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Gekata [30.6K]
3 years ago
9

If the volume of the expanding cube is increasing at the rate 24 cm3 / min , how fast is its surface area increasing when the su

rface area is 216 cm2 ?​
Mathematics
1 answer:
Georgia [21]3 years ago
7 0

Answer:

16 cm^2/min

Step-by-step explanation:

dV/dt=24

V=a^3, differentiate with respect to t

dV/dt=3a^2*da/dt, a^2*da/dt=8

S=6a^2, 216=6a^2. a=6. da/dt=(8/36)

dS/dt=12*a*da/dt=12*(8/6)=16 cm^2/min

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Answer:

a) 0.4770

b) 3.9945

c) z-statistics seem a large value

Step-by-step explanation:

<u>a. Find the standard deviation of the sample proportion based on the null hypothesis</u>

Based on the null hypothesis:

p_{0}: 0.35

and the standard deviation σ = \sqrt{p_{0} *(1-p_{0}) } =\sqrt{0.35 *0.65 } ≈0.4770

<u>b. Find the z statistic</u>

z-statistic is calculated as follows:

z=\frac{X-p_{o} }{\frac{s}{\sqrt{N} } } where

  • X is the proportion of employees in the survey who take advantage of the Credit Union (\frac{138}{300}=0.46)
  • p_{0} is the proportion in null hypothesis (0.35)
  • s is the standard deviation (0.4770)
  • N is the sample size (300)

putting the numbers in the formula:

z=\frac{0.46-0.35} }{\frac{0.4770}{\sqrt{300} } } = 3.9945

<u>c. Does the z statistic seem like a particularly large or small value?</u>

z-statistics seem a large value, which will cause us to reject the null hypothesis.

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How much time will Alex need to walk to his school, which is 2 1/4 miles away from his house, if he would walk with the speed of
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Juliette forgot to study for a test. Of the 150 questions on the test, she answered only 48% correctly. How many questions did
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Juliette answered 72 questions correctly

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