Math Counts Warm-Up #5-6 2017-2018

A pencil and 5 paper clips weigh the same as 2 erasers. A pencil weighs the same as 29 paper clips. How many paper clips weigh the same as an eraser?

___ paper clips

What is the maximum number of points of intersection of a right triangle with a square, assuming no side of the triangle is collinear with any side of the square?

___ points

If p(x) = ax² + bx + c is a quadratic polynomial satisfying p(0) = 4, p(1) =15, p(2) = 36,

what is the value of the product abc? ___

A certain sphere has a volume that is numerically equal to three times its surface area. What is the radius of this sphere?

___ units

A layered candle is made with 5 colors, shown here as candle A.

How many different candles can be made using the same 5 colors,

with BLUE as the middle layer, shown as candle B, and with no color

next to a color that it touched in candle A?

___ candles

Suppose Luke spins the pointer on a fair 3-color spinner twice. What is the probability that the pointer lands on the same color twice? Express your answer as a common fraction.

Kevin is playing basketball and up to now made 1 /3 of his attempted shots. If he makes his next 5 shots, he will improve his shooting percent to 50%. How many shots has Kevin attempted up to now, when he has a 1/3 success rate?

___ shots

What is 1100112 when rewritten in base eight? ___ base eight

If the point (8, 9) is the center of a circle of radius 10 units, at how many points does the circle intersect the coordinate axes?

___ points