22. Write the equation $y + 2 = \frac { 1 } { 4 } ( x + 3 )$ in the following forms: a. Slope-intercept form b. Standard form c. Standard form with a positive x-term d. Standard form with no fractions or decimals

Underline the pronoun in parentheses that correctly completes each sentence. The tomato, because of (its, their) versatility, is found in cuisines from many different parts of the world.

A spur gearset has 17 teeth on the pinion and 51 teeth on the gear. The pressure angle is $20^{\circ}$ and the overload factor $K_{o}=1$. The diametral pitch is 6 teeth/in and the face width is 2 in. The pinion speed is 1120 rev/min and its cycle life is to be $10^{8}$ revolutions at a reliability R = 0.99. The quality number is 5. The material is a through-hardened steel, grade 1, with Brinell hardnesses of 232 core and case of both gears. For a design factor of 2, rate the gearset for these conditions using the AGMA method.

A pressure-fed bearing has a journal diameter of 50.00 mm with a unilateral tolerance of -0.05 mm. The bushing bore diameter is 50.084 mm with a unilateral tolerance of 0.10 mm. The length of the bushing is 55 mm. Its central annular groove is 5 mm wide and is fed by SAE 30 oil is $55^{\circ} \mathrm{C}$ at 200 kPa supply gauge pressure. The journal speed is 2880 rev/min carrying a load of 10 kN. The sump can dissipate 300 watts per bearing if necessary. For minimum radial clearances, perform a design assessment using Trumpler's criteria.

The vertices of a triangle are P(-1, 2), Q(-1, 0), and R(2, 0). Rotate the triangle $180^{\circ}$ about the origin, and then reflect it in the x-axis. What are the coordinates of the image?

Solve an equation to answer the question. 19 is 95% of what?

Find $\lim _{x \rightarrow \infty} x \sin \frac{1}{x}$.

13 is what percent of 16?

Prove the reduction formulas in the text. For the third one write $\int \frac{d x}{\left(x^{2}+1\right)^{n}}=\int \frac{d x}{\left(x^{2}+1\right)^{n-1}}-\int \frac{x^{2} d x}{\left(x^{2}+1\right)^{n}}$ and work on the last integral. (Another possibility is to use the substitution x= tan u.)

Prove that if p and q are polynomials in x - a and $\lim _{x \rightarrow 0} R(x) /(x-a)^{n}=0$, then $p(q(x)+R(x))=p(q(x))+\bar{R}(x)$ where $\lim _{x \rightarrow 0} \bar{R}(x) /(x-a)^{n}=0$. Also note that if p is a polynomial in x - a having only terms of degree > n, and q is a polynomial in x - a whose constant term is 0, then all terms of p(q(x - a)) are of degree > n.

Show that if n is a positive integer, then $p(n) \leq(p(n-1)+p(n+1)) / 2.$

Decrypt the following message, which was enciphered using the Vigenere cipher with encrypting key TWAIN.

$$\begin{matrix} \text{PACWH} & \text{EZUAR} & \text{NLTEB} & \text{XPEZA}\\ \text{BJLMN} & \text{KJIVT} & \text{THLBU} & \text{TPIAG}\\ \text{TNNMQ} & \text{TXOCG} & \text{HQRWJ} & \text{GSOZY}\\ \text{AATPB} & \text{NOAVQ} & \text{LKFVN} & \text{MEOVF}\\ \text{TREIE} & \text{BOEVN} & \text{GZFTB} & \text{NNIAU}\\ \text{OWNQF} & \text{AADNE} & \text{HIIBZ} & \text{TPHMZ}\\ \text{THOVR} & \text{PKUTQ} & \text{HYCCC} & \text{RIEMV}\\ \text{EHIWA} & \text{RAAZF}\\ \end{matrix}$$

A family buys 4 airline tickets online. The family buys travel insurance that costs $19 per ticket. The total cost is$752. Let x represent the price of one ticket. a. Write an equation to represent this situation. b. What is the price of one ticket?

Let p and q be odd primes. Show that 2 is a primitive root of q, if q = 4 p + 1.