Can someone help me and explain how to do these probability questions?

Mathematics

2 answers:

Alex_Xolod [135]2 years ago

6 0

The answer to question A is 1/100 and 1%. For question B I think the answer is C but I’m not 100% sure on that unfortunately.

devlian [24]2 years ago

6 0

a. The probability is 1/100 since there are 10 possible digits (0-9) and you need the last two digits so $\frac{1}{10}*\frac{1}{10}=\frac{1}{100}$ .

This is 1%.

b. Let's start by calculating the probability of getting the right digits knowing that they are both even.

We have a total of 5 even digits (0, 2, 4, 6, 8). You need the last two so $\frac{1}{5}*\frac{1}{5} =\frac{1}{25}=\frac{4}{100}$ which is 4%.

Therefore the answer is a) It increases the probability that your choice is correct to 1/25, or 4%, because each digit could be 0, 2, 4, 6 or 8.

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ABCD is a rectangle. The measure of angle BCE is 4x-23 and the angle measure of angle DCE is 5+5x. Find the measure of angle BEC

Temka [501]

<h2>Explanation:</h2><h2></h2>

The diagram for this problem is shown below. Point E is the intersection of the two diagonals and we know that:

$\angle BCE=\beta \\ \\ \angle DCE=\theta$

Every internal angle of any rectangle measures 90 degrees, so:

$\beta +\alpha=90 \\ \\ (4x-23)+(5+5x)=90 \\ \\ \\ Isolating \ x: \\ \\ (4x+5x)+(5-23)=90 \\ \\ 9x-18=90 \\ \\ 9x=108 \\ \\ x=\frac{108}{9}=12$

So:

$\beta=4x-23=4(12)-23=25^{\circ}$

So the measure of angle BEC can be found as follows:

We know that triangle ΔCEB is an isosceles triangle because the diagonals of any rectangle measure the same. So

$\angle EBC=\beta$

The sum of internal angles of any triangle add up to 180 degrees, so:

$\beta + \beta+\angle BEC=180^{\circ} \\ \\ 2\beta+\angle BEC=180^{\circ} \\ \\ \angle BEC=180^{\circ}-2\beta \\ \\ \angle BEC=180^{\circ}-2(25^{\circ}) \\ \\ \angle BEC=180^{\circ}-50^{\circ} \\ \\ \boxed{\angle BEC=130^{\circ}}}$