Here you go. Should be solved
We will use the followin property of logarithms:
So, we have
If you multiply both sides by 4, you get
Suppose that the numbers that the boy being cast from the dice are 3 4 5 6.
3 stands for white, 4 stands for red, 5 stands for green and 6 stands for blue.
We need to interpret the statement given above. The set of numbers is 3 4 4 6 6 5.
First, we need to get the mean of this set. Add all the numbers and divide by the total number that the set has.
3+4+4+6+6+5= 28 / 6
= 4.67 The mean is 4.67
For the variance, we will use the mean above ( 4.67 )
1. Squared the mean and subtract how many numbers are present in the set.
4.67x4.67= 21.8089 /6 = 3.64 set aside this result
2. Next squared all the numbers present in the set and add the result
3x3= 9 , 4x4= 16, 4x4=16, 6x6=36, 6x6=36, 5x5=25
9+16+16+36+36+25= 138
3. Subtract the result of #2 with #1
138 - 3.64= 134.36 set this aside
4. Subtract 1 from the total numbers you have in your set
6 - 1= 5
5. Divide the result we have in #3 with the result of #4
134.36 / 5= 26. 872
So the variance is 26.872
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In this problem, you apply principles in trigonometry. Since it is not mentioned, you will not assume that the triangle is a special triangle such as the right triangle. Hence, you cannot use Pythagorean formulas. The only equations you can use is the Law of Sines and Law of Cosines.
For finding side a, you can answer this easily by the Law of Cosines. The equation is
a2=b2 +c2 -2bccosA
a2 = 11^2 + 8^2 -2(11)(8)(cos54)
a2 = 81.55
a = √81.55
a = 9
Then, we use the Law of Sines to find angles B and C. The formula would be
a/sinA = b/sinB = c/sinC
9/sin54° = 11/sinB
B = 80.4°
9/sin54° = 8/sinC
C = 45.6°
The answer would be: a ≈ 9, C ≈ 45.6, B ≈ 80.4
