True or False. A special case of the Law of Cosines is the Pythagorean Theorem.

Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is $30^{\circ},$ and from a second position 40 feet farther along this path it is $20^{\circ}.$ What is the height of the tree?

Solve equation $32 = 5 - 3t$

Find the function $y=a x^{2}+b x+c$ whose graph contains the points (1,-1), (3,-1), and (-2,14).

Find the inverse function $f^{-1}$ of each function f Find the range of and the domain and range of $f^{-1}.$ $f(x)=2 \cos (3 x+2) ;-\frac{2}{3} \leq x \leq-\frac{2}{3}+\frac{\pi}{3}$

Let p and q represent the following simple statements: p: The heater is working. q: The house is cold. Write each symbolic statement in words. $p \vee \sim q$

Show that the equation of the tangent to $y=2 x^{2}-1$ at the point where x = a, is $4 a x-y=2 a^{2}+1$.

Determine the unknown coefficient, $a$, in each function. a. $f(x) = 2x^{4} + x^{3}-14x^{2} -ax -6 \ \text{if} (x-3)$ is a linear factor. b. $f(x) = ax^{4} + 25x^{3} +21x^{2} -x -3 \ \text{if} (x+ 1)$ is a linear factor.

Give $L$-fucose (“Chemical Connections: A, B, AB, and O Blood Group Substances”) a name incorporating the prefix $deoxy$- that shows its relationship to galactose.

Mr. Whittaker earns b dollars biweekly. His employer is changing the pay procedure to monthly, but no annual salaries are changing. Express his monthly salary algebraically.

Use your calculator to write the following in the form $e^{k}$ where k is correct to 4 decimal places: 0.006

For each of the following data sets, make sure the data is ordered and then find: (i) the median (ii) the upper and lower quartiles (iii) the range (iv) the interquartile range. 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9

Sequence the steps in how a nerve impulse moves from one neuron to another neuron, by writing the numbers 1 to 5 in the squares to the left of the steps. ___ The neurotransmitter moves across the synapse and binds to receptors on the dendrite of a neighboring neuron. ___ An electrical impulse is sent along an axon, jumping from node to node in axons covered with myelin. ___ The neuron is at rest, with more sodium ions outside the cell and more potassium ions inside the cell. ___ The impulse reaches the synapse, where channels again open. Vesicles fuse with the plasma membrane and release a neurotransmitter by exocytosis. ___ The threshold for an action potential is reached at a dendrite, opening channels in the plasma membrane and causing a reversal in electrical charge.

The 2000 census reported that 66.4% of the households in Alaska were homeowners, and the remainder were renters. During the next decade, 37.2% of the homeowners became renters, and the rest continued to be homeowners. Similarly, 71.5% of the renters became homeowners, and the rest continued to rent. (A) Write the appropriate transition matrix. (B) According to this transition matrix, what percentage of households were homeowners in 2010? (C) If the transition matrix remains the same, what percentage of households will be homeowners in 2030?