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irina1246 [14]
3 years ago
11

Devon earns $35 per hour for a regular 40-hour work week. Sometimes, he works over 40 hours a week and earns "double time" for t

he extra hours worked. (That means that his hourly rate for the additional hours over 40 hours per week is double his normal hourly rate.)
Mathematics
1 answer:
Evgesh-ka [11]3 years ago
6 0

Answer:

Earnings = $1960

Step-by-step explanation:

The question is incomplete; however the missing part of the question asks his total earnings if he worked for 48 hours in a week

First, we need to determine the extra hour worked

Regular Hour = 40

Extra Hour = 48 - 40

Extra Hour = 8

Total Earnings is then calculated as follows:

Earnings = Regular Hours * Regular Charges + Extra Hours * Extra Charges

Earnings = 40 * 35 + 8 * Extra Charges

Since extra charges is twice regular charges, we have:

Earnings = 40 * 35 + 8 * 35 * 2

Earnings = 1400 + 560

Earnings = $1960

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snow_tiger [21]

Answer:

First question: LCL = 522, UCL = 1000.5

Second question: A sample size no smaller than 418 is needed.

Step-by-step explanation:

First question:

Lower bound:

0.36 of 1450. So

0.36*1450 = 522

Upper bound:

0.69 of 1450. So

0.69*1450 = 1000.5

LCL = 522, UCL = 1000.5

Second question:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

The project manager believes that p will turn out to be approximately 0.11.

This means that \pi = 0.11

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The project manager wants to estimate the proportion to within 0.03

This means that the sample size needed is given by n, and n is found when M = 0.03. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 1.96\sqrt{\frac{0.11*0.89}{n}}

0.03\sqrt{n} = 1.96\sqrt{0.11*0.89}

\sqrt{n} = \frac{1.96\sqrt{0.11*0.89}}{0.03}

(\sqrt{n})^2 = (\frac{1.96\sqrt{0.11*0.89}}{0.03})^2

n = 417.9

Rounding up

A sample size no smaller than 418 is needed.

6 0
3 years ago
Find the remainder when f(x) is divided by (x - k) <br> f(x) = 5x4 + 8x3 + 4x2 - 5x + 67; k = 2
yan [13]

It is to be solved by reminder thorem
f(x)/(x-k) will have reminder f(k), 
so, f(2) = 5*(2^4) + 8 *(2^3) +4* (2^2) -5(2) +67

             =5*16 + 8*8 +4*4 -5*2 +67
             =80 + 64 + 16 -10 +67

             = 217


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Answer:

1 6/7

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