Which of these constructions is impossible using only a compass and straightedge

From a group of 12 students, we want to select a random sample of 4 students to serve on a university committee. How many combin

borishaifa [10]

Answer:

495 combinations of 4 students can be selected.

Step-by-step explanation:

The order of the students in the sample 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.

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

How many combination of random samples of 4 students can be selected?

4 from a set of 12. So

$C_{n,x} = \frac{12!}{4!(8)!} = 495$

495 combinations of 4 students can be selected.

8 0

3 years ago

Christine performed the following experiment 20 times using a book that contains 462 pages.

wel

Using the probability concept, it is found that there is a 0.3 = 30% experimental probability that Christine will randomly choose a page that is divisible by 3.

<h3>What is a probability?</h3>

A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.

In an experimental probability, these number of outcomes are taken from previous trials.

In this problem:

The experiment was made 20 times.

Of those, in 6 experiments(81, 105, 171, 159, 297, 387) she choose a page that was divisible by 3.

Then:

$p = \frac{6}{20} = 0.3$

0.3 = 30% experimental probability that Christine will randomly choose a page that is divisible by 3.

You can learn more about the probability concept at brainly.com/question/15536019

7 0

2 years ago

1. Determine a rule that could be used to explain how the volume of a

Eva8 [605]

Answer:

See explanation

Step-by-step explanation:

Solution:-

- We will use the basic formulas for calculating the volumes of two solid bodies.

- The volume of a cylinder ( V_l ) is represented by:

$V_c = \pi *r^2*h$

- Similarly, the volume of cone ( V_c ) is represented by:

$V_c = \frac{1}{3}*\pi *r^2 * h$

Where,

r : The radius of cylinder / radius of circular base of the cone

h : The height of the cylinder / cone

- We will investigate the correlation between the volume of each of the two bodies wit the radius ( r ). We will assume that the height of cylinder/cone as a constant.

- We will represent a proportionality of Volume ( V ) with respect to ( r ):

$V = C*r^2$

Where,

C: The constant of proportionality

- Hence the proportional relation is expressed as:

V∝ r^2

- The volume ( V ) is proportional to the square of the radius. Now we will see the effect of multiplying the radius ( r ) with a positive number ( a ) on the volume of either of the two bodies:

$V = C*(a*r)^2\\\\V = C*a^2*r^2$

- Hence, we see a general rule frm above relation that multiplying the result by square of the multiple ( a^2 ) will give us the equivalent result as multiplying a multiple ( a ) with radius ( r ).

- Hence, the relations for each of the two bodies becomes:

$V = (\frac{1}{3} \pi *r^2*h)*a^2$