Not sure why such an old question is showing up on my feed...
Anyway, let
and
. Then we want to find the exact value of
.
Use the angle difference identity:
and right away we find
. By the Pythagorean theorem, we also find
. (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)
Meanwhile, if
, then (by Pythagorean theorem)
, so
. And from this,
.
So,
40.92 ounces.
You can find it by multiplying 124 by 0.33
If Karim ran one mile, Dan ran two miles.
If Karim ran three miles, Dan ran six miles.
Using the binomial distribution, it is found that there is a 0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.
For each free throw, there are only two possible outcomes, either he makes it, or he misses it. The results of free throws are independent from each other, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- He makes 90% of the free throws, hence
.
- He is going to shoot 3 free throws, hence
.
The probability that he makes exactly 1 is P(X = 1), hence:
0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.
To learn more about the binomial distribution, you can take a look at brainly.com/question/24863377
