Mathematics, 21.03.2020 10:03 orangeicecream

In a class of 100 students, 25 have hardcover and 75 students have paperback textbooks. If you randomly choose 15 students in this class, find the probability that 3 of them have hardcover texts.

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Answer from: esekvng4342

23.72% probability that 3 of them have hardcover texts.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the students are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

If you randomly choose 15 students in this class, find the probability that 3 of them have hardcover texts.

Desired outcomes:

3 with hardcover texts, from a set of 25.

15-3 = 12 with paperback texts, from a set of 75. So

$D = C_{25,3}*C_{75,12} = \frac{25!}{3!(22)!}*\frac{75!}{12!(63)!} = 6 \times 10^{16}$

Total outcomes:

15 students from a set of 100. So

$T = C_{100,15} = \frac{100!}{15!85!} = 2.53 \times 10^{17}$

Probability:

$P = \frac{D}{T} = \frac{6 \times 10^{16}}{2.53 \times 10^{17}} = 0.2372$

23.72% probability that 3 of them have hardcover texts.

Answer from: Quest

answer

a,b, and d

explanation

a reflection angle is more than

$\pi \: radians$

but less than;

$2 \pi \: radians$

an angle that measures

$\frac{4 \pi}{3} \: radians$

is a reflex angle.(true)

an angle that measures less than

$\frac{\pi}{2}$

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

$0 \leqslant \theta \: < \frac{\pi}{2}$

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

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