<h3>Answer: A. 5/12, 25/12</h3>
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Work Shown:
12*sin(2pi/5*x)+10 = 16
12*sin(2pi/5*x) = 16-10
12*sin(2pi/5*x) = 6
sin(2pi/5*x) = 6/12
sin(2pi/5*x) = 0.5
2pi/5*x = arcsin(0.5)
2pi/5*x = pi/6+2pi*n or 2pi/5*x = 5pi/6+2pi*n
2/5*x = 1/6+2*n or 2/5*x = 5/6+2*n
x = (5/2)*(1/6+2*n) or x = (5/2)*(5/6+2*n)
x = 5/12+5n or x = 25/12+5n
these equations form the set of all solutions. The n is any integer.
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The two smallest positive solutions occur when n = 0, so,
x = 5/12+5n or x = 25/12+5n
x = 5/12+5*0 or x = 25/12+5*0
x = 5/12 or x = 25/12
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Plugging either x value into the expression 12*sin(2pi/5*x)+10 should yield 16, which would confirm the two answers.
In an equilateral triangle, the measure of each angle is 60 degrees. Then the value of x and y is 17/3 and 65.
<h3>What is the triangle?</h3>
A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In trianlge ΔMNP, PM = 3x - 4, MN = 14, ∠N = 5y - 5.
In an equilateral triangle, all the sides and all the angles are equal.
MN = NP = PM
∠M = ∠N = ∠P
Then we have
PM = MN
3x - 4 = 14
x = 17/3
We know in an equilateral triangle, the measure of each angle is 60 degrees. Then we have
∠N = 60
5y - 5 = 60
5y = 65
y = 13
More about the triangle link is given below.
brainly.com/question/25813512
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To answer this question, we need to find the winning probability in either case.
Probability = no. of outcomes / total no. of possible outcomes
<u>When Hope pulled her defender :</u>
Total no. of games = 9
No. of games won = 3
Winning probability = 3/9 =1/3
<u>When Hope left her defender :</u>
Total no. of games = 10
No. of games won = 6
Winning probability = 6/10 = 3/5
We know that , 1/3 < 3/5.
So, Hope should not pull her defender, as the winning probability is better when Hope left her defender.
Answer : A. Hope should not pull her defender.
