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18 Weight (lbs.) 15 12 9 6 3 2 4 6 8 10 Age (months) This is a LINE GRAPH. It’s easy to see the baby’s weight changing as the months go by. Since Jill charges $25 per lawn each time, the “25” will not have a variable next to it. $18 for each hour means that the “18” should be multiplied by the “h”. Then, we simply add the 18h and the 25 together to get the total charge. Since all right angles must be 90o, the yellow angle is also 45o. Even though Leroy has rolled a “5” four times in a row, that won’t affect the probability of his next toss. The cube has 6 sides. Each side is equally likely to land facing up. The probability of any number being rolled is 1/6. Each can is a cylinder. Volume = p * r2 * h Volume = p * (1)2 2” 4” 5 Volume = 5p in3 5” cola * 10” The volume of the juice can is 8 times greater than the volume of the cola can. Volume = p * (2)2 * 10 Volume = 40p in3 juice When writing a number in scientific notation, you slip the decimal point in so that you’ve got a number between 1 and 10. Next, you see how far the decimal point needs to be moved in order to get it back to where it’s supposed to be. (Since we’re moving it to the LEFT, the exponent will be NEGATIVE.) When the shape is folded, these two segments will be joined together. Therefore, the circles and squares will need to be next to each other. 500 boxes total 35 boxes Each day, he loses 35 boxes. 35 boxes 35 boxes The area of this triangle = ½(3)(2) = 3 cm2 Since there are four identical triangles, their combined area is 12 cm2. The red rectangle is 6 cm x 3 cm, so its area is 18 cm2. The total area of the hexagon is 12 cm2 + 18 cm2 = 30 cm2. Since Pedro actually made more money, the group’s mean will increase. The nice thing about this problem is that you don’t have to add all the numbers together to solve it. Once the mistake was fixed, Pedro had earned an extra $16. Since there are 8 people in the group, that means we could simply take 16 8 to find how much the group’s mean increases by. If we multiply each number in the first column by 2, we’re always slightly too large. Subtracting 1 fixes this problem each time. Therefore, our formula for figure “n” is 2n-1 shaded squares. Notice how the numbers on the left side of the table go up by one, while the numbers on the right side go up by two each time. This tells us that the formula for finding the number of shaded squares must involve multiplication by 2. Figure Shaded Squares 1 1 2 3 3 5 4 7 5 9 6 11 7 13 n 2n-1 = 2(50) - 1 = 99 shaded squares Figure Shaded Squares 1 1 2 3 3 5 4 7 5 9 6 11 7 13 n 2n-1 50 99 Let’s convert them all to decimals… 7.75 7.625 7.071 7.82 Now, arrange them from least to greatest… 7.071 7.625 7.75 7.82 First, convert 18o C to Fahrenheit. F = (9/5)(18) + 32 F = 32.4 + 32 F = 64.4o The difference between high and low temperatures can be found by subtracting. 64.4o - 44.6o 19.8o F Next, convert 7o C to Fahrenheit. F = (9/5)(7) + 32 F = 12.6 + 32 F = 44.6o Add Add Add Add 6 21 7 28 8 36 9 45 10 55 2 3 4 5 If we continue this pattern, here’s what the table would look like… Other students may prefer to work with formulas. The number of cans can be found by using the formula ( L )( L+1 ) 2 For example… 6 21 7 28 8 36 ( 4 )( 4+1 ) 9 45 10 55 2 ( 7 )( 7+1 ) 2 ( 10 )( 10+1 ) 2 = = = ( 4 )( 5 ) 2 ( 7 )( 8 ) 2 ( 10 )( 11 ) 2 = 10 = 28 = 55 The residents’ concern is about the traffic volume during the 4-6 PM rush hour period only. It’s very possible that this intersection may not be used much at all during the rest of the day, so including nonrush hour data will make the intersection seem less busy. The department could get more accurate data if they would only monitor the intersection between 4-6 PM instead of taking an overall daily average. Parallel lines have the same slope. The slope of RW is ¼. Going up 1 block and over 4 blocks from point Q puts us at (-1,-3). (As you can see, we’ve formed a parallelogram.) h 0.4 meters 1.5 meters Volume = (length)(width)(height) 0.75 = (1.5)(0.4)(height) 0.75 = (0.6)(height) 0.6 0.6 height = 1.25 meters The best way is to try each formula to see whether or not it works. As luck would have it, choice A works all four times, so it’s the right answer. 1.15 (3) = 3.45 1.15 (5) = 5.75 1.15 (8) = 9.20 1.15 (12) = 13.80 If choice A would have failed, we would have gone to choice B, then choice C, etc. The correct answer must work all 4 times. (3)(5)(4) = 60 different meals First, make a proportion. Include units before you start. 50 7.5 meters kg = x 502.5 Next, cross-multiply and solve using Algebra. (7.5)(x) = (50)(502.5) 7.5x = 25125 x = 3350 meters kg Revenue Cost 13.60 x -5.80 x > 7.80 x 7.80 > x > 5.80 x + 120 -5.80 x 120 7.80 15.3846 Frank must sell at least 16 frames in order for his revenue to be greater than his costs. 6 2 Dropping down an altitude forms a 30o/60o/90o triangle. 6 8 = 9 n 6n = 72 n = 12 2 + 2(3) 8 2(2) + 3 7 (2)2 + (3)2 13 (2 + 3)2 25 Often times, the best way to solve a problem like this is to pick an even number and an odd number and simply try them out. Let’s make x = 2 and y = 3. We’ll round the values off as we go… Sun = 800 Mon = 350 Tue = 400 Wed = 350 Thur = 300 Fri = 400 Sat = 900 TOTAL = 3500 3500 customers 7 days = 500 each day This is a volume problem. V = (length)(width)(height) V = (22)(9)(8) V = 1584 in3 BE CAREFUL! This is not our final answer… …and it happens to be a choice. DON’T BE FOOLED! We need to take ¾ of 1584. 1188 in3 When an object travels at a constant rate, the graph will always be a straight line. The 34 employees with the lower salaries would be better off with the $500 raise. The 30 employees with the higher salaries would be better off with the 2% raise. If these employees voted, the $500 raise would be the likely winner. To figure the 2% raise, multiply the current salary by 1.02 Let’s compare both situations and see what the new salaries would be: New Salaries $500 raise 2% raise $19,000 $20,800 $24,600 $31,500 $42,500 $58,500 $71,500 $18,870 $20,706 $24,582 $31,620 $42,840 $59,160 $72,420 $18,500 * 1.02 = $18,870 $20,300 * 1.02 = $20,706 and so on… We’ll draw a “line of best fit” through the data points. Since the line has a positive slope, it’s obvious that the population is not going to decline or stay the same. 15 It’s unlikely that it will get above 120,000 in the next 10 years when it’s not even above 50,000 during the first 10 years. If we extend the line out, you can see from the graph that this is the obvious choice. OPP Starting from the shaded angle, label the 3 sides of the triangle: HYP ADJ Since it’s a trig problem, we’ll be using SOH CAH TOA The sides we’re dealing with are the OPPOSITE and the ADJACENT, so we’ll be using the TANGENT. tangent = opposite adjacent = 4 x n = 687.5 3 n = 229.16666 Here are my estimates: Superior = 31,000 Michigan = 22,000 Huron = 23,000 Erie = 10,000 Ontario = 8,000 Total = 94,000 If R and T are both midpoints, then SR = 14 and ST = 12. 14 12 These 2 triangles are similar. The orange triangle has sides which are twice as long as 14 the yellow triangle. Using 12 this scale factor, the bottom side of the yellow one is 14. 14 28 24 14 + 14 + 12 = 40 28 The final coordinates of the kite will be P”(1, 3), Q”(2, 4), R”(1, 7), and S”(0, 4). Some students may choose not to use a graph. Here’s what they’d need to do: P(-2, -1) Q(-1, -2) R(-2, -5) S(-3, -2). Reflecting the graph over the x-axis simply changes the signs on the y-coordinates. P’(-2, 1) Q’(-1, 2) R’(-2, 5) S’(-3, 2). Translating the graph 3 units right and 2 units up requires us to add 3 to each x-coordinate and 2 to each y-coordinate. P”(1, 3) Q”(2, 4) R”(1, 7) S”(0, 4). The final coordinates of the kite will be P”(1, 3), Q”(2, 4), R”(1, 7), and S”(0, 4). 2 n - w2 q 2/3 Do the exponents first. 1/9 - 36 2/3 Dividing by 2/3 is the same as multiplying by 3/2. 1/9 54 2 (1/3) - - (-6)2 = 8 -53 9 Probability = Probability = Hispanic males Total males 76,660 5,215,573 Probability = 0.0146982891 day #1 60 MPH x 9 hours 540 miles traveled 1244 miles total - 540 miles on day #1 704 miles to go day #2 704 miles 11 hours = 64 MPH average This presentation brought to you by Mr. Jeff Luce BBHHS Mathematics Dept.