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Art [367]
3 years ago
6

If m < nqm = 2x+8 and m < pqr = x+22 find the value of x

Mathematics
1 answer:
ArbitrLikvidat [17]3 years ago
8 0

Answer:

The value of x is 14

Step-by-step explanation:

see the attached figure to better understand the problem

we have that

m∠NQM=m∠PQR -----> given problem

substitute the given values and solve for x

2x+8=x+22

Group terms that contain the same variable and combine like terms

2x-x=22-8\\x=14

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The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day.
valina [46]

Answer:

A sample of 179 is needed.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.85}{2} = 0.075

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.075 = 0.925, so Z = 1.44.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

A previous study found that for an average family the variance is 1.69 gallon?

This means that \sigma = \sqrt{1.69} = 1.3

If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of water?

A sample of n is needed, and n is found for M = 0.14. So

M = z\frac{\sigma}{\sqrt{n}}

0.14 = 1.44\frac{1.3}{\sqrt{n}}

0.14\sqrt{n} = 1.44*1.3

\sqrt{n} = \frac{1.44*1.3}{0.14}

(\sqrt{n})^2 = (\frac{1.44*1.3}{0.14})^2

n = 178.8

Rounding up

A sample of 179 is needed.

7 0
3 years ago
Which line contains the point (3,6)
spayn [35]
Many lines do. One of them would be y = 2x
6 0
3 years ago
Will a 2 quart pitcher hold 8 cups,1/4 cup,and 1/3 cup
Ghella [55]

Yes it will. A 2 quart pitcher is equal to 8 cups, and since 1/4 and 1/3 are less it can still hold it.

8 0
3 years ago
there are 8 students at each of 4 rounds of tables in the cafeteria. there are 64 students at long tables. use the bar model to
Tomtit [17]

Step-by-step explanation:

there should be at least

4 0
3 years ago
A triangle has a height that is increasing at a rate of 2 cm/sec and its area is increasing at a rate of 4 cm2/sec. Find the rat
lesya [120]

Answer:

The value of rate of which the base is changing \frac{dB}{dt} = - 3 \frac{cm}{s}

Step-by-step explanation:

Area = 20 cm^{2}

height = 4 cm

\frac{dH}{dt} = 2 \frac{cm}{sec}

\frac{dA}{dt} =  2 \ \frac{cm^{2} }{sec}

we know that area of the triangle is given by

A= \frac{1}{2} B H

B = \frac{2A}{H}

B = \frac{2 (20)}{4}

B = 10 cm

Rate of change of area is given by

\frac{dA}{dT} = \frac{1}{2} [B\frac{dH}{dt} + H \frac{dB}{dt} ]

4 =  0.5 [10 × 2 + 4 \frac{dB}{dt} ]

\frac{dB}{dt} = - 3 \frac{cm}{s}

This is the value of rate of which the base is changing.

7 0
3 years ago
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