Answer:
A.The probability that exactly six of Nate's dates are women who prefer surgeons is 0.183.
B. The probability that at least 10 of Nate's dates are women who prefer surgeons is 0.0713.
C. The expected value of X is 6.75, and the standard deviation of X is 2.17.
Step-by-step explanation:
The appropiate distribution to us in this model is the binomial distribution, as there is a sample size of n=25 "trials" with probability p=0.25 of success.
With these parameters, the probability that exactly k dates are women who prefer surgeons can be calculated as:

A. P(x=6)

B. P(x≥10)




C. The expected value (mean) and standard deviation of this binomial distribution can be calculated as:

Answer:
Side x = 2.12132 = 3√2/2
Step-by-step explanation:
I used a triangle calculator to find side x
The function is L = 10m + 50
Here, we want to find out which of the functions is required to determine the number of lunches L prepared after m minutes
In the question, we already had 50 lunches prepared
We also know that he prepares 10 lunches in one minute
So after A-lunch begins, the number of lunches prepared will be 10 * m = 10m
Adding this to the 50 on ground, then we have the total L lunches
Mathematically, that would be;
L = 10m + 50