Mr. March sells popcorn at his theater. He uses 3 3/4 cups of unpopped corn to make 15 bags of popped corn. Write an equation for the number of bags of popcorn b that can be made with c cups of unpopped corn.​

The system of equations are y = 50 + 100x and y = 300 + 75x which is linear equations in two variables.

A straight line is a combination of endless points joined on both sides of the point.

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The linear equation can be written in form of:

y = mx + c

From the question:

The equation for Little Learners Pre-School:

y = 50 + 100x

The equation for Growing Place Pre-School:

y = 300 + 75x

Thus, the system of equations are y = 50 + 100x and y = 300 + 75x which is linear equations in two variables.

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Answer:

0.8 repeated

Step-by-step explanation:

Because it is

We can see from Steves rate of change that it was steeper than Peters. That means that it took more minutes per kilometer for each kilometer. It is easier to compare when seeing it on the graph. The steeper the line, the steeper the rate of change.

The data that represent a population is helpful when we have to find the information only about one field.

In the given question we have decide how well data represent a population.

The total group you want to make judgments about is referred to as a population. Data is a set of quantitive data which refers the population only in numbers. So the data is only helpful when we have to find the only in small amount and only one field.

Data collection from a large population is typically only simple when the population is small, approachable, and cooperative.

Example: Gathering information from a population

A high school administrator is looking for trends in the final exam results of all graduating seniors. They use the entire population dataset since they are only interested in applying their findings to the graduating seniors in this high school. So the data is useful.

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Answer:

Step-by-step explanation: 0.3

Answer:

Step-by-step explanation:

1. The answer is 0.3.

The measure of the other acute angle in the right triangle is 90 - 2y

The given parameters in the question are:

Shape = right triangle

Acute angle = 2y

The measures of acute angles in a right triangle add up to 90

This can be represented mathematically as

Acute angle + Other angle = 90

Substitute the known values in the above equation, so, we have the following representation

2y + Other angle = 90

This gives

Other angle = 90 - 2y

Hence, the other angle is 90 - 2y

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The missing parts of proof are:

In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector. By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.

Angle Bisector's Qualities:

Given,

KM is the bisector of ∠JKL

1. As per the definition of bisector, ∠JKM≅∠LKM

Given,

∠KXM and ∠KYM are right angles

∠KXM≅∠KYM because all right angles are congruent

2. Because of Reflexive Property of congruence, MK≅MK

3. Given △KXM≅△KYM, AAS congruence postulate

4. Given MX≅MY, this is according to CPCTE property

5. Given, Point M is equidistant from the sides of ∠JKL, as per the definition of equidistant

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The fraction form of 8 1/6 is 49/8 as the definition of fraction says, "An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided".

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction merely informs us of the number of parts that make up the whole. The slash that is written between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. 1/2, for instance, is a fraction.

Here,

8 1/6=(6*8+1)/8

=49/8

According to the definition of a fraction, which states that it is "a number represented mathematically as a quotient, where the numerator and denominator are divided," the fraction form of 8 1/6 is 49/8.

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To determine the next step, we need to slove the expression.

divide both sides by -1:

Square both sides of the equation:

A statement like that. An assertion is a single statement or comment. b: an information or idea report, 1 < 0.125= True, 125 > 0.12=True, and 126 < 0.125=True

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Answer:

scal factor = 1.5

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, that is

scale factor = [tex]\frac{C'D'}{CD}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5

(x-2) (x-6)

x(x-6)-2(x-6)

x²-6x-2x-12

X²-4x-12

Answer:

6x+3=5x-8

6x-5x= -8-3(match the like terms)

x= -11

We will have the following:

Here it is the Venn diagram for both; the statement is not valid, since they fall in different categories.

Answer:

4/5 or four fifths

Step-by-step explanation:

First you make 80% the fraction 80/100

Next you find the greatest common factor (GCF) which in each of them is 20

Finally you divide 80 and 100 by 20 and you get 4 and five now make them a fraction and you get 4/5

Answer: Width = 4.7 meters, Length = 6.7 meters

Step-by-step explanation:

Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].

[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]

we have the expression

Remember that

substitute

therefore

a=6

b=2

Answer:

The value of angle QXS is;

Explanation:

From the given diagram in question 1:

We can see that angle QXT equals the sum of angle SXT and angle QXS;

Given in the question is the value of angle SXT and angle QXS;

Substituting the values into the equation above;

Since angle QXT is equal to 125 degree, then;

We can now substitute the value of x to get the value of angle QXS;

Therefore, the value of angle QXS is;

The original statement is same as third statment and value of y is 27.

Writing the equation form for each statement -

Let the variable be represented as y.

1/3(30 - y) = 3/4

1/3×30 - y = 3/4

1/3×y - 30 = 3/4

1/3(30 - y) = 3/4

1/3(y - 30) = 3/4

Based on the interpretation of all the sentences in equation form, we find the statement 3 to be same as original statement. Solving the equation to get the value of y.

1/3(30 - y) = 3/4

10 - y/3 = 3/4

10 = 3/4 + y/3

10 = (3×4 + y×4)/12

10×12 = 12 + 4y

4y + 12 = 120

4y = 120 - 12

4y = 108

y = 27

Hence, the value of y is 27.

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Answer:

the answer is A.

1 over 3 (30 - y) = 3 over 4

Answer:

E

Step-by-step explanation:

[tex]3 \leq x-2 \\ \\ x-2 \geq 3 \\ \\ x \geq 5[/tex]

Answer:

E

Step-by-step explanation:

if it is supposed to be more or equal to then it has to add 5 or more. It has to add 5 or more because the 2 is negative and 5-2 is 3 so it has to be at least 5

Answer: 2.5, 5.3

Step-by-step explanation:

[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]

Answer:

the horizontal lines for #9 and those slanted ones for #10

Step-by-step explanation:

parallel lines are lines that never intercept. if these following lines continue infinetly they will never touch

y=10x-5 is the slope-intercept form

y-intercept= -5,

slope m= 10,

The slope-intercept formula y = mx + b, where m is the slope and b is the intercept.

y = y coordinate

m = slope

x = x coordinate

b = y intercept

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line.

the slope of the line to be examined and the point given is also the y-intercept (0, b)

by putting the given information in the question we get,

y=10x+(-5),

therefore,y=10x-5 is the slope-intercept form

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The width of the scale model given a height of 10 inches as in the task content is; 3.75 inches.

It follows from the task content that the width of the scale model is to be determined given a height of 10 inches.

According to the design, the lawnmower measures; 8 feet in height, 3 feet width, and 7 feet in length.

Hence, since 8 feet in height corresponds to 10 inches on the scale, the width on the scale can be determined by proportion as;

8/10 = 3/x

x = ( 10 × 3 ) / 8

x = 30/8

x = 3.75 inches.

Therefore, the width on the scale as required is; 3.75 inches.

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The equivalent expression as a base of 2¹⁰ is (2¹⁰)⁴

The mathematical statement in the question implies that

We rewrite 2^40 as a power in the base 2^10

Start by expressing the given number properly

So, we have

2⁴⁰

Express 40 as the product of 10 and 4

So, we have

2⁴⁰ = 2¹⁰ ˣ ⁴

Express as exponents

So, we have the following representation

2⁴⁰ = (2¹⁰)⁴

Hence, the new expression is (2¹⁰)⁴

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Solution

- 40% of peole would vote for the mMath teacher out f the 750 people. This implies that the number of people tahat would vote for him is

- We are also told that there is a margin of error of 4%. This implies that the number of people that vote for the math teacher is either 4% more or 4% less than the 300 people

- 4% margin of error can be gotten as follows:

- Thus, the number of people that vote for him is 300 give or take 30 people

The rule of the mean is

We will find the sum of the given numbers, then divide it by how many numbers

The given numbers are

4, 8, 14, 7, 0, 8, 2, 10, 3, 12

Their sum = 68

There are 10 numbers, then

To find the median we have to arrange the numbers from smallest to greatest, then take the middle number

0, 2, 3, 4, 7, 8, 8, 10, 12, 14

Since there are 10 numbers, then there are 2 numbers in the middle

Then we will find their average by adding them and dividing their sum by 2

The 2 middle numbers are the 5th and the 6th positions

The 2 middle numbers are 7 and 8

The answers are:

Sample mean = 6.8

The median = 7.5

The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.

An event that is certain to happen has a probability of 1.

Point slope form: y - 160 = 8(x-15)

Slope intercept form: y = 8x + 40

Explanation:

To write an equation of the line in point-slope form that passes through the given points in the table, we need to pick any two of the points in the table for x and y axis and find the changes of x and y

Points chosen: (20, 200) and (15, 160)

m = slope = (change in y)/ (change in x)

Point-slope form:

The equation in the slope intercept form:

Hence, Point slope form: y - 160 = 8(x-15)

Slope intercept form: y = 8x + 40