Given that XY is a line segment with the angle a = 48° and c = 59°, work out the value of the angle marked b.

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

6 0

Answer:

a+b+c = 180

48+59+b=180

107+b=180

b=180-107

b=73

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Look at this triangle work out length BC

Andreas93 [3]

Answer:

The length of BC is √105 cm or 10.2 cm.

Step-by-step explanation:

You have to apply Pythagoras Theorem, c² = a² + b² where c represents hypotenuse, a and b are the sides :

${c}^{2} = { a}^{2} + {b}^{2}$

$let \:a =BC \:, \: b = 8 \: , \: c = 13$

${13}^{2} = {BC}^{2} + {8}^{2}$

$169 = {BC}^{2} + 64$

${BC}^{2} = 169 - 64$

${BC}^{2} = 105$

$BC = \sqrt{105}$

$BC = 10.2 \: cm \: (3s.f)$

7 0

3 years ago

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3. Using the sample size of 800 and the proportion 0.47, calculate the margin of error associated with the estimate of the propo

salantis [7]

Answer:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346$

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

We assume for this case a confidence level of 95%. 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: