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3 years ago

PLEASE HELP!!

Mathematics

2 answers:

castortr0y [4]3 years ago

4 0

Answer:

x = 23

Step-by-step explanation:

6s² = 1944

Total area is given to be 1944

Since s = x - 5,

6(x - 5)² = 1944

Divide both sides by 6

(x - 5)² = 324

Square root both sides

x - 5 = +/- 18

Solve for x

x = 18 + 5 = 23

x = -18 + 5 = -13 (not possible because lengths can't be negative)

So, x = 23

Elden [556K]3 years ago

3 0

Answer:

x = 23

Step-by-step explanation:

We know that the surface area of a cube is denoted by S = 6s². In this case, we see that s = x - 5, so just plug x - 5 in for s in the formula:

S = 6(x - 5)²

We also know that the surface area is 1944, so S = 1944. Plug this in as well:

S = 6(x - 5)²

1944 = 6(x - 5)²

Now, we solve by expanding the right:

1944 = 6(x² - 10x + 25) = 6x² - 60x + 150

Subtract 1944 from both sides:

6x² - 60x - 1794 = 0

Divide by 6 from both sides for simplicity:

x² - 10x - 299 = 0

Factor:

(x - 23)(x + 13) = 0

x = 23 or x = -13

Obviously, we can't have a negative length, so -13 is wrong. We use x = 23 instead.

The answer is thus x = 23.

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Scores on a college entrance exam are normally distributed with a mean of 550 and a standard deviation of 100. Find the value th

Alinara [238K]

Answer:

The value that represents the 90th percentile of scores is 678.

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 550, \sigma = 100$