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pochemuha
3 years ago
15

Number of gallons of gas. Miles driven 0 0 2 62 4 124 10 310 How many gallons are used when the car has been driven 18 miles

Mathematics
1 answer:
Goryan [66]3 years ago
3 0

558 gallons are used when the car has been driven 18 miles.

<u>Step-by-step explanation:</u>

<u>From the given data, it can be determined that :</u>

  • The number of gallons for 2 miles = 62 gallons
  • The number of gallons for 4 miles = 124 gallons
  • The number of gallons for 10 miles = 310 gallons

Let, the number of gallons for 18 miles = 'x' gallons

<u>To find x :</u>

compare the given data with the unknown data,

62 gallons / 2 miles = x gallons / 18 miles

keep x alone on one side,

x = (62×18) / 2

x = 31×18

x = 558 gallons

Therefore, 558 gallons are used to drive 18 miles.

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If you divide both sides by -4 you get

y=-2x

So, you wrote the equation in the form y=kx, and in this form k is the constant of variation. So, the constant is -2.

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Oliver reads 28 1/2 pages of a book in 1 1/6 hours. Express his reading speed in pages per hour
Inessa05 [86]

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Mark wants to maintain an average of 70 on his math tests to remain eligible for sports. So far, he earned scores of 68, 75, 74,
Alex17521 [72]

Answer:

Step-by-step explanation:

(68+75+74+82+88+x)/6=70

(387+x)/6=70

x= 33

6 0
3 years ago
Factor completely 4x4 − 24x3 + 36x2.
ipn [44]

The previous answer from another person got deleted, so I'm here to put it back in my own words.

(Edit: The answer is A)

First of all, you can take 4 out of each, so simplify everything by 4.

4(x^4 - 6x^3 + 9x^2)

Next, you can see that you're able to take out x^2

4x^2(x^2 - 6x + 9)

You can see that both x^2 and 9 are perfect squares, meaning you can crunch them together like this

(x+3)^2 or (x-3)^2

Of course, only one would work, and as fate has it, (x-3)^ produces x^2 - 6x + 9

This would turn the now factored equation into :

4x^2(x-3)^2 or 4x^2(x-3)(x-3), this means the answer is A

6 0
3 years ago
A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly
Keith_Richards [23]

Answer:

0.7208 = 72.08% probability that this whole shipment will be accepted.

Step-by-step explanation:

For each tablet, there are only two possible outcomes. Either it meets the required specifications, or it does not. The probability of a tablet meeting the required specifications is independent of any other tablet, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

4% rate of defects

This means that p = 0.04

26 tablets

This means that n = 26

What is the probability that this whole shipment will be accepted?

Probability that at most one tablet does not meet the specifications, which is:

P(X \leq 1) = P(X = 0) + P(X = 1)

Thus

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{26,0}.(0.04)^{0}.(0.96)^{26} = 0.3460

P(X = 1) = C_{26,1}.(0.04)^{1}.(0.96)^{25} = 0.3748

Then

P(X \leq 1) = P(X = 0) + P(X = 1) = 0.3460 + 0.3748 = 0.7208

0.7208 = 72.08% probability that this whole shipment will be accepted.

3 0
3 years ago
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