3. Volunteer drivers are needed to bring 80 students to the championship baseball

game. Drivers either have cars, which can seat 4 students, or vans, which can seat 6

students. The equation 40 + 6v = 80 describes the relationship between the number

of cars, c, and number of vans, v, that can transport exactly 80 students.

Select all statements that are true about the situation.

A. If 12 cars go, then 2 vans are needed.

B. c = 14 and v= 4 are a pair of solutions to the equation.

C. If 6 cars go and 11 vans go, there will be extra space.

D. 10 cars and 8 vans isn't enough to transport all the students.

E. If 20 cars go, no vans are needed.

F. 8 vans and 8 cars are numbers that meet the constraints in this situation.

Answers

Answer 1

Answer:

Options (B), (C) and (E) are the correct options.

Step-by-step explanation:

Equation that represents relation between the number of cars c and the number of vans v to transport 80 students is,

4c + 6v = 80

Option A.

If c = 12,

4(12) + 6(v) = 80

48 + 6v = 80

6v = 32

[tex]v=\frac{16}{3}[/tex]

Which is not equal to 2.

Therefore, Option A is incorrect.

Option B

If c = 14,

4(14) + 6(v) = 80

56 + 6v = 80

6v = 24

v = 4

Therefore, c = 14 and v = 4 is a pair of solutions.

Option B is correct.

Option C.

If c = 6 and v = 11

4(6) + 6(11) = 24 + 66

                 = 90

This means with 6 cars and 11 vans 90 students can be transported. Therefore, there will be extra space.

Option C is correct.

Option D.

If c = 10 and v = 8

4(10) + 6(8) = 40 + 48

                  = 88

Therefore, 10 cars and 8 vans are enough to transport 80 students.

So option D is incorrect.

Option E.

If c = 20,

4(20) + 6(v) = 80

80 + 6v = 80

v = 0

Therefore, for 20 cars go no vans are needed.

Option E is correct.

Option F.

Constraints in this situation,

Minimum number of cars to be used = 20

c ≥ 20

Minimum number of vans to be used = [tex]\frac{80}{6}[/tex] ≈ 14

v ≥ 14

Therefore, Option (F) is incorrect.


Related Questions


can Yhu help me plzzz!!!!

Answers

Answer:

f^-1 (x) =7 − 21x

Step-by-step explanation:

Hope this helps!

Plz give brainliest

There are y boats on lake there are 6 people in each boat write an expression in terms of y for the total number of people in the boats

Answers

Answer:

6y

Step-by-step explanation:

There are 6 people in each boat and y boats. So, there would 6y people total.

ex:

There are 24 boats.

24 x 6 = 144

How much work is done if a person carries 5n of candy 25m when trick or treating

Answers

The amount of work done if a person carries 5n of candy 25m when trick or treating is 125.

In order to determine the amount of  work done we are going to multiply the force by the distance.

Using this formula

 

Work done = Force  x Distance

 

Where:

Force = 5n

Distance  = 25m

Let plug in the formula

Work done = 5 x 25

Work done= 125

Inconclusion the amount of work done if a person carries 5n of candy 25m when trick or treating is 125.

Learn more here:

https://brainly.com/question/18818154

The work done  if a person carries 5n of candy 25m when trick or treating is; 125 J.

We are given;

Force carried; F = 5n

Distance covered; d = 25 m

Now, the formula for work done is given as;

Work done = Force × Distance

Thus;

Work done = 5 × 25

Work done = 125 N.m

In conclusion, the work done  if a person carries 5n of candy 25m when trick or treating is 125 N.m or 125 J.

Read more at; https://brainly.com/question/18818154

Are any of these numbers an Integer?
15
20/5
44
13/19
-35.47
;w; help

Answers

Answer: 15, and 44 are integers.

Step-by-step explanation: For 15 to be an integer, 15 has to be a whole number. Furthermore, for 15 to be an integer, you should be able to write 15 without a fractional or decimal component. 15 is a whole number that can be written without a fractional component, thus 15 is an integer, as well as 44.

15 and 44

An integer is a whole number that is not a fraction since all the other numbers are not a whole your answer is 15 and 44.

NEED HELP!! 25 POINTSS!!!

Answers

Answer:0 is the answer duh it has the answer on it

Step-by-step explanation:

*I am kinda Confused by the question. . . because the answers are already on it*

Answer:

X(remainder)2  +  4 × "X"  +  3 = 0

X(remainder)2  -  5 × "X"  +4 = 0

X(remainder)2  -  49 = 0

4 × "X"(remainder)2  -  25 = 0

2 × "X"(remainder)2  +  7 × "X"  +  3 = 0

Explanation:

Sorry if it didn't Help at All, I tried . . . Sorry  :(

joey has 12 basketballs, which is three times as lisa. lisa has y basketballs. write this situation as an equation

Answers

Answer:

12x3=y

Step-by-step explanation:

i am sure there r other ways to write an equation  but this is mines: 12x3=y bc 12 is the number of the basketball joey has and they r saying lisa has 3 times more. it tells us the answer is is 3 times more then 12. i recommend u for these problems take them part by part and then set it up.

Answer:

12x3= what

Step-by-step explanation

there r multiple ways to solve this problem

Which is NOT a common denominator for 2/3 and 1/2 ?

A. 18
B. 12
C. 6
D. 3

Answers

Answer:

D: 3

Step-by-step explanation:

2 is not a factor of three

The number 3 can not be the common denominator for 2/3 and 1/2. The correct option is D.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. The number of components of a specific size is expressed as a fraction.

The fractions will have all the numbers 18, 12, and 6 as the common denominator but can not have 3 as a common denominator.

Therefore, the number 3 can not be the common denominator for 2/3 and 1/2. The correct option is D.

To know more about fractional expression follow

https://brainly.com/question/78672

#SPJ5

I need help fast .
(- 4, 2), (- 2, 5) and (0, 1) slides the triangle 3 units to the right to create an image . What are the vertices of the image ?

Answers

(-4,2) goes to (-1,2) (-2,5) goes to (1,5) and (0,1) translates to (3,1)

The expression 2.5a+2b gives the cost (in dollars) for a DVDs and b CDs at a moving sale. a. The cost for 1 DVD is $ and the cost for 1 CD is $ . b. The total cost for 4 DVDs and 4 CDs is $ . Question 2 c. Is $20 enough to buy 6 DVDs and 3 CDs?

Answers

Answer/Step-by-step Explanation:

Given:

a = no. of DVDs

b = no. of CDs

Total cost ($) for DVDs and CDs = [tex] 2.5a + 2b [/tex]

a. The cost for 1 DVD = 2.5(a) = 2.5(1) = $2.5

The cost for 1 CD = 2(b) = 2(1) = $2

b. Total cost for 4 DVDs and 4 CDs:

Substitute a = 4, and b = 4 into the equation.

[tex] 2.5(4) + 2(4) [/tex]

[tex] 10 + 8 = 18 [/tex]

Total cost for 4 DVDs and 4 CDs = $18

c. To find out if $20 would be enough to buy 6 DVDs and 3 CDs, substitute a = 6, and b = 3 into the equation. Solve for the total cost to see if it equals $20 or is less than $20. If it's greater than $20, then it won't be enough.

[tex] 2.5(6) + 2(3) [/tex]

[tex] 15 + 6 = 21 [/tex]

6 DVDs and 3 CDs cost more than $20, therefore, $20 is not enough.

10.
There are estimated 255 births every minute of every day. How many babies are born in the
world each hour?
255
6,120
12,250
15,300

Answers

Answer:

15,300

Step-by-step explanation:

multiply the estimated total number of births (255)

times 60 because there is 60 minutes in an hour

255*60= 15,300

Answer:

15,300

Step-by-step explanation:

1 hour: 60 minutes

60 x 255 = 15,300

following expression of -9(3x-7)

Answers

Answer:

-27x+63

Step-by-step explanation:

you do -9 times 3x then -9 times -7, two negatives creates a positive, and so 9 times 7 equals 63

hope this helps :^)

-9(3x-7)

Multiply each term in the parentheses by -9

-9×3x-9×(-7)

Calculate the product

-27x-9×(-7)

now we do the same thing only different way ok

-9×3x

Multiplying a negative and a positive equals a negative : (-)x(+)=(-)

-(9×3)x

Multiply the numbers

-27x

-9×3x-9×(-7)

Multiply the numbers

-27x+63

Now we do the same thing only different way ok

-9×(-7)

Multiply two negatives equals a positive: (-)×(-)=(+)

9 × 7

multiply the numbers

63

Solution: -23x+63

PLEASE MARK ME AS BRAINLIEST

Who can help me find the slope to the graph? Please help it’s due soon

Answers

1/2 cuz it goes down 1 and over 2

Tickets to the varsity basketball game cost $4 for students, but adults pay $6, and discount tickets are $5 for senior citizens and active military. At a recent game, 353 tickets were sold for a total of $1,660. If there were twice as many student tickets sold as adult tickets, what system of equations could be used to find how many of each type of ticket were sold?

Answers

Answer:

4s + 6a + 5c = 1,660

s = 2a

s + a + c = 353

Step-by-step explanation:

s = # of student tickets bought

a = # of adult tickets bought

c = # of senior citizen tickets bought

During summer, when the snow melts, the water level of the Yukon River increases. If the water level of the river increased by 84 centimeters in 6 days, what is the water level increase rate in centimeters per day?

Answers

Answer:

14 cm per day

Step-by-step explanation:

To find the water level increase rate in cm per day, divide 84 by 6, since it increased by 84 cm in 6 days:

84/6

= 14

So, the water level increase rate in 14 cm per day

whaty is the answer to the given qurestion

Answers

Answer: The answer is D, unless I am extremely dumb

Step-by-step explanation: The x is going by 2 so, the next would be 11, and the y is going by one so the next would be 19.

The distance between Walmart and Mrs. Stivers house is 8km. There are 1.6
km in 1 mile. How many miles apart is Mrs. Stivers house and Walmart?

Answers

Answer:

5 miles

Step-by-step explanation:

Divide 8 by 1.6 and the answer is 5. I hope this helped:)

If f(x)=-3x-8 find f(-1)?

Answers

f(-1)=3(-1)-8
f(-1) = -11
f = 11
:)

if Jonah needs 28 sec to fold 2 shirts how long would it take him to fold 5

Answers

It takes him 70 seconds.

Answer:

70 sec (1 min 10 sec)

Step-by-step explanation:divide 28 by 2 and get 14 and multiply that by 5 to get 70 sec

Show or tell work for brainlest and thank and 5.0 rate and follow

Before making invitations, katrina counted the supplies she bought for her party. She counted 36 water balloons and 81 beads to make bracelets. She then needed to decide how many invitations to make.

A. 6

B. 7

C. 9

D. 10

Answers

Answer:

9

Step-by-step explanation:

because they are both dividable by nine

Answer:

the answer is c.9

Step-by-step explanation:

if she has 36 water balloons divide 36 by 4 and then you get 9 then divide 81 9 and get 1 so 9 is the answer

James has $40 to spend. He wants to buy 2 tickets to a show. He has to spend $7 to get where tickets are sold. The following inequality can be used to find out the highest price James can afford to pay for each ticket. 2x+7 less than or equal to 40.
A.) x less than or equal to 23.5
B.) x less than or equal to 16.5
C.) x greater than or equal to 23.5
D.) x greater than or equal to 16.5

Answers

Answer:

B.) X less than or equal to 16.5

Step-by-step explanation:

If you take his limit, 40 and subtract the 7 dollars you will get 33. Then, divide that by two because he will need two tickets and you will get 16.5. It can't be greater than 16.5 because he will go over his budget.

Answer:

x ≤ 16.5

Step-by-step explanation:

40 ≤ 2t + 7 Subtract 7 from both sides.

40 - 7 ≤ 2t + 7 - 7

33 ≤ 2t Divide both sides by 2.

[tex]\frac{33}{2}[/tex] ≤ [tex]\frac{2t}{2}[/tex]

16.5 ≤ t or t ≥ 16.5

the give reasoning part for this is not correct. does anyone know the right answer

Answers

Answer:

80 degree angle while  second has a 50 degree angle(looks like an icecream cone)

Step-by-step explanation:

Answer:

They aren't equivalent, they're congruent. That's why it marked your answer wrong.

Step-by-step explanation:

by which rule are these triangles congruent ?
A) AAS
B) ASA
C) SAS
D) SSS

Answers

B ) ASA
I just solved that

Answer:

ASA

Step-by-step explanation:

Just answered this question

Find the vertex form,axis of symmetry,and vertex for y=2(x-2)^-3

Answers

hi there! here's my answer for you...

i do not think there is an answer since the equation you have given is not a conic section. therefore, there is no vertex form, axis of symmetry, or vertex.

hope this helped. have a good one!

Can anybody please help me

Answers

the answer to the question would be B

Answer: B

Step-by-step explanation:

We have to find the amount that Maya painted IN ALL, which means we must add 3/4 and 1/8. First, look for the answer choice that has 1/8 as a number (B and A). However, none of the answer choices have 3/4 as an answer, so we must convert it into an equivalent fraction, 6/8. You get 6/8 by multiplying both the numerator and denominator by 2. Therefore the answer is B.

which is the graph of the exponential function y=8(5)^x?

Answers

Answer:

y=8(5)^(x)

Step-by-step explanation:

please help me 30 points

Answers

Answer:

Hope your having a great day.

Step-by-step explanation:

God Bless, and try not to stress to much about school your doing great :)

A ball is dropped and bounces to a height of 5 feet. The ball rebounds to 70% of its previous height after each bounce The function that could be used to model the nth term in the sequence of heights of the ball after the initial drop is

Answers

Answer:

[tex]T_n = 7.143(0.7^n)[/tex]

Step-by-step explanation:

If a ball bounces to a height of 5feet, the initial drop = 5feet

If the ball rebounds to 70% of its previous height after each bounce, the next height after rebouncing will be expressed as;

= 70% of 5

= 70/100 * 5

= 0.7*5

= 3.5 feet

The next height will be 0.7*3.75 = 2.45 and so on

The  heights wil form a sequence as thus;

5, 3.5, 2.45...

This sequence forms a geometric progression.

To get the function that could be used to model the nth term in the sequence of heights of the ball after the initial drop, w will find the nth term of the sequence

[tex]T_n = ar^{n-1}[/tex]

a is the first term of the sequence

n is the number of terms

r is the common ratio

From the sequence:

a = 5

[tex]r = \frac{3.5}{5} = \frac{2.75}{3.5} = 0.7[/tex]

Substitute the given values into the formula

[tex]T_n = 5(0.7)^{n-1}\\T_n = 5(\frac{0.7^n}{0.7^1} )\\T_n = \frac{5}{0.7}\times 0.7^n \\T_n = 7.143(0.7^n)[/tex]

The nth tern=m required is [tex]T_n = 7.143(0.7^n)[/tex]

A giraffe's height is 5 meters 40 centimeters.

How tall is the giraffe in millimeters?

Answers

Answer:

5400 mm

Step-by-step explanation:

URGET! PLEASE HELP ASAP! WILL GIVE BRAINLIST! Complete the description of the piecewise function graphed below

Answers

Answer: f(x) = -3 if -4 ≤ x ≤ -1

Explanation: The filled in circles mean that solution is possible, so you use the equal to sign.

Hope this helps!

3.2% is equivalent to what fraction in reduced terms?

Answers

Answer:

3 1/5

Step-by-step explanation:

I think the fraction will be 16/5
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