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Helga [31]
3 years ago
7

What is the prime factorization of 312?

Mathematics
2 answers:
Fofino [41]3 years ago
5 0
You find the prime factorization by breaking the number down into other numbers that are prime.  Start by breaking up 312 into 39 * 8.  39 breaks up into 3 * 13, and 8 breaks up into 4 * 2 which breaks up into 2 * 2.  So the prime factorization of 312 is 3 * 13 * 2 * 2 * 2 or 3*13* 2^{3}.  When you multiply those together you'll get 312.
ratelena [41]3 years ago
4 0
The Prime Factorization of 312 is 3 x 13 x 2^3

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2x + y =8 and 4x -2y = 6
irakobra [83]

Answer:

x=1.25 and y=-5.5

Step-by-step explanation:

2x+y=-8, 2x=-y-8 or 4x=-2y-16. Plug this value in the second equation, we have - 2y-16-2y=6, y=-5.5. Plugging this in any equation we have, x=1.25

5 0
3 years ago
The average score of all golfers for a particular course has a mean of 75 and a standard deviation of 4. Suppose 64 golfers play
Vilka [71]

Answer:

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 75, \sigma = 4, n = 64, s = \frac{4}{\sqrt{64}} = 0.5

Find the probability that the average score of the 64 golfers exceeded 76.

This is 1 subtracted by the pvalue of Z when X = 64.

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{76 - 75}{0.5}

Z = 2

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that the average score of the 64 golfers exceeded 76.

6 0
3 years ago
What is the next number to follow 17, 18, 22, 31, 47, ?
Minchanka [31]

Answer:

  72

Step-by-step explanation:

First differences are ...

  18 -17 = 1

  22 -18 = 4

  31 -22 = 9

  47 -31 = 16

We observe that these are square numbers. The next square number is 25, so we expect the next number in sequence to be ...

  47 +25 = 72

3 0
2 years ago
To find the height of a tower, a surveyor positions a transit the is 2 meters tall at a spot of 40 meters from the base of the t
Mrac [35]
The height of the tower roughly equals 41.421 meters.
5 0
3 years ago
Ann car can go 117 miles on 3 gallons of gas. During a drive last weekend, Ann used 8 gallons of gas. How far did she drive?
Nitella [24]

Answer:

Ann drove 312 miles in 8 gallons.

Step-by-step explanation:

Distance covered by Ann's car = 117 miles

Gallons of gas spent by Ann's car to cover 117 miles = 3 gallons

Unit rate = 117 miles / 3 gallons

               = 39 miles per gallon

so Ann's car can go 39 miles in one gallon of gas.

  • Given that Ann used 8 gallons of gas.

Therefore,

Distance covered by Ann's car in 8 gallons = 39 × 8

                                                                         = 312 miles

Therefore, Ann drove 312 miles in 8 gallons.

6 0
3 years ago
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