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NARA [144]
3 years ago
12

A new car is purchased for 24600 dollars. The value of the car depreciates at 5.5% per year. To the nearest year, how long will

it be until the value of the car is 11300 dollars?
Mathematics
1 answer:
boyakko [2]3 years ago
4 0

Answer:

The number of years until the value of the car is 11300 dollars is 9 years.

Step-by-step explanation:

This can be calculated using the following formula:

Value of the Car = Purchase cost - (Annual depreciation expenses * N) ........ (1)

Where;

N = Number of years until the value of the car is 11300 dollars

Purchase cost = $24,600

Annual depreciation rate = 5.5%

Annual depreciation expenses = $24,600 * 5.5% = $1,353

Value of the car = $11,300

Substituting the value into equation (1) and solve for N, we have:

$11,300 = $24,000 - ($1,353 * N)

$1,353 * N = $24,000 - $11,300

$1,353 * N = $12,700

N = $12,700 / $1,353

N = 9.38654841093865

Rounding to the nearest year as required by the question, we have:

N = 9

Therefore, the number of years until the value of the car is 11300 dollars is 9 years.

Step-by-step explanation:

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Step-by-step explanation:

Data given and notation

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\sigma_{1}=12.5 represent the population standard deviation for the sample 1

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p_v represent the p value for the test (variable of interest)

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We need to conduct a hypothesis in order to check if the expenditure of households in City 1 is more than that of households in City 2, the system of hypothesis would be:

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Alternative hypothesis:\mu_{1}-\mu_{2}>0

We know the population deviations, so for this case is better apply a z test to compare means, and the statistic is given by:

z=\frac{(\bar X_{1}-\bar X_{2})-0}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}} (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Standard error

The standard error on this case is given by:

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Replacing the values that we have we got:

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We can replace in formula (1) the info given like this:

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P-value

Since is a one side right tailed test the p value would be:

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b. 0.03

Conclusion

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a. We can reject H(0) in favor of H(a)

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