At present the sum of monica's age and daughter's age is 44 years. after 2 years monica's age will be three times that if her daughter's age. find their present ages.

Monica's age = 34 years

Her daughter's age = 10 years

Step-by-step explanation:

Let Monica's age = x

Let her daughter'sage = y

x + y = 44   > equ 1

After 2 years:

Monica's age = x + 2

Her daughter's age = y + 2

x + 2 = 3 * (y+2)

x + 2 = 3y + 6

      x = 3y + 6 -2

      x = 3y + 4

Put x value in equ 1:

    3y + 4 + y = 44

            4y = 44 - 4

             4y = 40

               y = 40/4

               y = 10

x = 44 -10

x = 34

Monica' present age =34 years

Daughter's present age = 10 years

Step-by-step explanation:

Let x =  Monica's present age.

y= Her daughter's present age .

As per given , we have

After two years,

Monica's age = x+2

Daughter's age = y+2

According to the question,

Use (i) in (ii), we get

Put value of x in (i) , we get

Hence, Monica' present age =34 years

Daughter's present age = 10 years

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;