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2 years ago

What is the solution to the system of equations?

Mathematics

1 answer:

Natalka [10]2 years ago

5 0

Answer:

x = 1 y = 3 z = 1

Step-by-step explanation:

(1) x - 3y - z = -9 (2) -2x + y + 2z = 3 (3) 2x + y + 3z = 8

2x(1) <u>2x - 6y - 2z = -18</u> (2) <u>-2x + y + 2z = 3</u>

- 5y = -15 2y + 5z = 11

y = 3 2(3) + 5z = 11

6 + 5z = 11

5z = 5

z = 1

x - 3(3) - 1 = -9

x - 9 - 1 = -9

x - 10 = -9

x = 1

Note: If you write your equations across your paper, then the work can just flow down the paper. It makes it so much easier to show the work you have done. OK?

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The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed by a new machine. The mean an

Genrish500 [490]

Answer:

We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 mg .

Step-by-step explanation:

Given -

The sample size is large then we can use central limit theorem

n = 50 ,

Standard deviation $(\sigma)$ = 7.1

Mean $\overline{(y)}$ = 110

$\alpha =$ 1 - confidence interval = 1 - .98 = .02

$z_{\frac{\alpha}{2}}$ = 2.33

98% confidence interval for the mean caffeine content for cups dispensed by the machine = $\overline{(y)}\pm z_{\frac{\alpha}{2}}\frac{\sigma}\sqrt{n}$

= $110\pm z_{.01}\frac{7.1}\sqrt{50}$

= $110\pm 2.33\frac{7.1}\sqrt{50}$

First we take + sign

$110 + 2.33\frac{7.1}\sqrt{50}$ = 112.34

now we take - sign

$110 - 2.33\frac{7.1}\sqrt{50}$ = 107.66

We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 .

5 0

3 years ago

I will mark you brainliest! The value of a car decreases by 1/6 every year. What type or function represents this pattern?

d1i1m1o1n [39]

Answer:

Step-by-step explanation:

When the value of something decreases by a certain factor every unit of time, instead of by a set constant, then this is called exponential decay. When the rate is constant, this is called linear decay. Hope this helps!

3 0

3 years ago

Can someone help solve for b

icang [17]

Step-by-step explanation:

solved above 8n the diagrammm

5 0

4 years ago

What does PIN stand for?

ankoles [38]

Answer:

Personal Identification Number

7 0

3 years ago

Read 2 more answers

Can someone help me please

Anastaziya [24]

The first step to solve this problem is to compute first for the area of the bigger rectangle:

A = LW

A = 12m (10m)

A = 120 m^2

Next step is to find the area of the smaller rectangle:

A = LW

A = 7m (2m)

A = 14 m^2

The last step is to deduct the area of the smaller rectangle to the area of the larger rectangle:

Area of larger rectangle – Area of the smaller rectangle = Area of the shaded region

120 m^2 – 14 m^2 = 106 m^2

Therefore, the area of the shaded region is 106 square meters.

7 0

4 years ago