Two cars start from towns 800800 mi apart and travel toward each other. They meet after 88 hr. Find the speed of each car if one
1 answer:
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Answer:
- 4/13 h ≈ 0.308 h
- 22 9/13 km ≈ 22.7 km
Step-by-step explanation:
Mary and Amaruk are starting 35 -15 = 20 km apart. Their closing speed is 40 +25 = 65 km/h. The time it will take to close the gap between them is ...
t = (20 km)/(65 km/h) = 20/65 h = 4/13 h ≈ 0.308 h
They will pass each other after 4/13 hours, about 18 minutes 28 seconds.
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In that time, Mary will have increased her distance from Hall Beach by ...
d = (4/13 h)(25 km/h) = 100/13 km = 7 9/13 km
Her distance from Hall Beach when she passes Amaruk will be ...
15 km + 7 9/13 km = 22 9/13 km ≈ 22.7 km . . . . . distance from Hall Beach
Answer:
See the proof below.
Step-by-step explanation:
Assuming this complete question: "For each given p, let Z have a binomial distribution with parameters p and N. Suppose that N is itself binomially distributed with parameters q and M. Formulate Z as a random sum and show that Z has a binomial distribution with parameters pq and M."
Solution to the problem
For this case we can assume that we have N independent variables with the following distribution:
bernoulli on this case with probability of success p, and all the N variables are independent distributed. We can define the random variable Z like this:
From the info given we know that
We need to proof that by the definition of binomial random variable then we need to show that:
The deduction is based on the definition of independent random variables, we can do this:
And for the variance of Z we can do this:
And if we take common factor we got:
And as we can see then we can conclude that