Use a calculator to evaluate each expression to the nearest ten-thousandth.

$$log21$$

Simplify each expression. Justify each step with an operation or property. 4(y+6)+9

The joint probability mass function of the random variables X, Y, Z is

$$p ( 1,2,3 ) = p ( 2,1,1 ) = p ( 2,2,1 ) = p ( 2,3,2 ) = \frac { 1 } { 4 }$$

Find (a) E[XYZ], and (b) E[XY+XZ+YZ].

Assume a curve is given by the parametric equations x=f(t) and y=g(t), where f and g are twice differentiable. Use the Chain Rule to show that $y ^ { \prime \prime } ( x ) = \frac { f ^ { \prime } ( t ) g ^ { \prime \prime } ( t ) - g ^ { \prime } ( t ) f ^ { \prime \prime } ( t ) } { \left( f ^ { \prime } ( t ) \right) ^ { 3 } }$.

Four equal charges of

$$5.0 \mu \mathrm { C }$$

are placed at the vertices of a square of side 10 cm. a. Calculate the value of the electric potential at the centre of the square. b. Determine the electric field at the centre of the square. c. How do you reconcile your answers to a and b with the fact that the electric field is the derivative of the potential?

Without looking at the electron affinity table, arrange the following elements in order of decreasing electron affinities: C, O, Li, Na, Rb, and F.

Write and solve a proportion for each situation. A daffodil that is 1.2 feet tall casts a shadow that is 1.5 feet long. At the same time, a nearby lamppost casts a shadow that is 20 feet long. What is the height of the the lamppost?

Lane 1 at your local track is 0.25 mi long. You live 0.5 mi away from the track. Which of the following results in the shortest jog? F. jogging 6 times around the track in Lane 1 G. jogging to the track and then 5 times around the tracking Lane 1 H. jogging to the track, 3 times around the track in Lane 1, and then home I. jogging 8 times around the track in Lane 1

Find each limit algebraically. $\lim _{x \rightarrow-1}\left(8 x^{5}-7 x^{3}+8 x^{2}+x-4\right)$

Say whether l’Hospital’s rule applies. If is does, use it to evaluate the given limit. If not, use some other method. $\lim _{x \rightarrow-\infty} \frac{x^{2}+30 x}{2 x^{6}+10 x}$

Suppose

$$\Delta A B C \sim \Delta T U V.$$

Determine whether each pair of measures is equal. the ratios of the sides

$$\frac { B C } { U V } \text { and } \frac { A C } { T V }$$

Factor the polynomial by grouping.

$$2 s ^ { 3 } - 27 - 18 s + 3 s ^ { 2 }$$

Write the equation of a quadratic function in standard form for the parabola that passes through the given points (-1, 5), (4, 0), (5, -7)

Evaluate the given iterated integral. $\int_{0}^{4} \int_{0}^{1 / 2} \int_{0}^{x^{2}} \frac{1}{\sqrt{x^{2}-y^{2}}} d y d x d z$