1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
notsponge [240]
3 years ago
7

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
Other questions:
  • Solve the system by substitution: -4.5x-2y=-12.15 3.25x-y=-0.75
    15·1 answer
  • Need Help Badly!!!!!! The dot plot below shows the number of books 26 students read in a month: Dot plot labeled Number of Books
    10·1 answer
  • In order to figure out who will go first in a game, your friend asks you to pick a number between 1 and 25. What are the possibl
    9·1 answer
  • Jacob makes 20 baskets for every 35 times he shoots the ball. What is the ratio of baskets he makes to baskets he misses? Write
    14·1 answer
  • A sock drawer contains eight navy blue socks and five black socks with no other socks. If you reach in the drawer and take two s
    14·1 answer
  • Find the value of 3 square root of 1000​
    7·2 answers
  • Which line is it? help asap
    13·2 answers
  • Ram noticed three students used 1 2/10 dm of tape.what was the total used for three students???
    6·1 answer
  • Can someone please answer this question? I really need the answer please. Q:Two signs are on a street. One blinks every 10 s and
    7·1 answer
  • The scatter plot shows a scuba diver's depth in the ocean. The equation of the trend link shown is y = -3.29x - 10. Predict what
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!