1. Given any triangle ABC with sides BC=a, AC=b and AB=c, the following are true :
i) the larger the angle, the larger the side in front of it, and the other way around as well. (Sine Law) Let a=20 in, then the largest angle is angle A.
ii) Given the measures of the sides of a triangle. Then the cosines of any of the angles can be found by the following formula:
a^{2}=b ^{2}+c ^{2}-2bc(cosA)
2.
20^{2}=9 ^{2}+13 ^{2}-2*9*13(cosA) 400=81+169-234(cosA) 150=-234(cosA) cosA=150/-234= -0.641
3. m(A) = Arccos(-0.641)≈130°,
4. Remark: We calculate Arccos with a scientific calculator or computer software unless it is one of the well known values, ex Arccos(0.5)=60°, Arccos(-0.5)=120° etc
Answer:
Step-by-step explanation :The volume V of a prism is V = Bh, where B is the area of the base, h is the height of the prism.To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
At 0.01 significance level the hypothesis is rejected.
Null Hypothesis (H₀): The sample data occurs purely from chance.
Alternative Hypothesis (H₁): The sample data is influenced by some non-random cause.
If the p-value of the hypothesis test is less than some significance level (e.g. α = .01), then we can reject the null hypothesis and conclude that we have sufficient evidence to say that the alternative hypothesis is true.
Given that,
x = 28
s = 2.9
μ = 31
n = 8
α = 0.01
Then, the Null Hypothesis : H₀ = 31
The Alternate Hypothesis : H₁ < 31
The average number of cigeratte smoker per day is less than 31.
Test Statistics:
t = x -μ / s√n
= 28 - 31/ 2.9√8
= -3/ 8.41
= -0.356
Since the p-value of 0.0046 is less than the significance level of 0.01, the auditor rejects the null hypothesis.
Learn more about Null hypothesis:
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