Mastery Path

For a baobab tree habitat in South Africa, a scientist randomly selected $60$ baobab trees that were $18$ years old and randomly assigned them to two groups. Each group was subjected to a different watering pattern for $2$ consecutive years to observe whether the watering pattern affects the trees' growth rate. Based on the design of the study, what is the largest group to which these results can be applied?

Which expressions are factors of $3x^{2}+23x-70$? I. $x-10$ II. $3x-7$

A line segment that has a length of 123 centimeters (cm) is divided into three parts. One part is 49 cm long. The other two parts have lengths that are equal to each other. What is the length, in cm, of one of the other two parts of equal length?

A right circular cylinder has a height of 18 inches and a volume of 4,050Δ cubic inches. What is the radius, in inches, of this cylinder?

If $\frac{2a}{b} = 4.25$ and $\frac{a}{bn} = 8.5$, what is the value of $n$?

$$f(x) = (2.07)^{\frac{x}{4}}$$ The function $f$ is defined by the given equation. The equation can be rewritten as $f(x) = (1 + \frac{p}{100})^{x}$, where $p$ is a constant. Which of the following is closest to the value of $p$?

Data set A consists of the heights of 80 objects and has a mean of 30 meters. Data set B consists of the heights of 40 objects and has a mean of 60 meters. Data set C consists of the heights of the 120 objects from data sets A and B. What is the mean, in meters, of data set C?

Square A has side lengths that are 144 times the side lengths of square B. The area of square A is k times the area of square B. What is the value of k?

In the equation $T = 1200 + 20h$, $T$ represents Brittany’s total take-home pay, in dollars, for her first week of work, where $h$ represents the number of hours she worked that week and $1200$ represents a sign-on bonus. If Brittany’s total take-home pay was \1,880$, for how many hours was Brittany paid for her first week of work?

$684$ is $p\%$ greater than $9$. What is the value of $p$?

In triangle XYZ, angle Y is a right angle, point P lies on XZ, and point Q lies on YZ such that PQ is parallel to XY. If the measure of angle XZY is 57 degrees, what is the measure, in degrees, of angle XPQ?

$$f(x) = (x - 12)(x + 17)$$ The function $f$ is defined by the given equation. For what value of $x$ does $f(x)$ reach its minimum?

To study fluctuations in composition, samples of pumice were taken from 31 locations and cut in the shape of a cube. The length of the edge of one of these cubes is 4.000 centimeters. This cube has a density of 0.250 grams per cubic centimeter. What is the mass of this cube, in grams?

For the given system of equations, what is the value of $7(j - k)$? $$(j - k) - 16(m + l) = 689$$ and $$(j - k) + 12(m + l) = 1235$$

In triangle $ABC$, $AB = 4,920\text{ mm}$ and $BC = 4,920\text{ mm}$. Which statement is sufficient to prove that triangle $ABC$ is equilateral?

For the exponential function $f(x)=-2(3)^{x}-5$, how many real values of $x$ satisfy $f(x)=0$?

A line of best fit for data set $E$ is approximately $y=12+1.5x$. Data set $F$ multiplies each $y$-coordinate by $3.5$. Which equation could be a line of best fit for $F$?

$7kx + 13my = 20.4$ and $6kx + 5my = -48$. In the given system of equations, $k$ and $m$ are constants. The system has a solution of $(\frac{66}{43}, y)$. What is the value of $k$?

Segments $WZ$ and $XY$ intersect at $Q$, and $\angle QWX=\angle QYZ$. If $YQ=28$, $WQ=70$, $WX=60$, and $XQ=120$, what is the length of $YZ$?

The function f is defined by f(x) = |x - 4x|. What value of a satisfies f(6) - f(a) = -18?