Two points are selected randomly on a line of length 32 so as to be on opposite sides of the midpoint of the line. In other words, the two points X and Y are independent random variables such that X is uniformly distributed over [0,16) and Y is uniformly distributed over (16,32]. Find the probability that the distance between the two points is greater than 9.

Answers

Answer 1

Solution :

Let us consider the squares be [tex]$[1, 16] \times [16, 32]$[/tex]

If x ranges from the 0 to 16 and the y ranges from 16 to 32, we see that the boundary of the region[tex]$y-x \geq 9 \text{\ is}\ y - x = 9$[/tex]  which goes from the [tex]$(7, 16 ) \text{ to}\ (16, 25) $[/tex].

And so it is easier to find the area of region where [tex]$ y-x \leq 9$[/tex]. This is the triangle with points [tex]$(7,16),(16,25) \text{ and}\ (16,16)$[/tex] as its vertices.

The area if the triangle is =  [tex]$\frac{1}{2} \times 9 \times 9$[/tex]

                                         = [tex]$\frac{81}{2}$[/tex]

Now the entire area is [tex]$(16)^2$[/tex]  = 256

Then, [tex]$P(y-x \leq 9) = \frac{81/2}{256} =\frac{81}{512}$[/tex]

or [tex]$P(y-x \geq 9) = 1 - \frac{81}{512}=\frac{431}{512}$[/tex]

Thus the answer is [tex]$\frac{431}{512}$[/tex]


Related Questions

How to find the value of x

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71°. Both angles are the same because both sides are the same length (21). 180°, the total amount of degrees in a triangle, minus 38. 142 is what you get. Divide that by 2

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B 25% percent because 15/60 is 25
Answer: C
15 seats were empty, so 45 out of 60 seats were taken. 45 divided by 60 is 0.75, which is 75%

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Answer:

The answer is C

Step-by-step explanation:

Bruh. This guy lazy

2/3 divided by 2 1/2

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Step-by-step explanation:

Step 1: Multiply to get the lowest common denominator

Step 2: reciprocate thw second fraction(flipping the values)

Step 3: Cancel out values.

10. The table below shows the sales for a flower company for the years 2007 through 2012. Answer the given questions about
this table on your answer sheet.
14 -
A) Graph the data on the scatter plot and draw a line of best fit for the data.
FLOWER SALES
$420
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$395
Year
(in
thousands)
Sales in
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2007 $305
thousands)
2008
$345
$330
2009
$345
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2010
$370
$305
2007 2008 2009 2010 2011 2012
2011
$395
2012
$420
year
B) Write an equation for the line of best fit for this data.
Let x represent the years since 2007 and y represent the
sales, in thousands of dollars.
C) According to your equation, in what year will the
sales reach about $500 (in thousands)? Use
mathematics to explain how you determined your
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Five exterior angles of a hexagon are 41° 32°,67º 71°, and 55°, What is the measure of the sixth exterior
angle?
Can yo help me w this pls

i’m slow , can i get help on this asap please ?

Answers

140°
Pentagons add up to 540° so if you add all the degrees you get 400° and if subtracted from 540° you get 140°

Help??????????????????????

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Answer:

i think A diagonals

just a guess ok

I need help with 10 please!!!!!!!

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From the graph, [tex]y=mx+b[/tex] and m < 0 (The slope right here is less than 0.)

That means cut ( b ) and ( d ) choice, they both are wrong.

Now look at ( a ) and ( c ).

For ( a ) It's just f(x) = -2x but the graph that's shown here intercepts y-axis at (0,2).   f(x) = -2x is just slope and intercepts y-axis at (0,0)

So the answer is ( c )

What is 87B -179+957÷87

Answers

Answer:

8,677

Step-by-step explanation:

because the chemical in 87b is the same as 17yu so it would be 8,677.

When rolling a die what is the chance of getting a 3

Answers

The chance of rolling a die and landing on a three is 1/6. The reason for this is because there are 6 sides on a die, and only one 3 on the die.

What is Y

0.7+y=−1.34
y=

Answers

Answer:

y = -2.04

Step-by-step explanation:

0.7 + y = -1.34

~Subtract 0.7 to both sides

y = -2.04

Best of Luck!

The average weight of 6 people in an elevator is 173 pounds. A 7th person gets on and now the average weight is 165 pounds. How much did the 7th person weigh?

Answers

8 pounds because you divide

Find the distance between the points (-3, -6) and (1, -2).

Answers

Answer: -3 - 1 = -4

Your Answer I think is -4 Hope This helps If I'm Wrong I apoligize.

Consider random samples of size 900 from a population with proportion 0.65 . Find the standard error of the distribution of sample proportions.

Answers

Answer:

The value is [tex]\sigma_{p} = 0.022[/tex]

Step-by-step explanation:

From the question we are told that

   The sample size is  n  =  900

    The population proportion is  [tex]p = 0.65[/tex]

Generally the standard error of the distribution of sample proportion is mathematically represented as

       [tex]\sigma_{p} = \sqrt{\frac{ p(1 - p)}{ n} }[/tex]

=>     [tex]\sigma_{p} = \sqrt{\frac{ 0.65 (1 - 0.65 )}{ 900} }[/tex]

=>     [tex]\sigma_{p} = 0.022[/tex]

Write a fraction that is equal to 5

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Answer:

5/1

Step-by-step explanation:

Convert 49 degrees to radians. Use 3.14 for \piπ. Round to the nearest hundredth.

Answers

49° × π/180 = 0.8552 radians.
after rounding to nearest hundredth is 0.86

PLEASE ANSWER ASAP!!!!!!!
if 20% of some value is 400, then what is the missing value?

Answers

Answer:

Step-by-step explanation:

If 20% of some value is 400 in the missing values 80 20% x 400 is 80

The missing value is 2000 .

How to calculate the percentage of an amount ?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we imply that it is 50% of everything.As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any topic are calculated in terms of percentages in academics.

Calculations :

                  =       Based on the given conditions, formulate =  40/20%

                  =      Convert the percentage to decimals = 400/0.2

                  =      Multiply both the numerator and denominator

                          with the same integer =   4000/2

                  =      Cross out the common factor =  2000

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Which of the following is a biconditional statement?
Question 17 options:

A)

If x ≠ 5 then x2 ≠ 25

B)

If x2 = 25, then x = 5 or x = –5

C)

x = 5 if x2 = 25

D)

x = 5 if and only if x + 5 = 10

Answers

It is D

I just took the test and got it right

The biconditional statement is x = 5 if and only if x + 5 = 10.

Option D is the correct answer.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Biconditional statement.

This means,

The statement and its converse are both true.

Now,

x = 5 if and only if x + 5 = 10

This shows that both the statement and its converse are true.


Thus,

x = 5 if and only if x + 5 = 10 is a biconditional statement.

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not sure need help ​

Answers

Answer:

A (1,-3)

Step-by-step explanation:

it is asking where on the graph is each point. it even gives you where it is located.

The coordinates of the triangle A"B"C" are A"(3, 2), B"(-1, 4) and C"(2, 0).

From the given graph, the coordinates of triangle ABC are A(1, -3), B(5, -1) and C(2, -5).

1) We know that, the reflection of point (x, y) across the y-axis is (-x, y).

Here,

A(1, -3)→A'(-1, -3)

B(5, -1)→B'(-5, -1)

C(2, -5)→C'(-2, -5)

2) The transformation with <4, 5> are

A'(-1, -3)→A"(-1+4, -3+5)

= A"(3, 2)

B'(-5, -1)→B"(-5+4, -1+5)

= B"(-1, 4)

C'(-2, -5)→C"(-2+4, -5+5)

= C"(2, 0)

Therefore, the coordinates of the triangle A"B"C" are A"(3, 2), B"(-1, 4) and C"(2, 0).

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Tracey paid $130 for an item that was originally priced at $500. What percent of the original price did Tracey pay?

Answers

Answer:

2.6%

Step-by-step explanation:

Set up a proportion: [tex]\frac{130}{500} = \frac{x}{100}[/tex]  Cross multiply, then divide: 130 × 100 = 1300, 1300 ÷ 500 = 2.6So, Tracey spent 2.6% of the original price

I hope this helps!

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6.

the y-intercept is 4, which means the line crosses the y-axis at the point (0,4).

[just put a dot on the number four that's right under the letter y]

the slope of the line is positive, so it goes up from left to right.

Start at the y-intercept. Move up 2 and then move right 1.

You are now at the point (1,6).

[go to 1 for the horizontal line, then go up 6 spaces.] [connect two points]

7. y= -1/2-3

8. y=3x+4

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Answer:

0.15 or 3/20

Step-by-step explanation:

Answer:

3/20

Step-by-step explanation:

9/10 = 0.9

0.9/6 = 0.15

0.15 = 3/20

x + 3y = 13
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Answers

here x+3y=13

x=13-3y.....1st equation

-3x+2y=27......2nd euation

now putting the value of x from equation 1st in 2nd we will get

-3(13-3y)+2y=27

-49+9y+2y=27

11y=27+49

y=76÷11

y=6.9

now again putting the value of y in equation 1st we get

x=13-3×6.9

x=13-20.7

x=7.7

What is the relationship between the continental drift hypothesis and the theory of
plate tectonics?

Answers

Answer:

Plate tectonics explains why Earth's continents are moving; the theory of continental drift did not provide an explanation. Therefore, the theory of plate tectonics is more complete. It has gained widespread acceptance among scientists.

Step-by-step explanation:

Do some research on it.

What is an expression equivalent to 5x+10 using the distributive property?​

Answers

Answer:

5x + 10

Step-by-step explanation:

I did the math and checked. :)

Salvador is 15 years older than Elizabeth. In 6 years, the sum of their ages will be 87. How old are they now?​

please include and explantation

Answers

Answer:

????

Step-by-step explanation:

 

bla lee la. la la lee bla​

Answers

Answer:laaa vidas so las vi vi ras ony laa viras so las vi vi ras

Step-by-step explanation:laaaa vidas so las vi vi ras boty hastice hastice sola vi vi rasss*birb falling*

A spinner is divided into eight equal-sized sections, numbered from 1 to 8, inclusive. What is true about spinning the spinner one time? Select three options. S = {1, 2, 3, 4, 5, 6, 7, 8} If A is a subset of S, A could be {1, 2, 3}. If A is a subset of S, A could be {7, 8, 9}. If a subset A represents spinning a number less than 4,then A = {1, 2, 3, 4}. If a subset A represents the complement of spinning an odd number, then A = {2, 4, 6, 8}.

Answers

Answer: A, B, and E

Step-by-step explanation:

The true statements are (A) A could be {1, 2, 3} and (B) A could be {1, 2, 3, 4}, where A  is a subset of S

How to determine the true statements?

The sample space is given as:

S = {1, 2, 3, 4, 5, 6, 7, 8}

The possible subsets of S are as follows:

Even numbers = {2,4,6,8}Odd numbers = {1,3,5,7}Any number or group from 1 to 8, inclusive

Using the above highlights, the possible set of A are:

A could be {1, 2, 3}. A = {1, 2, 3, 4}.

Hence, the true statements are (A) and (B)

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The number of patients who reported that a new drug had relieved their pain. discrete or continuous?

Answers

Answer:

Continuously

Step-by-step explanation:

Continuously

Multiply two and four-fifths negative five and two-thirds

Answers

The answer is -25/3.



If you need it simplified let me know.
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