Using a separate sheet of graph paper, plot the solution sets to the following equations and inequalities: a. $x-y=10$ b. $x-y<10$ c. $y>x-10$ d. $y \geq x$ e. $x \geq y$ f. y = 5 g. y < 5 h. $x \geq 5$ i. $y \neq 1$ j. x = 0 k. x > 0 l. y < 0 m. $x^{2}-y=0$ n. $x^{2}+y^{2}>0$ o. $x y \leq 0$ Which ofthe inequalities in this exercise are linear inequalities?

What two enols are formed when 2-pentyne is treated with

$$\mathrm { H } _ { 2 } \mathrm { O } , \mathrm { H } _ { 2 } \mathrm { SO } _ { 4 } , \text { and } \mathrm { Hg } \mathrm { SO } _ { 4 } ?$$

Draw the ketones formed from these enols after tautomerization.

Simplify by combining similar terms. 6m-4n+(-7)m-(-5)n

Find dw/dt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before differentiating. w = cos(x - y), x = t², y = 1

Verify the identity algebraically. Use a graphing utility to check your result graphically. $\cos 3 \beta=\cos ^{3} \beta-3 \sin ^{2} \beta \cos \beta$

Let

$$S_n = x - x²/2 + x³/3 - x^4/4 + ... ±x^n/n$$

. Use a graphing utility to confirm the inequality graphically. Then complete the following x: 0.0, 0.2, 0.4, 0.6, 0.8, 1.0

$$S_n: (?)$$

, ln(x+1): (?),

$$S_{n+1}: (?)$$

to confirm the inequality numerically.

$$S_2 ≤ ln(x+1) ≤ S_3$$

A square garden has sides 50 ft long. You stretch a hose from one corner of the garden to another corner along the garden's diagonal. To the nearest tenth, how long is the hose?

(a) Calculate the critical angle for a diamond surrounded by air. (b) Calculate the critical angle for a diamond under water. (c) Explain why a diamond sparkles less under water then in air.

For a gas obeying the equation of state $p(v-b)=R T,$ where b is a positive constant, can the temperature be reduced in a Joule-Thomson expansion? Explain.

While waiting for a bus after school, Renae programmed her MP3 player to randomly play two songs from her play list, at right. Assume that the MP3 player will not play the same song twice. a. A sample space is a list of all possible outcomes for a probabilistic situation. List the sample space for all the combinations of two songs that Renae could select. The not matter for your list. How can you be sure that you listed all of the song combinations? b. Are each of the combinations of two songs equally likely? Why is that important? c. Find the probability that Renae will listen to two songs with the name "Mama" in the title. d. What is the probability that at least one of the songs will have the name "Mama" in the title? e. Why does it make sense that the probability in part (c) is higher than the probability in part (b)? $$ \begin{matrix} \text{PLAYLIST}\\ \text{I Love My Mama (country)}\\ \text{by the Strings of Heaven}\\ \text{}\\ \text{Don't Call Me Mama (country)}\\ \text{Duet by Sapphire and Hank Tumbleweed}\\ \text{}\\ \text{Carefree and Blue (R & B)}\\ \text{by Sapphire and Prism Escape}\\ \text{}\\ \text{Go Back To Mama (Rock)}\\ \text{Duet by Bjorn Free and Sapphire}\\ \text{}\\ \text{Smashing Lollipops (Rock)}\\ \text{by Sapphire}\\ \end{matrix} $$

Mrs. Morales wrote a test with 15 questions covering spelling and vocabulary. Spelling questions (x) are worth 5 points and vocabulary questions (y) are worth 10 points. The maximum number of points possible on the test is 100. a. Write an equation in slope -intercept form to represent the number of questions on the test. _ b. Write an equation in slope-intercept form to represent the total number of points on the test. _. c. Graph the solutions of both equations . d. Use your graph to te ll how many of each question type are on the test.

Use a graphing calculator to graph the funciton. Then determine whether the funciton is even, odd, or neither.

$$y = \frac { x ^ { 3 } } { 3 x ^ { 2 } + x ^ { 4 } }$$

A piece of copper wire is formed into a single circular loop of radius 12 cm. A magnetic field is oriented parallel to the normal to the loop, and it increases from 0 to 0.60 T in a time of 0.45 s. The wire has a resistance per unit length of

$$3.3 \times 10 ^ { - 2 } \Omega / m$$

What is the average electrical energy dissipated in the resistance of the wire?

Find the expected payoff of the game matrix

$$\left[\begin{array}{ll} 4 & 0\\ 2 & 3 \end{array}\right]$$

for the given strategies:

$$P=[0 \ \ 1]\quad Q=\left[\begin{array}{l} 0\\ 1 \end{array}\right]$$