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2 years ago

-2x-2y=-8 -4x-8y=-20

Mathematics

1 answer:

Citrus2011 [14]2 years ago

8 0

Answer:

-2x-2y=-8

-4x-8y=-20

From the 1st eqn

Dividing through by 2

you have

-x-y=-4

Multiply through by -(minus)

x+y=4

x=4-y

Substitute into eqn 2

-4x-8y=-20

-4(4-y)-8y=-20

-16 + 4y - 8y = -20

-4y = -20 +16

-4y = -4

y= 1

Substitute into any of the other eqn's to get x

x= 4-y

x= 4-1

x=3

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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

C. If one cubic foot contains about 7.5 gallons, how many gallons of water are in the pool? (3 points) I Water: gallons 3. A rec

Dominik [7]

Answer:

One Rectangular Pan

Step-by-step explanation:

Part C cannot be answered since the dimensions of the pool are not given. Please check the question.

The cake pans may be compared by calculating the volume of each shape:

Rectangular pan: Volume = Length x Width x Height

Volume Rectangle = (13")*(9")*(2") = 234 in^3

Round pan: Volume = $\pi r^{2} h$

Volume Round = (3.14)*(4")^2(2") = 100.5 in^3

Two round pans will hold 2*(100.5 in^3) or 201 in^3 of batter

One rectangular pan holds 234 in^3.

Go with the rectangular pan if you want more cake.

4 0

1 year ago

Multiply. 2x(x2 + 2x - 6)

Stels [109]

2x(x2 + 2x - 6)
First add what is in the "(" wich is 2x+2x
2x(4x - 6)
Second multiply the 2x by the 4x & -6
8x-12x
Now subtract the -12x from the 8x
8x-12x = -4x

8 0

3 years ago

Read 2 more answers

If the diameter of the circle is above 20mm what is the area

Phoenix [80]

Answer:

The area would be 314.16 mm squared

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3 years ago

A town population of children increased from 367 to 421 during the past year which equation showes how to find the percentage in

klemol [59]

Answer:

5.7%

Step-by-step explanation:

421-367=24

24/421x100=5.7%

6 0

2 years ago