Consider all four-digit numbers that can be made from the digits 0-8 (assume that numbers cannot start with 0). What is the probability of choosing a random number from this group that is greater than 7000

0.2498

Step-by-step explanation:

Number of 4 digit numbers that can be formed from the digit (0 - 8), assume number can't start from 0

Thus ;

First digit = (1, 2, 3, 4, 5, 6, 7, 8) = 8 ways

Next three digits = (0, 1, 2, 3, 4, 5, 6, 7, 8) = 9 ways

Hence,

Total possible outcomes = sample space = (8 * 9 * 9 * 9) = (8 * 9^3 ) = 8 * 729 = 5832

Required = number greater Than 7000

For number to be greater Than 7000, starting digit should be either 7 or 8

Hence,

First digit = 2 ways

Next three digits = 9 ways

Also excluding 7000

Hence, Number of digits above 7000;

2 * 9^3 = 2 * 729 = 1458 - 1 = 1457

Hence,

Probability = 1457 / 5832

= 0.2498285

= 0.2498

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.