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xz_007 [3.2K]
3 years ago
13

Point $(x,y)$ is randomly picked from the rectangular region with vertices at $(0,0),(2009,0),(2009,2010),$ and $(0,2010)$. What

is the probability that $x > 7y$? Express your answer as a common fraction.

Mathematics
2 answers:
Bezzdna [24]3 years ago
6 0

Answer: Probability that x>7y is \frac{287}{4020}

Step-by-step explanation:

Since we have given that

x>7y

And the coordinates are as follows:

(0,0),(2009,0),(2009,2010), and (0,2010)

We need to find the probability that x>7y

So, Required Probability is given by

\frac{\text{Area of triangle}}{\text{ Area of rectangle}}\\\\=\frac{0.5\times 2009\times 287}{2009\times 2010}\\\\=\frac{287}{4020}

Hence, Probability that x>7y is \frac{287}{4020}

pantera1 [17]3 years ago
6 0

Answer:

Hence, the probability is:

\dfrac{287}{4020}

Step-by-step explanation:

We know that probability of an event is defined as:

Probability=(Number of favourable events)/(Total number of events)

The probability that x > 7y is given by:

Here the number of favourable event is equal to the area covered by the triangle ΔABE

Area of triangle ABE= (1/2)×b×h=(1/2)×2009×287=288291.5

and the total outcome is equal to the area of the rectangle (i.e. rectangle ABCD)

Area of rectangle ABCD=2009×2010=4038090

Hence, probability=

\dfrac{288291.5}{4038090}=\dfrac{287}{4020}

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130 apples at the party. There were 3 times as many yellow apples as green apples, there were twice as many red apples as yellow
kipiarov [429]

Answer: There were 78 red apples at the party.

Step-by-step explanation:

This situation can be represented by the equation  

x + 3x + 2(3x) = 130    where x is the number of green apples, 3x is the number of  yellow apples and 2(3x) is the number  of red apples.

Now solve for x

x +3x +2(3x) =130

4x + 6x = 130

10x  = 130

x =  13  

Now we know that x is 13 so put it into the expression for red apples and solve for the actual number of red apples.

2 * (3*13)  = ?

2 * 39 = 78  

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3 years ago
What is the slope between the two points (8, -2) and (-7, 10)?
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Answer:

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Fantom [35]
2+5=7
7-3=4
so the answer is b 
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• Given the function, f(x) = x3 – 5x2 + 9x – 45, determine the number of roots and identify them.
dezoksy [38]
x3 - 5x2 + 9x - 45 = 0
 It is a polynomial of degree three, therefore, it has three roots.
 For this case, what we can do is factorize to write the polynomial in an easier way and thus be able to find the roots.
 Factoring we have:
 (x - 5) (x ^ 2 + 9) = 0
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 x = 3i
 x = -3i
 Answer: 
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 x = 5 
 x = 3i 
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