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3 years ago

Determine whether the sides given would form an acute,obtuse, or right triangle 7,7,12

Mathematics

1 answer:

Yuliya22 [10]3 years ago

5 0

Its a obtuse angle since 7^2 is 49 7^2 is 49 and 12^2 is 144
144 is bigger than 90 so its obtuse triangle

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How do you solve word problems with fractions?

Gelneren [198K]

You have to do what it says if you have to divide you divide if you have to multiply you multiply if you have to add you add and that is the same for subtraction as well.

I hope this helps you out.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Refer to Exercise 3.122. If it takes approximately ten minutes to serve each customer, find the mean and variance of the total s

garri49 [273]

Answer

a. The expected total service time for customers = 70 minutes

b. The variance for the total service time = 700 minutes

c. It is not likely that the total service time will exceed 2.5 hours

Step-by-step explanation:

This question is incomplete. I will give the complete version below and proceed with my solution.

Refer to Exercise 3.122. If it takes approximately ten minutes to serve each customer, find the mean and variance of the total service time for customers arriving during a 1-hour period. (Assume that a sufficient number of servers are available so that no customer must wait for service.) Is it likely that the total service time will exceed 2.5 hours?

Reference

Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour.

From the information supplied, we denote that

$X=$ Customers that arrive within the hour

and since $X$ follows a Poisson distribution with mean $\alpha$ = 7

Therefore,

$E(X)= 7$

$& V(X)=7$

Let $Y =$ the total service time for customers arriving during the 1 hour period.

Now, since it takes approximately ten minutes to serve each customer,

$Y=10X$

For a random variable $X$ and a constant $c$ ,

$E(cX)=cE(X)\\V(cX)=c^2V(X)$

Thus,

$E(Y)=E(10X)=10E(X)=10*7=70\\V(Y)=V(10X)=100V(X)=100*7=700$

Therefore the expected total service time for customers = 70 minutes

and the variance for serving time = 700 minutes

Also, the probability of the distribution $Y$ is,

$p_Y(y)=p_x(\frac{y}{10} )\frac{dx}{dy} =\frac{\alpha^{\frac{y}{10} } }{(\frac{y}{10})! }e^{-\alpha } \frac{1}{10}\\ =\frac{7^{\frac{y}{10} } }{(\frac{y}{10})! }e^{-7 } \frac{1}{10}$

So the probability that the total service time exceeds 2.5 hrs or 150 minutes is,

$P(Y>150)=\sum^{\infty}_{k=150} {p_Y} (k) =\sum^{\infty}_{k=150} \frac{7^{\frac{k}{10} }}{(\frac{k}{10})! }.e^{-7} .\frac{1}{10} \\=\frac{7^{\frac{150}{10} }}{(\frac{150}{10})! } .e^{-7}.\frac{1}{10} =0.002$

0.002 is small enough, and the function $\frac{7^{\frac{k}{10} }}{(\frac{k}{10} )!} .e^{-7}.\frac{1}{10}$ gets even smaller when $k$ increases. Hence the probability that the total service time exceeds 2.5 hours is not likely to happen.

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3 years ago

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Vikentia [17]

Step-by-step explanation:

area of trapezoid=(a+b)×h divided by 2

=(9+19)×4 divided by2

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3 years ago

Find a slope of each line (each block is one unit):

Darina [25.2K]

Answer:

The slope is -3

Step-by-step explanation:

We have two points

( -1,2) and (1,-4)

We can use the slope formula

m = ( y2-y1)/(x2-x1)

= ( -4 -2)/ ( 1 - -1)

= ( -4-2)/ (1+1)

= -6/2

= -3

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3 years ago

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statuscvo [17]

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4 years ago