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3 years ago

The perimeter of a rectangle is 36 meters. If the length of the rectangle is 10 meters, what is the width (in meters)?

2 answers:

8 0

The width is 8. The length is 10 so 10+10 equals 20. You subtract 20 from 36 you get 16. 16/2 is 8. If you add 8+8+10+10 you get 36.

Debora [2.8K]3 years ago

4 0

The width would have to be 8

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Six times the sum of three consecutive odd integers is 18.Find the integers 1st integers (smallest of 3): 2nd integers (middle o

OLga [1]

Answer:

-1, 1 and 3.

Step-by-step explanation:

Let the integers be n, n + 2 and n + 4, then

6( n + n+2 + n + 4) = 18

6(3n + 6) = 18 Divide through by 6:

3n + 6 = 3

3n = -3

n = -1

So the integers are -1, 1 and 3.

5 0

3 years ago

Solve and then use estimation to make sure your answer is reasonable.

Vinil7 [7]

114.5 hours = 6870 minutes
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3 0

3 years ago

According to 2013 report from Population Reference Bureau, the mean travel time to work of workers ages 16 and older who did not

gregori [183]

Answer:

a) 48.80% probability that his travel time to work is less than 30 minutes

b) The mean is 30.7 minutes and the standard deviation is of 3.83 minutes.

c) 13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

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:

$\mu = 30.7, \sigma = 23$

a. If a worker is selected at random, what is the probability that his travel time to work is less than 30 minutes?

This is the pvlaue of Z when X = 30. So

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

$Z = \frac{30 - 30.7}{23}$

$Z = -0.03$

$Z = -0.03$ has a pvalue of 0.4880.

48.80% probability that his travel time to work is less than 30 minutes

b. Specify the mean and the standard deviation of the sampling distribution of the sample means, for samples of size 36.

$n = 36$

Applying the Central Limit Theorem, the mean is 30.7 minutes and the standard deviation is $s = \frac{23}{\sqrt{36}} = 3.83$

c. What is the probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes?

This is 1 subtracted by the pvalue of Z when X = 35. So

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

By the Central Limit Theorem

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

$Z = \frac{35 - 30.7}{3.83}$

$Z = 1.12$

$Z = 1.12$ has a pvalue of 0.8687

1 - 0.8687 = 0.1313

13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

8 0

3 years ago

Find the inverse of the matrix <img src="https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-4%266%5C%5C8%26-12%5C%5C%

liraira [26]

Answer:

Step-by-step explanation:

If there is a 2x2 matrix as $\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]$

The determinant is given by $\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]$

<em>Now, if we calculate the value of "ad - bc", we see that:</em>

$(-4)(-12)-(8)(6)=0$

We can't calculate the inverse, the inverse doesn't exist. The answer is D.

4 0

3 years ago

781÷26<br>26×3=78<br>is answer 3 remainder 1 or 30 remainder 1

mamaluj [8]

Which one is the one you want, 781:-:(divison)26?

8 0

3 years ago