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2 years ago

Does someone mind helping me with this question? Thank you!

Mathematics

1 answer:

alukav5142 [94]2 years ago

6 0

Answer:

160 sq cm

Step-by-step explanation:

Since the two trapezoids are similar, you can use a ratio to find the area.

If we use x to represent the area of ABCD, then the ratio will look something like:

5/20 = 40/x

which then we can solve x to be 160 sq cm.

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Every time I use a piece of scrap paper, I crumple it up and try to shoot it inside the recycling bin across the room. I'm prett

valentinak56 [21]

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:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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 $\frac{211}{243}$ , hence the probability of making none, P(X = 0), is $\frac{232}{243}$ , hence:

$(1 - p)^5 = \frac{232}{243}$

$\sqrt[5]{(1 - p)^5} = \sqrt[5]{\frac{232}{243}}$

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:

$P(X \geq 2) = 1 - P(X < 2)$

In which:

[P(X < 2) = P(X = 0) + P(X = 1)

Then:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{6,0}.(0.0092)^{0}.(0.9908)^{6} = 0.9461$

$P(X = 1) = C_{6,1}.(0.0092)^{1}.(0.9908)^{5} = 0.0527$

Then:

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

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9988 = 0.0012$

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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