Answer: b. 0.8413
Step-by-step explanation:
Given : The average time taken to complete an exam, X, follows a normal probability distribution with 
and 
.
Then, the probability that a randomly chosen student will take more than 30 minutes to complete the exam will be :-
![P(x>30)=P(z>\dfrac{30-60}{30})\ \ [\because\ z=\dfrac{x-\mu}{\sigma} ]\\\\=P(z>-1)=P(z-z)=P(Z](https://tex.z-dn.net/?f=P%28x%3E30%29%3DP%28z%3E%5Cdfrac%7B30-60%7D%7B30%7D%29%5C%20%5C%20%5B%5Cbecause%5C%20z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%20%5D%5C%5C%5C%5C%3DP%28z%3E-1%29%3DP%28z%3C1%29%5C%20%5C%20%5C%20%5B%5Cbecause%5C%20P%28Z%3E-z%29%3DP%28Z%3Cz%29%5D%5C%5C%5C%5C%3D%200.8413)
[using z-value table]
Hence, the probability that a randomly chosen student will take more than 30 minutes to complete the exam = 0.8413
P = Number of ways of getting only 4 at the last trial / Total number of waysNumber of ways of getting only 4 at the last trial = 5 * 5 * 5 * 1 = 125 (for the first three trials, all but 4 is permissible (6 - 1 = 5 ways), and for the last trial, only 4 is permissible (1 way)).Total number of ways = 6 * 6 * 6 * 6 = 1296.P = 125/1296.
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General exponential equation
y = A(1+r)^x
where
A = initial value
r = rate increase (+) or decrease (-)
x = time period of the change
y = projected value
y = 300(1.05)^x
in this problem, x = years after 2017
we want to find an x that makes the value more than or equal to 650
650 <= 300(1.05)^x
Answer:
The equation is:
(2×π×r×4r)+(2×π×r^2)= A
The maximum radius of the can they will produce = 1.7 inches
Step-by-step explanation:
Please see the attached files for explanation
