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stealth61 [152]
2 years ago
11

Which point is a solution to y ≤ 3x- 4? O A. (0,4) O B. (-2, 0) OC. (0, 0) OD. (3,1)

Mathematics
2 answers:
Andrew [12]2 years ago
8 0
I’d say the answer is D. (3,1)
Nina [5.8K]2 years ago
4 0

Answer:

<em>(D). (3, 1) </em>

Step-by-step explanation:

y ≤ 3x - 4

<u><em>(A). (0, 4)</em></u>

4 ≤ 3(0) - 4

4 ≤ - 4 <u><em>(False statement)</em></u>

<u><em>(B). (-2, 0)</em></u>

0 ≤ 3(- 2) - 4

0 ≤ - 10 <u><em>(False statement) </em></u>

<u><em>(C). (0, 0)</em></u>

0 ≤ 3(0) - 4

0 ≤ - 4 <u><em>(False statement)</em></u>

<u><em>(D). (3, 1)</em></u>

1 ≤ 3(3) - 4

1 ≤ 5 <u><em>(True statement) </em></u>

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Answer:

The confidence interval for the mean is given by the following formula:  

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

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

Step-by-step explanation:

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 confidence interval for the mean is given by the following formula:  

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

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

3 0
3 years ago
Tannin and Dax bought a new video game for $48 to use the coupon for 25% off how much would the game cost if they paid full pric
olchik [2.2K]

Answer:

$64

Step-by-step explanation:

After using a 25% discount coupon, they paid 48 for the video game.

It means, <em>which number, decreased by 25%, would give us 48?</em>

<em />

First, 25% to decimal is:

25/100 = 0.25

Now, if we let the original price be "x", we can say:

x decreased by 0.25 of x would give us 48

Translating this to algebraic equation gives us:

x - 0.25x = 48

Now, we solve this:

x - 0.25x = 48\\0.75x=48\\x=\frac{48}{0.75}\\x=64

If they paid full price, the video game would cost $64

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