Sarah,Juan, are on the track team. Last week, Sarah ran 8.25 miles, Juan ran 11.8 miles, and Larry ran 9.3 miles. How many miles did they run altogether?

An equivalent expression for the given expression by combining like terms is 0.83b.

Given that, a student received a coupon for 17% off the total purchase price at a clothing store.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let b be the original price of the purchase.

So, new price =original price-17% of original price

⇒ new price =b - 17% of b

⇒ new price =b - 0.17b

= 0.83b

Therefore, an equivalent expression for the given expression by combining like terms is 0.83b.

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The function represented in the table is linear, so option A is correct.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given :

For x = 2, y = 4,

x = 4, y = 8...

As you can that the y is double of x,

So the equation of this condition is,

y = 2x

Hence, the function is dependent on x, and it is linearly dependent.

Therefore, The function represented in the table is linear.

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Answer:

$7500

Step-by-step explanation:

The required expression is  x + 2y = 2 (3/2 + y) that gives the value 3.

An algebraic expression is consists of variables, numbers with various mathematical operations,

To write the algebraic expression with variable x that has a value of 3.

Let x is a variable and y is another variable,

The expression for the x equal to 3 can be written as,

x + 2y = 2 (3/2 + y)

The expression x + 2y = 2 (3/2 + y) gives the value 3.

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Answer:

The rate of change in the function y=x+4 is _Equal_ the rate of change of the function represented in the table.

The required original cost of the in-line skates is given as $100.00.

Given that,
A pair of in-line skates are on sale for $90, this price represents a 9% discount from the original price, and the original price to the nearest cent is to be determined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
Let the original price of the in-line skates be x,
according to the question,
0.9 [x] = 90
x = 90 / 0.9
x =  $100

Thus,  The required original cost of the in-line skates is given as $100.00.

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Answer: C.2

Step-by-step explanation:

Given: Independent variable= Number of sides

To check how many of the remaining three columns represent a linear relationship, we need to check the rate of change of the three columns with respect to dependent variable.

For number of diagonals

The rate of change of diagonals w.r.t number of sides is constant and that is 1.

For Sum of all interior angles (degrees)

The rate of change of  Sum of all interior angles w.r.t number of sides is constant and that is 180°.

For measure of each angle (degrees)

The rate of change of  measure of each angle w.r.t number of sides is not constant and that is 180°.

Since for vertices 3 , measure of angle=60

vertices 4 , measure of angle=90

From vertices 3 to 4 change in measure of angle is 30

vertices 5 , measure of angle=108

From vertices 4 to 5 change in measure of angle is 18

Thus number of diagonals and Sum of all interior angles are the columns represent a linear relationship when compared with the independent variable.

Therefore there are 2 columns represent a linear relationship when compared with the independent variable.

Solution:

The equation of linear relationship is , y= k x

That is, [tex]\frac{y-value}{x-value}=k({\text{a constant})[/tex]

As, you can see that , ratio of

1.

[tex]\frac{\text{Sum of interior angles of a regular polygon}}{\text{number of sides of that polygon}}={\text{Measure of each interior angle of regular polygon}}[/tex]

2. Also, as number of sides increases, the smallest regular polygon is equilateral triangle(3 sides) , having 0, diagonal, the number of diagonal increases by 1.

→→Regular polygon having sides , n≥3=k, where k is number of diagonals=0,1,2,3,4,[ For example, for, n=3,k=1,n=4, k=2,...]

Column (2)

[tex]C_{4}-C_{3}=C_{3}-C_{2}=C_{2}-C_{1}=1[/tex]

Column (4)

[tex]C_{2}-C_{1}=90-60=30\\\\ C_{3}-C_{2}=108-90=18\\\\ C_{4}-C_{3}=120-108=12[/tex]

Column (3)

[tex]C_{4}-C_{3}=720-540=180\\\\ C_{3}-C_{2}=540-360=180\\\\ C_{2}-C_{1}=360-180=180[/tex]

In, Column (2) and Column(3) the difference between two consecutive values is same, while in column (4) difference between two consecutive values is not same.So, C(2) and C(3) shows linear relationship, column (4) do not.

Option (C) 2 is Right choice.

Answer:

50

Step-by-step explanation:

Answer: He would need [tex]3\dfrac{1}{3}[/tex] pounds to fill the container all the way.

Step-by-step explanation:

Since we have given that

Fraction of mashed potatoes he had to fill up a container = [tex]\dfrac{4}{5}[/tex]

Fraction of mashed potatoes he ended up using = [tex]2\dfrac{4}{6}=2\dfrac{2}{3}=\dfrac{8}{3}[/tex]

So, we need to find the number of pounds that he would need to fill the container all the way.

So, number of pounds would be

[tex]\dfrac{8}{3}\div \dfrac{4}{5}\\\\=\dfrac{8}{3}\times \dfrac{5}{4}\\\\=\dfrac{10}{3}\\\\=3\dfrac{1}{3}[/tex]

Hence, he would need [tex]3\dfrac{1}{3}[/tex] pounds to fill the container all the way.

Answer:

k/2 − 3/5

Step-by-step explanation:

To simplify the expression 2/5k - 3/5k + 1/10k, we combine the like terms and simplify the fractions. The simplified expression is -1/10k.

To simplify the expression 2/5k - 3/5k + 1/10k, we can combine like terms. Like terms have the same variable raised to the same power. In this case, the variable is 'k'. So, combining the fractions, we get:

(2/5 - 3/5 + 1/10)k

Now, let's simplify the fractions:

Therefore, the simplified expression is -1/10k.

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Answer:

Negative Slope

Step-by-step explanation:

The slope is the ratio of Change in height to the change in horizontal distance. It can also be define as tangent of angle made by that line and it is find by formula, [tex]slope (m)= \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

The slope is said to be a positive slope when a line is moving from left to right, the line rises.

The slope is said to be a negative slope when a line is moving from left to right, the line falls.

Here, Let the student earns be y marks in test

and let incorrect question be x

then y₁ = 98 , y₂ = 90 and x₁ = 1 , x₂ = 5

then [tex]slope (m)= \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

[tex]slope (m)= \frac{90 - 98}{5 - 1} [/tex]

⇒ m = -2

Hence, it has negative slope.

The rational number 7/50 is not equivalent to the other numbers listed (75%, 3/4, 0.75) as it converts to a decimal value of 0.14, which is distinct from 0.75.

The question asks which rational number is not equivalent to the others: 75%, 3/4, 0.75, or 7/50. To determine this, we can convert all the numbers to a common format, such as decimals or fractions, and compare their values.

First, 75% is equivalent to 0.75, as percent means "per hundred," so 75% is 75 per 100, which can be written as 75/100 and simplified to 3/4 or 0.75. Next, 3/4 is exactly 0.75 when converted to a decimal. This means that these three are equivalent to each other.

However, 7/50 is a different case. When we convert 7/50 to a decimal, we get 0.14, which is evidently different from 0.75. Therefore, 7/50 is not equivalent to the other rational numbers listed.

Answer: (3x1/3) x 42

Step-by-step explanation: trust me I took the test.

There are total 1638 marbles.

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

Given:

Number of jars = 3

Each bar contain = 42 marbles

Red marbles = 13

So, total number of marbles

= 3 x 13 x 42

= 1638.

Hence, there are total 1638 marbles.

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Final answer:

To find out how long it will take Nancy to paint the house alone, we calculate her work rate by subtracting Mary's rate from their combined rate. This gives us Nancy's work rate as 5/12 of a house per hour, which means Nancy would take 2.4 hours to paint the house by herself.

Explanation:

To determine how long it would take Nancy to paint the house by herself, we can set up an equation based on the rates of work done by Mary and Nancy together, and by Mary alone. We know that Mary can paint a house in 12 hours, so her work rate is 1/12 of a house per hour. When Nancy helps, together they can paint the house in 2 hours, so their combined work rate is 1/2 of a house per hour.

To find Nancy's work rate, we set up the equation:
1/12 + 1/N = 1/2

Now, we solve for N (Nancy's time to paint the house alone):
1/N = 1/2 - 1/12
1/N = 6/12 - 1/12
1/N = 5/12
N = 12/5
N = 2.4 hours

Therefore, it would take Nancy 2.4 hours to complete the same job by herself.