Question 1

Relative to the graph of $y=\ 3\sin x$ , what is the shift of the graph of $y=3\sin\left(x+\frac{\pi}{3}\right)$ ?

Accepted Answer

$\frac{\pi}{3}$ left

Answer

$\frac{\pi}{3}$ down

Answer

$\frac{\pi}{3}$ right

Answer

$\frac{\pi}{3}$ up

Question 2

A rabbit population doubles every $y=\ 3\sin x$ weeks. There are currently five rabbits in a restricted area. If $y=3\sin\left(x+\frac{\pi}{3}\right)$ represents the time, in weeks, and $P\left(t\right)$ is the population of rabbits with respect to time, about how many rabbits will there be in $98$ days?

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 3

When factored completely, $y=\ 3\sin x$ is equivalent to

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 4

If $y=\ 3\sin x$ , then $y=3\sin\left(x+\frac{\pi}{3}\right)$ equals

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 5

What is the solution to the system of equations $y=\ 3\sin x$ and $y=3\sin\left(x+\frac{\pi}{3}\right)$ where $P\left(t\right)$ is defined by the function below?

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 6

Which statement about statistical analysis is false?

Accepted Answer

Observational studies can determine cause and effect relationships.

Answer

Observational studies can suggest patterns and relationships in data.

Answer

Experiments can suggest patterns and relationships in data.

Answer

Experiments can determine cause and effect relationships.

Question 7

The expression $y=\ 3\sin x$ is equivalent to

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 8

What is the inverse of the function $y=\ 3\sin x$ ?

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 9

Gabriel performed an experiment to see if planting $y=\ 3\sin x$ tomato plants in black plastic mulch leads to larger tomatoes than if $y=3\sin\left(x+\frac{\pi}{3}\right)$ plants are planted without mulch. He observed that the average weight of the tomatoes from tomato plants grown in black plastic mulch was $P\left(t\right)$ ounces greater than those from the plants planted without mulch. To determine if the observed difference is statistically significant, he rerandomized the tomato groups $98$ times to study these random differences in the mean weights.

The output of his simulation is summarized in the dotplot below.

Given these results, what is an appropriate inference that can be drawn?

Accepted Answer

There was an effect observed that could be due to the random assignment of plants to the groups.

Answer

There is strong evidence to support the hypothesis that tomatoes from plants planted in black plastic mulch are larger than those planted without mulch.

Answer

There was no effect observed between the two groups.

Answer

There is strong evidence to support the hypothesis that tomatoes from plants planted without mulch are larger than those planted in black plastic mulch.

Question 10

If $y=\ 3\sin x$ and $y=3\sin\left(x+\frac{\pi}{3}\right)$ , then $P\left(t\right)$ equals

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 11

The solution to the equation $y=\ 3\sin x$ is

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 12

When $y=\ 3\sin x$ and $y=3\sin\left(x+\frac{\pi}{3}\right)$ are graphed on the same set of axes, which coordinates best approximate their point of intersection?

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 13

The price of a postage stamp in the years since the end of World War $y=\ 3\sin x$ is shown in the scatterplot below.

The equation that best models the price, in cents, of a postage stamp based on these data is

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 14

The eighth and tenth terms of a sequence are $y=\ 3\sin x$ and $y=3\sin\left(x+\frac{\pi}{3}\right)$ . If the sequence is either arithmetic or geometric, the ninth term can not be

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 15

The loudness of sound is measured in units called decibels $y=\ 3\sin x$ . These units are measured by first assigning an intensity $y=3\sin\left(x+\frac{\pi}{3}\right)$ to a very soft sound that is called the threshold sound. The sound to be measured is assigned an intensity, $P\left(t\right)$ , and the decibel rating, $98$ , of this sound is found using $d=10\log\frac{I}{I_0}$ . The threshold sound audible to the average person is $1.0 imes10^{-12}\$ $W/m^2$ (watts per square meter).

Consider the following sound level classifications:

How would a sound with intensity $6.3 imes10^{-3}$ $W/m^2$ be classified?

Accepted Answer

very loud

Answer

moderate

Answer

loud

Answer

deafening

Question 16

Pedro and Bobby each own an ant farm. Pedro starts with $y=\ 3\sin x$ ants and says his farm is growing exponentially at a rate of $y=3\sin\left(x+\frac{\pi}{3}\right)$ per month. Bobby starts with $P\left(t\right)$ ants and says his farm is steadily decreasing by $d=10\log\frac{I}{I_0}$ ants per month.

Assuming both boys are accurate in describing the population of their ant farms, after how many months will they both have approximately the same number of ants?

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 17

What is the solution, if any, of the equation $y=\ 3\sin x$ ?

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

all real numbers

Answer

no real solution

Question 18

In $y=\ 3\sin x$ , approximately $y=3\sin\left(x+\frac{\pi}{3}\right)$ million students took the Critical Reading portion of the SAT exam. The mean score, the modal score, and the standard deviation were calculated to be $P\left(t\right)$ , and $98$ , respectively.

Which interval reflects $95\%$ of the Critical Reading scores?

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 19

Which statement regarding the graphs of the functions below is untrue?

$f\left(x\right)=3\sin,$ from $-\pi h\left(x\right)=\log_2x$

$95\%$ $j\left(x\right)=-|4x-2|+3$

Accepted Answer

$\frac{\pi}{3}$ , and $j\left(x\right)$ have one $y$ -intercept.

Answer

$\frac{\pi}{3}$ and $j\left(x\right)$ have the same end behavior as $y$ .

Answer

$\frac{\pi}{3}$ and $j\left(x\right)$ have rational zeros.

Answer

$\frac{\pi}{3}$ and $j\left(x\right)$ have a maximum $y$ -value of $3$ .

Question 20

When $y=\ 3\sin x$ is divided by $y=3\sin\left(x+\frac{\pi}{3}\right)$ , the remainder is $P\left(t\right)$ . Given $98$ , which conclusion about $d=10\log\frac{I}{I_0}$ is true?

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

No conclusion can be made regarding $y=\ 3\sin x$ .

Answer

$\frac{\pi}{3}$ is a factor of $j\left(x\right)$ .

Question 21

Joelle has a credit card that has a $y=\ 3\sin x$ annual interest rate compounded monthly. She owes a total balance of $y=3\sin\left(x+\frac{\pi}{3}\right)$ dollars after $P\left(t\right)$ months. Assuming she makes no payments on her account, the table below illustrates the balance she owes after $98$ months.

Over which interval of time is her average rate of change for the balance on her credit card account the greatest?

Accepted Answer

month $y=\ 3\sin x$ to month $y=3\sin\left(x+\frac{\pi}{3}\right)$

Answer

month $y=\ 3\sin x$ to month $y=3\sin\left(x+\frac{\pi}{3}\right)$

Answer

month $y=\ 3\sin x$ to month $y=3\sin\left(x+\frac{\pi}{3}\right)$

Answer

month $y=\ 3\sin x$ to month $y=3\sin\left(x+\frac{\pi}{3}\right)$

Question 22

Which graph represents a cosine function with no horizontal shift, an amplitude of $y=\ 3\sin x$ , and a period of $y=3\sin\left(x+\frac{\pi}{3}\right)$ ?

Accepted Answer

https://uploads.quizalize.com/a8579f95-324b-44e7-9207-789e95af7b3b/question/28aa4b977fa0986910ad615a464f1bd2a7ba815e.png

Answer

https://uploads.quizalize.com/a8579f95-324b-44e7-9207-789e95af7b3b/question/d6451c281521fe67464b655022650e14c0e764fe.png

Answer

https://uploads.quizalize.com/a8579f95-324b-44e7-9207-789e95af7b3b/question/6e47e674b66e96324a60154c14990c283f447407.png

Answer

https://uploads.quizalize.com/a8579f95-324b-44e7-9207-789e95af7b3b/question/212b0a176f28d4fa995e6de7ccf115a39515c279.png

Question 23

According to a pricing website, Indroid phones lose $y=\ 3\sin x$ of their cash value over $y=3\sin\left(x+\frac{\pi}{3}\right)$ years. Which expression can be used to estimate the value of a $P\left(t\right)$ Indroid phone in $98$ years?

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Question 24

A cardboard box manufacturing company is building boxes with length represented by $y=\ 3\sin x$ , width by $y=3\sin\left(x+\frac{\pi}{3}\right)$ , and height by $P\left(t\right)$ . The volume of the box is modeled by the function below.

Over which interval is the volume of the box changing at the fastest average rate?

Accepted Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{3}$

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