Answer: 65%, 195 children
Step-by-step explanation: To get this, we just do 100-35 to get 65 percent. We can calculate this further, and do 300*0.65, and we get 195. Thus, there were 195 children.
Answer:
![(D)E[ X ] =np.](https://tex.z-dn.net/?f=%28D%29E%5B%20X%20%5D%20%3Dnp.)
Step-by-step explanation:
Given a binomial experiment with n trials and probability of success p,
Since each term of the summation is multiplied by x, the value of the term corresponding to x = 0 will be 0. Therefore the expected value becomes:
Now,
Substituting,
Factoring out the n and one p from the above expression:
Representing k=x-1 in the above gives us:
This can then be written by the Binomial Formula as:
![E[ X ] = (np) (p +(1 - p))^{n -1 }= np.](https://tex.z-dn.net/?f=E%5B%20X%20%5D%20%3D%20%28np%29%20%28p%20%2B%281%20-%20p%29%29%5E%7Bn%20-1%20%7D%3D%20np.)
Using the pythagorean identity, we can find the value of sin(A)
cos^2(A) + sin^2(A) = 1
(12/13)^2 + sin^2(A) = 1
144/169 + sin^2(A) = 1
sin^2(A) = 1 - 144/169
sin^2(A) = 169/169 - 144/169
sin^2(A) = (169 - 144)/169
sin^2(A) = 25/169
sin(A) = sqrt(25/169)
sin(A) = 5/13
Which is then used to find tan(A)
tan(A) = sin(A)/cos(A)
tan(A) = (5/13) divided by (12/13)
tan(A) = (5/13)*(13/12)
tan(A) = (5*13)/(13*12)
tan(A) = 5/12
The final answer is 5/12
Divide sale price by (1 - percent of discount):
15.75 / (1- 0.15) =
15.75 / 0.85 = 18.53
Answer = $18.53
The correct value is 720 ft of fencing.
Answer:
Max Area = 64800 sq.ft
Step-by-step explanation:
A square will always give us the maximum area.
Thus, one side would be;
720/4 = 180 feet
So, we want a square 180 ft by 180 ft
however, from the question, we are to use the creek as one side. So, we'll take the 180 ft that we don't need because of the creek and then add it to the opposite side to get 180 + 180 = 360 ft.
Thus,we now have a rectangle with dimensions: 180 ft by 360 ft
Area is given by;
area = length × width
Maximum Area = 180 × 360
Max Area = 64800 sq.ft
