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1 year ago

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Evelyn is buying a motorcycle that costs $14,000. The tax rate is 6.75%, and she plans to make a down payment of $1,500. The sal

es tax is
added before the down payment is applied. She is considering a three-year loan

1 answer:

Lostsunrise [7]1 year ago

3 0

Answer:

449.10

Step-by-step explanation:

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A random sample from a normal population is obtained, and the data are given below. Find a 90% confidence interval for . 114 157

melamori03 [73]

Answer:

$103.160 \leq \sigma \leq 187.476$

And the upper bound rounded to the nearest integer would be 187.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

Data given: 114 157 203 257 284 299 305 344 378 410 421 450 478 480 512 533 545

The confidence interval for the population variance $\sigma^2$ is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case we need to find the sample standard deviation with the following formula:

$s=sqrt{\frac{\sum_{i=1}^{17} (x_i -\bar x)^2}{n-1}}$

And in order to find the sample mean we just need to use this formula:

$\bar x =\frac{\sum_{i=1}^n x_i}{n}$

The sample mean obtained on this case is $\bar x= 362.941$ and the deviation s=132.250

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=17-1=16$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a tabel to find the critical values.

The excel commands would be: "=CHISQ.INV(0.05,16)" "=CHISQ.INV(0.95,16)". so for this case the critical values are:

$\chi^2_{\alpha/2}=26.296$

$\chi^2_{1- \alpha/2}=7.962$

And replacing into the formula for the interval we got:

$\frac{(16)(132.250)^2}{26.296} \leq \sigma \leq \frac{(16)(132.250)^2}{7.962}$

$10641.959 \leq \sigma^2 \leq 35147.074$

Now we just take square root on both sides of the interval and we got:

$103.160 \leq \sigma \leq 187.476$

And the upper bound rounded to the nearest integer would be 187.

4 0

2 years ago

Identify the explicit function for the sequence in the table.

juin [17]

14 - 9 = 5
19 - 14 = 5
24 - 19 = 5
29 - 24 = 5

It is an arithmetic sequence with differences, b = 5 and a = 9
a(n) = a + b(n - 1)
a(n) = 9 + 5(n - 1)

The answer is B

8 0

2 years ago

Read 2 more answers

When the net is folded into the rectangular prism shown beside it, which letters will be on the front and back of the rectangula

earnstyle [38]

<h2>Answer:</h2>

<u>The correct option is </u><u>The letter on the front will be N. The letter on the back will be L. </u>

<h2>Step-by-step explanation:</h2>

When we fold the given net, we will get Q,P,M and N on sides. Side M will come to the top, side Q on the right side, side P on the left and side O on the bottom. The side which comes to the front will be N of the observer and similarly the side L will come to the back of the rectangular prism.

4 0

2 years ago

Read 2 more answers

(b) The train is 61 cm long and travels at a speed of 18 cm/s.

xz_007 [3.2K]

Answer:

It goes 18 cm every second:

18 x 4 = 72 cm

The bridge is 72 cm long.

Hope this helps!

3 0

2 years ago

Read 2 more answers

Toby's Tiny Toys have fixed expenses of $53,900 for the production of their tiny toys. Toby's has a variable expense of $12.50 a

ipn [44]

The total cost of the factory will be the sum of its variable costs and it's fixed costs. The factory has fixed costs of $53,900 and variable costs of $12.50 per unit produced. Let $x$ be the number of toy's produced by this Toby's Tiny Toys, then the total variable costs will be $12.50x$ . From this information we can gather that the cost function for this factory is,

$C(x)=53\,900+12.50x.$

On the other hand, if we let $x$ be the number of toys sold, we can gather that at the selling price of 16.50, the revenue function will be ,

$R(x)=16.50x.$

Toby's Tiny Toys will reach their break even point when the total costs are equal to the total revenue. At this break even point ,we have that

$R(x)=C(x)\\\implies 16.50x=12.50x+53\,900\\\implies 16.50x-12.50x=53\,900\\\implies 4x=53\,900\\\implies x=\frac{53\,900}{4} \\\implies x=134\,750.$

The company has to sell 134 750 units to break even.

6 0

2 years ago