Answer:
d. The variance is 9.56 and the standard deviation is 3.09.
Step-by-step explanation:
From the above question, we are given the following data set.
3, 7, 8, 8, 8, 9, 10, 10, 13, 14
a) Mean = 3 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 13 + 14/ 10
= 90/10
= 9
b) Variance
The formula for sample Variance = (Mean - x)²/ n - 1
Mean = 9
n = 10
Sample Variance =
(3 - 9)² + (7 - 9)² + (8 - 9)² + (8 - 9)² + (8 - 9)² + (9 - 9)² + (10 - 9)² + (10 - 9)² + (13 - 9)² + (14 - 9)² / 10 - 1
= 36 + 4 + 1 + 1 + 1 + 0 + 1 + 1 + 16 + 25/9
= 86/9
= 9.555555556
≈ Approximately 9.56
Variance = 9.56
Sample Standard deviation = √Sample Variance
= √9.56
= 3.0919249667
≈ Approximately 3.09
Check the picture below.
since we know that x = 3/7, we can then plug that on either of the twin legs, since it's an isosceles, and get the length of each leg, so say let's plug it in 5x + 16
![5x + 16\implies 5\left( \cfrac{3}{7} \right)+16\implies \cfrac{38}{7}+16\implies \cfrac{38+112}{7}\implies \cfrac{150}{7}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\\stackrel{\textit{both legs}}{\cfrac{150}{7}+\cfrac{150}{7}}+\stackrel{\textit{base}}{6}\implies \cfrac{150+150+42}{7}\implies \cfrac{342}{7}\implies 48\frac{6}{7}\impliedby \textit{perimeter}](https://tex.z-dn.net/?f=5x%20%2B%2016%5Cimplies%205%5Cleft%28%20%5Ccfrac%7B3%7D%7B7%7D%20%5Cright%29%2B16%5Cimplies%20%5Ccfrac%7B38%7D%7B7%7D%2B16%5Cimplies%20%5Ccfrac%7B38%2B112%7D%7B7%7D%5Cimplies%20%5Ccfrac%7B150%7D%7B7%7D%5C%5C%5C%5C%5B-0.35em%5D%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%5Cstackrel%7B%5Ctextit%7Bboth%20legs%7D%7D%7B%5Ccfrac%7B150%7D%7B7%7D%2B%5Ccfrac%7B150%7D%7B7%7D%7D%2B%5Cstackrel%7B%5Ctextit%7Bbase%7D%7D%7B6%7D%5Cimplies%20%5Ccfrac%7B150%2B150%2B42%7D%7B7%7D%5Cimplies%20%5Ccfrac%7B342%7D%7B7%7D%5Cimplies%2048%5Cfrac%7B6%7D%7B7%7D%5Cimpliedby%20%5Ctextit%7Bperimeter%7D)
Answer:
He should buy lights that are 2088 inches long
Step-by-step explanation:
Craig has a rectangle wooden deck that measures 799 inches by 245 inches.
Let us say the length, L, is 799 inches and the breadth, B, is 245 inches.
He wants to put a string of lights around the deck.
This means that he needs to buy the length of lights that would be equal to the perimeter of the rectangular deck.
The perimeter of a rectangle is given as:
P = 2(L + B)
Hence, the length of lights he should buy is:
P = 2(799 + 245) = 2(1044)
P = 2088 inches
He should buy lights that are 2088 inches long.
The difference between causation and correlation is that, Causation is characterized by cause-and-effect while correlation establishes a probable relationship.
<h3>What is the difference between Causation and correlation?</h3>
While Causation is characterized by a situation in which an action certainly causes an outcome and hence, is described as a cause-and-effect relationship, Correlation on the other hand only establishes a relationship between the two events and doesn't necessarily ascertain the occurrence of the other event .
An example of two variables which may be correlated is; the height and weight of an individual in which case it is generally perceived that taller people are heavier.
Read more on correlation and causation;
brainly.com/question/964703
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Answer:
3 < c < 13
Step-by-step explanation:
A triangle is known to have 3 sides: Side a, Side b and Side c.
For a triangle, one of the three sides is longer than the other two sides. (The only exception is when we are told specifically that a triangle is an equilateral triangle, where all the 3 sides are equal to each other).
To solve the above question, we would be using the Triangle Inequality Theorem.
The Triangle Inequality Theorem states that the summation or addition of the lengths of any two sides of a triangle is greater than the length of the third side.
Side a + Side b > Side c
Side a + Side c > Side b
Side b + Side c > Side a
For the above question, we have 2 possible side lengths for the third side of the triangle. We are given in the above question,
side (a) = 5
side (b) = 8
Let's represent the third side as c
To solve for the above question,we would be having the following Inequality.
= b - a < c < b + a
= 8 - 5 < c < 8 + 5
= 3 < c < 13
