## Problem 1164

Is the selection a permutation, a combination, or neither?

A group of 10 friends sits in the same row in a movie theater.

Solution:-

Use the definition of permutation and combination to determine the type of selection mode.

A permutation of a set of n distinct objects is an arrangement of the objects in a specific order without repetition.

A combination of a set of n distinct objects in an arrangement of the objects without repetition where order is irrelevant.

In the selection process of the problem, the order in which the friends sit is important.

There will not be any repetition since a person cannot sir in multiple seats at the same time.

Use the fact that the selection process has no repetition and order is relevant to determine the type of selection.

The selection is a permutation.

## Problem 1162

Is the selection a permutation, a combination, or neither?

Sam rents 5 videos from a video store.

Solution:-

Use the definition of permutation and combination to determine the type of selection made.

A permutation of a set of n distinct object is an arrangement of the objects in a specific order without repetition.

A combination of a set of n distinct objects is an arrangement of the object without repetition where order is irrelevant.

In the selection process of the problem, the order that the video are rented is not important.

There will not be ant renting video form the video store because the student cannot rent the same copy of a movie multiple time at the same moment in time.

Use the fact that the selection process has no repetition and order is irrelevant to determine the type of selection.

The selection is a combination.

## Problem  453

Decide whether the pair of lines of lines is parallel. Perpendicular, or neither.

2x + 5y = 9

2x + 5y = 5

Solution

x coefficient and y coefficient are equal in both equations so lines are parallel.

Determine if f(x) = is linear, quadratic, or neither.

Solution

A  linear function can be written in the form f(x) = ax + b. The function f(x) is not currently in this form.

There is no way to rewrite f(x)without having a variable in the denominator.

So cannot be put in the form ax + b.

A quadratic function can be written in the form f(x) = a + bx +c.

The function f(x)is not currently in this form.

Since there is no way to rewrite f(x) without having a variable in the denominator, cannot be put in the form .

Therefore, f(x) is neither linear nor quadratic.