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3 years ago

A rectangle has a a perimeter of 72 ft. The length and width are scaled by a factor 3.5.

2 answers:

8 0

Formula for perimeter of rectangle:
P=2(L+w)
P=2L+2w
Here Perimeter, p= 72 ft
And scale factor of length and width=3.5 which means rectangle is enlarged.
So perimeter of rectangle= 3.5 x 72
P=252ft

Answer: 252 ft

Tasya [4]3 years ago

8 0

We know the perimeter of the original rectangle is 72ft.
We also know that the perimeter P of the rectangle is defined as:
P=2L+2W.
So P is directly proportional to L+W. This means that if L or W were to get bigger, P will get bigger, and if L or W were to get smaller P will get smaller.

The question also states that both L and W are scaled by the same factor of 3.5 .
This means the sum of the dimensions L+W is scaled by 3.5
It also means that the perimeter is upscaled by 3.5 as it is proportional to L+W.
P = 72 ft × 3.5 = 252 ft.

252 ft is the answer.

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Answer:

1. The set R ∪ S is the set of things that:

* have wheels or have engines

2. The set R ∩ S is the set of things that :

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Step-by-step explanation:

Let's complete the sentences:

1. The set R ∪ S is the set of things that:

* have wheels or have engines

Let's recall that the union of two sets, R and S for our case, is the set of elements which are in R or in S or in both.

2. The set R ∩ S is the set of things that :

* have wheels and have engines

Let's recall that the intersection of two sets, R and S, is the set of elements that are common to both R and S.

3. The set R′ is the set of things that :

* don't have wheels but do have engines

Let's recall that the complement of a set, R is the set of all elements that are in the universal set but are not in R. R' = {x ∈ U : x ∉ R}.

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3 years ago

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3 years ago

In 2011, New York City has a total of 11,232 motor vehicle accidents that occurred on Monday through Friday between the hours of

cestrela7 [59]

Answer:

$a. \ P(X=0)=5.574\times10^{-7}$

$b. \ \ P(X\leq 1)=8.584\times10^{-6}$

$c.\ \ \ P(X\geq 4)=0.9997$

Step-by-step explanation:

a. #We notice this is a Poisson probability function expressed as:

$f(x)=\frac{\mu^xe^{-\mu}}{x!}$

x-number of occurrences in a given interval.

$\mu$ -mean occurrences of the event

-The mean is calculated as:

$\mu=\frac{14.4}{4}=3.6$

#the probability of no accidents in a 15-minute period is :

$P(x)=\frac{\mu^xe^{-\mu}}{x!}\\\\P(X=0)=\frac{14.4^0e^{-14.4}}{0!}\\\\=5.574\times10^{-7}$

Hence, the probability of no accident in a 15-min period is $=5.574\times10^{-7}$

b. The the probability of at least one accident in a 15-minute period. is calculated as:

$P(x)=\frac{\mu^xe^{-\mu}}{x!}\\\\P(X\leq 1)=\frac{14.4^0e^{-14.4}}{0!}+\frac{14.4^1e^{-14.4}}{1!}\\\\=5.574\times10^{-7}+8.026\times 10^{-6}\\\\=8.584\times 10^{-6}$

Hence, the probability of at least one accident in a 15-minute period is $8.584\times10^{-6}$

c. The probability of four or more accidents in a 15-minute period is calculated as:

$P(X\geq 4)=1-P(X\leq 3)=1-[P(X=0)+P(X1)+P(X=2)+P(X=3)]\\\\=1-[5.574\times10^{-7}+a. \ 8.026\times10^{-6}+\frac{14.4^2e^{-14.4}}{2!}+\frac{14.4^3e^{-14.4}}{3!}]\\\\=1-[8.584\times 10^{-6}+5.779\times10^{-5}+2.774\times10^{-4}]\\\\=0.9997$

Hence,the probability of four or more accidents in a 15-minute period. is 0.9997

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3 years ago