Toll booths on the New York State Thruway are often congested because of the large number of cars waiting to pay. A consultant w
1 answer:
Answer:
The proportion of cars can get through the toll booth in less than 3 minutes is 67%.
Step-by-step explanation:
Let the random variable <em>X</em> be defined as the service times at a tool booth.
The random variable <em>X</em> follows an Exponential distribution with parameter <em>μ</em> = 2.7 minutes.
The probability density function of <em>X</em> is:
Compute the probability that a car can get through the toll booth in less than 3 minutes as follows:
Thus, the proportion of cars can get through the toll booth in less than 3 minutes is 67%.
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A1) One possible set of inequalities is
x +y > 2
y -x < 4
A2) The lines are graphed as though the inequality were an equal sign. Since the inequality does not include the "or equal to" case, the lines are drawn dashed. In each case, the area to the right of the line is shaded.
B) Points A and B are solutions to the system if they are in the doubly-shaded region (which they are). In the graph here, that region is darker orange. (For this purpose, you need to ignore the green region, which overlaps part of the solution space.
C) The houses Billy is interested in are found by graphing the inequality and identifying the houses in its solution space. (Those houses are B and C.) Alternatively, you can evaluate the inequality for each of the house coordinates and see which ones give "true."
x +y > 2
y -x < 4
A2) The lines are graphed as though the inequality were an equal sign. Since the inequality does not include the "or equal to" case, the lines are drawn dashed. In each case, the area to the right of the line is shaded.
B) Points A and B are solutions to the system if they are in the doubly-shaded region (which they are). In the graph here, that region is darker orange. (For this purpose, you need to ignore the green region, which overlaps part of the solution space.
C) The houses Billy is interested in are found by graphing the inequality and identifying the houses in its solution space. (Those houses are B and C.) Alternatively, you can evaluate the inequality for each of the house coordinates and see which ones give "true."
According to the information given in the exercise:
- The office equipment was purchased for $20,000.
- The scrap value is assumed to be $2,000 after 10 years.
- -It's depreciated linearly from $20,000 to $2,000.
(a) The Slope-Intercept Form of the equation of a line is:
Where "m" is the slope of the line and "b" is the y-intercept.
Let be "V" the value (in dollars) and "t" the time (in years).
Analyzing the information given in the exercise, you can set up that the equation will have this form:
Where "m" is the slope and "b" is the y-intercept.
Notice that you have these two points:
Then, you can apply the formula for calculating the slope:
You can say that:
Substituting and evaluating, you get:
To find "b", you need to remember that the value of "x" is zero when the line intersects the y-axis. Therefore, knowing that one of the points is:
You can determine that:
Hence, the equation is:
(b) To find the value of the equipment after 6 years, you need to set up that:
Then, substituting this value into the equation and evaluating, you get:
Therefore, the answers are:
(a)
(b) $9,200