Aset of equations is shown above. which method eliminates one of the variables? a) multiply equation a by -1/3 and add the result to equation b. b) multiply equation b by 3 and add the result to equation a. c) multply equation a by 2 and equation b by -6 and add the results together. d) multiply equation b by 5 and equation a by 4 and add the results together.

Step-by-step explanation:

Multiplying Equation A by (1/3) and adding the result to Equation B will do the trick.  Let's actually solve the problem!

Equation A:  (5/3)x + 3y = 12

Equation B:    4x     -  3y = 8

                     (5/3 + 12/3)x = 15        Note how this has eliminated the variable

                            (17/3)x = 15           y.

                                   x = (3/17)(15)

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;