Exam 1: The Nature of Problem Solving

If you take 7 cards from a deck of 52 cards, how many cards do you have? ​ __________ cards ​

If an island's only residents are penguins and bears, and if there are 16 heads and 38 feet on the island, how many penguins and how many bears are on the island? ​

Write the number in fixed-point notation. ​ ​

Perform the operations. ​ ​

If a family has 7 children, in how many ways could the parents have 3 boys and 4 girls as children? ​

If a country's annual production of sugar is 39,000,000 tons, estimate the number of grains of sugar produced in a year in that country. Use scientific notation. Round your answer to 4 decimal places. (Note: There are 2,000 lb per ton. Assume there are 2,260,000 grains in a pound of sugar.)

Consider the pattern: ​ 9 × 1 - 1 = 8 9 × 21 - 1 = 188 9 × 321 - 1 = 2888 9 × 4321 - 1 = 38888 ​ Use this pattern to find .

Compute the result. Leave your answer in scientific notation. ​

Consider the pattern: ​ 123456789 × 9 = 1111111101 123456789 × 18 = 2222222202 123456789 × 27 = 3333333303 ​ Use this pattern to find .

Compute the result. Leave your answer in scientific notation. ​

If an island's only residents are penguins and bears, and if there are 17 heads and 38 feet on the island, how many penguins and how many bears are on the island? ​ The number of bears is __________. ​ The number of penguins is __________. ​

Imagine that you have written down the numbers from 1 to 300. What is the total number of zeros you have recorded? ​ __________ zeros

If a family has 4 children, in how many ways could the parents have 2 boys and 2 girls as children? ​ __________ ways ​

Compute the result. Leave your answer in scientific notation. Round your answer to 1 decimal place. ​

Find the first five terms of the seven pattern.

How many 1-cent stamps are there in a dozen? ​ __________ stamps ​

Compute the result. ​ ​

Write the number in fixed-point notation. Write your answer as a circulating fraction. Round your answer to 3 decimal places.

Use Euler circles to check the validity of the argument. ​ All candy is fattening. All candy is delicious. Therefore, all fattening food is delicious. ​ The argument is __________. ​

Thoth, an ancient Egyptian god of wisdom and learning, has abducted Ahmes, a famous Egyptian scribe, in order to assess his intellectual prowess. Thoth places Ahmes before a large funnel set in the ground (see figure below). It has a circular opening 1,000 ft in diameter, and its walls are quite slippery. If Ahmes attempts to enter the funnel, he will slip down the wall. At the bottom of the funnel is a sleep-inducing liquid that will instantly put Ahmes to sleep for eight hours if he touches it. Thoth hands Ahmes two objects: a rope 1,006.28 ft in length and the skull of a chicken. Thoth says to Ahmes, "If you are able to get to the central tower and touch it, we will live in harmony for the next millennium. If not, I will detain you for further testing. Please note that with each passing hour, I will decrease the rope's length by a foot. Is it possible to reach the central ankh tower and touch it? ​ ​ Ahmes' dilemma. Note that there are two ankhshaped towers. One stands on a cylindrical platform in the center of the funnel. The platform's surface is at ground level. The distance from the platform surface to the liquid is 500 ft. The other ankh tower is on land, at the edge of the funnel. ​