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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

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3 years ago
The rectangle is 3 3⁄4 centimeters long and 2 1⁄2 centimeters wide. What is the area of this rectangle?
scZoUnD [109]

Answer:

The answer to your question is    Area = 9 3/8

Step-by-step explanation:

Data

length = 3 3/4 cm

width = 2 1/2 cm

Process

1.- Write the equation of the Area of a rectangle

   Area = length x width

2.- Convert the values to improper fractions

     3 3/4 = (12 + 3)/ 4 = 15/4

     2 1/2 = (4 + 1) / 2 = 5/2

3.- Substitution

      Area = (15/4)(5/2)

4.- Simplification

      Area = 75/8

5.- Convert to a mixed fraction

                       9

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                        3

6.- Result

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Step-by-step explanation:

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Find x for both compound shapes. Please show your working out.
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Q1  Perimeter = sum of all the sides

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Q2

unmarked sides = x - 8 and  and 5 - 2 = 3

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