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3 years ago

DEF is a right triangle. A. True B. False

Mathematics

2 answers:

Vika [28.1K]3 years ago

8 0

------------ False-----------

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Sonbull [250]3 years ago

5 0

Given triangle DEF with the lengths of all sides. If you want to check whether this triangle is right, use the Pythagorean theorem. The greatest side is EF, then only this side could be the hypotenuse.

Check, whether

$EF^2=ED^2+DF^2.$

Substitute ED=25, EF=48 and DF=27:

$DF^2+DE^2=27^2+25^2=729+625=1354,\\ \\EF^2=48^2=2304.$

Since $1354\neq 2304,$ the triangle DEF is not right triangle.

Answer: correct choice is B

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Translate the following problem into an equation: (1) together Jon and Amy spent $29 dollars on a birthday gift. (2) Jon spent $

kolbaska11 [484]

Let the money spent by John = y
and Amy=x

ATQ

x+y = $29

It is given that jon spend 5 more than Amy. SO he spend

x +5

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2x = 29-5

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4 0

3 years ago

Suppose that 20% of the subscribers of a cable television company watch the shopping channel at least once a week. The cable com

riadik2000 [5.3K]

Answer:

4.01% probability that the cable company will keep the shopping channel.

Step-by-step explanation:

For each subscriber, there are only two possible outcomes. Either they watch the shopping channel at least once a week, or they do not. This means that we can solve this problem using the binomial probability distribution.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 100, p = 0.20$

$E(X) = 100*0.20 = 20$

$\sqrt{V(X)} = \sqrt{100*0.20*0.80} = 4$

The cable company has decided to keep the shopping channel if the sample proportion is greater than 0.27. What is the approximate probability that the cable company will keep the shopping channel, even though the true proportion who watch it is only 0.20?

This probability is 1 subtracted by the pvalue of Z when $X = 0.27*100 = 27$ . So