MATHEMATICS HIGH SCHOOL

The gas mileage for a certain model of car is known to have a standard deviation of 6 mi/gallon. A simple random sample of 64 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gallon. Construct a 97.5% confidence interval for the mean gas mileage for this car model.

Answers

Answer 1

Answer:

Answer: confidence interval = 27.5 +/- 1.68

= ( 25.82, 29.18)

Step-by-step explanation:

Given;

Number of samples n = 64

Standard deviation r = 6mi/gallon

Mean x = 27.5mi/gallon

Confidence interval of 97.5%

Z' = t(0.0125) = 2.24

Confidence interval = x +/- Z'(r/√n)

= 27.5 +/- 2.24(6/√64)

= 27.5 +/- 1.68

= ( 25.82, 29.18)

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Find the mean of the following data set. 42, 45, 58, 63

Answers

The mean of the given data will be equal to 52.

What is mean?

Mean is defined as the ratio of the sum of the given data to the number of the counts of the data.

Given that:-

42, 45, 58, 63

The mean will be calculated as:-

Mean = Sum of the data sets ÷ Number of the data sets

Mean = ( 42 + 45 + 58 + 63 ) ÷ 4

Mean = 208 ÷ 4

Mean = 52

Therefore the mean of the given data will be equal to 52.

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To find the Mean you have to add all the numbers from the data set,
$42+45+58+63=208$
Next you divide the sum by the amount of numbers in the set,
$208/4=52$
Final Answer: 52

A major concern with Social Security is the possibility that funds will not be available when today’s tax-payers retire to become beneficiaries. According to the Social Security Trustee’s report, an increase of 1.89% in the Social Security payroll tax would keep the account full for the next 75 years. To achieve similar results, benefits would have to be decreased from the current 42% of the ending salary to 29% of the salary.Cindy is relatively new to the workforce. She has 32 years until she can retire. Her current annual salary is $45,000.

1a) Calculate how much Cindy will have to pay in Social Security tax (6.2%) based on this salary.
1b) Calculate how much Cindy will have to pay in Social Security tax if the tax was increased by 1.89%.

2a) Calculate Cindy’s annual Social Security benefit (about 42%) if her salary remains unchanged until she retires (annual average is $45,000).
2b) Calculate Cindy’s annual Social Security benefit if her salary remains unchanged but benefits (based on her annual salary of $45,000) were cut from 42% to 29%.

3) If Cindy were given a choice between the increase in Social Security tax now or the decrease in Social Security benefits when she retires, which would you recommend she choose? Explain your answer thoroughly.

Answers

1a) 45,000 * 6.2% = 2,790
1b) 45,000 * (6.2% + 1.89%) = 45,000 * 8.09% = 3,640.50

2a) 45,000 * 42% = 18,900
2b) 45,000 * 29% = 13,050

3) I think it would be better to have an increase in Social Security tax now and receive 18,900 as annual pension rather than the decrease in Social Security benefits when she retires.

Answer:

1a) $45,000 * 0.062 = $2,790

1b) 6.2% + 1.89% = 8.09%; $45,000 * 0.0809 = $3640.50

2a) $45,000 * 0.42 = $18,900

2b) 42% - 13% = 29% $45,000 * 0.029 = $13,050

3) You should probably recommend she pay the extra taxes now. If the tax were increased by 1.89%. Cindy would have to pay an extra $3640.50 - $2,790 = $850.50 per year for the 32 years before she retires. This adds up to $27,216 over the length of 32 years. On the other hand, if benefits were decreased from 42% of her salary to 29% of her salary the time of Cindy’s retirement (approximations), she would receive $18,900 - $13,050 = $5,850 less per year after she retires. This adds up to $58,500 in just 10 years.

Step-by-step explanation:

This is the answer they have given me.

Perimeter of a hexagon with 3.25 m sides

Answers

If it is a regular hexagon, then it will have 6 3.25metre sides.

So the perimeter is simply:
6x3.25 = 19.5Metres.

Answer:REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Step-by-step explanation:

If I walk outside with my umbrella, then it will rain. Decide whether the given conditional statement is true or false. If it is false, explain why the logic is faulty and rewrite the statement so it is true. If it is true,explain why it is true and write two additional true statements of your choice

Answers

Answer:

False

Step-by-step explanation:

Umbrellas could be used for different reasons besides rain.

Kent worked in the housewares section of a department store this year he set a record high for vacuum sales with 567 vacuum sold the previous high was last year when 540 vacuums were sold what is the percent of increased in sales from last year to this year?

Answers

The percent increase in vacuum sales from last year to this year is 5%. This means that there was a 5% increase in the number of vacuums sold this year compared to last year's sales.

To calculate the percent increase in vacuum sales from last year to this year, we can use the following formula:

Percent Increase = [(New Value - Old Value) / Old Value] * 100

Where:

New Value = 567 (vacuums sold this year)

Old Value = 540 (vacuums sold last year)

Now, let's plug in the values and calculate:

Percent Increase = [(567 - 540) / 540] * 100

Percent Increase = (27 / 540) * 100

Percent Increase = 0.05 * 100

Percent Increase = 5%

The percent increase in vacuum sales from last year to this year is 5%. This means that there was a 5% increase in the number of vacuums sold this year compared to last year's sales.

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One percent of 540 is 5.4 (540\100) now divide 567 by that number which gives you 105% take the original 100% away, it's an increase of 5%

the sum of two numbers is 60. the larger number is 12 more than the smaller number. what is the number?

Answers

The larger number is: 36
The smaller number is: 24

Firstly, if a number is 12 more than the other, that means that the difference between the two numbers is 12

If you divide 60 by 2, you get two 30's. Then, if you add 6 to one of the 30's and then subtract 6 to the other 30, resulting in 36 and 24, you get set of numbers which equal 60 and also have a difference of 12.

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