Assume that 20 percent of students have taken calculus in high school. of those who have taken calculus in high school, 80 percent plan to major in science. of those who did not take calculus in high school, only 30 percent plan to major in science. what is the probability that a randomly selected student plans to major in science?

The probability that a randomly selected student plans to major in science is 40%

Step-by-step explanation:

Students who take calculus in high school = 20% or 0.2

Of these students, 80% or 0.8 plan to major in science.

That means of these students,

(100 -80) = 20% or 0.2 do not plan to major in science

Students who do not take calculus in high school = (100 -20)= 80% or 0.8

Of these students, 30% or 0.3 plan to major in science.

That means of these students,

(100 -30) = 70% or 0.7 do not plan to major in science.

The probability of students who take calculus in high school and plan to major in science = 0.2 * 0.8

= 0.16

= 16%

The probability of students who take calculus in high school and do not plan to major in science = 0.2 * 0.2

= 0.04

= 4%

The probability of students who do not take calculus in high school and plan to major in science = 0.8 * 0.3

= 0.24

= 24%

The probability of students who do not take calculus in high school and do not plan to major in science

= 0.8 * 0.7

= 0.56

= 56%

All of these probabilities will give 100% of the population.

(16+4+24+56)% = 100%

Therefore, the probability that a randomly selected student plans to major in science = 16% + 24%

= 40%

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~