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2 years ago

If e5x = k, where k is any positive number, then what is the value of X?

Advanced Placement (AP)

1 answer:

AlladinOne [14]2 years ago

4 0

Answer:

$x = \frac{ln(k)}{5}$

Explanation:

Given

$e^{5x} = k$

Required

Solve for x

$e^{5x} = k$

Take natural logarithm of both sides:

$ln(e^{5x}) = ln(k)$

Apply law of logarithm:

$ln(e^{f(x)}) = f(x)$

So, we have:

$ln(e^{5x}) = ln(k)$

$5x = ln(k)$

Divide through by 5

$x = \frac{ln(k)}{5}$

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Maddie's nominal income was $33,000 in 2012. In 2013, because of her excellent work ethic, she received a raise that increased h

Trava [24]

Answer:

-6.7 %; Hurt

Explanation:

1. Calculate Maddie's inflation adjusted income

$\text{Inflation adjusted income} = \text{2012 income} \times \dfrac{\text{2013 CPI}}{\text{2012 CPI}}\\\\= 33 000 \times \dfrac{125}{110} = \$37 500$

Maddie should be earning $37 500 in 2013 just to keep up with inflation.

2. Calculate the percent change in Maddie's real income.

Maddie is "real" salary is only $35 000.

$\text{\% Change} = \dfrac{\text{real - expected}}{\text{expected}} \times 100 \, \%\\\\= \dfrac{35 000 - 37 500 }{37 500} \times \, 100 \% = \dfrac{-2500}{37 500} \times 100 \, \% = \mathbf{-6.7 \, \%}$

The percent change in Maddie's real income is -6.7 %.

Maddie was certainly hurt by this inflation.

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2 years ago

Eleni and Analisa are driving to Ms. A's wedding. Eleni is going east at a rate of 50 mph and Analisa is driving south at 38 mph

Yuki888 [10]

Answer :

-62.8 miles per hour .

*hope this helped*

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2 years ago

Kiona is in fifth grade and goes to a private school. Liam is in his second year at college at a public university. Ava is a sen

dexar [7]

D. Ava Liam Kiona Asher

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2 years ago

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Kathy and her brother Clay recently ran in a local marathon. The distribution of finishing time for women was approximately norm

xxMikexx [17]

Answer:

<u>The proportion of women who ran the marathon and had a finishing time less than Kathy's is 66% (rounding to the next whole)</u>

Explanation:

1. Let's review the information given to us to answer the question properly:

μ of finishing time for women = 259 minutes

σ of finishing time for women = 32 minutes

Finishing time for Kathy = 272 minutes

2. What proportion of women who ran the marathon had a finishing time less than Kathy's? Show your work.

Let's calculate the z-score for the finishing time for Kathy, as follows:

z-score = (272 - 259)/32

z-score = 13/32 = 0.41 (rounding to the next hundredth)

Using the z-table, now we can calculate the proportion of women who ran the marathon had a finishing time less than Kathy's:

p (z=0.41) = 0.6591

<u>The proportion of women who ran the marathon and had a finishing time less than Kathy's is 66% (rounding to the next whole)</u>

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2 years ago

Categorize the actions according to whether Hayek would be likely to agree or disagree with them

andrew11 [14]

Answer:

<h3>Economist Friedrich August Hayek propagated and believed in free market private investment. </h3>

Explanation:

Economist Friedrich August Hayek <u>propagated and believed in free market and private investment. </u>His economic model revolved around private entrepreneurship and capitalism.

Hayek advocated <u>against government intervention</u>. Therefore, he would most likely agree to private investment and private enhancement and disagree to governmental initiatives or interventions.

Agree: eliminate the minimum wage, decrease overall taxes, reduce import taxes on goods imported into the U.S. from japan, let prices naturally increase as resources become scarce.

Disagree: Increase government spending during economic turndowns to improve the economy, increase the money supply, pass a law requiring stricter emission standards for all cars, limit the price of gasoline, government creates jobs to employ the unemployed, government pays for all levels of education for every citizen.

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2 years ago