The vectors {u, v, w} are linearly independent.

Find the derivatives.
${\displaystyle y=(x^2+6x+2)(\frac{2}{x^4}+\sqrt[3]{x^5}+3)}$

MODELING REAL LIFE. You mix 0.25 cup of juice concentrate for every 2 cus of water to make 18 cups of juice. How much juice concentrate do you use? How much water do you use? You use ___ cups of juice concentrate and ___ cups of water.

Refer to the Journal of Experimental Social Psychology (Vol. 45, 2009) study of whether buying gifts truly buys love. Recall that study participants were randomly assigned to play the role of gift giver or gift receiver. Gift receivers were asked to provide the level of appreciation (measured on a 7-point scale where 1 = "not at all" and 7 = "to a great extent") they had for the last birthday gift they received from a loved one. Gift givers were asked to recall the last birthday gift they gave to a loved one and to provide the level of appreciation the loved one had for the gift. The researchers wanted to know if the average level of appreciation is higher for birthday gift givers than for birthday gift receivers. a. Why is this study designed? b. Specify the key elements of the study: experimental unit, response variable, factor, and treatments.

In a statistics class of 100 students, the mean score on the midterm was 98. In another class of 23 students, the mean score was 8. What was the mean score of the two classes combined?

Graph the sets of points whose polar coordinates satisfy the equations and inequalities ${\displaystyle 1\le r\le 2}$