ACT Math Hard practice

A farmer wants to fence a rectangular area along a river. He has 120 meters of fence and does not need to fence the side along the river. What is the maximum area he can enclose?

A store increases a price by 30%, then later decreases that new price by 30%. Compared to the original price, the final price is:

For what values of $x$ is the quadratic $x^2-5x+6<0$?

Solve for $x$: ${\log }_3(x)=4$

A store sells two products. Product X has a profit of \5$perunitandProductYhasaprofitof$$8$ per unit. The store can produce at most 200 units total, and must produce at least 60 units of Product X. If the store produces $x$ units of X and $y$ units of Y, which constraint set correctly models the situation?

A car's value depreciates by 15% each year. The car was purchased for \24{,}000$.Whichexpressiongivestheca{r}^{\prime }svalue$V$after$t$ years?

A recipe requires $\frac{3}{4}$ cup of sugar to make 24 cookies. A baker wants to make 60 cookies. How many cups of sugar are needed?

Two pipes fill a pool. Pipe A can fill the pool alone in 6 hours; Pipe B alone in 4 hours. Working together, how many hours does it take to fill the pool?

A sphere has volume $\frac{4}{3}\pi r^3$. If the radius is doubled, by what factor does the volume increase?

A 10-foot ladder leans against a wall. The base of the ladder is 6 feet from the wall. How high up the wall does the ladder reach?

The function $f(x)=2^x$ is transformed to $g(x)=2^{x-3}+5$. Compared to $f$, the graph of $g$ is:

A researcher models the spread of a rumor in a school of 800 students with the equation $N(t)=\frac{800}{1+799e^{-0.5t}}$, where $t$ is hours. Approximately how many students know the rumor after 10 hours?

(Use $e^{-5}\approx 0.0067$)

The height $h$ (in feet) of a projectile launched upward is given by $h(t)=-16t^2+80t+6$, where $t$ is time in seconds. At what time does the projectile hit the ground?