1. If we trace this point to the point that it corresponds to in the x axis we have x = 3 and we have the required points as (3, 1).

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Answer:

y = -4x-9

Step-by-step explanation:

The slope must stay the same for parallel lines, which is -4. Now we will plug the point into slope-intercept form(y=mx+b) where m is the slope and b is the y-intercept. Plugging in -4 for the slope and (-3, 3) for x and y, we get [tex]3=-4*13 + b[/tex], or [tex]3 = 12 + b[/tex]. Subtracting 12 from sides gives us that b = -9, which is the y-intercept! We know have both the slope and y-intercept, so we get that the equation is y = -4x - 9.

Hope this helps!

Hence, the slope of equation is [tex]f(x)=-0.25x+2[/tex].

What is the slope of the line?

The slope is always estimated by determining the ratio of the “vertical change” to the “horizontal change” between any two different points on a line.

Suppose that the amount of water in the tank after a certain number of minutes.

Let [tex]x[/tex] be any value. So, after the [tex]x[/tex] minutes the tank has lost [tex]0.25x[/tex] gallons from the original [tex]2[/tex] .

So, the [tex]f(x)=2-0.25x[/tex] where [tex]f(x)[/tex] is the number of gallons remaining after [tex]x[/tex] minutes and here [tex]x[/tex] is the number of minutes.

[tex]f(x)=2-0.25x\\\\f(x)=-0.25x+2[/tex]

Hence, the slope of equation is [tex]f(x)=-0.25x+2[/tex].

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Answer:

32

Step-by-step explanation:

we have to find the side of the bigger triangle by making a ratio

5/8=7/x

cross multiply

5x=7(8)

5x=56

/5.  /5

x=11.2

now for the other side

5/8=8/x

5x=8(8)

5x=64

/5. /5

x=12.8

we know all three sides 11.2, 12.8 and 8 so we add them

11.2+12.8+8

24+8

32

hopes this helps

since the border is 4 inches wide and there are 2 sides to the border , the expression in factored form that represents the area of border = 8 x (length of border)

The area of a rectangle is the amount of two-dimensional space that the rectangle occupies. It is calculated by multiplying the length of the rectangle by its width.

The perimeter of a rectangle is the distance around the outside of the rectangle.

(4 inches) * (2 sides) * (length of border) = 8 inches * (length of border)

To write this expression in factored form, we can factor out the 8 inches:

8 inches * (length of border) = 8 inches * (length of border)

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Answer:

12

Step-by-step explanation:

3*4=12

Answer:

-3/14

Step-by-step explanation:

Step 1) Convert into -7/14 + 4/14

Step 2) -7/14 + 4/14= -3/14

The statement that best describes the changes in air pressure and wind speed is C. When a high- and a low-pressure air mass are far apart, air moves slowly from high to low pressure.

The weight of air molecules pressing down on the Earth is referred to as air pressure. As you ascend from sea level into the atmosphere, the pressure of the air molecules changes. The greatest pressure exists at sea level, where the density of air molecules is greatest.

Atmospheric pressure, also known as barometric pressure, is the pressure that exists within Earth's atmosphere. The region with low pressure will always get winds from the high pressure. This means that the region of low will attract winds from the high pressure and vice versa.

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The order pair will be greater than (-2,5) because when substituted the value (-2,5) will give 11 that will be false.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it can be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers. Two variables are frequently represented by ordered pairs. (x, y) = (7, - 2) means that x = 7 and y = -2. The x-coordinate is the number that corresponds to the value of x, and the y-coordinate is the number that corresponds to the value of y.

Here,

The given inequality,

-3x+y<11

at (0,0)

0<11

it is true.

at (1,1)

-3+1<11

-2<11

it is true.

Because 11 will be false when the value (-2,5) is substituted, the order pair will be greater than (-2,5).

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Answer: y= -2/3x + 0

Explanation: y= mx +b

Y-intercept at (o,o), so b is 0

Let's pick 2 points (-3,2) ( 0,0), so the slope is -2/3

So the equation is y=-2/3x + 0

Answer: 13/15

Step-by-step explanation:

2/3 x 5 = 10/15

1/5 x 3 =3/15

3/15 + 10/15 =13/15

Answer:

13/15

Step-by-step explanation:

2/3 = 15/3 = 10 this is because 5 and three have common factors. So I now have 10/15.
1/5 = 3/15.

3/15 + 10/15 = 13/15.

The equation of line of c and y intercept are y = 100x +400 and 400 respectively.

The equation, y = mx + b, is in slant capture structure for the situation of a line. At the point when a condition is here, the slant of the line is given by m and the y-capture is situated at b. For instance, a line with the situation y = 2x + 4 has a slant of 2 and a y-catch of 4.

Let take two random points lying on the line.

(0, 400) and (1, 500)

we know that,

Slope(m) = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = (500-400)/(1-0) = 100

And y-intersect from the graph is c = 400

Then,

Y = mx + c

y = 100x +400

Y-intercept represent the number of phones produce in a day.

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For the mileage of 80 miles company A will charge less than company B.

So, the inequality is m≤80.

A variety of notations are available to denote different kinds of inequalities. An inequality in mathematics is a relationship between two expressions or values that is not equal. To resolve an inequality, follow these steps: First, multiply each term by the total of the least common denominators of all the fractions to be subtracted. Step 2: Combine similar terms on both sides to simplify the inequality. Step 3: Calculate the unknown by adding or subtracting the amounts from the numbers on either side.

Charge for company A=$131

Charge for company B=$75+0.70m

75+0.70m≤131

0.70m≤56

m≤(56/0.7)

m≤80

Therefore, for the mileage of 80 miles company A will charge less than company B.

So, the inequality is m≤80.

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Answer:

x = 3

Step-by-step explanation:

CD is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is

[tex]\frac{BD}{AD}[/tex] = [tex]\frac{BC}{AC}[/tex] ( substitute values )

[tex]\frac{x}{2.25}[/tex] = [tex]\frac{4}{3}[/tex] ( cross- multiply )

3x = 4 × 2.25 = 9 ( divide both sides by 3 )

x = 3

Answer:

-60q+20

Step-by-step explanation:

(a) The joint probability distribution of the two points will be 1/x, 0<x<1, 0<y<1

(b) The expectation of the product of the two points will be 1/6

(c) The marginal distribution of the point your friend picks will be (-1/2) lny^2

We have, X=(0,1)

Y | X=X=(0, X)

a) Let f(x,y) be the joint probability distribution of the two points will be:

f(X)=1

f(Y|X)=1/x

[tex]$$\begin{aligned}& f(x, y)=f(X) f(Y \mid X=x)=1 / x, 0 < x < 1,0 < y < x\end{aligned}$$[/tex]

b) Let E(XY) be the expectation of the product of the two points.

[tex]$$\begin{aligned}E(XY)=& \int_0^1 \int_0^x \frac{x y}{x} d y d x=\frac{1}{6} \quad \text { (Decimal : } 0.16667 \ldots \text { ) }\end{aligned}$$[/tex]

c) Let f(y) be the marginal distribution of the point your friend picks.

So, the value of f(y) will be:

[tex]$$\begin{aligned}& \mathrm{f}(\mathrm{y})= \\& \int_y^1 \frac{1}{x} d x=-\frac{1}{2} \ln \left(y^2\right)\end{aligned}$$[/tex]

d)for 0<y<1

[tex]$$\begin{aligned}& f(y) > =0 \\& \int_0^1-\frac{1}{2} \ln \left(y^2\right) d y=1\end{aligned}$$[/tex]

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