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
g100num [7]
3 years ago
13

A random number is selected from the interval [6.35, 10]. Find the probability that the number is within a distance of 0.25 from

an even integer. (Answer as a decimal number, and round to 4 decimal places).
Mathematics
1 answer:
exis [7]3 years ago
6 0

Let <em>X</em> be a random number selected from the interval. Then the probability density for the random variable <em>X</em> is

f_X(x)=\begin{cases}\dfrac1{10-6.35}=\dfrac1{3.65}\approx0.2740&\text{if }6.35\le x\le 10\\0&\text{otherwise}\end{cases}

8 and 10 are the only even integers that fit the given criterion (6 is more than 0.25 away from 6.35), so that we're looking to compute

P(|<em>X</em> - 8| < 0.25) + P(|<em>X</em> - 10| < 0.25)

… = P(7.75 < <em>X</em> < 8.25) + P(9.75 < <em>X</em> < 10.25)

… = P(7.75 < <em>X</em> < 8.25) + P(9.75 < <em>X</em> < 10)

(since P(<em>X</em> > 10) = 0)

… = 0.2740 (8.25 - 7.75) + 0.2740 (10 - 9.75)

… = 0.2055

You might be interested in
Brockman Corporation's earnings per share were $3.50 last year, and its growth rate during the prior 5 years was 7.0% per year.
fredd [130]

Answer:

The number of years it would take is  n  =  2 \ years

Step-by-step explanation:

From the question we are told that

         The earning per share  is  P = $3.50

          The growth rate is  r  =  7.0%

           The duration is t =  5 \ years

Generally the future value is mathematically represented as

          A =  P(1 + \frac{r}{100} )^n

 Where P is the present value

              n is the time period

         A is the future value which is mathematically evaluated as

               A =  3 * P

substituting value

            A =  3 * 3.50

            A = $ 10.5 0

So

      A =  P(1 + \frac{r}{100} )^n

       10.5 =  3.5(1 + \frac{7}{100} )^n

       10.5 = 3.225^n

Taking log of both sides

       log 10.5 = nlog 3.225

        1.0212 = n(0.5085)

         n  =   \frac{1.0212}{(0.5085)}

         n  =  2 \ years

     

4 0
3 years ago
The base value is the <br><br> A. New value <br><br> B. Current value
Andrei [34K]
The base value is the current value

Good luck! I hope this helps!
6 0
3 years ago
Pls help me and show work pls
ElenaW [278]
3/6 cause there are 3 evens and 3 odds on a dice
3 0
2 years ago
Write 6,392,094,003 in word form
sattari [20]
Six billion three hundred ninety-two million ninety-four thousand and three
6 0
3 years ago
Read 2 more answers
6 decigrams = milligrams
malfutka [58]
1 decigram = 100 milligrams

6 decigrams = 600 milligrams
6 0
3 years ago
Other questions:
  • The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than a certain number of inches
    14·1 answer
  • Which of the following statements is true? A. A tangent is never a secant. B. A secant is always a chord. C. A chord is always a
    13·1 answer
  • We toss two dice 1,000 times. How many times do we expect to have the sum of the two dice equal to 4?
    5·1 answer
  • 3.3333 as a simplified fraction
    15·2 answers
  • How can you find the least common denominator for 1/8 and 2/9
    7·1 answer
  • What is 2+2-1+4-2+1-5+20<br><br><br><br><br><br> -Quick Maths
    15·2 answers
  • Help Please Just with part B...PLEASE!!!
    8·1 answer
  • 36
    5·2 answers
  • 2x+y=5 solve for y (please show work)
    6·1 answer
  • Ill brainlist anyone who anwsers this
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!