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Answer:
Mean = 30.9
Range = 80
Interquartile Range = 36
Step-by-step explanation:
The mean of a set of numbers is the sum divided by the number of terms. In other words that means 2, 22, 4, 36, 82, 44, 65, 30, 8, 16 go over a fraction like this. There are 10 numbers here so this is our denominator.
For the range, all we do is subtract the minimum value from the maximum which is 82 - 2. That gives us 80.
For the IQ Range....
Arrange the terms in ascending order.
2, 4, 8, 16, 22, 30, 36, 44, 65, 82
Then we need to find the median which is the average of the two middle terms.
So for the lower half of data 2, 4, 8, 16, 22 we have the median of 8
And for the upper half 30, 36, 44, 65, 82 we have the median of 44.
To find the IQ Range it is the difference between the first quartile (8) and the third (44)
So 44 - 8 = 36
<span>11. Find the exact value by using a half-angle identity.
</span><span>sin (22.5)
</span><span>the sine half-angle formula
</span>
12. Find all solutions to the equation in the interval [0, 2π)
</span>cos x = sin 2x
cosx-sin 2x=0
<span>using a graphical tool
</span>in the interval [0, 2π)
</span></span>
</span></span>
</span><span>sin (22.5)
</span><span>the sine half-angle formula
</span>
sin<span>(x/2)</span>=±((1−cos(x))/2) ^0.5 cos 45=(2^0.5)/2
sin(22.5)=±((1−cos(45))/2) ^0.5
sin(22.5)=±((2-2^0.5))^0.5/2
sin(22.5)=±0.3826834324
<span>12. Find all solutions to the equation in the interval [0, 2π)
</span>cos x = sin 2x
cosx-sin 2x=0
<span>using a graphical tool
</span>in the interval [0, 2π)
<span>the solutions are
x1=0----------------not
solution
x2=</span>π/6------------ not solution<span>
x3=</span>π/2------------ is a solution<span>
x4=5</span>π/6---------- not solution<span>
x5=3</span>π/2---------- is a solution
</span></span>
13. Rewrite with only sin x and cos x. sin(2x) = 2*sin(x)*cos(x)
sin 2x - cos x=2*sin(x)*cos(x)- cos x= cos x*(2*sin(x)-1)
<span>the answer is the letter <span>c) cos x (2 sin x - 1)</span></span>
<span>14. Verify the
identity.
cosine of x divided by quantity one plus sine of x plus quantity one plus sine
of x divided by cosine of x equals two times secant of x</span>.
cosx/(1+sinx) + (1+sinx)/cosx
<span>
= (cosx * cosx + (1+sinx)(1+sinx)) / (cosx (1+sinx))
= (cos²x + sin²x + 2 sinx + 1) / (cosx (1+sinx))
= (1 + 2 sinx + 1) / (cosx (1+sinx))
= (2 + 2 sinx) / (cosx (1+sinx))
= 2 (1+sinx) / (cosx (1+sinx))
= 2/cosx
<span>= 2 secx Ok is correct</span></span>