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LiRa [457]
2 years ago
14

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

y good at it: If I shoot $5$ pieces of paper at the recycling bin, at least one of them will make it inside the recycling bin with probability $\frac{211}{243}$. If I shoot $6$ pieces of paper at the recycling bin, what's the probability at least two of them make it inside the recycling bin
Mathematics
1 answer:
valentinak56 [21]2 years ago
7 0

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

#SPJ1

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o-na [289]

Answer:

=$61,472.00

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3 years ago
If f(x) = g(x), then what does 7x - 12 = -3x + 10?​
Bumek [7]

Answer:

x = 2.2

Step-by-step explanation:

Comment

f(x) = g(x) I don't think has any meaning for this question. I will just solve the equation.

Solution

7x - 12 = - 3x  + 10                    Add 3x to both sides

7x + 3x  -12 = - 3x + 3x +10    Combine

10x - 12 = 10                            Add 12 to both sides

10x -12 + 12 = 10 + 12              Combine

10x = 22                                  Divide by 10

10x/10 = 22/10

x = 2.2

3 0
1 year ago
BRAINLIEST ANSWER (please do it right)
Naddika [18.5K]

Answer:

55 performances

Step-by-step explanation:

The first equation will be the total cost. The total cost has $88,000 already and then $5,900 is added with each performance. So the equation would be 88,000+5,900x because x will represent the number of performances.

y = 88,000 + 5,900x

The next equation will be how much the performances earn. If they earn $7,500 with each performance then the equation will be 7,500x, with x representing the number of performances

y = 7,500x

Now set the equations equal to each other and solve for x

7,500x = 88,000 + 5,900x

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x = 55

They need to have 55 performances for the cost and the revenue to break even.

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3 years ago
Can someone help me with this
katrin [286]

Half  the length of the curve which separates the 2 halves = 1/2 circumference of a circle with diameter 6 mm.  = 1/2 * pi * d = 3pi mm

So the length of the line = 6pi =  18.85 mm to nearest hundredth. answer

The area of shaded region = 1/2 area of the circle = 1/2 pi r^2

= 1/2 * pi * 6^2

=  56.55 mm^2  to nearest hundredth  answer


8 0
3 years ago
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kirill [66]

Answer:

B. 3.45

Step-by-step explanation:

The radius is half the diameter

8 0
3 years ago
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