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3 years ago

Which of the following proportions can be used to prove AE || DK in the proof below? Select all that apply.

Mathematics

2 answers:

Ira Lisetskai [31]3 years ago

8 0

Triangle AEF and triangle DFK are similar to each other, this implies that the ratio of the corresponding sides are equal. Hence:
Using the proportions and ratio we have
the correct statement is:
b

Galina-37 [17]3 years ago

5 0

Answer: DA:FA=KE:EF, DF:DA=KF:KE and FA:DA=EF:KE are correct.

Explanation: Since, $\triangle EFA$ and $\triangle KFD$ are similar triangles.

Because, $\angle FAE= \angle FDK$ and $\angle FEA= \angle FKD$ (because EA and KD are parallels. And, $\angle F$ is common angle for these triangles.

Therefore, according to the property of similar triangles.

FE:EK= FA:AD, FE:FK=FA:FD and DF:DA=KF:KE .

Thus, first, second and third options are correct.

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3 years ago

preliminary sample of 100 labourers was selected from a population of 5000 labourers by simple random sampling. It was found tha

VladimirAG [237]

Answer:

$n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79$

n=369

Step-by-step explanation:

1) Notation and definitions

$X=40$ number of the selected labourers opt for a new incentive scheme.

$n=100$ random sample taken

$\hat p=\frac{40}{100}=0.4$ estimated proportion of the selected labourers opt for a new incentive scheme.

$p$ true population proportion of the selected labourers opt for a new incentive scheme.

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

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

2) Solution tot he 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: