Solve. Be sure to check.

$$\dfrac{1}{4} y-\dfrac{2}{3} y=5$$

The allowable blood loss $L$ is the amount of blood that a patient can lose before a transfusion is necessary. This can be estimated by

$$L=\frac{E\left(H_i-H_f\right)}{H_i}$$

where $E$ is the estimated blood volume of the patient, in milliliters, $H_i$ is the initial hemoglobin level, and $\mathrm{H}_f$ is the lowest acceptable final hemoglobin level. What is the estimated blood volume of a patient with an allowable blood loss of $1470 \mathrm{~mL}$, an initial hemoglobin of $13 \mathrm{~g} / \mathrm{dL}$, and the lowest final hemoglobin of $7 \mathrm{~g} / \mathrm{dL}$? Chess Ratings. The formula

$$R=r+\frac{400(W-L)}{N}$$

is used to establish a chess player's rating $R$, after he or she has played $N$ games, where $W$ are the number of wins, $L$ is the number of losses, and $r$ is the average rating of the opponents. Data: U.S. Chess Federation

Use roster notation to write the set. The set of all even natural numbers

Solve. Be sure to check.

$$3 x-7 x=60$$

Intel Corporation has invented silicon-based connections that use lasers to move data at a rate of 50 gigabytes per second. The printed collection of the U.S. Library of Congress contains 10 terabytes of information. How long would it take to copy the Library of Congress using these connections?

Simplify and write scientific notation for the answer. Use the correct number of significant digits.

$$\dfrac{1.2 \times 10^{-12}}{6.1 \times 10^{-7}}$$

Write an equivalent expression without negative exponents and, if possible, simplify.

$$\frac{5 a^{-3} b c^{-1}}{d^{-6} f^2}$$

Use roster notation to write the set. The set of all odd natural numbers

Baseball. Baseball analysts use the formula $r=0.3 b-0.6 c$ to estimate the number of runs $r$ due to stolen bases for a runner who stole $b$ bases and was caught stealing $c$ times. In 2011, Ichiro Suzuki stole 40 bases and was credited with $7.8$ stolen-base runs. How often was he discovered stealing?

Write an equivalent expression without negative exponents and, if possible, simplify.

$$\frac{p q^{-2} r^{-3}}{2 u^5 v^{-4}}$$

A musical note's pitch is related to the frequency of the wave producing the sound, which is in turn related to the length of the sound wave. By varying lengths, different notes can be produced by an instrument as simple as a piece of PVC pipe. The frequency $f$ of the note produced by striking a pipe of length $L$ and radius $r$ is given by

$$f=\dfrac{2 r+c}{2 L},$$

where $c$ is the speed of sound, which is approximately $13,500 \mathrm{in}$. /sec. The following table shows some frequencies and related pipe lengths for PVC pipe with a radius of $1 \mathrm{in}$. What length pipe should be used in order to create the lowest note on an 88-key piano (an A), which has a frequency of $27.5$ hertz?

International Data Corporation estimated that 988 exabytes of information was generated in 2010 by the worldwide population of $6.8$ billion people. Given that 1 exabyte is $10^{12}$ megabytes, the average amount of data produced per person in 2010 in terms of megabytes.

Find the opposite, or additive inverse.

$$0$$

Simplify and write scientific notation for the answer. Use the correct number of significant digits.

$$\left(8.7 \times 10^{-9}\right) \times\left(4.3 \times 10^{15}\right)$$