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galben [10]
3 years ago
13

A bathtub is draining at a constant rate. After 2 minutes, it holds 30 gallons of water. Three minutes later, it holds 12 gallon

s of water. Write an equation the represents the number of y of gallons of water in the tub after x minutes.
Mathematics
1 answer:
aliya0001 [1]3 years ago
5 0
Let x, represent the number of minutes and y represents the number of gallons of water in the tub, then the ordered pairs (2, 30) and (5, 12) satisfies the equation.

Therefore the equation is given by: (y - 30)/(x - 2) = (12 - 30)/(5 - 2)
(y - 30)/(x - 2) = -18/3 x = -6
y - 30 =  -6(x - 2) = -6x + 12
y = -6x + 42

Required equation is y + 6x = 42.
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Answer:

a) P(X ≤ 4) = 0.9

b) P(X>7) = 0

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d) P(X>4) = 0.1

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Step-by-step explanation:

Hello!

Given the distribution of cumulative probability

        0        for  X < 1

F(x)  0.7     for 1 ≤ X < 4

       0.9     for  4 ≤ X < 7

         1        for 7 ≤ X

To determine each of the asked probabilities you have to select the probability corresponding to the defined intervals for X:

a) P(X ≤ 4) = 0.9

This value of X is included the interval "4 ≤ X < 7" so the corresponding probability is 0.9

b) P(X>7) = 0

This is equal to the expression:

1 - P(X≤7)

This expression is included in the last interval so the probability is 1

1 - 1 = 0

c) P(X ≤ 5) = 0.9

5 is included in the third interval "4 ≤ X < 7" so the corresponding probability is 0.9

d) P(X>4) = 0.1

P(X>4) = 1 - P(X≤4)

P(X≤4) is in the interval of definition "4 ≤ X < 7" so the corresponding probability is 0.9

1 - 0.9 = 0.1

e) P(X≤2)= 0.7

The value X=2 is included in the second interval "for 1 ≤ X < 4", so the probability is 0.7

I hope it helps!

4 0
3 years ago
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