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3 years ago

What is the factored form of 9X^2-64

2 answers:

8 0

This should be recognized as the difference of perfect squares which is of the form:

(a^2-b^2) and the difference of squares always factors to:

(a-b)(a+b) in this case:

(3x-8)(3x+8)

emmasim [6.3K]3 years ago

4 0

(3x-8)(3x+8) would be the factored form of 9x^2-62

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The mathematics section of a standardized college entrance exam had a mean of 19.8 and an SD of 5.1 for a recent year. Assume th

Fudgin [204]

Answer:

a) 0.84% of students scored over 32

b) 29.12% of students scored under 17

c) 70.04% of students scored between 17 and 32.

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:

$\mu = 19.8, \sigma = 5.1$

a) About what percent of students scored over 32?

This is 1 subtracted by the pvalue of Z when X = 32. So

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

$Z = \frac{32 - 19.8}{5.1}$

$Z = 2.39$

$Z = 2.39$ has a pvalue of 0.9916

1 - 0.9916 = 0.0084

So 0.84% of students scored over 32

b) About what percent of students scored under 17?

This is the pvalue of Z when X = 17. So

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

$Z = \frac{17 - 19.8}{5.1}$

$Z = -0.55$

$Z = -0.55$ has a pvalue of 0.2912

So 29.12% of students scored under 17

c) About what percent of students scored between 17 and 32?

This is the pvalue of Z when X = 32 subtracted by the pvalue of Z when X = 12. So

X = 32

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

$Z = \frac{32 - 19.8}{5.1}$

$Z = 2.39$

$Z = 2.39$ has a pvalue of 0.9916

X = 17

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

$Z = \frac{17 - 19.8}{5.1}$

$Z = -0.55$

$Z = -0.55$ has a pvalue of 0.2912

0.9916 - 0.2912 = 0.7004

70.04% of students scored between 17 and 32.

5 0

3 years ago

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $65. A season pass costs $400. The skier

Vlad [161]

Let x be the number of days.

Daily pass:
65x + 30x
95x

Season pass:
400 + 30x

95x > 400 + 30x
65x > 400
x > 6.15

The number of days can't be 6.15, so you must round. You can't go down because then the price will be more expensive, so you have to round up.

It would take 7 days until the season pass is less expensive than the daily pass.
----------------------
You can check this by plugging in the x.

95x > 400 + 30x
95(7) > 400 + 30(7)
665 > 400 + 210
665 > 600
The daily pass is more expensive than the season pass.

3 0

3 years ago

Pierre had $42 before he paid his club dues. Evaluate the expression 42 − d for d = 25 to find how much money Pierre had left af

Step2247 [10]

Answer:

$17

Step-by-step explanation:

This is simply stated as a function.

We can rewrite this problem out as --> f(d) = -d + 42

If we simply say that he spent d, the problem states that d is equivalent to 25.

So the function looks like this --> f(d) = -25 + 42

Therefore your answer becomes --> f(d) = 17