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OlgaM077 [116]
3 years ago
6

If MNOP is a rectangle, and m

Mathematics
2 answers:
GenaCL600 [577]3 years ago
7 0

Answer:

B-60 APEX!!!!!

vivado [14]3 years ago
6 0

Answer:

(B) 60

Step-by-step explanation:

From the figure, it is given that MNOP is a rectangle and ∠MON=60°.

Now, Since from the properties of rectangle, the diagonals are congruent and bisect each other, therefore ∠PNO=60°.

Now, using the angle sum property in ΔNDO, we have

{\angle}DNO+{\angle}DON+{\angle}NDO=180^{\circ}

Substituting the given values, we get

⇒60^{\circ}+60^{\circ}+{\angle}NDO=180^{\circ}

⇒120^{\circ}+{\angle}NDO=180^{\circ}

⇒{\angle}NDO=180-120

⇒{\angle}NDO=60^{\circ}

Now, since x={\angle}NDO=60^{\circ}( Vertically opposite angle)

Thus, the value of x is 60°

Hence, option B is correct.

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In a survey, the planning value for the population proportion is . How large a sample should be taken to provide a confidence in
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Answer:

n=350

Step-by-step explanation:

Notation and definitions

n random sample taken  (variable of interest)

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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.  

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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:

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The margin of error for the proportion interval is given by this formula:  

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

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n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.586  

And rounded up we have that n=350

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