91Ó°ÊÓ

Express the statement as an inequality. (a) \(x\) is negative. (b) \(y\) is nonnegative. (c) \(q\) is less than or equal to \(\pi\). (d) \(d\) is between 4 and 2 . (e) \(t\) is not less than 5 . (f) The negative of \(z\) is not greater than 3 . (g) The quotient of \(p\) and \(q\) is at most 7. (h) The reciprocal of \(w\) is at least 9 . (i) The absolute value of \(x\) is greater than 7 .

Use the quadratic formula to factor the expressions. \(15 x^{2}+34 x-16\)

Exer. 33-40: Replace the symbol \(\square\) with elther = or \(\neq\) to make the resulting statement true for all real numbers \(a, b\) \(c,\) and \(d,\) whenever the expressions are defined. $$-(a+b) \square-a+b$$

Solve the equation or inequality. Express the solutions in terms of intervals whenever possible. $$|4 x-1|=7$$

Express the number In decimal form. (a) \(2.3 \times 10^{7}\) (b) \(7.01 \times 10^{-9}\) (c) \(1.23 \times 10^{10}\)

The number of hydrogen atoms in a mole is Avogadro's number, \(6.02 \times 10^{23} .\) If one mole of the gas has a mass of 1.01 grams, estimate the mass of a hydrogen atom.

Highway travel A north-south highway intersects an eastwest highway at a point \(P .\) An automobile crosses \(P\) at 10 A.M., traveling east at a constant rate of \(20 \mathrm{mi} / \mathrm{hr}\). At the same instant another automobile is 2 miles north of \(P\), traveling south at \(50 \mathrm{mi} / \mathrm{hr}\). (a) Find a formula for the distance \(d\) between the automobiles \(t\) hours after 10: 00 A.M. (b) At approximately what time will the automobiles be 104 miles apart?

Archeologists can determine the height of a human without having a complete skeleton. If an archeologist finds only a humerus, then the height of the individual can be determined by using a simple linear relationship. (The humerus is the bone between the shoulder and the elbow.) For a female, if \(x\) is the length of the humerus (in centimeters), then her height \(h\) (in centimeters) can be determined using the formula \(h=65+3.14 x .\) For a male, \(h=73.6+3.0 x\) should be used. (a) A female skeleton having a 30 -centimeter humerus is found. Find the woman's height at death. (b) A person's height will typically decrease by 0.06 centimeter each year after age \(30 .\) A complete male skeleton is found. The humerus is 34 centimeters, and the man's height was 174 centimeters. Determine his approximate age at death.

A person's body surface area \(S\) (in square feet) can be approximated by $$S=(0.1091) w^{1423} h^{0.723}$$ where height \(h\) is in inches and weight \(w\) is in pounds. (a) Estimate \(S\) for a person 6 feet tall weighing 175 pounds. (b) If a person is 5 feet 6 inches tall, what effect does a \(10 \%\) increase in weight have on \(S ?\)