A recent study indicates that the annual cost of maintaining and repairing a car in a town in Ontario averages 200 with a variance of 260. A tax of 20% is introduced on all items associated with the maintenance and repair of cars (i.e., everything is made 20% more expensive). Calculate the variance of the annual cost of maintaining and repairing a car after the tax is introduced.

Answers

Answer 1

Answer:

Answer:

374.4

Step-by-step explanation:

All items related to the maintenance are 20% more expensive, it means that each datum is 20% bigger including the average.

The variance its a dispersion measurof the data and its calculated of this way:

$\sigma^(2) =(1)/(n) \sum\limits^n_(i=1) (x_(i)-\var{x})^2\n$

Here n is the number of data, $\var{x}$ is the average and $x_(i)$ represent each datum. The increment in 20% in each parameter can be represented multiplying for 1.2, of this way

$\sigma_(20\%)^(2) =(1)/(n) \sum\limits^n_(i=1) (1.2x_(i)-1.2\var{x})^2\n$

Factorizing the 1.2 we have:

$\sigma_(20\%)^(2) =(1)/(n) \sum\limits^n_(i=1) (1.2(x_(i)-\var{x}))^2$

$\sigma_(20\%)^(2) =(1)/(n) \sum\limits^n_(i=1)1.2^(2) (x_(i)-\var{x})^2$

$\sigma_(20\%)^(2) =(1.2^(2))/(n) \sum\limits^n_(i=1) (x_(i)-\var{x})^2\n$

That is:

$1.2^(2)\sigma^(2)=\sigma_(20\%)^(2)$

The new variance is $1.2^(2) \sigma^(2) =1.44*260=374.4$

Answer 2

Answer:

Final answer:

To calculate the variance of the annual cost of maintaining and repairing a car after the tax is introduced, we can use the formula var(X + c) = var(X), where X is the original cost and c is the tax rate. In this case, the tax rate is 20%, so c = 0.2. The variance of the original cost is 260, so the variance of the cost after the tax is introduced is also 260.

Explanation:

To calculate the variance of the annual cost of maintaining and repairing a car after the tax is introduced, we can use the formula var(X + c) = var(X), where X is the original cost and c is the tax rate. In this case, the tax rate is 20%, so c = 0.2. The variance of the original cost is 260, so the variance of the cost after the tax is introduced is also 260.

Learn more about variance of annual cost here:

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Mason has to mow 6 lawns today. So far, he has mowed 1 1/2 of them. How many does he have left to do?

Answers

He has left 4 1/2 lawns to mow. As there are total 6 lawns, Mason has mowed 1 1/2 lawns. The remaining lawns are 6 - 1 1/2 = 6 - 1.5 = 4.5 = 4 1/2

Answer:

4 1/2 is the answer! Hope this helps!

Step-by-step explanation:

What is the value of x?

Enter your answer in the box.

x =

Answers

Answer:

x = 4

Step-by-step explanation:

Let's find the length of JL as a first step. Knowing the result, we can easily find x.

|JL| 1

sin 30 degrees = ----------------- = --------

8√2 2

Then 2 |JL| = 8√2, or |JL| = 4√2

Next, find x: sin 45 degrees = x / |JL| = x / [4√2], and since sin 45 degrees is 1 / [√2],

x / [4√2] = -------- which results in x = 4

√2

The rainfall total two years ago was 10.2 inches. Last year's total was 20% greater. What was last year's rainfall total?

Answers

basically, to answer this question, you have to increase 10.2 by 20%.hence,

10.2×20= 204
204÷100= 2.04
10.2+2.04= 12.24
answer- 12.24inches

10.2+10.2*20/100= 12.24 inches

What is the length of segment LP?

Answers

In the image, as denoted by similar sides OP and MN, we can conclude that the 2 triangles are similar triangles. To look for the value of x (which we can substitute later to find the length of segment LP), we relate the relations of segments LO and LP to segments LM and LN. This relation is shown below:

LO/LP = LM/LN

22 / x+12 = 30 / x+12 + 5
22 / x+12 = 30 / x+17

Cross-multiplying:
30x + 360 = 22x + 374

Isolating x to one side of the equation by subtracting 22x and 360 from both sides:

30x + 360 - 360 - 22x = 22x + 374 - 360 - 22x
8x = 14
x = 1.75

Since we now have the value of x, we substitute this to the equation of LP:
LP = x + 12
LP = 1.75 + 12
LP = 13.75

Therefore the value of LP is 13.75 in.

In the figure, m∠2 = (20x + 52)° and m∠7 = (40x – 48)°For what value of x is line m parallel to line n?
18

5

44

3