Barry spent 1/5 of his monthly salary for rent and 1/8 of his monthly salary for his utility bill. If $1188 was left, what was his monthly salary

$1,760

Step-by-step explanation:

Let his salary be x.

He spent 1/5 of his salary, or x/5, and 1/8 of his salary, or x/8.

His salary was x. He spent x/5 and x/8, so we subtract those two amounts from his salary.

x - x/5 - x/8 is the amount he still has. He still has $1188. We equate the two and have an equation.

x - x/5 - x/8 = 1188

x/1 - x/5 - x/8 = 1188

We need to combine the three fractions on the left side, so we need to use a common denominator. The least common multiple of 1, 5, and 8 is 40, so 40 is the LCD.

40x/40 - 8x/40 - 5x/40 = 1188

27x/40 = 1188

Multiply both sides by 40.

27x = 47,520

Divide both sides by 27.

x = 1,760

His monthly salary is $1,760.

Check:

1/5 of his salary is 1760/5 = 352

1/8 of his salary is 1760/8 = 220

Now we subtract 352 and 220 from 1760.

1760 - 352 - 220 = 1188 which is what the problem stated.

Our answer, $1760, is correct.

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;

1) the property is   ixi = a ⇔x = a   o x = -a

4(x-5)+3= 15⇒4x-20+3 = 15⇒4x-17= 15⇒4x = 15+17⇒4x = 32⇒x =32/4= 8

4(x-5) +3= -15⇒4x-20 +3 = -15⇒4x-17= -15⇒4x =-15+17⇒4x = 2⇒x =2/4= 1/2

the values are x =8 and x = 0,5