Given:
To find:
The exact value of cos 15°.
Solution:
Using half-angle identity:
Using the trigonometric identity:
Let us first solve the fraction in the numerator.
Using fraction rule:
Apply radical rule:
Using :
Complete Question
In a study of the accuracy of fast food drive-through orders, one restaurant had 32 orders that were not accurate among 367 orders observed. Use a 0.05 significance level to test the claim that the rate of inaccurate orders is equal to 10%. Does the accuracy rate appear to be acceptable?
Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence to show that the rate of inaccurate orders is equal to 10%
Step-by-step explanation:
Generally from the question we are told that
The sample size is n = 367
The number of orders that were not accurate is
The population proportion for rate of inaccurate orders is p = 0.10
The null hypothesis is
The alternative hypothesis is
Generally the sample proportion is mathematically represented as
=>
=>
Generally the test statistics is mathematically represented as
=>
=>
From the z table the area under the normal curve to the left corresponding to -0.8174 is
Generally the p-value is mathematically represented as
=>
From the value obtained we see that hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence to show that the rate of inaccurate orders is equal to 10%