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3 years ago

Which set of side lengths form a right triangle?

1 answer:

4 0

Since we don't want to use the Pythagorean Theorem on all of these, first we look for some Pythagorean Triples. Its very helpful to know some of the common ones, so here's a list:

3, 4, 5
5, 12, 13
7, 24, 25
8, 15, 17

So we either look for these or a multiple of these numbers.

The last one is the only one that fits because 15, 20, 25 is a multiple of the triple 3, 4, 5 by multiplying all of them by 5.

Thus, 15, 20, 25 forms a right triangle.

You might be interested in

Suppose that the relation T is defined as follows.

stepladder [879]

The domain is all of the x values which are the first number in each set of parentheses and the range is all of the y values therefore domain = {2, 1, 5, 3} and range= {2, -7, 3, 0}

3 0

3 years ago

Customers enter the waiting line at a cafeteria on a first-come, first-served basis. The arrival rate follows a Poisson distribu

Veseljchak [2.6K]

Answer:

The average number of customers waiting in line behind the person being served is 0.7619.

Step-by-step explanation:

In queueing problem, an M/M/1 queue model is an arrangement with a single queue, where arrivals at the queue are approximated by a Poisson distribution with mean λ and the service times follows an exponential distribution with mean μ.

The mean number of arrivals in this system is given by:

$\text{Average number of customers}=\frac{\rho}{1-\rho}$

Here the variable ρ is defined as:

$\rho=\frac{\lambda}{\mu}$

From the average number of arrivals in the system, we can calculate the average number of arrivals in the queue by subtracting the average number of arrivals in service.

That is,

$\text{Average number of customers in the queue}=\frac{\rho}{1-\rho}-\rho =\frac{\rho^{2}}{1-\rho}$

The information provided is:

The average number of arrivals of customers is, λ = 4.

The average service rate of a single server is, μ = 7.

Compute the average number of customers waiting in line behind the person being served as follows:

$\text{Average number of customers in the queue}=\frac{\rho}{1-\rho}-\rho =\frac{\rho^{2}}{1-\rho}$

$=\frac{(4/7)^{2}}{1-(4/7)}\\\\=\frac{(4/7)^{2}}{(7-4)/7}\\\\ =\frac{16}{49}\times \frac{7}{3}\\\\=0.7619$

Thus, the average number of customers waiting in line behind the person being served is 0.7619.

3 0

4 years ago

Find the area of the circle. Round your answer to the nearest hundredth.

vichka [17]

Answer:

7.07 in²

Step-by-step explanation:

pi x radius²

pi × 1.5²

4 0

3 years ago

45 students preferred cats in a servey. This was 30% of the number of students surveyed. How many students took the survey

Nikolay [14]

Answer:

$30 \div 45$

7 0

4 years ago

What number would you add to both sides of x^2+7x=4 to complete the square?

emmainna [20.7K]

Answer:

49/4

Step-by-step explanation:

x^2+7x=4

Take the coefficient of x

Divide by 2

7/2

Then square it

(7/2) ^2 = 49/4

Add this to both sides of the equation to complete the square

3 0

4 years ago