Right angle/90° angle, i believe
Answer:
__63.81 inches__< μ <___65.87 inches__
Step-by-step explanation:
To calculate at 95% confidence interval, we need the Mean of the sample= 64.84
Sample size=32
Standard Deviation=2.9592
95% Confidence Interval: 64.84 ± 1.03
(63.81 inches to 65.87 inches)
"With 95% confidence the population mean is between 63.81 and 65.87, based on 32 samples."
Use the identity:
P(A or B)=P(A)+P(B)-P(A and B)
Substitute given values,
0.88=0.62+0.47-P(A and B)
=>
P(A and B)=0.62+0.47-0.88=0.21
<span>To be both complex and imaginary, the answer would have to include "i" as well as have the form "a + bi". The first example, 3i - 5, fits. This would look to be the only example that does fit. The negative square root of 14 would be imaginary, but not complex.</span>
Answer:
See explanation
Step-by-step explanation:
Let a,b, and c be real numbers.
The distributive property says that:
![a(b + c) = ab + ac](https://tex.z-dn.net/?f=a%28b%20%2B%20c%29%20%3D%20ab%20%2B%20ac)
Assuming we want to simplify:
![10(5*10^{-1}+150*10^{-3})](https://tex.z-dn.net/?f=10%285%2A10%5E%7B-1%7D%2B150%2A10%5E%7B-3%7D%29)
We apply the distributive property to get:
![10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10+150*10^{-3} \times 10](https://tex.z-dn.net/?f=10%285%2A10%5E%7B-1%7D%2B150%2A10%5E%7B-3%7D%29%20%3D%205%2A10%5E%7B-1%7D%20%5Ctimes%2010%2B150%2A10%5E%7B-3%7D%20%5Ctimes%2010)
We can now use rules of exponents to simplify further:
![10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10^{1} +150*10^{-3} \times 10^{1}](https://tex.z-dn.net/?f=10%285%2A10%5E%7B-1%7D%2B150%2A10%5E%7B-3%7D%29%20%3D%205%2A10%5E%7B-1%7D%20%5Ctimes%2010%5E%7B1%7D%20%2B150%2A10%5E%7B-3%7D%20%5Ctimes%2010%5E%7B1%7D%20)
![10(5*10^{-1}+150*10^{-3}) = 5*10^{-1 + 1} +150*10^{-3 + 1}](https://tex.z-dn.net/?f=10%285%2A10%5E%7B-1%7D%2B150%2A10%5E%7B-3%7D%29%20%3D%205%2A10%5E%7B-1%20%2B%201%7D%20%2B150%2A10%5E%7B-3%20%2B%201%7D)
![10(5*10^{-1}+150*10^{-3}) = 5*10^{0} +150*10^{-2}](https://tex.z-dn.net/?f=10%285%2A10%5E%7B-1%7D%2B150%2A10%5E%7B-3%7D%29%20%3D%205%2A10%5E%7B0%7D%20%2B150%2A10%5E%7B-2%7D)
![10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2}x {10}^{2}](https://tex.z-dn.net/?f=10%285%2A10%5E%7B-1%7D%2B150%2A10%5E%7B-3%7D%29%20%3D%205%2A1%2B1.50%2A10%5E%7B-2%7Dx%20%7B10%7D%5E%7B2%7D%20)
![10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2 + 2}](https://tex.z-dn.net/?f=10%285%2A10%5E%7B-1%7D%2B150%2A10%5E%7B-3%7D%29%20%3D%205%2A1%2B1.50%2A10%5E%7B-2%20%2B%202%7D)
![10(5*10^{-1}+150*10^{-3}) = 5+1.50*10^{0} = 6.5 \times {10}^{0}](https://tex.z-dn.net/?f=10%285%2A10%5E%7B-1%7D%2B150%2A10%5E%7B-3%7D%29%20%3D%205%2B1.50%2A10%5E%7B0%7D%20%3D%206.5%20%5Ctimes%20%20%7B10%7D%5E%7B0%7D%20)