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3 years ago

8

Darren has gotten 2 offers for jobs in the alternative energy industry. offer #1 pays $31,000 per year with 2,000 raise each yea

r. Offer #2 pays $26,000 per year with $2,500 raise each year. Use guess and check or any other method to solve.
A) financially, which job should he take?

B) At what point in time does offer #2 become a better offer?

1 answer:

katovenus [111]3 years ago

6 0

Answer: Darren

A) Job Offer #1 would be better financially until job offer 2 (in 12 years) would be a better and have more income, so IMO job offer #1 would set you better off financially

B) it would take 12 years for job offer #2 to become a better offer (you can also express this in your own words if needed)

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You have measured the systolic blood pressure of a random sample of 25 employees of a company located near you. A 95% confidence

Alla [95]

Answer:

$122 \leq \mu \leq 138$

The 95% confidence interval would be given by (122;138)

And the correct interpretation for this case is:

c. If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % where by a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.06$

Now we have everything in order to replace into formula (1), for this case we got:

$122 \leq \mu \leq 138$

The 95% confidence interval would be given by (122;138)

And the correct interpretation for this case is:

c. If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

6 0

3 years ago

Please help i will give brainly :

Lubov Fominskaja [6]

1) The x-axis represents the energy ( $E$ ), in joules. The y-axis represents the amplitude ( $x$ ), in milimeters.

2) The curve depicts an <em>monotonous decrecent</em> rate of change.

3) The amplitude is directly proportional to the root square of the energy.

<h3>How to analyze a graph relationship between two variables</h3>

In this question we have a relationship between two variables, in which we must apply principles of <em>functional</em> analysis to respond three questions presented in the statement.

Now we proceed to answer the three questions below:

<em>What is on the x-axis? The y-axis?</em> R/ The x-axis represents the energy ( $E$ ), in joules. The y-axis represents the amplitude ( $x$ ), in milimeters.
<em>How would you describe the rate of change of the line?</em> R/ The curve depicts an <em>monotonous decrecent</em> rate of change, that is, the slope converges to zero when the energy tends to infinite.
<em>What does this tell you about the relationship between amplitude and energy?</em> R/ The curve show a strong similarity with a function of the form $x = A\cdot \sqrt{E}$ . Hence, the amplitude is directly proportional to the root square of the energy.

To learn more on functions, we kindly invite to check this verified question: brainly.com/question/12431044

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2 years ago

If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

Cloud [144]

Answer:

The largest possible volume of the box is 2000000 cubic meters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, of the box with a square base are described below:

$A_{s} = l^{2}+h\cdot l$ (1)

$V = l^{2}\cdot h$ (2)

Where:

$l$ - Side length of the base, in centimeters.

$h$ - Height of the box, in centimeters.

By (2), we clear $h$ within the formula:

$h = \frac{V}{l^{2}}$

And we apply in (1) and simplify the resulting expression:

$A_{s} = l^{2}+ \frac{V}{l}$

$A_{s}\cdot l = l^{3}+V$

$V = A_{s}\cdot l -l^{3}$ (3)

Then, we find the first and second derivatives of this expression:

$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find the critical value of the side length of the base is:

$30000-3\cdot l^{2} = 0$

$3\cdot l^{2} = 30000$

$l = 100\,cm$

Then, we evaluate this result in the expression of the second derivative:

$V'' = -600$

By Second Derivative Test, we conclude that critical value leads to an absolute maximum. The maximum possible volume of the box is:

$V = 30000\cdot l - l^{3}$

$V = 2000000\,cm^{3}$

The largest possible volume of the box is 2000000 cubic meters.

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2 years ago

Simplify and expression for the perimeter of the the rectangle shown.

erma4kov [3.2K]

Answer:

Step-by-step explanation:

l = 8.6 x + 3

b = 5.2

perimeter =

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3 years ago

Someone solve this for me please: Find a vector v such that || v || = 10 and v is in same direction as 2i + 3j

drek231 [11]

Answer:

Step-by-step explanation:

$\overrightarrow{a}=2*\overrightarrow{i}+3*\overrightarrow{j}\\\\||\overrightarrow{a}||=\sqrt{2^2+3^2} =\sqrt{13} \\\\\boxed{\overrightarrow{v}=\dfrac{20}{\sqrt{13}}*\overrightarrow{i}+\dfrac{30}{\sqrt{13}}*\overrightarrow{j}} \\\\\\||\overrightarrow{a}||=\sqrt{(\dfrac{20}{\sqrt{13}})^2+(\dfrac{30}{\sqrt{13}})^2} =\sqrt{\dfrac{400+900}{13} }==\sqrt{\dfrac{1300}{13} }=\sqrt{100}=10 \\$

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2 years ago