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3 years ago

Reduce the fraction to lowest terms m^2/m^2-n^2

Mathematics

2 answers:

Softa [21]3 years ago

4 0

Answer:

$\boxed{\bold{\frac{m^2}{\left(m+n\right)\left(m-n\right)}}}$

Step-by-step explanation:

Factor $\bold{m^2-n^2}$

$\bold{\left(m+n\right)\left(m-n\right)}$

Rewrite Equation

$\bold{\frac{m^2}{\left(m+n\right)\left(m-n\right)}}$

AVprozaik [17]3 years ago

4 0

Answer:

$\frac{m^2}{(m+n)(m-n)}$

Step-by-step explanation:

Here we have to simplify the denominator of the expression given in the question.

We will use the formula for

Difference of the squares which us given as under

$a^2-b^2=(a+b)(a-b)$

Let us now simplify the denominator

$m^2-n^2=(m+n)(m-n)$

Hence

Our answer is

$\frac{m^2}{(m+n)(m-n)}$

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2 years ago

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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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2 years ago

Bill plans to save for a pair of headphones that are 89.00.The sales tax rate is 8% how much will bill need to save

umka21 [38]

Answer: 96.12

Step-by-step explanation:

The amount that Bill will need to save will be for the cost of the headphones and the sales tax that will be applied. This will be:

= 89 + (8% × 89)

= 89 + (0.08 × 89)

= 89 + 7.12

= 96.12

Therefore, Bill will need to save 96.12.

5 0

2 years ago