2022 (Aug.): NY Regents - Algebra 2

The Hot and Tasty Coffee chain conducts a survey of its customers at its location at the Staten Island ferry terminal. After the survey is completed, the statistical consultant states that 70% of customers who took the survey said the most important factor in choosing where to get their coffee is how fast they are served. Based on this result, Hot and Tasty Coffee can infer that

Given that i is the imaginary unit, the expression (x-2i)^2 is equivalent to

The equation below can be used to model the height of a tide in feet, H(t), on a beach at t hours.

H(t)=4.8\mathrm{sin}\big(\frac{\pi}{6}(t+3)\big)+5.1

Using this function, the amplitude of the tide is

In watching auditions for lead singer in a band, Liem became curious as to whether there is an association between how animated the lead singer is and the amount of applause from the audience. He decided to watch each singer and rate the singer on a scale of 1 to 5, where 1 is the least animated and 5 is the most animated. He did this for all 5 nights of auditions and found that the more animated singers did receive louder applause.

The study Liem conducted would be best described as

In the diagram of a unit circle below, point A, \big(-\frac{\sqrt{3}}{2},\frac{1}{2}\big), represents the point where the terminal side of \theta intersects the unit circle.

What is \mathrm{m}\angle{\theta}?

Consider the function f(x)=2x^{3}+x^{2}-18x-9. Which statement is true?

Which sketch could represent the function m(x)=-\log_{100}(x-2)?

Which equation has roots of 3+i and 3-i?

A local university has a current enrollment of 12,000 students. The enrollment is increasing continuously at a rate of 2.5% each year. Which logarithm is equal to the number of years it will take for the population to increase to 15,000 students?

What is the total number of points of intersection of the graphs of the equations y=e^x and xy=20?

The amount of a substance, A(t), in grams, remaining after t days is modeled by A(t)=50(0.5)^\frac{t}{3}. Which statement is false?

A parabola that has a vertex at (2,1) and a focus of (2,-3) has an equation of

The expression \big(a\sqrt[3]{2b^{2}}\big)\big(\sqrt[3]{4a^{2}b}\big) is equivalent to

Given f(x)=3^{x-1}+2, as x \rightarrow -\infin

For all values of x for which the expression is defined, \frac{x^{2}+3x}{x^{2}+5x+6} is equivalent to

A recursive formula for the sequence 64, 48, 36, ... is

Which expression is equivalent to \frac{x^{3}-2}{x-2}?

What is the solution set of the equation \frac{4}{k^{2}-8k+12}=\frac{k}{k-2}+\frac{1}{k-6}?

Given the polynomial identity x^{6}+y^{6}=(x^{2}+y^{2})(x^{4}-x^{2}y^{2}+y^{4}), which equation must also be true for all values of x and y?

Given p(\theta)=3\mathrm{sin}(\frac{1}{2}\theta) on the interval -\pi<\theta<\pi, the function p

A company fired several employees in order to save money. The amount of money the company saved per year over five years following the loss of employees is shown in the table below.

Which expression determines the total amount of money saved by the company over 5 years?

A rush-hour commuter train has arrived on time 64 of its first 80 days. As arrivals continue, which equation can be used to find x, the number of consecutive days that the train must arrive on schedule to raise its on-time performance rate to 90%?

Given f(x)=-\frac{2}{5}x+4, which statement is true of the inverse function f^{-1}(x)?

The amount of a substance, A(t), that remains after t days can be given by the equation A(t)=A_{0}(0.5)^\frac{t}{0.0803}, where A_0 represents the initial amount of the substance. An equivalent form of this equation is

Determine the average rate of change, in mph, from 2 to 4 hours on the graph shown below.

Factor the expression x^{3}-2x^{2}-9x+18 completely.

Solve algebraically for all values of x:

\sqrt{4x+1}=11-x

Given that \Bigg(\frac{y^{\frac{17}{8}}}{y^{\frac{5}{4}}}\Bigg)^{-4}=y^{n}, where y>0, determine the value of n.

Given \mathrm{cos} A=\frac{3}{\sqrt{10}} and \mathrm{cot} A=-3, determine the value of \mathrm{sin} A in radical form.

According to a study done at a hospital, the average weight of a newborn baby is 3.39 kg, with a standard deviation of 0.55 kg. The weights of all the newborns in this hospital closely follow a normal distribution. Last year, 9256 babies were born at this hospital. Determine to the nearest integer, approximately how many babies weighed more than 4 kg.

The table below shows the results of gender and music preference.

Based on these data, determine if the events “the person is female” and “the person prefers classic rock” are independent of each other.

Justify your answer.

Algebraically determine the solution set for the system of equations below.

y=2x^{2}-7x+4

y=11-2x