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shtirl [24]
3 years ago
15

Show work please! I don't understand how to get this answer! I will give brainliest to the best answer!

Mathematics
1 answer:
Marina86 [1]3 years ago
4 0

Answer:

(x,y,z) = (2,-2,1)

Step-by-step explanation:

Three equations with three variables are given. Take two equations at a time to eliminate one variable.

                      x + y - z = -1                       .....(1)

                   4x -3y + 2z = 16                   .....(2)

                    2x - 2y - 3z = 5                   ......(3)

Solve (1) and (3) to eliminate z.

To do that multiply (1) by 2 and add (1) and (2). We get:

                        4x - 5z = 3                       ......(4)

Now, solve (2) and (3) and subtract them. We get:

                        2x + 13z = 17                    ......(5)

Solve (4) and (5). Multiply (5) by 2 and subtract. We get:

                                        z  = 1

Substituting z = 1, in (4) we get:  x = 2.

Now to find y, substitute values of x and y in (1).

⇒ x + y - z = -1 ⇒ 2 + y - 1 = -1

⇒ y = -2

∴ Values of (x, y, z) = (2, -2, 1).

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3 years ago
Based on information from Consumer Reports, a random sample of 35 thirty-gram cookies had a sample mean of 146 calories. The sta
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Using the z-distribution, it is found that the 90% confidence interval for mean calories in a 30-gram serving of all chocolate chip cookies is (143, 149).

We are given the <em>standard deviation</em> for the population, which is why the <em>z-distribution </em>is used to solve this question.

The information given is:

  • Sample mean of \overline{x} = 146.
  • Population standard deviation of \sigma = 12.
  • Sample size of n = 65.

The confidence interval is:

\overline{x} \pm z\frac{\sigma}{\sqrt{n}}

The critical value, using a z-distribution calculator, for a <u>95% confidence interval</u> is z = 1.645, hence:

\overline{x} - z\frac{\sigma}{\sqrt{n}} = 146 - 1.645\frac{12}{\sqrt{35}} = 143

\overline{x} + z\frac{\sigma}{\sqrt{n}} = 146 + 1.645\frac{12}{\sqrt{35}} = 149

The 90% confidence interval for mean calories in a 30-gram serving of all chocolate chip cookies is (143, 149).

A similar problem is given at brainly.com/question/16807970

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