Answer:
The constant of proportionality for this situation is 3.2
Step-by-step explanation:
For the given situation we can say that, the amount spent to fill the gas directly varies with the number of gallons of gas filled.
We can say,
where is the constant of proportionality which is nothing but the units rate of gas in dollars per gallon.
Dividing both sides by 22.5 to find
∴
Unit rate of gas = $3.2/gallon
∴ The constant of proportionality for this situation is 3.2.
Answer:
Probability that the wait time is greater than 37 minutes is 0.3474.
Step-by-step explanation:
We are given that the random variable X is known to be exponentially distributed and X be the waiting time for a car to pass by on a country road, where X has an average value of 35 minutes.
<u><em>Let X = waiting time for a car to pass by on a country road</em></u>
The probability distribution function of exponential distribution is given by;
where,
= parameter of distribution.
Now, the mean of exponential distribution is = which is given to us as 35 minutes that means
.
So, X ~ Exp( )
Also, we know that Cumulative distribution function (CDF) of Exponential distribution is given as;
, x > 0
Now, Probability that the wait time is greater than 37 minutes is given by = P(X > 37 min) = 1 - P(X 37 min)
P(X 37 min) =
{Using CDF}
= 1 - 0.3474 = 0.6525
So, P(X > 37 min) = 1 - 0.6525 = 0.3474
Therefore, probability that the wait time is greater than 37 minutes is 0.3474.
Answer:
-7/12
Step-by-step explanation:
1. so you add (3/12) + 1/12= 4/12
2. 4/12-11/12= -7/12
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