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Unformatted text preview: s, and twice as many blue marbles as green marbles. If these are the only colors of marbles in the bag, what is the probability of randomly picking a blue marble from the bag? (A) (B) (C) (D) (E)
1 6 2 9 1 4 2 7 1 3 www.petersons.com 304 Chapter 16 SOLUTIONS TO PRACTICE EXERCISES
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1. (B) Since the figure shows a 45°45°90° 4. (E)
y2 − y1 1 − 3 −2 = = = −1 . Substitute the (x,y) x 2 − x1 4 − 2 2 The line’s slope (m) = triangle in which the length of one leg is known, you can easily apply either the sine or cosine function to determine the length of the hypotenuse. Applying the function sin45° =
2 , set the value of this function equal to 2 5 opposite x hypotenuse , then solve for x: 25 10 10 2 = ; 2 x = 10 ; x = = =5 2. 2 x 2 2 pair for either point to define the equation of the line. Using the pair (2,3):
y = −x + b 3 = −2 + b 5=b 2. (D) Since the figure shows a 30°60°90° 5. The line’s equation is y = –x + 5. To determine which of the five answer choices provides a point that also lies on this line, plug in the values of x and y provided each answer choice, in turn. Only choice (E) provides a solution to the equation: –1 = –6 + 5. (B) The slope of AB = y2 − y1 3 − (−3) 6 3 = == x 2 − x1 4 − (−4) 8 4 . The slope of the line
3 4 triangle, you can easily apply either the sine or the cosine function to determine the length of the hypotenuse. Applying the function sin30° =
1 2 4 x perpendicular to AB is the negative reciprocal of 4 , which is – 3 . 6. (D) Given any two xycoordinate points, a
y −y , set the value of this function equal to
14 opposite hypotenuse , then solve for x: 2 = x ; x = 8 . 3. (C) Since the hexagon is regular (all sides are congruent), the area of ∆AOP in the following figure is 3 — one sixth the area of the hexagon. 1 2 line’s slope m = x − x . Accordingly, 1 2 1 5 − (−3) = . Simplify, then crossmultiply to 3 a−2 solve for a:
1 8 = 3 a−2 a − 2 = (3)(8) a − 2 = 24 a = 26 7. ∆AOP is equilateral; hence you can divide it into two 1: 3 :2 triangles, as shown in the figure. Sinc...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at EmbryRiddle FL/AZ.
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