What is the solution to the system? {x+3y-z=6 {4x-2y+2z= -10 {6x+z= -12 a. (2, 1, -3) b. (-3, 5, 6) c. (0,-2,-12)

B. (-3, 5, 6)

Step-by-step explanation:

The system of equations is:

x + 3y - z = 6 ... (i)

4x - 2y + 2z = -10 ... (ii)

6x + z = -12 ... (iii)

The value of z in (iii) is;

z = -12 - 6x

Replacing z in (i) and (ii) gives:

x + 3y - (-12 - 6x) = 6 ... (i)

4x - 2y + 2(-12 - 6x) = -10 ... (ii)

Simplifying gives;

7x + 3y = -6 ... (i)

-8x - 2y = 14 ... (ii)

Multiplying (i) by 2 and (ii) by 3 gives;

14x + 6y = -12 ... (i)

-24x - 6y = 42 ... (ii)

Adding (i) and (ii) gives;

-10x = 30

x = -3

Replacing x = -3 in (i) gives;

7(-3) + 3y = -6

3y = 21 - 6

y = = 5

Replacing x = -3 in (iii) gives;

6(-3) + z = -12

z = -12 + 18 = 6

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;

answer. d.289 hope that