Warm-Up 14.pdf Click on the file aboveDo problems 199, 191, and 193 ONLY!I NEED THE WORK WITH THE ANSWERS!!!

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Warm-Up 14

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)

m

m + n = 25 m – n

and m > n. What is the value of n ?

m-n 4 m+n

Express your answer as a common fraction.

193. ________ For non-negative integers m and n,

cm3 How many cubic centimeters of silver are needed to cover just the faces of a cube with a

194. ________

layer of silver that is 1 mm thick if the cube has edges of length 6 cm? Express your answer

to the nearest whole number.

195. ________ Stage 1 of a pattern is a black square of side length 2015 units. At stage 2, a white square

of side length 2014 units is placed on top of the square in stage 1 and positioned so that

the upper left vertices of the squares coincide. The pattern continues with alternating white

and black squares placed and positioned in this manner at each stage. Each new square

placed has sides 1 unit shorter than the square placed at the previous stage. The ?rst ?ve

stages are shown. At stage 2015, what portion of the ?gure will be black? Express your

answer as a common fraction.

Stage 1

Stage 2

Stage 3

Stage 4

Stage 5

integers The domain of f (x) = x2 – 3 is {-4, -3, …, 3, 4}. How many integers are in both the range

196. ________

and the domain of f ?

feet

197. ________

12 ft

5 ft

?

The lamp of a streetlight is 12 feet above the street below. A girl who is

5 feet tall stands at a point 6 feet from the spot directly below the light.

How long is her shadow? Express your answer as a mixed number.

6 ft

integers How many positive integers have the same digits in the same order when written in base 7

198. ________

and in base 13?

199. ________ Maggie writes the numbers 1, 2, 3,
, 10 on separate slips of paper and tosses the

10 slips into a hat. She then randomly pulls three slips from the hat at the same time. What

is the probability that the arithmetic mean of the three selected values is in fact written on

one of those same three slips? Express your answer as a common fraction.

200. ________ If 2015 + a = b for positive integers a and b, both of which are palindromes, what is the

smallest possible value of a?

28

MATHCOUNTS 2014-2015

in

In the equilateral triangle, each downward facing white triangle has its vertices at

the midpoints of the sides of the larger upward facing triangle that just contains

it. What fraction of the entire ?gure is white? Express your answer as a common

fraction.

192._________

36

in2 Two concentric circles and a line segment tangent to the smaller circle are shown. If

191._________

the length of the line segment is 36 inches, what is the area of the region between

the circles? Express your answer in terms of p.

…

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