In ΔIJK, j = 940 inches, ∠J=20° and ∠K=50°. Find the length of i, to the nearest inch.

Mathematics

1 answer:

zzz [600]3 years ago

6 0

Answer:

5170 inches

Step-by-step explanation:

To solve this problem, we need to figure out a.), the angle measurement of I, and b.), the amount of inches per degree, which will lead us to c.), the final answer.

1) Add the measurements of J and K.

20 + 50 = 70

2) Subtract from 180 to find the measurement of I

180 - 70 = 110

∠I = 110°

3) Divide 940 by 20 to find the amount of inches per degree.

940/20 = 47

4) Multiply 47 by 110 to get the measurement of I.

47 * 110 = 5170

Final answer: I = 5170 inches

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An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume

Lynna [10]

Answer:

a) $21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

b) $ME=2.58\frac{52}{\sqrt{350}}=7.17$

c) $ME=2.58\frac{52}{\sqrt{100}}=13.42$

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

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".

Part a

$\bar X=21$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=52$ represent the population standard deviation

n=350 represent the sample size

99% confidence interval

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 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$