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RideAnS [48]
3 years ago
5

Find x when y = 2 for y = -x + 5

Mathematics
2 answers:
Ganezh [65]3 years ago
8 0
Hope this helps with the answer to your question

bija089 [108]3 years ago
6 0

Answer:

x = 3

Step-by-step explanation:

<u>Step 1:  Solve for x </u>

<em>Set y equal to 2 </em>

y = -x + 5

2 = -x + 5

<em>Subtract 5 from both sides </em>

2 - 5 = -x + 5 - 5

-3 = -x

<em> </em>

<em>Divide both sides by -1 </em>

-3 / -1 = -x / -1

3 = x

Answer:  x = 3

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12. Using the value of 0.538 for the proportion of those surveyed who said they exercise at least 30 minutes three or more days
ICE Princess25 [194]

Answer:

ME=1.96\sqrt{\frac{0.538 (1-0.538)}{15235}}=0.00792    

The margin of error on this case is approximated \pm 0.792\% who is very clos to the +1% reported by the Gallup.

Step-by-step explanation:

Assuming this previous info : "Results are based on telephone interview conducted as part of the Gallup-Healthways Well-Being Index survey June 1–30,2013, with a random sample of 15,235 adults, aged 18 and older, living in all 50 U.S. states and the District of Columbia.

For results based on the total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is ±1 percentage point."

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The estimated proportion on this case is \hat p =0.538 and n =15235, the margin of error is given by:

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)

And if we replace we got:

ME=1.96\sqrt{\frac{0.538 (1-0.538)}{15235}}=0.00792    

The margin of error on this case is approximated \pm 0.792\% who is very clos to the +1% reported by the Gallup.

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2 years ago
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Select the two values of x that are roots of this equation.
makkiz [27]

Answer:

\implies x = (-2) \qquad or\qquad x = \dfrac{-3}{2}

Step-by-step explanation:

<u>Given </u><u>:</u><u>-</u><u> </u>

  • A quadratic equation is given to us.
  • The equation is 2x² + 7x +6=0

And we need to find out the roots of the given equation. We can use the middle term splitting method to find out the roots as ,

<u>Given </u><u>equation</u><u> </u><u>:</u><u>-</u>

\implies 2x^2 + 7x +6=0

Step 1: <u>Find</u><u> out</u><u> the</u><u> </u><u>factors</u><u> </u><u>of </u><u>1</u><u>2</u><u> </u><u>:</u><u>-</u><u> </u>

We will choose the two factors such that their sum equals to the coefficient of x i.e. 7 .The factors are , 1×12 , 2×6 , 3×4 .

  • And 3 + 4 = 7. So we will break the middle term into 3x and 4x .

Step 2 :<u> Breaking</u><u> the</u><u> </u><u>middle</u><u> term</u><u> </u><u>:</u><u>-</u><u> </u>

\implies 2x^2 + 3x+4x +6=0

Step 3: <u>Take </u><u>out </u><u>common</u><u> </u><u>from </u><u>terms </u><u>:</u><u>-</u>

\implies x(2x + 3) +2(2x +3)=0

\implies ( x +2)(2x+3)=0

Step 4 : <u>Equate </u><u>them </u><u>with </u><u>0</u><u> </u><u>:</u><u>-</u><u> </u>

\implies x = (-2) \qquad or\qquad x = \dfrac{-3}{2}

<u>Hence </u><u>the</u><u> </u><u>correct</u><u> </u><u>options </u><u>are </u><u>C </u><u>and </u><u>D </u><u>.</u>

5 0
2 years ago
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