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kramer
1 month ago
15

The Polk Company reported that the average age of a car on U.S. roads in a recent year was 7.5 years. Suppose the distribution o

f ages of cars on U.S. roads is approximately bell-shaped. (a) If 99.7% of the ages are between 1 year and 14 years, what is the standard deviation of car age? (5 points) (b) Suppose
Mathematics
2 answers:
babunello [11.8K]1 month ago
8 0
Answer: 2.167. Step-by-step explanation: Given that 99.7% of data is within three standard deviations around the mean, we calculate that 6.5 years is the total deviation (derived from either 14 - 7.5 or 7.5 - 1). Dividing that by 3 gives a standard deviation of 2.167.
PIT_PIT [12.4K]1 month ago
8 0
Answer: The car age's standard deviation is 2.17 years. Step-by-step explanation: The Empirical Rule indicates that for a normally distributed random variable: 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three. In this context, given a mean of 7.5 years, with 99.7% of car ages ranging from 1 to 14 years implies that 1 year is three standard deviations below the mean while 14 years is three above. Thus, the calculation for standard deviation yields 2.17 years.
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Explain the error in the solution below. What additional step needs to be completed? log x – log53 = 2log53 log x = 3log53 log x
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The mistake lies in the fact that the logarithms have different bases. The one-to-one property of logarithms cannot be applied unless the bases are identical. <span>To correct this, the change of base formula should be used to express the logarithms with a uniform base.
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5 0
3 months ago
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Karl records the number of city blocks from his house to each of his friends houses. which statement is supported by the data?
AnnZ [12381]

Response:

Thorough analysis:

I believe that option 4 is the right choice

5 0
3 months ago
(2 thousands 7 tens) times 10
babunello [11817]

You may either multiply the numbers or the place value, and both methods will yield the same answer.

(2 thousands, 7 tens) multiplied by 10 results in

... (20 thousands, 70 tens)

or

... (2 ten-thousands, 7 hundreds)

8 0
2 months ago
Linda found that the cost to get a swimming pool installed in her backyard is a linear function of the pool's area. A swimming p
lawyer [12517]

Answer:

The equation for the line is C = 30A + 9000

Step-by-step explanation:

Let A denote Area and C stand for Cost, we can deduce that:

For an area of A = 1500 square feet, the cost amounts to C = 54000

If A = 700, then, C = 30000

Since the cost equation represents a function of area, this establishes a linear connection, necessitating the formulation of the line's equation.

C = mA + b

Where:

m denotes the slope of the line

b indicates the intercept with the C axis..

We possess two coordinates:

(700, 30000)

(1500, 54000)

Using these points, we calculate the slope via the formula:

m = \frac{y_2 -y_1}{x_2-x_1}\\\\m = \frac{54000-30000}{1500-700}\\\\m = 30

Consequently, the equation concludes with:

C = 30A +b

To find b, we substitute the point (700, 30000) into the equation

30000 = 30(700) + b\\\\30000 -21000=b

b = 9000

Thus

C = 30A + 9000

The linear equation's graph is depicted in the provided image

3 0
1 month ago
Find the interest for each loan. $252 at 8% for 2 years: ________ $400 at 2% for 6 months:________ $5,000 at 3.5% for 1 year:___
lawyer [12517]

Hello! I'm here to assist you! To calculate interest, we apply the formula prt, which involves multiplying the principal (the amount of money initially), the rate (the interest rate), and the time (typically in years). Here are the results:

$252 at 8% over 2 years yields $40.32
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For period calculations, we convert months into decimals: 6 months equals 0.5 years, and 9 months equals 0.75 years. Simply multiply the principal amount by the percentage in decimal form and by the time, and that’s it!

4 0
2 months ago
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