stanley semester 2 final exam\n8. newtons second law, $f = mcdot a$, describes the relationship between an…

stanley semester 2 final exam\n8. newtons second law, $f = mcdot a$, describes the relationship between an objects mass, a force acting on it, and the resulting acceleration, where:\n$f$ is force, in newtons\n$m$ is mass, in kilograms\n$a$ is acceleration, in meters per second squared\na young boy and his tricycle have a combined mass of 30 kilograms. if the boys sister gives him a push with a force of 60 newtons, what is his acceleration?\na. $\frac{1}{2}$ meter per second squared\nb. 2 meters per second squared\nc. 30 meters per second squared\nd. 90 meters per second squared\n9. what is the average rate of change for the function $f(x)=2x^{2}+4$ on the interval $0leq xleq2$?\n10. a coffee shop sells two types of coffee: regular and decaf. each cup of regular coffee costs $2 and each cup of decaf coffee costs $3. the coffee shop sold a total of 100 cups of coffee on a particular day and made $250.\nthe augmented matrix representing the given situation is as shown.\n$\\begin{bmatrix}1&1&|&p\\2&3&|&q\\end{bmatrix}$\nwhat are the values of $p$ and $q$ in the given matrix?\na. $p = 100, q = 250$\nb. $p = 250, q = 100$\nc. $p = 200, q = 750$\nd. $p = 750, q = 200$\n11. which of these would best be studied using a survey?\nselect two correct answers.\na. a software developer wants user feedback on a newly developed mobile app.\nb. a dance teacher wants to analyze the confidence of students while dancing on stage.\nc. a researcher wants to determine if broccoli consumption affects ldl cholesterol level.\nd. a psychologist wants to know the impact of music on mood regulations of his patients.\ne. a physical education teacher of a school wants to determine the most popular sports among the students.

stanley semester 2 final exam\n8. newtons second law, $f = mcdot a$, describes the relationship between an objects mass, a force acting on it, and the resulting acceleration, where:\n$f$ is force, in newtons\n$m$ is mass, in kilograms\n$a$ is acceleration, in meters per second squared\na young boy and his tricycle have a combined mass of 30 kilograms. if the boys sister gives him a push with a force of 60 newtons, what is his acceleration?\na. $\frac{1}{2}$ meter per second squared\nb. 2 meters per second squared\nc. 30 meters per second squared\nd. 90 meters per second squared\n9. what is the average rate of change for the function $f(x)=2x^{2}+4$ on the interval $0leq xleq2$?\n10. a coffee shop sells two types of coffee: regular and decaf. each cup of regular coffee costs $2 and each cup of decaf coffee costs $3. the coffee shop sold a total of 100 cups of coffee on a particular day and made $250.\nthe augmented matrix representing the given situation is as shown.\n$\\begin{bmatrix}1&1&|&p\\2&3&|&q\\end{bmatrix}$\nwhat are the values of $p$ and $q$ in the given matrix?\na. $p = 100, q = 250$\nb. $p = 250, q = 100$\nc. $p = 200, q = 750$\nd. $p = 750, q = 200$\n11. which of these would best be studied using a survey?\nselect two correct answers.\na. a software developer wants user feedback on a newly developed mobile app.\nb. a dance teacher wants to analyze the confidence of students while dancing on stage.\nc. a researcher wants to determine if broccoli consumption affects ldl cholesterol level.\nd. a psychologist wants to know the impact of music on mood regulations of his patients.\ne. a physical education teacher of a school wants to determine the most popular sports among the students.

Answer

8.

Explanation:

Step1: Identify values in formula

Given $F = m\cdot a$, $F = 60$ N, $m=30$ kg.

Step2: Solve for $a$

$a=\frac{F}{m}=\frac{60}{30}=2$ m/s².

Answer:

B. 2 meters per second squared

9.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 0$, $b = 2$, and $f(x)=2x^{2}+4$.

Step2: Calculate $f(0)$ and $f(2)$

$f(0)=2(0)^{2}+4 = 4$, $f(2)=2(2)^{2}+4=2\times4 + 4=12$.

Step3: Calculate average rate of change

$\frac{f(2)-f(0)}{2 - 0}=\frac{12 - 4}{2}=\frac{8}{2}=4$.

Answer:

4

10.

Explanation:

Step1: Define variables

Let $x$ be the number of regular - coffee cups and $y$ be the number of decaf - coffee cups. We know that $x + y=100$ (total number of cups) and $2x + 3y=250$ (total money made).

Step2: Match with augmented matrix

The augmented matrix for the system $\left{\begin{array}{l}x + y=p\2x+3y = q\end{array}\right.$ has $p = 100$ (total number of cups) and $q = 250$ (total money made).

Answer:

A. $p = 100$, $q = 250$

11.

Brief Explanations:

A survey is useful for gathering opinions, preferences, and self - reported data. A software developer can use a survey to get user feedback on a mobile app. A physical education teacher can use a survey to find out the most popular sports among students. Analyzing confidence while dancing on stage may require direct observation, determining the impact of broccoli on cholesterol may need a controlled experiment, and studying the impact of music on mood may involve a combination of experiments and self - reporting but not just a simple survey.

Answer:

A. A software developer wants user feedback on a newly developed mobile app. E. A physical education teacher of a school wants to determine the most popular sports among the students.