Solve the problem. Peanuts cost $2 per pound .and cashews cost$4 per pound. A 50-pound mixture costs $164. How many pounds of each kind of nut are in the mixture?

Solve the problem. Suppose you want to make a mixture of peanuts and walnuts that costs $2.70 per pound. How many pounds of peanuts at$1.50 per pound should be mixed with 24 pounds of walnuts at $3.50 per pound?

Solve the problem. Peanuts cost $2.50 per pound and walnuts cost$5.00 per pound. If you mix 4 pounds of peanuts and 4 pounds of walnuts, what is the cost of one pound of the mixture?

$5 \$$ A snack mix is made from peanuts that cost$\$3$ per pound and caramel popcorn that costs $\$ 2.20$ per pound. The mixture costs $\$ 2.50$ per pound. Does the mixture contain more peanuts or more popcorn?

Decide whether the statement is true or false. You might be MORTIFIED if you get the lowest test score in the class.

Simplify each square root.

A 5.0-kg solid cylinder of radius 0.25 m is free to rotate about an axle that runs along the cylinder’s length and passes through its center. A thread wrapped around the cylinder is weighed down by a mass of 2.0 kg so as to unwrap and make the cylinder rotate as this mass falls. If there is no slippage between the thread and the cylinder, and the cylinder starts from rest at $t _ { i } = 0$, calculate (a) its rotational velocity at $t _ { f } = 5.0 \mathrm { s }$ and (b) the angle through which it has turned in this interval. Ignore any friction in the axle.

How do migrating birds find their way?

On a summer day, you keep the air conditioner in your room running. From the list numbered 1 to 4, choose the bot reservoir and the cold reservoir. 1. the air outside, 2. the compartment inside the air conditioner where the air is compressed, 3. the freon gas that is the working substance (expands and compresses in each cycle), 4. the air in the room. (a) 1 is the hot reservoir, 2 is the cold reservoir. (b) 1 is the hot reservoir, 3 is the cold reservoir. (c) 1 is the hot reservoir, 4 is the cold reservoir. (d) 2 is the bot reservoir, 3 is the cold reservoir. (e) 2 is the hot reservoir, 4 is the cold reservoir. (f) 3 is the hot reservoir, 4 is the cold reservoir.

Solve using a proportion. A bicyclist completes a 120-mile race in 4 hours 30 minutes. What is the average speed, in miles per hour, of the bicyclist?

A store sells cashews for $5.00 per pound and peanuts for$1.50 per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?

Terrell noticed that if he adds the first terms, second terms, third terms, etc. of the two arithmetic series at right, he gets a brand new series!

$$\begin{array} { l } { \text { original series } \rightarrow } \\ { \text { new series } \rightarrow } \end{array} \left\{ \begin{array} { l } { 1 + 2 + 3 + 4 + \ldots + n } \\ { \frac { 2 + 4 + 6 + 8 + \ldots + 2 n } { 3 + 6 + 9 + 12 + \ldots + 3 n } } \end{array} \right.$$

a. Describe his new series. Is it arithmetic? How many terms does it have? b. Use the expressions for the sums of the original series to find an expression for the sum of the new series. c. Is there another way you could have found the expression for the sum of the series $3 + 6 + 9 + \ldots + 3 n ?$ Be prepared to explain your strategy to the class. d. If you have not done so already, verify that your strategy in part (c) resulted in an expression equivalent to your expression from part (b).

A contractor must tile a rectangular kitchen that is 4 ft longer than it is wide, and the perimeter of the kitchen is 48 ft. (A) Find the dimensions of the kitchen. (B) How many square feet of tile should be ordered if the contractor adds an additional 10% to account for waste? (C) Determine the total cost if the tile costs $12/ft^2 and sales tax is 6%.

Account for the fact that the line that separates the metals from the nonmetals on the periodic table is diagonal downward to the right instead of horizontal or vertical.