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?
bmk,nl
Question #1:
To find the probability, we first need to determine the total number of possible outcomes. Since we are choosing two students at random from a group of 50, the total number of possible outcomes is given by the combination formula, denoted as C(50, 2), which is calculated as:
C(50, 2) = 50! / (2! * (50-2)!)
Now, let's find the probabilities for each case:
a) Both students walked:
To find the probability that both students walked, we need to determine the number of favorable outcomes, which is the number of students who walked. According to the information given, 5 students traveled by car and walked, but did not use a bus. Therefore, there are 5 students who walked. Since we are choosing two students at random, the number of favorable outcomes is given by C(5, 2). Therefore, the probability is:
P(both walked) = C(5, 2) / C(50, 2)
b) Only one of the students walked:
To find the probability that only one of the students walked, we need to determine the number of favorable outcomes, which is the number of students who walked but did not use any other form of travel. According to the information given, 5 students traveled by car and walked, but did not use a bus, and 10 students traveled by bus and walked but did not use a car. Therefore, there are 5 + 10 = 15 students who walked but did not use any other form of travel. Since we are choosing two students at random, the number of favorable outcomes is given by C(15, 1) * C(35, 1). Therefore, the probability is:
P(one walked) = C(15, 1) * C(35, 1) / C(50, 2)
Now you can substitute the values in these formulas to find the probabilities.
Question #2:
In the surface area of a cylinder, (dA)/(dr) represents the derivative of the surface area with respect to the radius. It is used to find the rate of change of the surface area as the radius changes.
To calculate this, you differentiate the formula for the surface area of a cylinder, which is given by:
A = 2πrh + 2πr²
Taking the derivative of this formula with respect to the radius (r) gives us:
(dA)/(dr) = 2πh + 4πr
Therefore, (dA)/(dr) represents the rate at which the surface area of the cylinder changes with respect to a change in the radius.