The area A of the rectangle shown is described with the inequality 100 ≤ A ≤ 1,000. Write and solve a compound inequality for x.
2 answers:
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Answer:
The piece-wise function is;
Step-by-step explanation:
The flat rate for renting the car = $35 per day
The amount charged as insurance fee per day for renting the car for 3 days or less = $10
The insurance fee charged per day when the car is rented for more than 3 days = $5
Let the number of days = x
Therefore, we have;
For x ≤ 3, f(x) = 35 × x + 10 × x = x × (35+10) = 45·x
For x > 3, f(x) = 35 × x + 5 × x = x × (35+5) = 40·x
Therefore;
The charge rate for renting the car for less than or equal to 3 days = 45·x
The charge rate for renting the car for more than 3 days = 40·x
The piece-wise function can be presented as follows;
Answer:
The probability of a selection of 50 pages will contain no errors is 0.368
The probability that the selection of the random pages will contain at least two errors is 0.2644
Step-by-step explanation:
From the information given:
Let q represent the no of typographical errors.
Suppose that there are exactly 10 such errors randomly located on a textbook of 500 pages. Let be the random variable that follows a Poisson distribution, then mean
and the mean that the random selection of 50 pages will contain no error is
∴
Pr(q =0) = 0.368
The probability of a selection of 50 pages will contain no errors is 0.368
The probability that 50 randomly page contains at least 2 errors is computed as follows:
P(X ≥ 2) = 1 - P( X < 2)
P(X ≥ 2) = 1 - [ P(X = 0) + P (X =1 )] since it is less than 2
P(X ≥ 2) = 0.2644
The probability that the selection of the random pages will contain at least two errors is 0.2644
The student's statement about area is incorrect because by joining suitable lines, we can divide the region into 3 rectangles and we can find its area.
Please check the attached figure.
From the figure, we can easily observe that the area of the shaded region = Area of the rectangle A + Area of the rectangle B - Area of the rectangle C.
