91Ó°ÊÓ

A power company charges one household \(\$ 0.12\) per kilowatt-hour \((\mathrm{kWh})\) and \(\$ 14.89\) in monthly taxes. a. Write a formula for the monthly charge \(C\) for this household if it uses \(k\) kilowatt-hour. b. Compute the monthly charge if the household uses \(1200 \mathrm{kWh}\)

Write the expression using rational exponents. Assume that all variables represent positive real numbers. \(\sqrt[5]{a^{3}}\)

Refer to \(B=\left\\{\frac{\pi}{2}, 0,-4,0 . \overline{48}, 1,-\sqrt{13}, 9.4\right\\} .\) Determine which elements belong to the given set. a. \(\mathbb{N}\) b. \(\mathbb{W}\) c. \(\mathbb{Z}\) d. \(\mathbb{Q}\) e. \(\mathbb{H}\) f. \(\mathbb{R}\)

A utility company charges a base rate for water usage of \(\$ 13.50\) per month, plus \(\$ 3.58\) for every additional 1000 gal of water used over a 2000 -gal base. a. Write a formula for the monthly charge \(C\) for a household that uses \(n\) thousand gallons over the 2000-gal base. b. Compute the cost for a family that uses a total of 5000 gal of water for a given month.

Write the expression using rational exponents. Assume that all variables represent positive real numbers. \(\sqrt[7]{z^{4}}\)

Write the expanded form for \((a+b)(a-b)\).

Write the expression using rational exponents. Assume that all variables represent positive real numbers. \(\sqrt{6 x}\)

Write each statement as an inequality. \(a\) is at least \(5 .\)

The \(\operatorname{cost} C\) (in \$) to rent an apartment is \(\$ 640\) per month, plus a \(\$ 500\) nonrefundable security deposit, plus a \(\$ 200\) deposit for each dog or cat. a. Write a formula for the total cost to rent an apartment for \(m\) months with \(n\) cats/dogs. b. Determine the cost to rent the apartment for 12 months, with 2 cats and 1 dog.

Perform the indicated operations and simplify. $$ (4 x-5)(4 x+5) $$