Solve each equation. Check your solution.

$$4w + 10 = 6 w - 13$$

Determine whether or not the given vectors are perpendicular. (4, -2, -4), (1, -2, 2)

Asample of 20 engineers employed with a company for three years has been rank ordered with respect to managerial potential. Some of the engineers attended the company’s management-development course, others attended an off-site management-development program at a local university, and the remainder did not attend any program. Use the following rankings and $\alpha =$ .025 to test for a significant difference in the managerial potential of the three groups.

$$\begin{matrix} \text{No Program} & \text{Company Program} & \text{Off-Site Program}\\ \text{16} & \text{12} & \text{7}\\ \text{9} & \text{20} & \text{1}\\ \text{10} & \text{17} & \text{4}\\ \text{15} & \text{19} & \text{2}\\ \text{11} & \text{6} & \text{3}\\ \text{13} & \text{18} & \text{8}\\ \text{ } & \text{14} & \text{5}\\ \end{matrix}$$

What genre is "Of Mice and Men" book?

As an avid biker, you’ve come to realize that your top speed is really an air speed, not a ground speed, because air resistance is very noticeable when you ride fast. You like to ride at top speed for exactly an hour every day, and you know that on a calm day, you can ride 20 km before having to turn around and come back the same way. Today, though, you have a 20-km/h head wind for the first leg of the trip (which of course is a tailwind on the way back). You must be back home in an hour, so you look at your map.

Summarize the events at the end of the story. Do you think it is an effective ending? Explain.

Describe a dilation with center (0, 0) that would produce an image such that every image point is closer to (0, 0) than its corresponding preimage point.

A coin is tossed and a number cube is rolled. What is the probability of heads and a number greater than three?

All members of the junior class at a local high school took the PSAT exam. The distribution of the results of the mathematics section was found to be approximately normal, with a mean score of 52 and a standard deviation of 6.8. Stephan claimed that he scored better than 90% of the students in the junior class. Use z-sore and your z-table to determine what score Stephan must have earned to be correct.

A historian discovers a nineteenth-century notebook in which some observations, dated 1822, were recorded on a substance thought to be a new element. Here are some of the data recorded in the notebook: "Ductile, silver-white, metallic looking. Softer than lead. Unaffected by water. Stable in air. Melting point:

$$153 ^ { \circ } \mathrm { C }$$

Den sity:

$$7.3 \ g/cm^3$$

Electrical conductivity: 20% that of copper. Hardness: About 1 % as hard as iron. When 4.20 g of the unknown is h eated in an excess of oxygen, 5.08 g of a white solid is formed. The solid could be sublimed by heating to over

$$800 ^ { \circ } \mathrm { C }$$

" Using information in the text and the CRC Handbook of Chemistry and Physics, and making allowances for possible variations in numbers from current values, identify the element reported.

Find the limit by interpreting the expression as an appropriate derivative. (a)

$$\lim _ { x \rightarrow 0 } \frac { \ln ( 1 + 3 x ) } { x }$$

, (b)

$$\lim _ { x \rightarrow 0 } \frac { \ln ( 1 - 5 x ) } { x }$$

Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. $\int \frac { d x } { \sqrt { 4 - x ^ { 2 } } }$

Show that the inverse of

$$A=\left[\begin{array}{rr} a&b \\ c&d \end{array}\right]$$

is given by the formula

$$A^{-1}=\left[\begin{array}{rr} \dfrac d{\Delta}& \dfrac {-b}{\Delta} \\\\ \dfrac {-c}{\Delta}&\dfrac {a}{\Delta} \end{array}\right]$$

where $\Delta =ad-bc \neq 0$. The number $\Delta$ is called the determinant of A.

Independence of events is not always obvious. Toss two balanced coins independently. The four possible combinations of heads and tails in order each have probability 0.25. The events A = head on the first toss B = both tosses have the same outcome may seem intuitively related. Show that P(B|A) = P(B), so that A and B are in fact independent.