All categories

3 years ago

The number a is smaller than the number b by 1/5 of b. By what part of a is b bigger than a?

Mathematics

1 answer:

Ira Lisetskai [31]3 years ago

7 0

Answer:

The number b is bigger than the number a by $\dfrac{1}{4}$ of a.

Step-by-step explanation:

1. If the number a is smaller than the number b by 1/5 of b, then

$a+\dfrac{1}{5}b=b.$

Thus,

$a=b-\dfrac{1}{5}b=\dfrac{4}{5}b,\\ \\b=\dfrac{5}{4}a.$

2. Consider the expression $b=\dfrac{5}{4}a:$

$b=\dfrac{5}{4}a=\dfrac{4}{4}a+\dfrac{1}{4}a=a+\dfrac{1}{4}a.$

This gives you that the number b is bigger than the number a by $\dfrac{1}{4}$ of a.

You might be interested in

What is the expontential form of √13

kaheart [24]

The answer is (13)^1/2

6 0

3 years ago

Read 2 more answers

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:

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

3 0

3 years ago

If a rope is 36 feet long and cut into 8 sections what is the length in feet of each section

tigry1 [53]

Answer:

The length of feet in each section is 4 4/8 which is then reduced to 4 1/2

Step-by-step explanation:

In order to get the answer, you will divided 36 by 8. When you divide, you then get 4 4/8 which is then reduced to 4 1/2. Hope this helps! :)

<h2>CloutAnswers</h2>

3 0

3 years ago

Read 2 more answers

Which of these figures has rational symmetry?

Nana76 [90]

Answer:

a is the answer parallelogram is a rotational symmetry

4 0

2 years ago

Read 2 more answers

F (x) = 20 - (1.27)<br> growth or decay ?

RideAnS [48]

Answer:

Decay...? Read below

Step-by-step explanation:

Assuming you meant to put 20 - (1.27)x, it is decay. As the x increases, the y decreases, making it decay.

8 0

3 years ago