Question #1
50 students total.
12 students travelled by car only
7 students travelled by bus only
5 students travelled by car and walked,but did not use a bus
10 students travelled by bus and walked,but did not use a car
3 students used all three forms of travel
I drew a Venn diagram.
Two students are chosen at random from all 50 students.
- Find the probability that
a) Both students walked
b) only one of the students walked
Question #2
What does (dA)/(dr) mean in the surface area of cylinder the problem?
I too made a Venn diagram and after filling in the given information , found two missing sections
1. Those that only walked
2. Those that took the bus or the car, but did not walk
confirm this please
#2, dA/dr means the rate of change of the surface area with respect to the radius.
Question 1:
To find the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes. Here's how we can find the probabilities for the given scenarios:
a) Both students walked:
Since we know that 3 students used all three forms of travel, we can subtract this number from the total number of students who walked. The remaining students who walked only and didn't use any other form of travel are (5 - 3) + (10 - 3) = 9.
To find the probability that both students walked, we need to calculate the probability of choosing one student who walked, and multiply it by the probability of choosing another student who walked from the remaining students who walked.
The probability for the first student to walk is 9/50, and for the second student to walk is 8/49 (since there is now one less student available). Multiplying these probabilities together, we get (9/50) * (8/49) = 72/2450.
b) Only one of the students walked:
Here, we need to calculate the probability of choosing one student who walked and the other who didn't walk.
The number of students who walked only is 9 (as we determined in the previous part). To find the probability that only one student walked, we need to multiply the probability of choosing one student who walked by the probability of choosing the other student who didn't walk.
The probability for the first student to walk is 9/50, and the probability for the second student to not walk is (50 - 9)/49 (since there is now one less student available). Multiplying these probabilities together, we get (9/50) * (41/49) = 369/2450.
Question 2:
In the surface area of a cylinder, (dA)/(dr) represents the rate of change of the surface area with respect to the radius. The letter "d" traditionally represents a small change or infinitesimal difference, so (dA)/(dr) means the change in the surface area divided by the change in radius.
For example, let's say we have a cylinder, and we increase the radius by a small amount. The resulting change in the surface area divided by the change in radius will give us the rate at which the surface area is changing relative to the radius change. This rate is referred to as the derivative of the surface area with respect to the radius. In mathematical terms, (dA)/(dr) represents the derivative of the surface area function with respect to the radius.