Bill and Sam go to a casino. They each have the same amour of money. After an hour bill had won $20 and Sam lost the same amount. The next hour bill had lost two thirds of all his money and Sam had won the same amount. At that point Sam had four times as much as bill. How much money did they each have before they started?

They each have $180 before they started.

Step-by-step explanation:

Let x represents the amount they each have before they started. Therefore, we have:

Amount with Bill after one hour = x + $20

Amount with Sam after one hour = x - $20

Amount with Bill after two hours = (x + $20) - (x + $20)(2 / 3)

Amount with Sam after two hours = (x - $20) + (x - $20)(2 / 3) = 4((x + $20) - (x + $20)(2 / 3)) (1)

From equation (1), we can solve for x as follows:

(x - $20) + (x - $20)(2 / 3) = 4((x + $20) - (x + $20)(2 / 3))

(x - $20) + (x - $20)0.666666666666667= 4((x + $20) - (x + $20) 0.666666666666667)

x - $20 + 0.666666666666667x - $13.3333333333333= 4(x + $20 - 0.666666666666667x - $13.3333333333333)

x - $20 + 0.666666666666667x - $13.3333333333333= 4x + $80 - 2.66666666666667x - $ 53.3333333333332

Collecting the like terms, we have:

x + 0.666666666666667x - 4x + 2.66666666666667x = $80 - $53.3333333333332+ $20 + $13.3333333333333

(1 + 0.666666666666667- 4 + 2.66666666666667)x = $60

0.333333333333337x = $60

x = $60 / 0.333333333333337

x = $180

Therefore, they each have $180 before they started.

man its nopq i just guessed and got it right so uhh

g00d lucc

step-by-step explanation:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;