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1 year ago

The length of a rectangle is 3 inches more than three times the width. the perimeter is 94 inches. find the length and width.

1 answer:

3 0

Let length be (l) and width be (w).

According to the question, l=3w+3......equation1
And perimeter that is 2(l+w) =94........equation2

Solve these two equations, you get your answer.
l=36
w=11

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How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winner

Liula [17]

Answer:

The 95% confidence interval would be given by (14444.04;33657.30)

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 means 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.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Data: $26,650 $6,060 $52,820 $8,490 $13,660$25,840 $49,840 $23,790 $51,480 $18,960$990 $11,450 $41,810 $21,060 $7,860

We can calculate the mean and the deviation from these data with the following formulas:

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

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

$\bar X=24050.67$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=17386.13 represent the sample standard deviation

n=15 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=15-1=14$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,14)".And we see that $t_{\alpha/2}=2.14$

Now we have everything in order to replace into formula (1):

$24050.67-2.14\frac{17386.13}{\sqrt{15}}=14444.04$

$24050.67+2.14\frac{17386.13}{\sqrt{15}}=33657.30$

So on this case the 95% confidence interval would be given by (14444.04;33657.30)

6 0

1 year ago

Given 8x-3y=-21, 3x+y=-10; Prove x=-3

Mashcka [7]

The numbers start from the top

3 0

1 year ago

An Epson inkjet printer ad advertises that the black ink cartridge will provide enough ink for an average of 245 pages. Assume t

Neko [114]

Answer:

35.2% probability that the sample mean will be 246 pages or more

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 245 \sigma = 15, n = 33, s = \frac{15}{\sqrt{33}} = 2.61$

What the probability that the sample mean will be 246 pages or more?

This is 1 subtracted by the pvalue of Z when X = 246. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{246 - 245}{2.61}$

$Z = 0.38$

$Z = 0.38$ has a pvalue of 0.6480.

1 - 0.6480 = 0.3520

35.2% probability that the sample mean will be 246 pages or more

4 0

1 year ago

Six pipes are laid end to form a row.each pipe is 9 1/3 inches long.how long is the row of pipes in feet?

laiz [17]

six pipes are laid end to end to form a row. Each pipe is 9 1/3 inches long. how long is the row of pipes, in feet?

Answer:

4.67 feet or 4 feet 8 inches or $4\frac{2}{3}$ feet

Step-by-step explanation:

Let x be the length of the row pipes.

Given:

Number of pipes = 6

Each pipe has length $9\frac{1}{3}$ inches. and six pipes are laid end to end to form a row.

The total length of the row is equal to length of the 6 pipes.

So, total length of row = Number of pipes $\times$ Length of the pipe

$x=\frac{28}{3}\times 6$

$x=28\times 2$

$x=56$ inches

convert inch into feet.

$x=\frac{56}{12}$

$x=4.67 feet$

Therefore, The length of the row is 4.67 feet or 4 feet 8 inches or $4\frac{2}{3}$ feet .

3 0

2 years ago

it takes you approximately 1/3 hour to type a memo. if you plan to work for 6 hours, how many memos can you type? a. 18 b. 6 (c.

Harrizon [31]

U would actually do both...because when ur dividing fractions, u end up multiplying....but u start with dividing.
6 / (1/3) =
6 * 3 = 18 <== ur answer

6 0

2 years ago

Read 2 more answers