Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The inequality

$$\frac { x - 2 } { x + 3 } < 2$$

can be solved by multiplying both sides by x + 3 resulting in the equivalent inequality

$$x - 2 < 2 ( x + 3 ).$$

Write <, =, or > to make a true sentence. -6 + 5 $\underline{?}$ -5 + 7

Use any analytical method to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. You do not need to use the definition of the Taylor series coefficients.

What is the purpose of the AC adapter on the end of the cord used for mobile phones?

Prove the validity of the second-derivative test in the case that $f^{\prime\prime}(c)<0$.

In aqueous solution , hydrogen sulfide reduces $\mathrm { Br } _ { 2 }$ to $\mathrm { Br } ^ { - }$ In all cases, under appropriate conditions, the product is elemental sulfur. Write a balanced net ionic equation for each reaction.

Let $X$ and $Y$ each have support $(0,1)$ marginally, and suppose that the joint PDF $f_{X,Y}$ of $X$ and $Y$ is positive for $0 < x < y$ and 0 otherwise. (a) What is the support of the conditional PDF of $Y$ given $X = x$? (b) Show that $X$ and $Y$ can’t be independent.

The wavelength of absorbed electromagnetic radiation for $\mathrm { CoBr } _ { 4 } ^ { 2 - }$ is $3.4 \times 10 ^ { - 6 }\ \mathrm { m } .$ Will the complex ion $\mathrm { CoBr } _ { 6 } ^ { 4 - }$ absorb electromagnetic radiation having a wavelength longer or shorter than $3.4 \times 10 ^ { - 6 }\ \mathrm { m } ?$ Explain.

Distinguish between living donor transplants and deceased donor transplants. Which type is more common?

Find the product or quotient.

$$\frac { 4 x ^ { 9 } y } { 3 x ^ { 3 } } \cdot \frac { 2 x y } { 8 y ^ { 2 } }$$

In I 899, Charles M. "Mile a Minute" Murphy set a record for speed on a bicycle by pedaling for a mile at an average of 62.3 mi/h (27.8 m/s) on a 3 mi track of plywood planks set over railroad ties in the draft of a Long Island Railroad train. In 1985, a record was set for this type of "motor pacing" by Olympic cyclist John Howard who raced at 152.2 mi/h (68.04 m/s) in the wake of a race car at Bonneville Salt Flats. The race car had a modified tail assembly designed to reduce the air drag on the cyclist. What was the kinetic energy of the bicycle plus rider in each of these feats? Assume that the mass of bicycle plus rider is 70.5 kg in each case.

Use the Quotient Rule to differentiate the function f(x)=tanx-1/secx, Simplify the expression for f(x) by writing it in terms of sinx and cosx, and then find f'(x). show that your answer are equivalent.

Read this passage and then answer. (1) American history has many famous heroes, but Sybil Ludington is one who is less well known. (2) In 1777, Sybil was just 16 years old. (3) Her father was an officer in the New York militia. (4) One night, the British attacked a nearby town. (5) Someone had to alert the militiamen in the area. (6) Sybil volunteered to call the soldiers to arms. (7) She rode 40 miles that night. Choose the correct way to add a participial phrase to sentence 4. A. One night, the British attacked a nearby town; the colonists had stored supplies there. B. One night, the British attacked a nearby town and stole supplies. C. One night, the British attacked a nearby town, stealing colonists’ supplies. D. One night, the British attacked a nearby town where the colonists had stored supplies.