Find the error and explain why:

Mathematics

1 answer:

Sloan [31]2 years ago

5 0

1) 9x + 2 = x + 5 ---> 9x + 2 = 6

subtracted X from one side but not the other

2) 3(x-4) + 5 = 12 ---> 3x + 4 + 5 = 12

didn't distribute correctly: 3(x-4)

multiplied the X by 3 but not the -4

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Find the area of sector AOB. Express your answer in terms of pi and rounded to the nearest tenth.

STatiana [176]

63 $\pi$

The sector is $\frac{70}{360}$ ; there are 360 degrees in a circle.
You use the formula $\pi r^{2}$ .
18cm is the radius, and then you square it to get 324.
Multiply 324 by $\frac{70}{360}$
You get 63 $\pi$

7 0

2 years ago

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 $Z = 1.28$