Answer:
Option A) Discrete and quantitative
Step-by-step explanation:
We are given the following situation in the question:
In a study of the effect of handedness on athletic ability.
Variable 1: Handedness - right-handed, left-handed, and ambidextrous
Variable 2: Athletic ability measured on a 12-point scale.
Dependent Variable:
- The dependent variable is the response variable and its value depends on the independent variable.
- A change in independent variable leads to a change in the dependent variable.
For the given case the athlete ability is the dependent variable that depends on the independent variable of handedness.
Athletic ability is measured on a 12 point scale. thus, it can take numerical values from 0 to 12.
Thus, it is a quantitative variable.
Since theses values are always expressed in whole numbers and not in decimals so they cannot take all the values within an interval.
Thus, it is a discrete variable.
Option A) Discrete and quantitative
To find the acceleration of the bicycle rider, we are going to use the acceleration formula:
![a= \frac{v_{f}-v_{i}}{t}](https://tex.z-dn.net/?f=a%3D%20%5Cfrac%7Bv_%7Bf%7D-v_%7Bi%7D%7D%7Bt%7D%20)
where
![a](https://tex.z-dn.net/?f=a)
is the acceleration
![v_{i}](https://tex.z-dn.net/?f=v_%7Bi%7D)
is the initial speed
![v_{f}](https://tex.z-dn.net/?f=v_%7Bf%7D)
is the final speed
![t](https://tex.z-dn.net/?f=t)
is the time
We know from our problem that increases his speed from 5 m/s to 15 m/s in 10 seconds, so his initial speed is 5 m/s and his final speed is 15 m/s; therefore,
![v_{i}=5](https://tex.z-dn.net/?f=v_%7Bi%7D%3D5)
,
![v_{f}=15](https://tex.z-dn.net/?f=v_%7Bf%7D%3D15)
, and
![t=10](https://tex.z-dn.net/?f=t%3D10)
. Lets replace those values in our formula:
![a= \frac{v_{f}-v_{i}}{t}](https://tex.z-dn.net/?f=a%3D%20%5Cfrac%7Bv_%7Bf%7D-v_%7Bi%7D%7D%7Bt%7D%20)
![a= \frac{15-5}{10}](https://tex.z-dn.net/?f=a%3D%20%5Cfrac%7B15-5%7D%7B10%7D%20)
![a= \frac{10}{10}](https://tex.z-dn.net/?f=a%3D%20%5Cfrac%7B10%7D%7B10%7D%20)
We can conclude that the acceleration of the bicycle rider 1 m/s^2
V = 1/3 * pi r^2 h
V = 1/3 * pi * 5/2^2 * 6
V = 1/3 * pi * 25/4 *6
V = 2 * pi *25/4
V = 25/2 pi
Answer: (12.5*pi)in^3 or 39.27 in^3