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Ivenika [448]
3 years ago
5

Find the angel x in d diagram above with a well structured solution.Thanks​

Mathematics
1 answer:
Tom [10]3 years ago
5 0

Step-by-step answer:

Please refer to attached image.

1. Quad PQRS is cyclic (all vertices on the same circle), so opposite angles are supplementary, meaning

  that

  angles QPS and QRS are supplementary =>

  QPS+QRS=180   =>

  QRS = 180 - 74 = 106

2. Triangle RSQ is isosceles with RS=RQ =>

   angles RSQ and RQS are congruent.

3. Angle RSQ = (180 - 106) /2 = 74 / 2  = 37

4. QP is a diameter => angle QSP is a right-angle.

5. From (3) and (4) above,

  angle RSP = 37+90 = 127

6. Since PQRS is cyclic, angles RQP  and RSP are supplementary =>

   RQP+RSP = 180   =>

   x + 127 = 180   =>

   x = 180 - 127 = 53 degrees.

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One stats class consists of 52 women and 28 men. Assume the average exam score on Exam 1 was 74 (σ = 10.43; assume the whole cla
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Answer:

(A) What is the z- score of the sample mean?

The z- score of the sample mean is 0.0959

(B) Is this sample significantly different from the population?

No; at 0.05 alpha level (95% confidence) and (n-1 =79) degrees of freedom, the sample mean is NOT significantly different from the population mean.

Step -by- step explanation:

(A) To find the z- score of the sample mean,

X = 75 which is the raw score

¶ = 74 which is the population mean

S. D. = 10.43 which is the population standard deviation of/from the mean

Z = [X-¶] ÷ S. D.

Z = [75-74] ÷ 10.43 = 0.0959

Hence, the sample raw score of 75 is only 0.0959 standard deviations from the population mean. [This is close to the population mean value].

(B) To test for whether this sample is significantly different from the population, use the One Sample T- test. This parametric test compares the sample mean to the given population mean.

The estimated standard error of the mean is s/√n

S. E. = 16/√80 = 16/8.94 = 1.789

The Absolute (Calculated) t value is now: [75-74] ÷ 1.789 = 1 ÷ 1.789 = 0.559

Setting up the hypotheses,

Null hypothesis: Sample is not significantly different from population

Alternative hypothesis: Sample is significantly different from population

Having gotten T- cal, T- tab is found thus:

The Critical (Table) t value is found using

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- (n - 1) degrees of freedom; where n is the total number of observations or items in the population

- the standard t- distribution table

Alpha level = 0.05

1 - (0.05 ÷ 2) = 0.975

Checking the column of 0.975 on the t table and tracing it down to the row with 79 degrees of freedom;

The critical t value is 1.990

Since T- cal < T- tab (0.559 < 1.990), refute the alternative hypothesis and accept the null hypothesis.

Hence, with 95% confidence, it is derived that the sample is not significantly different from the population.

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Answer:

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Using the cosine ratio in the right triangle

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Answer:

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