In three dimensions, the location of a point can be represented by the ordered triple (x, y, z). a) Find the coordinates of the midpoint of the line segment with endpoints A(2, 3, 1) and B(6, 7, 5). b) Write an expression for the coordinates of the midpoint of the line segment with endpoints $\left( x _ { 1 } , y _ { 1 } , z _ { 1 } \right)$ and $\left( x _ { 2 } , y _ { 2 } , z _ { 2 } \right)$

Find the effective rate corresponding to the given nominal rate. a.$8\%/\text{year}$ compounded monthly b.$8\%/\text{year}$ compounded daily

The following table gives the number of families under the poverty level in the U.S. in recent years. Source: U.S. Census Bureau. $$ \begin{array}{|c|c|}\hline \text {Year} & \begin{array}\text {Families Below Poverty}\\ \text {Level (in thousands)} \end{array} \\\hline {2000} & \qquad{6400} \\ \hline {2001} & \qquad{6813} \\ \hline {2002} & \qquad{7229} \\ \hline {2003} & \qquad{7607} \\ \hline {2004} & \qquad{7623} \\ \hline {2005} & \qquad{7657} \\ \hline {2007} & \qquad{7668} \\ \hline {2007} & \qquad{7835} \\\hline {2008} & \qquad{8147} \\ \hline\end{array} $$ $a.$ Find a linear equation for the number of families below poverty level (in thousands) in terms of , the number of years since $2000$, using the data for $2000$ and $2008$. an almanac or other reference. Is the result in general agreement with the previous results? $b.$ Repeat part a, using the data for 2004 and 2008. $c.$ Find the equation of the least squares line using all the data. Then plot the data and the three lines from parts a–c on a graphing calculator. $d.$ Discuss which of the three lines found in parts a–c best describes the data, as well as to what extent a linear model accurately describes the data

Write an equation perpendicular to the given line through the given point. perpendicular to y = 5x + 14 through (5, -3)

Work uniforms include pants or a skirt, a shirt, and a tie or a vest. There are 3 pairs of pants, 5 skirts, 10 shirts, 2 ties, and 1 vest in a wardrobe. a. What is the probability of choosing a pair of pants, a shirt, and a tie? b. The pants and shirt from the previous day must be washed, but the tie returns to the wardrobe. What is the probability of choosing pants, a shirt, and a tie next day?

Determine which matrices are in reduced echelon form and which others are only in echelon form.

$$\left[ \begin{array}{ccccc}{0} & {1} & {1} & {1} & {1} \\ {0} & {0} & {2} & {2} & {2} \\ {0} & {0} & {0} & {0} & {3} \\ {0} & {0} & {0} & {0} & {0}\end{array}\right]$$

Under what conditions might a financial adviser advise investing in bonds even in the situation described in the article? What would be the reasons for the advice?

Choose the blank that marks the most reasonable place to insert ellipsis points. The speaker remembers _____ seeing them "alone, at work, and _____ at home."

The number of arrangements of five letters from the word magnetic that contain the word net is A. 60 B. 100 C. 360 D. 630 E. 720

a) Draw the triangle with vertices Q(-2, 0), R(2, 8), and S(7, 3). Then, construct the right bisector of each side. b) Verify algebraically that the three right bisectors intersect at a single point, the circumcentre of $\triangle \mathrm { QRS }$ c) Find the distance from each vertex of $\triangle \mathrm { QRS }$ o the circumcentre. d) Describe the circle that passes through the vertices of $\triangle \mathrm { QRS }$ e) Describe how you would use geometry software to answer parts a) to d).

Dylan and Indira are hiking on the Caledon Hills section of the Bruce Trail. They have reached the point that has coordinates (6, 8) on their map of the trail. They want to hike out to the straight section of Hockley Road that joins points (4, 7) and (6, 5). a) At what point will they reach Hockley Road if they take the shortest possible route? b) Explain why the shortest route might not be the best route.

In $\triangle \mathrm { ABC }$ P(0, 2) is the midpoint of side AB, Q(2, 4) is the midpoint of BC, and R(1, 0) is the midpoint of AC. a) Find the coordinates of A, B, and C. b) Use the midpoint formula to check the coordinates you calculated in part a).

Use a counterexample to show that this statement is false: “Every circle with a radius greater than 1 has at least one point with integer coordinates.”

Sally has hidden her brother’s birthday present somewhere in the backyard. When writing instructions for finding the present, she used a coordinate system with each unit on the grid representing 1 m. The positive y-axis of this grid points north. The instructions read “Start at the origin, walk halfway to (8, 6), turn $90 ^ { \circ }$ left, and then walk twice as far.” Where is the present? How far is it from the origin?