Answer:
The answer to your question is the third choice secФ = 41/40
Step-by-step explanation:
Data
Opposite side = 9
Adjacent side = 40
hypotenuse = 41
Process
To solve this problem use trigonometric functions. The secant is the trigonometric function that relates the hypotenuse and the adjacent side.
sec Ф = hypotenuse / adjacent side
hypotenuse = 41
adjacent side = 40
then,
secФ = 41/40
Using the binomial distribution, it is found that there is a 0.0012 = 0.12% probability at least two of them make it inside the recycling bin.
<h3>What is the binomial distribution formula?</h3>
The formula is:


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.
With 5 shoots, the probability of making at least one is
, hence the probability of making none, P(X = 0), is
, hence:

![\sqrt[5]{(1 - p)^5} = \sqrt[5]{\frac{232}{243}}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B%281%20-%20p%29%5E5%7D%20%3D%20%5Csqrt%5B5%5D%7B%5Cfrac%7B232%7D%7B243%7D%7D)
1 - p = 0.9908
p = 0.0092
Then, with 6 shoots, the parameters are:
n = 6, p = 0.0092.
The probability that at least two of them make it inside the recycling bin is:

In which:
[P(X < 2) = P(X = 0) + P(X = 1)
Then:



Then:
P(X < 2) = P(X = 0) + P(X = 1) = 0.9461 + 0.0527 = 0.9988

0.0012 = 0.12% probability at least two of them make it inside the recycling bin.
More can be learned about the binomial distribution at brainly.com/question/24863377
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Let +n+ = number of bottles of cranberry juice needed
+2n+ = number of bottles of ginger ale needed
---------------------------
+3.2n+%2B+.9%2A%28+2n+%29+=+20+
+3.2n+%2B+1.8n+=+20+
+32n+%2B+18n+=+200+
+50n+=+200+
+n+=+4+
and
+2n+=+8+
----------------
The most bottles of cranberry juice is 4