At a constant rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?

Answers

Answer 1

Answer:

Answer: 12 minutes

Step-by-step explanation:

This is a standard Work Formula question (2 or more 'entities' that work on a task together). When there are just 2 entities and there are no 'twists' to the question, we can use the Work Formula to get to the correct answer.

Work = (A)(B)/(A+B) where A and B are the individual times needed to complete the task.

We're told that two hoses take 20 minutes and 30 minutes, respectively, to fill a pool. We're asked how long it takes the two hoses, working together, to fill the pool.

(20)(30)/(20+30) = 600/50 = 12 minutes to fill the pool.

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The total commission, in dollars, Jessie earned on selling cars at a dealership in two weeks is given by the expression 800+400x. She earns the same amount of commission per car each week. Which situation could be described by this expression?Jessie earned a total commission of $800 in the first week and x dollars in the second week.Jessie sold 2 cars in the first week and x number of cars in the second week, earning a commission of $400 on each car.Jessie sold 1 car in the first week, earning $800, and x number of cars in the second week, earning a total commission of $1,200.Jessie earned a commission of $800 on each car in the first week and $400 on each car in the second week, selling x number of cars each week.

Distance between -5.4 and -3.8

Answers

Answer:

1.6

Step-by-step explanation:

In order to find the distance all you need to do is subtract the two numbers

so you would:

-5.4-(-3.8)=-1.6 or 1.6 since distance is not negative number.

A interesting fact to note is when you are subtracting negatives you can also just add the number as a positive

Ex.

5 - (-2) =7

5+2=7

Final answer:

The distance between -5.4 and -3.8 is found by taking the absolute difference of these two numbers, which results in 1.6.

Explanation:

To find the distance between two numbers on a number line, we subtract the smaller number from the larger one and take the absolute value. Here, the smaller number is -5.4, and the larger number is -3.8. Therefore the absolute difference or distance between these two numbers would be |-5.4 - (-3.8)| which equals to |-5.4 + 3.8| = |-1.6|= 1.6. Hence, the distance between -5.4 and -3.8 is 1.6.

Learn more about distance between numbers here:

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If the function h(x) represents the number of full hours that it takes a person to assemble x sets of tires in a factory, which would be an appropriate domain for the function?1) the set of real numbers
2) the set of negative integers
3) the set of integers
4) the set of non-negative integers

Why?

Answers

Of course the D answer is correct.
The number of sets of tires must be a whole number. It can't be real number because it is impossible to assemble for example 3.2321 set of tires.The negative -- it certainly also isn't possible. The amount can't be a negative number that's why C isn't correct as well.

On 4-7 how do you write the ratio and find the answer?

Answers

Basic trig concepts you have to keep in mind:
SOH CAH TOA
Sine: Opposite of the angle over the hypotenuse
Cosine: Adjacent over hypotenuse
Tangent: Opposite over adjacent
I'll do one of the problems, you should be able to do the rest (It's good practice ;))
$sin(L) = 12/15$

A grocery store manager uses 1/2 crate of apples for every 3/4 crate if oranges in a fruit display. How many crates of oranges will she need if she uses 2 1/2 crates of apples?

Answers

Answer:

15/4

Step-by-step explanation:

This is a proportion question

It says 1/2 crates of apple are used for every 3/4 crates of oranges

For 5/2 crates of apple, x crates of oranges will be needed.

To get x, we simply multiply 1/2 by x and equate it to 3/4 multiplied by 5/2

This means: 0.5x = 0.75 × 2.5

x = ( 0.75 × 2.5 ) ÷ 0.5 = 3.75

Hence for 5/2 crates for apple, she will need 15/4 crates of oranges.

Answer:

Step-by-step explanation:

You would first make a proportion.

.5/.75 = 2.5/x

So, .5x = 1.875

x = 15/4

If we divide the polynomial x4 + 4x3 + 2x2 + x + 4 by x2 + 3x, what will be the remainder?

Answers

$x^4+4x^3+2x^2+x+4 = Q(x)\cdot (x^2+3x)+ax+b,\;we\;need\;to\;find\;a,\;and\;b;\n\nx^4+4x^3+2x^2+x+4 = Q(x)\cdot x\cdot (x+3)+ax+b$

If you choose x = 0, then we have 4 = Q(0)*0 + a*0 + b, therefore b = 4.

If we choose x = -3, then we have:

$(-3)^4+4\cdot (-3)^3+2 \cdot (-3)^2-3+4 = Q(-3)\cdot (-3)\cdot (-3+3)-3a+4\Rightarrow 81-108+18+1=4-3a,\;or\;-12=-3a,\;so\;a=4.$

The remainder is: 4x+4.

Green eyes.

. Lisa spent $67 for a skateboard and $25 for a protective helmet.. . . . What percent of the total amount that Lisa spent was the price of the skateboard? A. . . 62.7%. . . . . . . . .
B. . . 72.8%. . . . . . . . .
C. . . 75%. . . . . . . . .
D. . . 81.7%. .

Answers

Total amount: $67 + $25 = $92
p = ( 67 x 100 ) : 92 = 72.826 ≈ 72.8 %
Answer: 72.8 %

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