Question

Identify whether each of the following statements is true or false.

1. Relative frequency and experimental probability represent the same ratio.

2. A function is a relation in which each input has at least one output.

3. The x-axis on a coordinate plane is the vertical axis.

4. In a direct variation, the constant of proportionality, constant of variation, and unit rate represent the same value.

Answer 1

1) True 2) False 3) False 4) True

Explanation:

1) True

A Relative Frequency is a ratio given by
`f_(i)=(n_(i))/(N)`. Where
`n_(i)` = "number of favorable outcomes" over N="Total Outcomes" and it provides a relative quantity of how many times some event occurs. This quantity belongs to this interval [0,1]

An Experimental Probability for its turn is also a ratio where on the numerator goes: "number of times the event occurred" over "number of trials". We will have another ratio on this interval [0,1]

2) False

A function is a relation in which each input (x ∈ A) uniquely has one output (f(x)∈ B). Whether it is an injective (one to one function) or not.

3) False

The x-axis on a coordinate plane is the horizontal axis, also called abscissa.

4) True

When we mention Direct Variation, we are saying that y varies directly with and proportionally to x. In other words, y=kx. Every time we increase the quantity of x, by making k=2, or k=3 we increase y.

Suppose

y=kx

k=2 then y=2x

k=3 then y=3x

10=2k

K is called Constant of Proportionality or Constant of Variation.

Unit Rate represents how much of something per unit.

In short: it all refers to quantities related to K.

e.g.

y=10 people, x=2 hours. K= 5 people per hour (Unit rate)

Answer 2

1. TRUE

2. FALSE, A function can only have one output for each input.

3. FALSE, The X - Axis is always the horizontal plane.

4. TRUE