Answer:68.3 degrees
Step-by-step explanation:
The diagram of the triangle ABC is shown in the attached photo. We would determine the length of side AB. It is equal to a. We would apply the cosine rule which is expressed as follows
c^2 = a^2 + b^2 - 2abCos C
Looking at the triangle,
b = 75 miles
a = 80 miles.
Angle ACB = 180 - 42 = 138 degrees. Therefore
c^2 = 80^2 + 75^2 - 2 × 80 × 75Cos 138
c^2 = 6400 + 5625 - 12000Cos 138
c^2 = 6400 + 5625 - 12000 × -0.7431
c^2 = 12025 + 8917.2
c = √20942.2 = 144.7
To determine A, we will apply sine rule
a/SinA = b/SinB = c/SinC. Therefore,
80/SinA = 144.7/Sin 138
80Sin 138 = 144.7 SinA
SinA = 53.528/144.7 = 0.3699
A = 21.7 degrees
Therefore, theta = 90 - 21.7
= 68.3 degees
Answer:
$83 million
Step-by-step explanation:
29% of the charity's donated funds.
$24.1 million = donation
Let x = the total amount of donated funds
29/100 • x = 24.1
x = 24.1 • 100/29
x = 83.10
=83
Hope this helps :)
Answer:
Step-by-step explanation:
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Answer:
P=0.54.
Step-by-step explanation:
We know that in a sample of 6500 automobiles found that 1560 of the automobiles were black, 3120 of the automobiles were sedans, and 1170 of the automobiles were black sedans.
We calculate the number of sedans that are not black:
3120-1170=1950
We calculate the number of black cars that are not sedans:
1560-1170=390
The number of automobiles which are black or a sedan is
1950+390+1170=3510.
The probability that the automobile is black or a sedan is:
P=3510/6500
P=0.54.
