Answer:
The answer to your question is
A = 29.6°
B = 115.4°
C = 35°
Step-by-step explanation:
Process
1.- Use the Cosines law to answer this question
c² = a² + b² - 2abcosФ
Solve for cos Ф
cos Ф = (c² - a² - b² )/ -2ab
Substitution
cosФ = (7² - 6² - 11²) / (-2)(6)(11)
cosФ = (49 - 36 - 121) / -132
cos Ф = -108 / -132
cos Ф = 0.818
Ф = 35° = C
Find B
cos Ф = (b² - a² - c²) / (-2ac)
cos Ф = (11² - 6² - 7²) / (-2)(6)(7)
cos Ф = ( 121 - 36 - 49) / -84
cos Ф = 36 / -84
cos Ф = -0.429
Ф = 115.4° = B
2.- Find a
The sum of the internal angles in a triangle equals 180°
A + B + C = 180
A + 115.4 + 35 = 180
A = 180 - 115.4 - 35
A = 29.6°
we can simply put both fractions with the same denominator, and thus then we can just compare which numerator is larger.
we can do so by <u>multiplying each fraction by the other's denominator</u>, let's proceed.
We are given the following variables:
μ = the sample mean = 152 pounds
σ = the standard deviation = 26 pounds
x = the sample value we want to test = 180 pounds
n = the sample size = unknown
MOE = margin of error = 4% = 0.04
Confidence level = 96%
The first thing we can do is to find for the value of z
using the formula:
z = (x – μ) / σ
z = (180 – 152) / 26
z = 1.0769 = 1.08
Since we are looking for the people who weigh more than
180 pounds, therefore this is a right tailed z test. The p value is:
p = 0.1401
Then we can use the formula below to solve for n:
n = z^2 * p * (1 – p) / (MOE)^2
n = 1.08^2 * 0.1401 * (1 – 0.1401) / (0.04)^2
n = 87.82 = 88
Therefore around 88 people must be surveyed.
Step-by-step explanation:
32/3+21/5÷7
14.87÷7
2.124