A high school janitor has 140 keys on his key chain. Of these 140 keys, 100 open classroom doors, 80 open the
door to the teachers' lounge, and 60 open classroom doors and the teachers' lounge.

1. P(C) =  5/7

2. P(T) =  4/7

3. P(C and T) =  3/7

4. P(C or T) =  6/7

Correct statement and question:

A high school janitor has 140 keys on his key chain. Of these 140 keys, 100 open classroom doors, 80 open the door to the teachers' lounge, and 60 open classroom doors and the teachers' lounge. Using this information, answer each of the following questions.

Let C be the event that a randomly selected key opens a classroom and T be the event that a randomly selected key opens the teachers' lounge.

1. What is P(C), the probability that a key opens a classroom?

2. What is P(T), the probability that a key opens the teachers' lounge?

3. What is P(C and T), the probability that a key opens a classroom and the teachers' lounge?

4. What is P(C or T), the probability that a key opens a classroom or the teachers' lounge?

Source:

Question that can be found at chegg dot com

Step-by-step explanation:

1. Let's review the information given to us to answer the problem correctly:

Number of keys the high-school janitor has = 140

Number of keys that open classroom doors = 100

Number of keys that open   teachers' lounge = 80

Number of keys that open both = 60

2. What is P(C), the probability that a key opens a classroom?  

Let's recall the formula of probability:

Probability = Number of favorable outcomes/Total of possible outcomes

Substituting with the real given values:

P(C) = 100/140 = 5/7 (Dividing by 20 numerator and denominator)

P(C) =  5/7

3. What is P(T), the probability that a key opens the teachers' lounge?

Substituting with the real given values:

P(T) = 80/140 = 4/7 (Dividing by 20 numerator and denominator)

P(T) =  4/7

4. What is P(C and T), the probability that a key opens a classroom and the teachers' lounge?

Substituting with the real given values:

P(C and T) = 60/140 = 3/7 (Dividing by 20 numerator and denominator)

P(C and T) =  3/7

5. What is P(C or T), the probability that a key opens a classroom or the teachers' lounge?

P(C or T) = P(C) + P(T) - P(C and T)

Substituting with the real given values:

P(C or T) = 5/7 + 4/7 - 3/7

P(C or T) =  6/7

3,750 deer

step-by-step explanation:

1,500 is 15 times larger than 100

lets make 250 15 times larger.

3750 deer

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.