Answer:
75 feet
Step-by-step explanation:
the shadow to the object would be a 4:5 ratio
since the shadow of the flagpole is 60 ft,
4x=60 so x would =15
then you multiply 15 by 5 and end up with 75
Answer: 0.8461
Step-by-step explanation:
Let p be the proportion of residents are against the increase of taxes to fund alternatives to drug addiction treatment.
As per given , we have p=0.40
A random sample is taken with size : n= 400
Expecting sample proportion : ![\hat{p}=\dfrac{150}{400}=0.375](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7B150%7D%7B400%7D%3D0.375)
Now , the probability that more than 150 of the residents surveyed will be against increasing taxes if a random sample of 400 residents are surveyed will be :
![P(p>0.375)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.375-0.40}{\sqrt{\dfrac{0.40(0.60)}{400}}})](https://tex.z-dn.net/?f=P%28p%3E0.375%29%3DP%28%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%3E%5Cdfrac%7B0.375-0.40%7D%7B%5Csqrt%7B%5Cdfrac%7B0.40%280.60%29%7D%7B400%7D%7D%7D%29)
![=P(z>\dfrac{0.375-0.40}{\sqrt{\dfrac{0.40(0.60)}{400}}})\ \ [\because\ z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]](https://tex.z-dn.net/?f=%3DP%28z%3E%5Cdfrac%7B0.375-0.40%7D%7B%5Csqrt%7B%5Cdfrac%7B0.40%280.60%29%7D%7B400%7D%7D%7D%29%5C%20%5C%20%5B%5Cbecause%5C%20z%3D%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%5D)
![=P(z>-1.02)=P(z-z)=P(Z](https://tex.z-dn.net/?f=%3DP%28z%3E-1.02%29%3DP%28z%3C1.02%29%5C%20%5C%20%5B%5Cbecause%20%5C%20P%28Z%3E-z%29%3DP%28Z%3Cz%29%5D)
[By z-table]
Hence, the approximate probability that more than 150 of the residents surveyed will be against increasing taxes if a random sample of 400 residents are surveyed is 0.8461 .
Answer:
I think that the answer is A.
Step-by-step explanation:
Answer:
93 degrees
Step-by-step explanation:
The angles in a triangle add to be 180 so
180-56-31=x
x=93
Answer:
60
Step-by-step explanation:
Set up a ratio problem
15/25 = 36/x
15x = 900
x = 60