Answer:
0.4375
Step-by-step explanation:
Lets say that X is the random varaible that determine the arrival time of Bob and Y the random variable that determine the arrival time of Alice. Bot X and Y are Independent random variables with uniform [0,1] distribution. 15 minutes is the quarter of an hour, so we want to calculate P(|X-Y|) < 0.25.
Note that P(|X-Y| < 0.25) = P(|X-Y| < 0.25 | X ≥ Y) * P(X≥ Y) + P(|X-Y| < 0.25 | Y ≥ X) * P(Y ≥ X) = P(X-Y < 0.25 | X ≥Y) * P(X≥Y) + P(Y-X < 0.25 | Y≥X)*P(Y ≥ X).
For a simmetry argument, that expression is equivalent to 2*P(Y-X < 0.25 | Y≥X)*P(Y ≥ X) = 2*P(0 < Y-X < 0.25). The region 0 < Y-X < 0.25 is, for X between 0 and 0.75, a parallelogram, of base 0.75 and height 0.25, and for X between 0.75 and 1, it is a Triangle of base and height equal to 0.25. Therefore P(0 < Y-X < 0.25) = 0.25*0.75 + 0.25² * 0.5 = 7/32. Hence 2*P(0 < Y-X < 0.25) = 14/32 = 0.4375.
They will meet for lunch with probability 0.4375
Answer:
f(x) = (x + 6)² - 29
Step-by-step explanation:
Given
f(x) = x² + 12x + 7
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² + 12x
x² + 2(6)x + 36 - 36 + 7
= (x + 6)² - 29, thus
f(x) = (x + 6)² - 29
Answer:
2<x>7
Step-by-step explanation:
The greater than symbol shows that one or more numbers are larger or 'greater' than a given value. The less than symbol is written as <. The less than symbol shows that one or more numbers are smaller or 'less' than a given value
I hope this helps!
The expression of the polynomials with like terms grouped together is (c) [-4x²] + 2xy² + [10x²y + (-4x²y)]
<h3>How to group the polynomial by like terms?</h3>
We have:
10x²y + 2xy² - 4x² - 4x²y
Collect the like terms
- 4x² + 2xy² + 10x²y - 4x²y
Put each group in bracket
- 4x² + 2xy² + [10x²y - 4x²y]
Express as positives
[-4x²] + 2xy² + [10x²y + (-4x²y)]
Hence, the expression of the polynomials with like terms grouped together is (c) [-4x²] + 2xy² + [10x²y + (-4x²y)]
Read more about polynomials at:
brainly.com/question/4142886
#SPJ1
Hey there!
“Write a expression for b plus 4”
Key term(s): “b plus 4”
• b = b (which is an UNKNOWN know)
• plus let’s us know that we’re adding
• 4 let’s us know what we’re COMPARING to “b”
Equation/Answer: “b + 4” would most likely be your expression
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)