A fast-food company advertises that the pre-cooked weight for its burgers is, on average, 0.2\text{ kg}0.2 kg0, point, 2, start text, space, k, g, end text. The company runs a regular quality control test that involves weighing a sample of burgers to see if the burgers are too light or too heavy. If the sample mean weight is significantly different than 0.2 \text{ kg}0.2 kg0, point, 2, start text, space, k, g, end text, then they recycle the entire batch. What are appropriate hypotheses for the company's significance test?

The appropriate hypotheses for the company's significance test is:

H₀: μ = 0.20 vs. Hₐ: μ ≠ 0.20.

Step-by-step explanation:

The advertisement made by a fast-food company is that the precooked weight for its burgers is, on average, 0.20 kg.

To check this, the company runs a regular quality control test that involves weighing a sample of burgers to see if the burgers are too light or too heavy.

They decided that if the ample mean weight is significantly different than 0.20 kg then they would recycle the entire batch.

A two-tailed single mean test can be performed to determine whether the mean weight is different from 0.20 kg or not.

The hypothesis can be defined as follows:

H₀: The precooked weight for the burgers is, on average 0.20 kg, i.e. μ = 0.20.

Hₐ: The precooked weight for the burgers, on average, is different from 0.20 kg, i.e. μ ≠ 0.20.

Thus, the appropriate hypotheses for the company's significance test is:

H₀: μ = 0.20 vs. Hₐ: μ ≠ 0.20.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1