Question

question 9
if the volume for 3 - d polyhedra a is 200 cm³ and the volume for 3 - d polyhedral b is 800 cm³, how many times bigger is the volume of pyramid b than pyramid a?

a 0.4%

b 4%

c 40%

d 400%

e i have not learned this yet.

question 10
which statement accurately describes a step function?

a a step function consists of any linear function including horizontal and vertical lines.

b each piece of a step function is represented by a linear function with a slope greater than 0.

c the domain and range of a step function is all real numbers

d each piece of a step function is represented by a linear function with a slope equal to zero.

e i have not learned this yet.

Explanation:

Question 9

Step1: Find the ratio of volumes

To find how many times bigger the volume of B is than A, we calculate the ratio of the volume of B to the volume of A. The volume of A is \(200\space cm^3\) and the volume of B is \(800\space cm^3\). So the ratio is \(\frac{800}{200}\).
\(\frac{800}{200}=4\)

Step2: Convert the ratio to a percentage

To convert the ratio to a percentage, we multiply by \(100\%\). So \(4\times100\% = 400\%\).

• Option a: A step function is not just any linear function; vertical lines are not functions, and step functions have horizontal segments (constant) and jumps, not general linear functions. Eliminate a.
• Option b: Step function pieces are constant (slope 0), not with slope greater than 0. Eliminate b.
• Option c: The range of a step function is a set of discrete values (not all real numbers), and the domain can be all real numbers but the range is not. Eliminate c.
• Option d: Each piece of a step function is a horizontal line segment, which is a linear function with slope \(0\) (since \(y = c\) has slope \(0\)). This is correct.
• Option e: Not applicable as we can determine the answer.

Answer:

d. 400%

Question 10