Mathematics, 13.01.2020 08:31 mattgraham366

Aschool committee consists of 2 teachers and 4 students. the number of different committees that can be formed from 5 teachers
and 10 students is
a. 10
b. 15
c. 2100
d. 8

Answers: 2

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Answer from: gabriellabadon2

Option C

2100 different committees that can be formed from 5 teachers and 10 students

Solution:

A school committee consists of 2 teachers and 4 students

The number of different committees that can be formed from 5 teachers and 10 students is to be found

This is a combination problem

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected

The formula to calculate combinations is:

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

where n represents the number of items, and r represents the number of items being chosen at a time

Here we have to choose 2 teacher from 5 teacher and 4 student from 10 student

Hence we get,

Number of committees = $5C_2 \times 10C_4$

$\begin{aligned}&5 C_{2} \times 10 C_{4}=\frac{5 !}{2 !(5-2) !} \times \frac{10 !}{4 !(10-4) !}\\\\&5 C_{2} \times 10 C_{4}=\frac{5 !}{2 ! \times 3 !} \times \frac{10 !}{4 ! \times 6 !}\end{aligned}$

To get the factorial of a number n the given formula is used,

$n !=n \times(n-1) \times(n-2) \ldots \times 2 \times 1$

Therefore,

$5 C_{2} \times 10 C_{4}=\frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 3 \times 2 \times 1} \times \frac{10 \times 9 \times \ldots . \times 2 \times 1}{4 \times 3 \times 2 \times 1 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}$

$5 C_{2} \times 10 C_{4}=2100$

Thus 2100 different committees that can be formed from 5 teachers and 10 students

Answer from: Quest

The correct answer would be the function g(x) increased at a faster rate

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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