Answer:
a

b

c
Option A is correct
Step-by-step explanation:
From the question we are told that
The sample size is n = 15
The probability of success is 
The number of success we are considering is r = 10
Now the probability of failure is mathematically evaluated as

substituting value


Now using the binomial distribution to find the probability of exactly 10 successes we have that
![P(X = r ) = [\left n } \atop {r}} \right. ] * p^r * q^{n- r}](https://tex.z-dn.net/?f=P%28X%20%3D%20%20r%20%29%20%3D%20%20%5B%5Cleft%20n%20%7D%20%5Catop%20%7Br%7D%7D%20%5Cright.%20%5D%20%2A%20p%5Er%20%2A%20%20q%5E%7Bn-%20r%7D)
substituting values
![P(X = 10 ) = [\left 15 } \atop {10}} \right. ] * p^{10}* q^{15- 10}](https://tex.z-dn.net/?f=P%28X%20%3D%20%2010%20%29%20%3D%20%20%5B%5Cleft%2015%20%7D%20%5Catop%20%7B10%7D%7D%20%5Cright.%20%5D%20%2A%20p%5E%7B10%7D%2A%20%20q%5E%7B15-%2010%7D)
Where
mean 15 combination 10 which is evaluated with a calculator to obtain
![[\left 15 } \atop {10}} \right. ] = 3003](https://tex.z-dn.net/?f=%5B%5Cleft%2015%20%7D%20%5Catop%20%7B10%7D%7D%20%5Cright.%20%5D%20%20%3D%203003)
So


Now using the normal distribution to approximate the probability of exactly 10 successes, we have that

Applying continuity correction

substituting values


Standardizing

The where
is the mean which is mathematically represented as

substituting values


The standard deviation is evaluated as

substituting values


Thus



From the normal distribution table we obtain the
as

And the 

There value can also be obtained from a probability of z calculator at (Calculator dot net website)
So


Looking at the calculated values for question a and b we see that the values are fairly different.
In a 45-45-90 triangle, the two legs are congruent. Let's call them x. The hypotenuse is equal to 1 as we're using the unit circle. The hypotenuse of the triangle is the same as the radius of the unit circle.
a = x
b = x
c = 1
Use those values in the Pythagorean theorem to solve for x.
a^2 + b^2 = c^2
x^2 + x^2 = 1^2
2x^2 = 1
x^2 = 1/2
x = sqrt( 1/2 )
x = sqrt(1)/sqrt(2)
x = 1/sqrt(2)
x = sqrt(2)/2 ... rationalizing the denominator
So this right triangle has legs that are sqrt(2)/2 units long. Once we know the legs of the triangle, we can divide them over the hypotenuse to find the sine and cosine values.
sin(angle) = opposite/hypotenuse
sin(45) = (sqrt(2)/2) / 1
sin(45) = sqrt(2)/2
and
cos(angle) = adjacent/hypotenuse
cos(45) = (sqrt(2)/2) / 1
cos(45) = sqrt(2)/2
------------------------------------------------------
For a 30-60-90 triangle, we would have
a = 1
b = x
c = 2
so,
a^2+b^2 = c^2
1^2+x^2 = 2^2
1+x^2 = 4
x^2 = 4-1
x^2 = 3
x = sqrt(3)
The missing leg is sqrt(3) units long.
Once we know the three sides of the 30-60-90 triangle, you should be able to see that
sin(30) = 1/2
sin(60) = sqrt(3)/2
cos(30) = sqrt(3)/2
cos(60) = 1/2
Answer:
D)$660
Step-by-step explanation:
Add all of them up and you get $658.29 the number in the tens place is 5 and the number on the right is 8 so you round up.