Solving a Two-Step Matrix Equation
Solve the equation:

Step-by-step explanation:

Solve the following equation:

-In order to solve a pair of equations by using substitution, you first need to solve one of the equations for one of variables and then you would substitute the result for that variable in the other equation:

-First equation:

-Second equation:

-Choose one of the two following equations, which I choose the first one, then you solve for by isolating

-Subtract to both sides:

-Subtract to both sides:

-Divide both sides by :

-Multiply by :

-Substitute for in the second equation, which is :

Multiply by :

-Combine like terms:

-Subtract to both sides:

-Multiply both sides by :

-After you have the value of , substitute for onto this equation, which is :

-Multiply and :

-Since both and have the same denominator, then add the numerators together. Also, after you have added both numerators together, reduce the fraction to the lowest term:

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;