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3 years ago

Determine the coordinates for the intersection of the diagonals in RSTU with vertices at R(-8,-2),S(-6,7), T(6,7) and U(4,-2)

Mathematics

2 answers:

irina [24]3 years ago

6 0

It is answer choice A. (-1, 2.5)

Kamila [148]3 years ago

6 0

Answer:

A. (-1,2.5)

Step-by-step explanation:

We have been the coordinates of a an quadrilateral RSTU with vertices at R(-8,-2),S(-6,7), T(6,7) and U(4,-2). We are asked to find the coordinates for the intersection of the diagonals of RSTU.

First of let us draw the quadrilateral on coordinate plane.

Please find the attachment for the quadrilateral.

We can see that our given quadrilateral is a parallelogram. Now let us draw diagonals of our parallelogram.

We can see that both diagonals are intersecting at point (-1,2.5), therefore, option A is the correct choice.

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2 years ago

Two trains, Train A and Train B, simultaneously depart Station A and Station B. Station A and Station B are 252.5 miles apart fr

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3 years ago

A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.

denpristay [2]

Answer:

We conclude that the population mean light bulb life is at least 500 hours at the significance level of 0.01.

Step-by-step explanation:

We are given that a manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly. The population standard deviation is 50 hours and the light bulb life is normally distributed.

You select a sample of 100 light bulbs and find mean bulb life is 490 hours.

Let $\mu$ = population mean light bulb life.

So, Null Hypothesis, $H_0$ : $\mu \geq$ 500 hours {means that the population mean light bulb life is at least 500 hours}

Alternate Hypothesis, $H_A$ : $\mu$ < 500 hours {means that the population mean light bulb life is below 500 hours}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean bulb life = 490 hours

σ = population standard deviation = 50 hours

n = sample of light bulbs = 100

So, the test statistics = $\frac{490-500}{\frac{50}{\sqrt{100} } }$

= -2

The value of z test statistics is -2.

Now, at 0.01 significance level the z table gives critical value of -2.33 for left-tailed test.

Since our test statistic is higher than the critical value of z as -2 > -2.33, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the population mean light bulb life is at least 500 hours.

7 0

3 years ago

Jim has received scores of 72 72 and 77 77 on his first two 100 point tests. what score must he get on his third 100 point test

Alisiya [41]

77+72=149
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through the process of elimination, I found that Jim needs to get an 88 or higher to receive an average of 79 or greater.

77+72+88=237
237/3=79

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3 years ago