Recall that
sin(<em>a</em> + <em>b</em>) = sin(<em>a</em>) cos(<em>b</em>) + cos(<em>a</em>) sin(<em>b</em>)
sin(<em>a</em> - <em>b</em>) = sin(<em>a</em>) cos(<em>b</em>) - cos(<em>a</em>) sin(<em>b</em>)
Adding these together gives
sin(<em>a</em> + <em>b</em>) + sin(<em>a</em> - <em>b</em>) = 2 sin(<em>a</em>) cos(<em>b</em>)
To get 14 cos(39<em>x</em>) sin(19<em>x</em>) on the right side, multiply both sides by 7 and replace <em>a</em> = 19<em>x</em> and <em>b</em> = 39<em>x</em> :
7 (sin(19<em>x</em> + 39<em>x</em>) + sin(19<em>x</em> - 39<em>x</em>)) = 14 cos(39<em>x</em>) sin(19<em>x</em>)
7 (sin(58<em>x</em>) + sin(-20<em>x</em>)) = 14 cos(39<em>x</em>) sin(19<em>x</em>)
7 (sin(58<em>x</em>) - sin(20<em>x</em>)) = 14 cos(39<em>x</em>) sin(19<em>x</em>)
Answer:
And if we use the values obtained we got:
For this case this value means that the expected score is about 7.48
Step-by-step explanation:
For this case we assume the following probability distribution:
X 5 6 7 8 9 10
P(X) 0.05 0.15 0.33 0.28 0.12 0.07
First we need to find the expected value (first moment) and the second moment in order to find the variance and then the standard deviation.
In order to calculate the expected value we can use the following formula:
And if we use the values obtained we got:
For this case this value means that the expected score is about 7.48
In order to find the standard deviation we need to find first the second moment, given by :
And using the formula we got:
Then we can find the variance with the following formula:
![Var(X)=E(X^2)-[E(X)]^2 =57.46-(7.48)^2 =1.5096](https://tex.z-dn.net/?f=Var%28X%29%3DE%28X%5E2%29-%5BE%28X%29%5D%5E2%20%3D57.46-%287.48%29%5E2%20%3D1.5096)
And then the standard deviation would be given by:
<span>Since it's even, the integral from -7 to -1 is the same as the integral from 1 to 7.
</span><span>think about
x^2
from 0..1,its 1/3
from 0..7 its 7^3/3
from -1..7 its 7^3/3+1/3
</span>
<span>from -7..-1 of x^2 its -1/3+7^3/3 to get this without integrating we just do 7^3/3-1/3 which is the integral from 0..7 minus the integral from 0..1
</span><span>So the integral from 1 to 0 f(x) dx = 5 changes to the integral from 0 to 1 f(x) dx = -5 and you add it to the integral from 0 to 7 which is 1 making -4</span>
The second answer choice.
Answer:
0.91 because 8/10 as a decimal is 0.8
Step-by-step explanation:
so 0.91 is bigger than 0.8
