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Alexxx [7]
3 years ago
11

I have to find the length of the angle indicated for the trapezoid

Mathematics
1 answer:
Stels [109]3 years ago
6 0
That is not a trapezoid, it is a general quadrilateral.  All 2-dimensional, 4-sided figures have an internal angle sum of 360 (triangles are 180).  So if you assume angles P and Q are right, they are each equal to 90 degrees, for a total of 180.
Subtract: 360 - 180 = 180.  We know that S + R must equal 180.  If you subtract 180 - 65, you get 115, which is obtuse (greater than 90 degrees).  This matches the drawing as the unknown angle is clearly greater than 90.  So the answer is 115 degrees.
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Step-by-step explanation:

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A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.
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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 = <u><em>population mean light bulb life.</em></u>

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 <u>One-sample z test statistics</u> 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, <u><em>the test statistics</em></u>  =  \frac{490-500}{\frac{50}{\sqrt{100} } }

                                     =  -2

The value of z test statistics is -2.

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

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 <u>we fail to reject our null hypothesis.</u>

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

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