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Korolek [52]
3 years ago
5

The seventh- grade class is building a mini- golf game for the school carnival. The end of the putting green will be a circle if

the circle is 10 feet in diameter, how many square feet of grass carpet will they need to buy the cover the circle
Mathematics
1 answer:
Serga [27]3 years ago
6 0

Answer:

78.5 square feet of grass carpet will they need to buy to cover the circle.

Step-by-step explanation:

Given

Diameter of a circle = 10 feet.

To find:

The grass carpet area need to cover the circular part.

Solution:

For circular part area is given as

\textrm{area of circle} = \pi \times r^{2}

where r is the radius of the circle

d be the diameter of circle.

Also we know the radius is equal to half of the diameter.

∴ r = \frac{d}{2} \\r = \frac{10}{2}\\r = 5\ feet

substituting the value of r i.e radius in the above formula we get

\textrm{area of circle} = \pi \times 5^{2}

= 3.14\times 25\\= 78.5\ square\ feet

Therefore,78.5 square feet of grass carpet will they need to buy to cover the circle.

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Let’s start with “five more than a number x.” This translates to:

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According to Harper's Index, 55% of all federal inmates are serving time for drug dealing. A random sample of 16 federal inmates
Salsk061 [2.6K]

Answer:

a)P(X\geq 11) = 0.198

b)P(X\leq 2) = 0.000565

c) Mean = 8.8

Step-by-step explanation:

1) Previous concepts

Binomial Distribution is a "discrete probability distribution which is used to calculate the probabilities for the independent trials and for each trial there is only two outcomes success or failure and probability for each success remains constant throughout each trial".

The Binomial distribution is a type of Bernoulli experiment with following properties:

a)There are two possible outcomes; success or failure.

b) Outcomes are independent on preceding result of a trial.

c) The probability of success remains constant throughout the experiment.

d)The number of successes are fixed.

The probability mass function for the Binomial distribution is given by:

P(X=a)=(nCa)(p)^x (1-p)^{n-x}

Where p is the probability of success, n the number of trials and x the number of successes that we want on the n trials.

X represent the number federal inmates that are serving time for drug dealing

p=0.55 represent the proportion of federal inmates that are serving time for drug dealing

n=16 random sample selected

2) Part a

The random variable X follows this distribution X \sim Binom(n,p)

On this case we want the following probability, and since says greater or equal than 11 we can express like this:

P(X \geq 11)=P(X=11)+P(x=12)+P(x=13)+P(x=14)+P(x=15)+P(x=16)

P(X=11)=(16C11)(0.55)^{11} (1-0.55)^{5} =0.112

P(X=12)=(16C12)(0.55)^{12} (1-0.55)^{4} =0.0572

P(X=13)=(16C13)(0.55)^{13} (1-0.55)^{3} =0.0215

P(X=14)=(16C14)(0.55)^{14} (1-0.55)^{2} =0.00563

P(X=15)=(16C15)(0.55)^{15} (1-0.55)^{1} =0.000918

P(X=16)=(16C16)(0.55)^{16} (1-0.55)^{0} =0.00007011

P(X \geq 11)=0.112+0.0572+0.0215+0.00563+0.000918+0.00007011=0.198

3) Part b

P(X \leq 2)=P(X=0)+P(x=1)+P(x=2)

P(X=0)=(16C0)(0.55)^{0} (1-0.55)^{16} =0.00000283

P(X=1)=(16C1)(0.55)^{1} (1-0.55)^{15} =0.0000552

P(X=2)=(16C2)(0.55)^{2} (1-0.55)^{14} =0.000507

P(X \leq 2)=0.00000283+0.0000552+0.000507=0.000565

4) Part c

The expected value for the binomial distribution is given by the following formula:

E(X)=np=16*0.55=8.8

So then the average number of federal inmates that are serving time for drug dealing on a sample of 16 is approximately 9.

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