21 people are going to the show. They have 3 vans and 1 car. If 6 people fit in each van, how many will have to ride in a car?

Question 8 options:

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6

0.4(3b +10) = 19

1.2b + 4 = 19

1.2b = 15

b = 15 / 1.2

b = 12.5

Lines r and s are parallel based on the given measure of angles 2 and 6.

Based on the given information, if the measure of angle 2 is 110° and the measure of angle 6 is also 110°, then it can be concluded that lines r and s are parallel. This conclusion is based on the Alternate Interior Angles Theorem, which states that if a transversal intersects two parallel lines, then the alternate interior angles are congruent.

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After setting up a system of equations and solving them simultaneously, the two numbers are found to be 42 and 48.

To find the two numbers where the sum is 90 and where 20 added to three times the smaller number exceeds twice the larger number by 50, we can set up a system of equations. Let x be the smaller number and y be the larger number. The first equation based on the sum of the numbers will be:

x + y = 90

The second equation derived from the condition involving multiplication and addition will be:

3x + 20 = 2y + 50

Solving these two equations simultaneously, we start by rearranging the first equation to find y:

y = 90 - x

Next, we substitute this expression for y into the second equation:

3x + 20 = 2(90 - x) + 50

Simplify and solve for x:

3x + 20 = 180 - 2x + 50

5x = 210

x = 42

Now substitute x back into the equation for y:

y = 90 - 42

y = 48

The two numbers are 42 and 48.

A. [tex]\[ T = C + G \times P \][/tex]

B. they will spend $748.95 before sales tax.

C. [tex]\[ T = C + G \times P + K \times R \][/tex]  

D. The total cost before sales tax if Homer and Bart purchase one computer, five games, and three extra controllers would be $823.92.

PART A:

Let us define the variables:

- C: Cost of the computer ($499.00)

-  G : Number of games

-  P : Cost of one game ($49.99)

-  T : Total cost before sales tax

The algebraic expression to describe how much they will spend before sales tax based on purchasing the computer and the number of games is:

[tex]\[ T = C + G \times P \][/tex]

PART B:

If they purchase one computer and five games, we substitute G = 5  into the expression:

[tex]\[ T = 499 + 5 \times 49.99 \][/tex]

Now, we can calculate:

[tex]\[ T = 499 + 5 \times 49.99 \]\[ T = 499 + 249.95 \]\[ T = 748.95 \][/tex]

So, they will spend $748.95 before sales tax.

PART C:

Let's define an additional variable:

-  K : Number of extra controllers

-  R: Cost of one extra controller ($24.99)

The algebraic expression to describe how much they spend in total before sales tax when they purchase one computer, any number of games, and any number of extra controllers is:

[tex]\[ T = C + G \times P + K \times R \][/tex]

If they purchase one computer, five games, and three extra controllers, we substitute  G = 5  and  K = 3  into the expression:

[tex]\[ T = 499 + 5 \times 49.99 + 3 \times 24.99 \][/tex]

PART D:

Now, we can calculate:

[tex]\[ T = 499 + 5 \times 49.99 + 3 \times 24.99 \]\[ T = 499 + 249.95 + 74.97 \]\[ T = 499 + 324.92 \]\[ T = 823.92 \][/tex]

So, the total cost before sales tax if Homer and Bart purchase one computer, five games, and  three extra controllers would be $823.92.

Answer: 6.121212121212... = 202/33

Step-by-step explanation:

(612 - 6)/99 = 606/99 = 202/33 = 6.12121212121212... ∈ ℚ

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.  

Since 6.121212121212... is a number whose digits are periodic (12) , we can express it as a fraction 202/33, therefore is a rational number ∈ℚ.

[tex]\textit{\textbf{Spymore}}[/tex]

Answer:

The value of the equation for y is [tex]y=\frac{-\pi+7x}{2}[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex] \pi=7x-2y[/tex]  

We need to solve the equation for y.

Subtract 7x to both sides of the equation.

[tex] \pi-7x=7x-7x-2y[/tex]  

[tex] \pi-7x=-2y[/tex]

Divide both the sides by -2.

[tex] \frac{\pi-7x}{-2}=\frac{-2y}{-2}[/tex]

[tex]y= \frac{\pi-7x}{-2}[/tex]  

[tex]y=\frac{-\pi+7x}{2}[/tex]  

Hence, the value of the equation for y is [tex]y=\frac{-\pi+7x}{2}[/tex].

Tom volunteered 18 hours at the Salvation Army, 37 hours at the Red Cross, and 45 hours at the Rescue Mission.

Let S represent the number of hours Tom served at the Salvation Army.

Since the total number of hours Tom served is 100, we have,

S + R + M = 100

Substitute R and M with the expressions in terms of S:

S + (S + 19) + (S + 19 + 8) = 100

S + S + 19 + S + 27 = 100
3S + 46 = 100
3S = 54
S = 18

So, Tom served 18 hours at the Salvation Army. Now, we find the hours for the other two charities,

In summary, Tom volunteered 18 hours at the Salvation Army, 37 hours at the Red Cross, and 45 hours at the Rescue Mission.

Complete question-
Tom performed a total of 100 hours of community service. He served at three charities – Salvation Army, Red Cross and Rescue Mission. The number of hours he served at the Red Cross was 19 hours more than at the Salvation Army. The number of hours he served at the Rescue Mission was 8 hours more than what he served at the Red Cross. Find the number of hours he volunteered at each charity.

Two lengths within the average range for a ladybug could be 0.2 inches and 0.35 inches, both of which are between the minimum of 0.08 inches and the maximum of 0.4 inches.

The average length of a ladybug can range from 0.08 to 0.4 inch. To find two lengths that are within the given span, we can select any two numbers that fall between these two values. For instance:

These lengths are examples of measurements that would fall within the typical size range of a ladybug.

Final answer:

To find how many cans and bottles Reggie collected, we consider the 360 cans and bottles Tanner collected as 40% of Reggie's collection. After setting up an equation and solving it, we determine that Reggie collected a total of 900 cans and bottles.

Explanation:

Tanner collected 360 cans and bottles, which was 40% of what Reggie collected. To find out how many cans and bottles Reggie collected, we'll use the concept of percentage. Since 40% equals 0.40 in decimal form, we can represent the total number Reggie collected as 100%, which is 1 when converted to decimal form.

Therefore, if Tanner collected 360 cans and bottles and this is 40% of Reggie's amount, we can set up the equation:

360 = 0.40 × (Total number of cans and bottles Reggie collected)

To solve for the total number, we divide both sides of the equation by 0.40:

Total number of cans and bottles Reggie collected = 360 ÷ 0.40

After the division, we find that:

Total number of cans and bottles Reggie collected = 900

Answer:

its A

Step-by-step explanation:

n/6 = 10/15

n = 10/15 * 6

n = 10*6 =60,  60/15 = 4

n = 4