MATHEMATICS HIGH SCHOOL

Manny's cleaning supply store receives a mixture of 80% detergent and 20% water in 15-gallon buckets. Manny would like a mixture of 60 detergent and 40% water in a 5 gallon buckets. To make this he combined some 80/20 mixture with some pure water in each 5 gallon bucket. How much gallons of pure water does Manny add to each 5 gallon bucket.

Answers

Answer 1
Answer:

Answer:

1.67 gallons

Step-by-step explanation:

Given that:

Original mixture contains 80% detergent and 20% water in a 15 gallon bucket.

New Mixture to contain 60% detergent and 40% water of 5 gallon bucket.

To find:

Volume of Pure water to be added to each 5 gallon bucket to obtain the new mixture.

Solution:

First of all, let us calculate the answer by adding pure water to 15 gallon bucket.

Let the number of gallon of water to be added = x

New volume = (15+x) gallons

Now, let us compare the number of gallons of water in the mixture before and after.

15* 20\% + x = (15+x)* 40\%\n\Rightarrow (3+x)* 5 = (15+x)* 2\n\Rightarrow 15+5x=30+2x\n\Rightarrow 3x=15\n\Rightarrow x =5\ gallons

Therefore, to a 15 gallon bucket (80% detergent and 20% water)of detergent mixture, if we add 5 gallons of pure water , it will become 60% detergent and 40% water.

To a 5 gallon bucket, the number of gallons of water to be added = (5)/(3) =\bold{1.67\ gallons}

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Ellie is going to a carnival that has games and rides. Each game costs $2.50 and each ride costs $3.50. How much would Ellie have to pay if she wanted to play 5 games and go on 7 rides? How much would Ellie have to pay if she wanted to play xx games and go on yy rides?5 games and 7 rides:

Answers

1 game (x) = 2.50

1 ride (y) = 3.50

5x + 7y

5(2.50) + 7(3.50)

12.50 + 24.50

37

Ellie would have to pay $37 to play 5 games and go on 7 rides.

Hope this helps!! :)

Answer:

$37

Step-by-step explanation:

You are given the prices of the games and the rides.

First you find the games. Since there are 5 games, you do 2.50 * 5. This gives you 12.5. She would have to have $12.50 to spend.

Next, you do the rides. There are 7 rides, each for 3.50, so you do 3.50 * 7, giving you 24.50. She would have to have $24.50 to spend on rides.

Now the question asks how much she would have to pay to do both. This means you add your values:

12.5 + 24.5 = $37.

If a certain medicine cures 90% of the people who take it, what is the probability that if 9 people take the medicine that 6 will be cured?A) 0.01
B) 0.02
C) 0.04
D) 0.33

Answers

This is an example of binomial distribution probability. The probability that a person gets cured by the medicine (p) is 90% or 0.9. The probability that a person does not get cured by the medicine (q) is 100 - 90 = 10% = 0.1. The probability of a binomial distribution is given by nCx (p)^x (q)^(n - x); where n is the sample size, x is the number of success, p is the probability of success, and q is the probability of failure. Therefore, the probability that out of 9 people that takes the medicine, 6 will be cured is given by 9C6 (0.9)^6 (0.1)^3 = 84 x 0.531441 x 0.001 = 0.0446. Therefore, option C (0.04) is the correct answer.

option C (0.04) is the correct answer

What is the highest common factor of 12 and 49?

Answers

12|2\n.\ 6|2\n.\ 3|3\n.\ 1|\n==========\n49|7\n.\ 7|7\n.\ 1|\n==========\n\nHCF(12;\ 49)=1
Factors of 12 . . . . . 1, 2, 3, 4, 6, 12

Factors of 49 . . . . . 1, 7, 49

Common factors . . . 1

Highest common factor . . . 1

35, 0.68, 0.20, 0.31 ordered greatest to least

Answers

0.20, 0.31, 0.68, 35.0

By what fraction name for 1 must 2/3 be multiplied to form a fraction with a denominator of 15

Answers

If you are asking what I think than it should be 5/5 because 3*5=15 so in that case the denominator would be 15 making the whole answer 10/15 although that could still be simplified to 2/3) (that's what happens when you multiply by one) 

Or you may be asking 1/x forms a denominator of 15.
In this case you would still have 5 as your number (or really 1/5), if would just mean when they are multiplied together you would get 2/15 instead....

I NEED HELP ASAP (A new pizza shop opened up and started out$5,344.46 in the hole. Their first month being open they sold 61 pizzas ($3.06 profit each) and 89 sodas ($1.42 profit each). Thier bills for the first month were $1,208.01. How much money do they still need to make to break even?

Answers

Answer:

$894.97 is needed more to break even

Step-by-step explanation:

In this question, we want to know how much money the pizza shop need so that their profits will equal their expenses.

Let’s calculate their profit

This can be calculated from the pizza sales

That would be;

61(3.06) + 89(1.42) = $186.66 + $126.38 = $313.04

Now, given that their bills for the first month is $1,208.01, the amount still needed to break even would be the amount of their bills minus the profit made from selling soda and pizza

That would be 1,208.01 - 313.04 = $894.97
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