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3 years ago

What is the solution to this system of linear equations? x + y = 4 x − y = 6 A: (4, 6) B: (6, 4) C: (5, −1) D: (−1, 5)

Mathematics

1 answer:

zhuklara [117]3 years ago

4 0

Answer:

Step-by-step explanation:

Given the 2 equations

x + y = 4 → (1)

x - y = 6 → (2)

Add the 2 equations term by term to eliminate y, that is

2x = 10 ( divide both sides by 2 )

x = 5

Substitute x = 5 into either of the 2 equations and evaluate for y

Substituting into (1)

5 + y = 4 ( subtract 5 from both sides )

y = - 1

solution is (5, - 1 ) → C

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Consolidated Power, a large electric power utility, has just built a modern nuclear power plant. This plant discharges waste wat

Gemiola [76]

Answer:

We conclude that the plant should shut down.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 60

Sample mean, $\bar{x}$ = 61.498

Sample size, n = 100

Alpha, α = 0.05

Population standard deviation, σ = 6

a) First, we design the null and the alternate hypothesis such that the power plant will be shut down when the null hypothesis is rejected.

$H_{0}: \mu \leq 60\\H_A: \mu > 60$

We use One-tailed(right) z test to perform this hypothesis.

b) Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{61.498 - 60}{\frac{6}{\sqrt{100}} } = 2.49$

Now, $z_{critical} \text{ at 0.05 level of significance } = 1.64$

Since,

$z_{stat} > z_{critical}$

We reject the null hypothesis and accept the alternate hypothesis. Thus, the temperature of waste water discharged is greater than 60°F. We conclude that the power plant will shut down.

Calculating the p-value from the z-table:

P-value = 0.0063

Since,

P-value < Significance level

We reject the null hypothesis and accept the alternate hypothesis. Thus, the temperature of waste water discharged is greater than 60°F. We conclude that the power plant will shut down.

7 0

4 years ago

Find the amount of social security deducted from the check: $835 biweekly.

Inga [223]

Normally 8% is deducted as social security tax.

So,
8% of 835 = 8/100 x 835
= $56.36 (approx.)

4 0

3 years ago

1 + 1 = ? <br> I am a Collage Student and i have ZERO idea what this is.

Effectus [21]

Answer: 2
Explanation: common sense math lol

6 0

3 years ago

I need help will give brainliest for correct answer

Alex777 [14]

Answer:

x=-2

Step-by-step explanation:

To solve this, let's set the two exponents so that they have the same base. We know that 9 is 3², so we can rewrite the left side as (3²)^(x-8), which simplifies to 3^(2x-16). Now, we have 3^(2x-16) = 3^(4x-12). Since the bases are equal, the exponents are also equal. Therefore, 2x-16 = 4x-12. When we solve, we get -2x = 4, so x=-2. Hope this helps!

6 0

3 years ago

Read 2 more answers

4. Find the measure of the missing angle

soldier1979 [14.2K]

Wouldnt it also be 40 like if it’s the same as the top angle

5 0

3 years ago