Answer:

Step-by-step explanation:
There is a formula that can be used to find the x-value of the vertex of the parabola. This formula is 
We have the function 
From this function, we can find that

We can plug in our know values into the formula to get

Then we can plug in our x-value to find the y-value of the vertex

This means that the vertex would be 
Answer:
Therefore, the probability that at least half of them need to wait more than 10 minutes is <em>0.0031</em>.
Step-by-step explanation:
The formula for the probability of an exponential distribution is:
P(x < b) = 1 - e^(b/3)
Using the complement rule, we can determine the probability of a customer having to wait more than 10 minutes, by:
p = P(x > 10)
= 1 - P(x < 10)
= 1 - (1 - e^(-10/10) )
= e⁻¹
= 0.3679
The z-score is the difference in sample size and the population mean, divided by the standard deviation:
z = (p' - p) / √[p(1 - p) / n]
= (0.5 - 0.3679) / √[0.3679(1 - 0.3679) / 100)]
= 2.7393
Therefore, using the probability table, you find that the corresponding probability is:
P(p' ≥ 0.5) = P(z > 2.7393)
<em>P(p' ≥ 0.5) = 0.0031</em>
<em></em>
Therefore, the probability that at least half of them need to wait more than 10 minutes is <em>0.0031</em>.
Answer:
Melanie can translate the figure, rotate the figure, or reflect the figure. The figure would still be congruent.
Step-by-step explanation:
Hope that helps.... sorry if it doesn't..
If you mean 1/3 the answer is -15.5
1/3(-32.48-14.02) = 1/3(-46.5) = (-15.5)