Answer:
Step-by-step explanation:
According to congruent chords and arcs theorem, if 
then 
.
This means that 
Thus:
(full circle = 360°)
Plug in the values into the equation
Add like terms
Subtract 36 on both sides
Divide both sides by 12
Answer:
Mean = 8
Variance = 7.36
Standard Deviation = 2.7129
Step-by-step explanation:
This is a binomial distribution with parameters, n and p.
Where
n is sample size (given as 100)
p is the probability of success, or probability of defective (given as 8% or 0.08)
The mean, variance, standard deviation formula for binomial distribution is shown below:
Mean = 
Variance = 
Standard Deviation = 
Where q would be probability of failure, or "1 - p"
Thus,
n = 100
p = 0.08
q = 1 - 0.08 = 0.92
SO, we have:
Mean = 
Variance = 
Standard Deviation = 
When we are given 3 sides, we try to solve the angles first by using the
law of cosines
cos (A) = [b^2 + c^2 - a^2] / (2 * b * c)
cos (A) = [43^2 + 17^2 -27^2] / (2 * 43 * 17)
cos (A) = [1,849 + 289 -729] /
<span>
<span>
<span>
1,462
</span></span></span>cos (A) = 1,409 / 1,462
cos (A) =
<span>
<span>
<span>
0.96374829001368
Angle A = 15.475
Now that we have one angle, we next can use the
Law of Sines
sin(B) / side b = sin(A) / side a
sin(B) = sin(A) * sideb / sidea
</span></span></span><span>sin(B) = sin(15.475) * 43 / 27
</span><span>sin(B) = 0.26682 * 43 / 27
sin (B) = </span><span>0.424935555555</span>
Angle B = 25.147 Degrees
Remember the arc sine (<span>0.424935555555) also equals </span>
<span>
<span>
<span>
154.85
</span></span></span>Finally, calculating the third angle is quite easy
Angle C = 180 - Angle (A) - Angle(B)
Angle C = 180 - 15.475 - 154.85
Angle C = 9.675
Source:
http://www.1728.org/trigtut2.htm
Answer:
x = 6
Step-by-step explanation:
move all terms to the left:
-1.5x+12-(2.5x-12)=0
get rid of parentheses
-1.5x-2.5x+12+12=0
add all the numbers together, and all the variable.
-4x+24=0
move all terms containing x to the left, all other terms to the right
-4x=-24
x=-24/-4 - divide
x=+6
