# Solve equilibrium of price, estimate population, and dimension of rectangular

Need assistance in solving the attached problems. My answers are falling short of the choices given in the problem. Please explain the steps to get answers.

Thank you.

1. Find the equilibrium price.

Suppose the price p of bolts is related to the quantity q that is demanded by: P=520-5q^2 where q is measured in hundreds of bolts. Suppose the supply function for bolts is given by p=5q^2, where q is the number of bolts (in hundreds) that are supplied at price: a. $7 b. $260 c. $275 d. $520.

2. Solve the problem.

The growth in the population of a certain rodent at a dump site fits the exponential function A(t)=336e0.031t, where t is the number of years since 1963. Estimate the population in the year 2000.

a. 529

b. 1058

c. 1091

d. 347

3. Solve the problem.

An open box is to be made from a rectangular piece of tin by cutting two inch squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin.

a. 4 in. by 9 in.

b. 5 in. by 10 in.

c. Not enough information

d. 5 in. by 9 in.

4. Five cards are drawn at random from an ordinary deck of 52 cards. In how many ways is it possible to draw all black cards?

a. 32,890

b. 65,780

c. 263,120

d. 131,560

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