Answer:
![\dfrac{1}{9}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B9%7D)
Step-by-step explanation:
4 people use all three facilities, then
- 16 - 4 = 12 people use the gym and the track and do not use the pool;
- 9 - 4 = 5 people use the pool and the track and do not use the gym;
- 19 - 4 = 15 people use the gym and the pool and do not use the track.
At least two facilities use 4 + 12 + 5 + 15 = 36 people, 4 of them use all three facilities. Thus, the probability that a randomly selected person which uses at least two facilities, uses all the facilities is
![\dfrac{4}{36}=\dfrac{1}{9}](https://tex.z-dn.net/?f=%5Cdfrac%7B4%7D%7B36%7D%3D%5Cdfrac%7B1%7D%7B9%7D)
Well the only thing that would make these triangles not congruent is dilation, Thus, translation, reflection, and rotations all make the triangles congruent.
The bottom one and third one are not congruent while everything else is.
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Answer:
Step-by-step explanation:
Given that the housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 38 bids from potential buyers to estimate the average loss in home value.
s = sample std deviation = 3000
Sample mean = 9379
Sample size n = 38
df = 37
Std error of sample mean = ![\frac{s}{\sqrt{n} } \\=486.66](https://tex.z-dn.net/?f=%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%20%7D%20%5C%5C%3D486.66)
confidence interval 95% = Mean ± t critical * std error
=Mean ±1.687*486.66 = Mean ±821.003
=(8557.997, 10200.003)
a) If std deviation changes to 9000 instead of 3000, margin of error becomes 3 times
Hence 2463.008
b) The more the std deviation the more the width of confidence interval.
length = 12 yd
width = 10 yd
height = 12 yd
diagonal = 19.697715603592 yd
total surface area = 768 yd2
lateral surface area = 528 yd2
bottom surface area = 120 yd2
volume = 1440 yd3