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9966 [12]
3 years ago
10

3

Mathematics
1 answer:
adoni [48]3 years ago
8 0

Answer:

The solution set is (5,6).

Step-by-step explanation:

Given equations are:

-6x + 6y= 6         Eqn 1

-6x + 3y=-12      Eqn 2

Subtracting Eqn 2 from Eqn 1

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

-6x+6y+6x-3y=6+12

3y = 18

Dividing both sides by 3

\frac{3y}{3}=\frac{18}{3}\\y=6

Putting y=6 in Eqn 1

-6x+6(6)=6

-6x+36=6

-6x=6-36

-6x=-30

\frac{-6x}{-6}=\frac{-30}{-6}\\x=5

Hence,

The solution set is (5,6).

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3 years ago
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e
Viefleur [7K]

Answer:

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. So 1537 - 1184 = 353 read at or below this level. Then

n = 1537, \pi = \frac{353}{1537} = 0.2297

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 - 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2087

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 + 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2507

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).

7 0
3 years ago
Is <img src="https://tex.z-dn.net/?f=1-2x%5E%7B2%7D" id="TexFormula1" title="1-2x^{2}" alt="1-2x^{2}" align="absmiddle" class="l
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Answer:

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Step-by-step explanation:

This is a quadratic expression.  If you want this expression in standard form, write the terms in descending order of powers of x:  -2x^2 + 1.

This   -2x^2 + 1   has not yet been factored.

-2x^2 + 1 is in standard form.

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Answer:

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Step-by-step explanation:

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