Suppose you had 7 counselors available. How many campers could you have?

In 1962, the average cost of 1 gallon of gasoline in the United States was $0.31. The cost of gasoline increased by an average o

Kobotan [32]

Answer:

3*10=30.

Step-by-step explanation:

increased by 3% each year for 10 years

increased 30%.

0.31*0.30= .92

7 0

3 years ago

the length of a side of a square is 10x+4 units. If the perimeter is 96 units. What is the area of the square?

dmitriy555 [2]

Answer:

576 Units

Step-by-step explanation:

The way your teacher wants you to do it:

1. We know that multiplying a length by four gives us the perimeter of a square.

1a. Thus, we multiply the given length by four. 4(10x+4)=40x+16

1b. We know the perimeter is 96. So: 40x+16=96

2. Solving for x, we get x=2

3. Plugging our solved x into the given length (10x+4), we see that the length of a side of the square is 10*2+4=24.

4. We know that the area of a square can be found by squaring the side of a square.

4a. 24*24=576.

5. The area is 576 units.

--------------------------------------------------------------

Easier Solution:

1. We know that the perimeter is length*4.

2. We set L to length.

2a. 4L=96

2b. L=24

3. We know that the length square is area.

4. 24*24=576.

4 0

3 years ago

A student committee is to consist of 2 freshmen, 5 sophomores, 4 juniors, and 3 seniors. If 6 freshmen, 13 sophomores, 8 juniors

mezya [45]

<h3>Answer: 491,891,400</h3>

Delete the commas if necessary.

============================================================

Explanation:

There are 6 freshmen total and we want to pick 2 of them, where order doesn't matter. The reason it doesn't matter is because each seat on the committee is the same. No member outranks any other. If the positions were labeled "president", "vice president", "secretary", etc, then the order would matter.

Plug n = 6 and r = 2 into the nCr combination formula below

$n C r = \frac{n!}{r!(n-r)!}\\\\6 C 2 = \frac{6!}{2!*(6-2)!}\\\\6 C 2 = \frac{6!}{2!*4!}\\\\6 C 2 = \frac{6*5*4!}{2!*4!}\\\\ 6 C 2 = \frac{6*5}{2!}\\\\ 6 C 2 = \frac{6*5}{2*1}\\\\ 6 C 2 = \frac{30}{2}\\\\ 6 C 2 = 15\\\\$

This tells us there are 15 ways to pick the 2 freshmen from a pool of 6 total.

Repeat those steps for the other grade levels.

n = 13 sophomores, r = 5 selections leads to nCr = 13C5 = 1287. This is the number of ways to pick the sophomores.

You would follow the same type of steps shown above to get 1287. Let me know if you need to see these steps.

Similarly, 8C4 = 70 is the number of ways to pick the juniors.

Lastly, 14C3 = 364 is the number of ways to pick the seniors.

-----------------------------

To recap, we have...

15 ways to pick the freshmen
1287 ways to pick the sophomores
70 ways to pick the juniors
364 ways to pick the seniors

Multiply out those values to get to the final answer.

15*1287*70*364 = 491,891,400

This massive number is a little under 492 million.

7 0

2 years ago

Nathaniel has $2 worth of dimes and quarters. He has 6 more dimes than quarters. By following the steps below, determine the num

Aleksandr-060686 [28]

Answer:

10 dimes and 4 quarters

Step-by-step explanation:

Number of dimes = d, each d = 10 c
Number of quarters = q, each q = 25 c
Total = $2 = 200 c

<u>Equations according the given:</u>

10d + 25q = 200
d = q + 6

<u>Solve for q by substitution:</u>

10(q + 6) + 25q = 200
10q + 60 + 25q = 200
35q = 140
q = 140/35
q = 4

<u>Find the value of d:</u>

d = 4 + 6 = 10

Nathaniel has 10 dimes and 4 quarters

8 0

3 years ago

What is 8 meters increased by 20%

NeX [460]

8 increased by 20% is 9.6 i hope this helps :)

8 0

3 years ago