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Ganezh [65]
3 years ago
14

Complete the two column proof Given: 22= 24,m_2 = 110°

Mathematics
1 answer:
Savatey [412]3 years ago
6 0

Step-by-step explanation:

I took 3 indicated as 5 and its adjacent angle to be 3

<2 = <4

As <2 =<3( corresponding angle)

And <3 = <4 ( Vertically opp.angle)

hence <2 = <4

<2 =>110

so , <4 = 110

So, <4 =>110

As <4 and <5 form linear pair

So <4 + <5 =>180

<5 = 180 -110 =>70

As i took <5 as replacing angle to <3

So According to Question fig

<3 =>70

Hence proved

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Answer:

<em>m=-1/2</em>

Step-by-step explanation:

The equation is in y=mx+b form. M is the slope. In this equation, -1/2 is m.

Therefore the slope is -1/2.

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Noa hopes to pick the winning ticket during her math class’s raffle. the student who picks the ticket with a true statement will
Natali5045456 [20]

Answer: The winning ticket is 2(x-6)=-35 is equivalent to 2x=-23.



Step-by-step explanation:

Let's check all the options

4(x-5)=35 is not equivalent to 4x=40

\text{since }4(x-5)=35\\\Rightarrow4x-20=35\\\Rightarrow4x=35+20\\\Rightarrow4x=55

8(x-7)=35 is not equivalent to 8x=28


\text{since }8(x-7)=35\\\Rightarrow8x-56=35\\\Rightarrow8x=35+56\\\Rightarrow8x=91

2(x-6)=-35 is equivalent to 2x=-23


\text{since }2(x-6)=-35\\\Rightarrow2x-12=-35\\\Rightarrow2x=-35+12\\\Rightarrow2x=-23

9(x-6)=-35 is not equivalent to 9x=-29

\text{since }9(x-5)=-35\\\Rightarrow9x--40=-35\\\Rightarrow9x=-35+40\\\Rightarrow9x=5

Thus, the winning ticket is 2(x-6)=-35 is equivalent to 2x=-23.

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Our faucet is broken, and a plumber has been called. The arrival time of the plumber is uniformly distributed between 1pm and 7p
Ymorist [56]

Answer:

E(A+B) = E(A)+E(B)=4+0.5 =4.5 hours

Var(A+B)= Var(A)+Var(B)=3+0.25 hours^2=3.25 hours^2

Step-by-step explanation:

Let A the random variable that represent "The arrival time of the plumber ". And we know that the distribution of A is given by:

A\sim Uniform(1 ,7)

And let B the random variable that represent "The time required to fix the broken faucet". And we know the distribution of B, given by:

B\sim Exp(\lambda=\frac{1}{30 min})

Supposing that the two times are independent, find the expected value and the variance of the time at which the plumber completes the project.

So we are interested on the expected value of A+B, like this

E(A +B)

Since the two random variables are assumed independent, then we have this

E(A+B) = E(A)+E(B)

So we can find the individual expected values for each distribution and then we can add it.

For ths uniform distribution the expected value is given by E(X) =\frac{a+b}{2} where X is the random variable, and a,b represent the limits for the distribution. If we apply this for our case we got:

E(A)=\frac{1+7}{2}=4 hours

The expected value for the exponential distirbution is given by :

E(X)= \int_{0}^\infty x \lambda e^{-\lambda x} dx

If we use the substitution y=\lambda x we have this:

E(X)=\frac{1}{\lambda} \int_{0}^\infty y e^{-\lambda y} dy =\frac{1}{\lambda}

Where X represent the random variable and \lambda the parameter. If we apply this formula to our case we got:

E(B) =\frac{1}{\lambda}=\frac{1}{\frac{1}{30}}=30min

We can convert this into hours and we got E(B) =0.5 hours, and then we can find:

E(A+B) = E(A)+E(B)=4+0.5 =4.5 hours

And in order to find the variance for the random variable A+B we can find the individual variances:

Var(A)= \frac{(b-a)^2}{12}=\frac{(7-1)^2}{12}=3 hours^2

Var(B) =\frac{1}{\lambda^2}=\frac{1}{(\frac{1}{30})^2}=900 min^2 x\frac{1hr^2}{3600 min^2}=0.25 hours^2

We have the following property:

Var(X+Y)= Var(X)+Var(Y) +2 Cov(X,Y)

Since we have independnet variable the Cov(A,B)=0, so then:

Var(A+B)= Var(A)+Var(B)=3+0.25 hours^2=3.25 hours^2

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