Based on the given information, let x represent the grade for the fifth quiz.
(79+88+95+71+x)/5=85
(333+x)/5=85
333+x=425
x=92
Jackson would have to earn a 92 on his fifth quiz to earn an average of 85.
Answer:
is a factor of 
Step-by-step explanation:
is a factor of
We will prove this with the help of principal of mathematical induction.
For n = 1, is a factor , which is true.
Let the given statement be true for n = k that is is a factor of 
.
Thus, can be written equal to 
, where y is an integer.
Now, we will prove that the given statement is true for n = k+1
Thus, is divisible by .
Hence, by principle of mathematical induction, the given statement is true for all natural numbers,n.
The value is given in question.... put the corresponding value in the equation in place of "x" and you will obtain the value of "y"
Answer:
central angle, in radians
Step-by-step explanation:
The ratio s/r is equal to the central angle, which must be in radians.
<span> sin20 * sin40 * sin60 * sin80
since sin 60 = </span><span> √3/2
</span>√3/<span>2 (sin 20 * sin 40 * sin 80)
</span>√3/<span>2 (sin 20) [sin 40 * sin 80]
</span>
Using identity: <span>sin A sin B = (1/2) [ cos(A - B) - cos(A + B) ]
</span>√3/<span>2 (sin 20) (1 / 2) [cos 40 - cos 120]
</span>√3/4<span> (sin 20) [cos 40 + cos 60]
</span>
Since cos 60 = 1/2:
√3/4<span> (sin 20) [cos 40 + (1/2)]
</span>√3/4 (sin 20)(cos 40) + √3/8<span> (sin 20)
</span>
Using identity: <span> sin A cos B = 1/2 [ sin(A + B) + sin(A - B) ]
</span>√<span>3/4 (1 / 2) [sin 60 + sin (-20)] + </span>√3/8<span> (sin 20)
</span>
Since sin 60 = √3/<span>2
</span>√3/8 [√3/2 - sin 20] + √3/8 (sin 20)
3/16 - √3/8 sin 20 + √3/8<span> sin 20
</span>
Cancelling out the 2 terms:
3/16
Therefore, sin20 * sin40 * sin60 * <span>sin80 = 3/16</span>
