MATHCOUNTS Valentine

On some graph paper, graph the following segments:

y = x, for 0 ≤ x ≤ 2
y = 2x − 2, for 2 ≤ x ≤ 3
x = 3, for 4 ≤ y ≤ 6
y = −x + 9, for 2 ≤ x ≤ 3
y = 7, for 1 ≤ x ≤ 2
y = x + 6, for 0 ≤ x ≤ 1

Now reflect each of the segments over the y-axis.  What popular shape have you drawn?

 

Hot Air Balloons

Fall is a beautiful time of year to take a hot air balloon ride! You may not be able to take a balloon ride, but we hope you enjoy solving this week’s problems.

Melrose’s hot air balloon is a sphere of diameter 100 feet. How many cubic feet of air will Melrose’s hot air balloon hold when completely filled? Express your answer as a decimal to the nearest tenth.

Moving Day

The summer months are the most popular time to move to a new home. Janet’s family is moving, and she suddenly realizes just how much stuff they have in their current home. Once the moving company finishes packing everything in boxes, they begin the task of numbering them. A sticker is placed on every box and on every item that is too large to fit in a box. Janet notices that stickers in three distinct colors are used. There are blue stickers numbered 239 through 262, green stickers numbered 163 through 178 and yellow stickers numbered 453 through 492.

Road Work Ahead

A construction crew places orange barrels on both sides of a particular road to indicate a work zone. On each side of the road, the distance between the centers of consecutive barrels is 15 feet. If this work zone is 1.5 miles long, what is the total number of barrels that will be used?

Happy Pi Day

 

This Wednesday (3/14) was Pi Day. Here are a few questions in honor of the day.

If Celia ate 1/4 of 2/3 of 1/2 of a pie, what fraction of the whole pie did she eat? Express your answer as a common fraction.

Celia ate (1/4)(2/3)(1/2) = 1/12 of the whole pie.