Three of four numbers have a sum of 22. If the average of the four numbers is 8, what is the fourth number?

Answers

Answer 1

Answer: $a+b+c=22\n \n (a+b+c+x)/(4)=8\n \n a+b+c+x=32\n \n 22+x=32\n \n \boxed{x=10}$

Answer 2

Answer:

Answer:

Step-by-step explanation:

Let's call the four numbers x1, x2, x3, and x4. Their average is (x1 + x2 + x3 + x4)/4 = 8, so x1 + x2 + x3 + x4 = 4 × 8 = 32. And we know that three of the numbers have a sum of 22, so x1 + x2 + x3 = 22.

Subtracting this last equation from the first equation, we have:

$\sf:\implies{x4 = 32 - (x1 + x2 + x3) = }$

$\sf:\implies{32 - 22 = 10}$

So the fourth number is 10.

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Which of the following points lie in the solution set to the following system of inequalities?y < −3x + 3
y < x + 2
(1, −5)
(1, 5)
(5, 1)
(−1, 5)

Answers

Answer with Step-by-step explanation:

We have to find the points which lie in the solution set of the following system of inequalities:

y < −3x + 3

y < x + 2

(1, −5)

when x=1

y < −3x + 3⇒ y<0

y < x + 2⇒ y<3

and y= -5 satisfies the above inequalities

So, it lies in the solution set

(1, 5)

when x=1

y < −3x + 3⇒ y<0

y < x + 2⇒ y<3

and y= 5 does not satisfy the above inequalities

So, it does not lie in the solution set

(5, 1)

when x=5

y < −3x + 3⇒ y< -12

y < x + 2⇒ y<7

and y= 1 does not satisfy the above inequalities

So, it does not lie in the solution set

(−1, 5)

when x= -1

y < −3x + 3⇒ y<6

y < x + 2⇒ y<1

and y= 5 does not satisfy the above inequalities

So, it does not lie in the solution set

Hence, Correct answer is:

(1,-5)

(1,-5) would be the answer. I used a graphing calculator to solve this. I plugged in the equation and looked at the intersection of the 2 graphs. Hope this helps.

A basketball player makes 75% of her free throws. If she made 84 free throws this season, how many has she attempted?

Answers

If you would like to know how many free throws did a basketball player attempted, you can calculate this using the following steps:

75% of x is 84
75% * x = 84
75/100 * x = 84
x = 84 * 100 / 75
x = 112 free throws

The correct result would be 112 free throws.

A bowling alley charges $3.50 per game plus $5 to rent shoes. A second bowling alley charges $5 per game plus $2 to rent shoes. Howmany games would a person have to play for the two bowling alleys to cost the same amount?

Answers

Answer:

2 games for both bowling alleys to cost the same amount

Ryan has some nickels and dimes. Altogether, he has 34 coins that total $2.60. Write the system of equations to determine how many of each coin he has.

Answers

34= n+d
2.60=.05n+.1d

To find the amount of dimes that Ryan uses, I used (2.60/0.10) to get 26 dimes, meaning that there are also 8 nickels.

So in total, you have 26 dimes and 8 nickels

Hope this helps

PLEASE HELPPP!You’re buying hand lotion. The lotion comes in rectangular pyramid-shaped bottles. Bottle A has a base of 1 in x 2 in, and a height of 6 in. Bottle B is a wider bottle with a base of 1.5 in x 3 in, and a height of 4 inches. Which bottle has more lotion?

Answers

Answer:

Bottle B has a larger volume of lotion therefore the correct answer

Step-by-step explanation:

1×2×6=12/3=4 Bottle A

1.5×3×4=18/3=6 Bottle B

Answer:

Bottle B contains 6 in3 of lotion, and Bottle A contains 4 in3. Bottle B contains more.

Step-by-step explanation:

What is 25% of 860 i remember percentages just need touch up how to do them

Answers

The thing you need to remember is that 25% means 0.25 .
That's the whole problem. The rest is easy.

0.25 x 860 = 215

To find 25% of something you have to divide it by 4. So 860 divided by 4 = 215
Hope this helped! :)
Remember:
100% = 1 = 1
75% = 3/4 = 0.75
50% = 1/2 = 0.5
25% = 1/4 = 0.25
10% = 1/10 or 10/100 = 0.1
1% = 1/100 = 0.01

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