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3 years ago

Bryan worked 32 hours last week. His regular hourly wage is $7.50 per hour. Calculate his gross earnings for the week.

1 answer:

galina1969 [7]3 years ago

4 0

multiply the number of hours worked by the hourly wage. Once you have that number multiply that by the percent deducted. Subtract the percent deducted number from the gross pay and you have your answer.

Note: each deduction is taken out of the total gross pay.

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A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.93. Assume indepen

noname [10]

Answer:

There is a 99.99998% probability that at least one valve opens.

Step-by-step explanation:

For each valve there are only two possible outcomes. Either it opens on demand, or it does not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$n = 5, p = 0.93$

Calculate P(at least one valve opens).

This is $P(X \geq 1)$

Either no valves open, or at least one does. The sum of the probabilities of these events is decimal 1. So:

$P(X = 0) + P(X \geq 1) = 1$

$P(X \geq 1) = 1 - P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{5,0}.(0.93)^{0}.(0.07)^{5} = 0.0000016807$

Finally

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000016807 = 0.9999983193$

There is a 99.99998% probability that at least one valve opens.

5 0

3 years ago

Read 2 more answers

-2- 3(7-k) =-4(2k-1)

Ivan

Answer:

k=27/11

Step-by-step explanation:

7 0

3 years ago

In order to ensure efficient usage of a server, it is necessary to estimate the mean number

juin [17]

Answer:

a. [36.19;39.21]

b. Reject the null hypothesis. The population mean of users that are connected at the same time is greater than 35.

Step-by-step explanation:

Hello!

Your study variable is,

X: "number of users of one server at a time"

The objective is to estimate the mean, for this, a sample of n=100 times was taken and the standard deviation S= 9.2 and the sample mean is X[bar]= 37.7 were calculated.

You need to study the population mean, for this you need your variable to have at least normal distribution. Since you don't have information about its distribution, but the sample is big enough (n≥30) you can apply the Central Limit Theorem and approximate the distribution of the sample mean X[bar] to normal:

X[bar]≈N(μ;σ²/n)

a. With this approximation, you can construct the 90% Confidence Interval using the approximate Z

[X[bar] ± $Z_{1-\alpha /2}$ * S/√n]

$Z_{1-\alpha /2}$ = $Z_{0.95}$ = 1.64

[37.7± 1.64* 9.2/√100]

[36.19;39.21]

b. You need to test if the population mean is greater than 35 with a level of significance of 1%.

The hypothesis is:

H₀: μ ≤ 35

H₁: μ > 35

α: 0.01

This is a one-tailed test so you have only one critical level (right tail):

$Z_{1\alpha } = Z_{0.99} = 2.33$

This means that if the value of the calculated statistic is equal or greater than 2.33 you will reject the null Hypothesis.

If the value is less than 2.33 you will support the null hypothesis.

The statistic is:

Z= X[bar] - μ = 37.7 - 35 = 2.93

S/√n 9.2/10

The value 2.93 > 2.33, so you reject the null hypothesis. This means that the population mean of users that are connected at the same time is greater than 35.

Note: To make the decision using the interval calculated on a), the hypothesis should have been two-tailed and the confidence and significance levels complementary.

I hope it helps!

7 0

3 years ago

What is the value of x? 40° (6x + 2)

Anvisha [2.4K]

Answer:

x = 8

Step-by-step explanation:

40 + 6x + 2 = 90 {Complementary angles}

Combine like terms

40+ 2 + 6x = 90

42 +6x = 90 {Subtract 42 form both sides}

6x = 90 - 42

6x = 48 {divide both sides by 6}

6x/6 = 48/6

x = 8

6 0

4 years ago

Read 2 more answers

At what points is the function y= cosx/4x continuous

Naya [18.7K]

There is a discontinuity at 0 since you can’t divide cos x by 0. So that would be represented in interval notation at (-infinity, 0) U (0, infinity) replace infinity with the symbol

5 0

3 years ago