For the point P(2,-14) and Q(9,-9) find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ
1 answer:
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So I went ahead and divided up the figure so that you would understand what I'm going to tell you. Let's start with the red rectangle.
The distance from point R to point I is 6 units and the distance from Point R to point S is 5 units. 6*5 = 30 so that red rectangle has an area of 30 units
Now let's calculate triangle AVI. Area of a triangle is Base * Height. The base is 1 and the height is 5 which means the area of triangle AVI is 5.
Next, triangle ALT. From Point A to point L is 4 unit. From Point L to point T is 3 units. 4*3 is 12. So triangle ALT has an area of 12.
Triangle TSI. From Point T to point L is 3 units. From Point L to X is 2. Triangle TSI has an area of 6.
Now we add all of them up. 30+5+12+6 = 53. In total, RSTUV has an area of 53
The distance from point R to point I is 6 units and the distance from Point R to point S is 5 units. 6*5 = 30 so that red rectangle has an area of 30 units
Now let's calculate triangle AVI. Area of a triangle is Base * Height. The base is 1 and the height is 5 which means the area of triangle AVI is 5.
Next, triangle ALT. From Point A to point L is 4 unit. From Point L to point T is 3 units. 4*3 is 12. So triangle ALT has an area of 12.
Triangle TSI. From Point T to point L is 3 units. From Point L to X is 2. Triangle TSI has an area of 6.
Now we add all of them up. 30+5+12+6 = 53. In total, RSTUV has an area of 53
Answer:
(a) Explained below.
(b) 0.0294
(c) 0.0173
(d) 0.09827
(e) 0.0452
Step-by-step explanation:
The complete question is:
According to an airline, flights on a certain route are on time 80% of the time. Suppose 25 flights are randomly selected and the number of on-time flights is recorded.
(a) Explain why this is a binomial experiment.
(b) Find and interpret the probability that exactly 16 flights are on time.
(c) Find and interpret the probability that fewer than 16 flights are on time.
(d) Find and interpret the probability that at least 16 flights are on time.
(e) Find and interpret the probability that between 14 and 16 flights, inclusive, are on time.
Solution:
(a)
Let the random variable <em>X</em> be defined as the number of on-time flights.
A Binomial experiment has the following properties:
- There are a fixed number of trials (n).
- Each trial are independent of the others.
- Each trial has only two outcomes: Success and Failure
- Each trial has the same probability of success (p).
If a random variable <em>X</em> is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.
All of these properties can be confirmed for the random variable <em>X</em>.
Thus, this is a binomial experiment.
(b)
Compute the probability that exactly 16 flights are on time as follows:
Thus, the probability that exactly 16 flights are on time is 0.0294.
(c)
Compute the probability that fewer than 16 flights are on time as follows:
Thus, the probability that fewer than 16 flights are on time is 0.0173.
(d)
Compute the probability that at least 16 flights are on time as follows:
(e)
Compute the probability that between 14 and 16 flights, inclusive, are on time as follows:
Thus, the probability that between 14 and 16 flights, inclusive, are on time is 0.0452.