Machines at a factory produce circular washers with a specified diameter. The quality control manager at the factory periodically tests a random sample of washers to be sure that greater than 90 percent of the washers are produced with the specified diameter. The null hypothesis of the test is that the proportion of all washers produced with the specified diameter is equal to 90 percent. The alternative hypothesis is that the proportion of all washers produced with the specified diameter is greater than 90 percent.

C) The test provides the convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%.

Step-by-step explanation:

Options are missing from the question. The complete question with its options is shown in the image below.

We need to describe about the Type 1 error. In Statistics there are two main errors: Type 1 error and Type 2 error.

In the given case the Null Hypothesis is:

The proportion of all washers produced with the specified diameter is equal to 90 percent.

The Type 1 error will occur when the test results will reject the Null hypothesis and accept that the specified diameter is greater than 90% , when infact the Null hypothesis is true and actual proportion is equal to 90%.

Therefore, the correct option will be:

C) The test provides the convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47