Question

4,10,18,4,4,5,6,5
what is the median of the data set shown?
a) 4
b) 5
c) 7
d) 14

a right circular cylinder has a volume of 432 cubic centimeters. the area of the base of the cylinder is 24 square centimeters. what is the height, in centimeters, of the cylinder?
a) 18
b) 24
c) 216
d) 10,368

$x^{2}=-841$
how many distinct real solutions does the given equation have?
a) exactly one
b) exactly two
c) infinitely many
d) zero

line $k$ is defined by $y = 2x+\frac{1}{8}$. line $j$ is perpendicular to line $k$ in the $xy$-plane. what is the slope of line $j$?
a) -8
b) $-\frac{1}{7}$
c) $\frac{1}{8}$
d) 7

Explanation:

First problem (median of data set \(4,10,18,4,4,5,6,5\))

Step1: Sort the data set

Sort the data set \(4,10,18,4,4,5,6,5\) in ascending order: \(4,4,4,5,5,6,10,18\)

Step2: Find the median

Since there are \(n = 8\) (even number of data points), the median is the average of the \(\frac{n}{2}\) - th and \((\frac{n}{2}+1)\) - th values. \(\frac{n}{2}=4\) and \(\frac{n}{2}+1 = 5\). The \(4\) - th value is \(5\) and the \(5\) - th value is \(5\). The median is \(\frac{5 + 5}{2}=5\)

For any real number \(x\), \(x^{2}\geq0\). The equation \(x^{2}=- 841\) implies that we are looking for a real number \(x\) such that its square is negative. But since the square of a real number is non - negative, there are no real solutions.

Step1: Use the formula for the volume of a cylinder

The formula for the volume of a cylinder is \(V=Ah\), where \(V\) is the volume, \(A\) is the base area, and \(h\) is the height.

Step2: Solve for \(h\)

We know \(V = 432\) and \(A = 24\). Substitute into the formula \(h=\frac{V}{A}\). So \(h=\frac{432}{24}=18\)

Answer:

B. \(5\)

Second problem (\(x^{2}=-841\))