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3 years ago

Find the missing lengths of the sides

Mathematics

2 answers:

SCORPION-xisa [38]3 years ago

8 0

That's a 30-60-90 triangle, so the hypotenuse will always be 2x, the shorter leg will be x and the longer leg will be x√3. In this case, we are given the longer leg and we can deduce that x = 9. So, a = x = 9 and c = 2x = 18. Your answer is A, a = 9 yd, c = 18 yd.

Mandarinka [93]3 years ago

8 0

Answer:

a) a = 9d, c = 18 yd

Step-by-step explanation:

The given triangle is a 30-60-90 triangle. The ratio of the sides of the triangle is 1x: 2x: √3x.

Here the hypotenuse is 2x, the shorter leg is x and the longer leg is √3x.

In given figure, we are given the longer leg.

√3x = 9√3

From this we can find the value of x, which is the shorter leg.

Dividing both sides by √3, we get

x = 9

The shorter side, a = 9 yd

Now let's find the hypotenuse.

Plug in x = 9, in 2x, we get

= 2*9

= 18 yd

The hypotenuse "c" = 18 yd.

So the answer is a) a = 9d, c = 18 yd

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3 years ago

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Natasha2012 [34]

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4 years ago

A realtor would like to create a 95% confidence interval for the average price of a house in Franklin County, Ohio. To accomplis

VMariaS [17]

Answer:

$320128-1.96\frac{50324}{\sqrt{529}}=315839.52$

$320128+1.96\frac{50324}{\sqrt{529}}=324416.48$

So on this case the 95% confidence interval would be given by (315839.52;324416.48)

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".

$\bar X=320128$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=50324$ represent the population standard deviation

n=529 represent the sample size

Solution to the problem

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$320128-1.96\frac{50324}{\sqrt{529}}=315839.52$

$320128+1.96\frac{50324}{\sqrt{529}}=324416.48$

So on this case the 95% confidence interval would be given by (315839.52;324416.48)

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Answer:

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almond37 [142]

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3 years ago