Answer:
The probability of observing between 43 and 64 successes=0.93132
Step-by-step explanation:
We are given that
n=100
p=0.50
We have to find the probability of observing between 43 and 64 successes.
Let X be the random variable which represent the success of population.
It follows binomial distribution .
Therefore,
Mean,
Standard deviation , 
![\sigma=\sqrt{100\times 0.50(1-0.50)]](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B100%5Ctimes%200.50%281-0.50%29%5D)
Now,
Hence, the probability of observing between 43 and 64 successes=0.93132
Answer:
320 in.²
Step-by-step explanation:
Let's think of the shape as a normal rectangle with a height of 16 inches. Now all we need is the length. If you look at the right corner, it looks like a piece has been cut out. Since that piece has the same length and height of 8 inches, it is a square. This tells us the missing length of the entire length of the rectangle. Now the length of the rectangle is 16 inches + 8 inches, which is 24 inches.
The total area of the rectangle is 16 × 24, which is 384.
Then from the total area, we just need to subtract the area of the cut-out part. The area of the cut-out square is 8 × 8, which is 64.
384 - 64 = 320
The total surface area of the following complex shape is 320 in.²
Answer:
x = 2.5 inches. Or
x = 5/2
Step-by-step explanation:
Length: 7 + 2x
Width: 5 + 2x
Note that you have to add x at each end of the picture and onto each part of the width.
The entire area is 120 square inches.
Formula
L*W = Area
(2x + 7)(2x + 5) = 120
Solution
4x^2 + 10x + 14x + 35 = 120 Subtract 120 from both sides. Add xs
4x^2 + 24x + 35 - 120 = 0
4x^2 + 24x - 85 = 0 Factor
(2x + 17)(2x - 5)
2x + 17 has no meaning. It will give - 8.5 which is not possible.
2x - 5 =0
2x = 5 Divide by 2
x = 5/2
x = 2.5
Note: I don't know which one the computer is looking for.
