Which expressions are equivalent to 16x4 − 64? Check all that apply.

Mathematics

2 answers:

Cerrena [4.2K]2 years ago

8 0

Answer:

First, Third, and Fourth to be short

Step-by-step explanation:

he basically explained everything else

Dmitry_Shevchenko [17]2 years ago

7 0

The first one is one, because 16x and -16x cancel eachother out, the second one on the other hand is not because 2 negatives do not cancel each other, but instead, add together. the third one yes, because when you foil 4x2 times 4x2 = 16x4. the -8 x 4x2 and 8 x 4x2 cancel eachother out, leaving you with -8 x 8, which equals -64, thus 16x4 - 64. the 4th one yes, because 16x2 x x2 = 16x4, and 16 x 2 = 32, x -2 equals -64.the last one, no because while 4 x 4x4 IS 16x4, 4 x -8 is 32

You might be interested in

Sick-leave time used by employees of a firm in a course of one month has approximately normal distribution, with a mean of 200 h

Usimov [2.4K]

Answer:

a)0.62% probability that total sick leave for next month will be less than 150 hours.

b) 225.6 hours should be budgeted for sick leave if that amount is to be exceeded with a probability of only 0.10.

Step-by-step explanation:

Problems of normally distributed samples can be 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:

$\mu = 200, \sigma = \sqrt{400} = 20$

a.Find the probability that total sick leave for next month will be less than 150 hours.

This probability is the pvalue of Z when X = 150. So:

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

$Z = \frac{150 - 200}{20}$

$Z = -2.5$

$Z = -2.5$ has a pvalue of 0.0062.

So there is a 0.62% probability that total sick leave for next month will be less than 150 hours.

b.In planning schedules for next month, how much time should be budgeted for sick leave if that amount is to be exceeded with a probability of only 0.10.

This is the value of X when Z has a pvalue of 0.90. So $Z = 1.28$