Answer:
the probability that the sample variance exceeds 3.10 is 0.02020 ( 2,02%)
Step-by-step explanation:
since the variance S² of the batch follows a normal distribution , then for a sample n of 20 distributions , then the random variable Z:
Z= S²*(n-1)/σ²
follows a χ² ( chi-squared) distribution with (n-1) degrees of freedom
since
S² > 3.10 , σ²= 1.75 , n= 20
thus
Z > 33.65
then from χ² distribution tables:
P(Z > 33.65) = 0.02020
therefore the probability that the sample variance exceeds 3.10 is 0.02020 ( 2,02%)
The sides of a triangle must satisfy the triangle inequality, which states the sum of the lengths of any two sides is strictly greater than the length of the remaining side.
We really only have to check if the sum of the two smaller sides exceeds the largest side.
A. 5+6>7, ok
B. 6+6>10, ok
C. 7+7=14 Not ok, this is a degenerate triangle not a real triangle
D. 4+6>8 ok
Answer: C
well, putting the movie in fifths, she watched 3/5, the whole movie will be 5/5 = 1.
![\begin{array}{ccll} \stackrel{movie}{fraction}&hour\\ \cline{1-2} \frac{3}{5}&\frac{5}{8}\\[1em] \underset{whole}{1}&x \end{array}\implies \cfrac{~~ \frac{3}{5}~~}{1}=\cfrac{~~ \frac{5}{8}~~}{x}\implies \cfrac{3}{5}x=\cfrac{5}{8}\implies \cfrac{3x}{5}=\cfrac{5}{8} \\\\\\ 24x=25\implies x = \cfrac{25}{24}\implies x = 1\frac{1}{24}\qquad \textit{1 hour, 2 minutes and 30 seconds}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccll%7D%20%5Cstackrel%7Bmovie%7D%7Bfraction%7D%26hour%5C%5C%20%5Ccline%7B1-2%7D%20%5Cfrac%7B3%7D%7B5%7D%26%5Cfrac%7B5%7D%7B8%7D%5C%5C%5B1em%5D%20%5Cunderset%7Bwhole%7D%7B1%7D%26x%20%5Cend%7Barray%7D%5Cimplies%20%5Ccfrac%7B~~%20%5Cfrac%7B3%7D%7B5%7D~~%7D%7B1%7D%3D%5Ccfrac%7B~~%20%5Cfrac%7B5%7D%7B8%7D~~%7D%7Bx%7D%5Cimplies%20%5Ccfrac%7B3%7D%7B5%7Dx%3D%5Ccfrac%7B5%7D%7B8%7D%5Cimplies%20%5Ccfrac%7B3x%7D%7B5%7D%3D%5Ccfrac%7B5%7D%7B8%7D%20%5C%5C%5C%5C%5C%5C%2024x%3D25%5Cimplies%20x%20%3D%20%5Ccfrac%7B25%7D%7B24%7D%5Cimplies%20x%20%3D%201%5Cfrac%7B1%7D%7B24%7D%5Cqquad%20%5Ctextit%7B1%20hour%2C%202%20minutes%20and%2030%20seconds%7D)
39 it's an arithmetic sequence in which the common difference is +7
