The converse of the hinge theorem is also true: If the two sides of one triangle are congruent<span> to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second .</span>
Answer:
The answer is b ($9.74)
Step-by-step explanation:
I got it right (:
Machine C makes 75 candies per minute.
Machine D makes 130 candies per minute.
Difference is 55
55 * 11 minutes = 605 candies.
Answer:
Check Explanation
Step-by-step explanation:
A) The null hypothesis would be that the proportion of newly hired candidates that are not white is not significantly different from the proportion of the applicants that are not white & there is no significant evidence that the company's hiring practices are discriminatory.
Mathematically,
H₀: μ₀ = 0.53
And the alternative hypothesis would be that there is a significant difference between the proportion of newly hired candidates that are not white is not significantly different from the proportion of the applicants that are not white. More specifically, that the proportion of newly hired candidates that are not white is significantly less than the proportion of applicants that are not white & there is significant evidence that the company's hiring practices are indeed discriminatory.
Mathematically,
Hₐ: μ₀ < 0.53
B) The two errors that can come up in this hypothesis testing include -
Type I error: We reject the null hypothesis because we obtain that the proportion of newly hired candidates that are not white is significantly less than the proportion of applicants that are not white and conclude that there is indeed significant evidence that the company's hiring practices are discriminatory when in reality, there is no significant difference and hence, no discrimination.
Type II error: We accept the null hypothesis (fail to reject the null hypothesis) because we obtained that there is no significant difference between the proportion of newly hired candidates that are not white & th proportion of applicants that are not white and conclude that there is no discrimination in the company's hiring practices when in reality, there is significant difference in the stated proportions above and significant evidence that there is indeed significant evidence that the company's hiring practices are discriminatory.
C) The power of the test increases as the significance level reduces. This is because t-statistic increases as significance level reduces.
D) The standard error of the mean used in computing the t-score is given as
σₓ = (σ/√n)
It is evident that as the value of n increases, the standard error reduces and this widens the effect of the test, hence, the power of the test increases.
Hope this Helps!!!
Answer:
cos(F) = 9/41
Step-by-step explanation:
The triangles are similar, so you know that ...
... cos(D) = cos(A) = 40/41.
From trig relations, you know ...
... cos(F) = sin(D)
and
... sin(D)² +cos(D)² = 1
So ...
... cos(F) = sin(D) = √(1 -cos(D)²) = √(1 -(40/41)²) = √(81/1681)
... cos(F) = 9/41
_____
The ratio for cos(A) tells you that you can consider AB=40, AC=41. Then, using the Pythagorean theorem, you can find BC = √(41² -40²) = √81 = 9.
From the definition of the cosine, you know cos(C) = BC/AC = 9/41. Because the triangles are similar, you know
... cos(F) = cos(C) = 9/41
