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If m and n are directly proportional, and m = -2 when n = 6,

If m and n are directly proportional, and m = -2 when n = 6, Then what is the value of m when n = -12? A) -36 B) -6 C) -3 D) 2 E) 4. If m and n are directly proportional, and m = -2 when n = 6, Then what is the value of m when n = -12?

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If m and n are directly proportional, and m = -2 when n = 6,

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  1. If m and n are directly proportional, and m = -2 when n = 6, • Then what is the value of m when n = -12? • A) -36 B) -6 C) -3 D) 2 E) 4

  2. If m and n are directly proportional, and m = -2 when n = 6, Then what is the value of m when n = -12? A) -36 B) -6 C) -3 D) 2 E) 4 Directly proportional means either that n = km, or that n/m is a constant (quotient is constant; as one gets bigger, the other gets bigger) / m = 6 / -2 = -12 / m 24 = 6m  m = 4 (e)

  3. If m and n are inversely proportional, and m = -2 when n = 6, • Then what is the value of m when n = -12? • -6 B) -3 C) 1 D) 2 E) 4

  4. If m and n are inversely proportional, and m = -2 when n = 6, • Then what is the value of m when n = -12? • -6 B) -3 C) 1 D) 2 E) 4 • Inversely proportional means either that n = k/m, or mn = k (product is constant: when one gets bigger, the other gets smaller)) • mn = -2(6) = m(-12)  m = 1

  5. What is the area of the shaded portion? Assume that these are indeed circles. You may leave it in terms of π. 4 6 10 12

  6. What is the area of the shaded portion? Assume that these are indeed circles. You may leave it in terms of π. 4 - - 6 Area of triangle = ½(12)(20) = 120 Area of small circle = 9 π Area of large circle = 25π Shaded area = 120 - 34π 10 12

  7. Thought for the Day If a turtle loses its shell, is it naked or homeless?

  8. Riddle of the Day My first is a number, my second another, And each, I assure you, will rhyme with the other. My first you will find is one-fifth of my second, And truly my whole, a long period reckoned. Yet my first and my second (nay, think not I cozen), When added together, will make but two dozen.

  9. If this figure is made of identical squares, and the area of the entire figure is 125, then what is the perimeter?

  10. If this figure is made of identical squares, and the area of the entire figure is 125, then what is the perimeter? Five identical squares means the area of each one is 125 / 5 = 25 Since Area = s2, then the side will be √25 = 5 There are twelve exterior sides, so the perimeter will be 12 ∙ 5 = 60

  11. What is the numerator of (1/2 + 1/6) – (1/12 + 1/3) in simplest terms?

  12. What is the numerator of (1/2 + 1/6) – (1/12 + 1/3) in simplest terms? (1/2 + 1/6) = (6/12 + 2/12) = 8/12 1/12 + 1/3 =1/12 + 4/12 = 5/12 8/12 – 5/12 = 3/12 = ¼ Answer: 1

  13. How many odd integers are between 10/3 and 83/4? A) 8 B) 9 C) 10 D) 18 E) 19

  14. How many odd integers are between 10/3 and 83/4? • 8 B) 9 C) 10 D) 18 E) 19 • 10/3 = 3.33 • 83/4 = 20.75 • Thus, between them: 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19

  15. Word of the day: Aibohphobia: Fear of Palindromes

  16. Word of the day: Aibohphobia: Fear of Palindromes (just kidding!)

  17. 1.2 hr B) 1.3 hr C) 1.8 hr D) 2.4 hr E) 3.0 hr • Phil paints ¼ of the job per hour • His son paints 1/6 of the job per hour • Together, they paint ¼ + 1/6 = 3/12 + 2/12 = 5/12 • But, Phil already finished ¼ of the job in his hour alone, so ¼ + x(5/12) = 1 whole job • ¾ = 5x / 12 • 9/12 = 5x / 12  x = 9/5..they work 1.8 hours together

  18. Poor Hoggs—they now have to repaint after the Groundhog day celebration.. It would take Phil 4 hours to paint alone, while his son would take 6 hours to paint alone. Phil works one hour alone, and then they work together to finish. How long did they have to paint together to finish the job? A) 1.2 hr B) 1.3 hr C) 1.8 hr D) 2.4 hr E) 3.0 hr

  19. Poor Hoggs—they now have to repaint after the Groundhog day celebration.. It would take Phil 4 hours to paint alone, while his son would take 6 hours to paint alone. Phil works one hour alone, and then they work together to finish. How long did they have to paint together to finish the job? Hint: how much of the job did Phil finish alone? How much was left to paint together? A) 1.2 hr B) 1.3 hr C) 1.8 hr D) 2.4 hr E) 3.0 hr

  20. Finish this for tomorrow! A) 1.2 hr B) 1.3 hr C) 1.8 hr D) 2.4 hr E) 3.0 hr

  21. 1.2 hr B) 1.3 hr C) 1.8 hr D) 2.4 hr E) 3.0 hr • Phil paints ¼ of the job per hour • His son paints 1/6 of the job per hour • Together, they paint ¼ + 1/6 = 3/12 + 2/12 = 5/12 • But, Phil already finished ¼ of the job in his hour alone, so ¼ + x(5/12) = 1 whole job • ¾ = 5x / 12 • 9/12 = 5x / 12  x = 9/5..they work 1.8 hours together

  22. After the huge Groundhog Day celebration, the Hoggs are left to clean up the grounds. If Phil works alone, he finishes in 4 hours; his wife working alone finishes in 3 hours, and their son can finish in 6 hours. If they all pitch in, how long will it take them to clean up? A) .8 hr B) 1.3 hr C) 2 hr D) 2.8 hr E) 3.6 hr

  23. After the huge Groundhog Day celebration, the Hoggs are left to clean up the grounds. If Phil works alone, he finishes in 4 hours; his wife working alone finishes in 3 hours, and their son can finish in 6 hours. If they all pitch in, how long will it take them to clean up? • .8 hr B) 1.3 hr C) 2 hr D) 2.8 hr E) 3.6 hr • ¼ + 1/3 + 1/6 = 3/12 + 4/12 + 2/12 = 9/12 = ¾ • Together, they clean ¾ of the grounds per hour • Thus, 1 / (3/4) = 4/3 working together

  24. Phil G. Hogg takes 4 hours to clean his home, and his wife, Mrs. G. Hogg, takes 2 hours. How long will it take them working together to clean up? • 1.3 hour B) 2.2 hours C) 3 hours D) 3.5 hours • E) 6 hours

  25. Phil G. Hogg takes 4 hours to clean his home, and his wife, Mrs. G. Hogg, takes 2 hours. How long will it take them working together to clean up? A) 1.3 hr B) 2.2 hr C) 3 hr D) 3.5 hr E)6 hr Phil cleans ¼ per hour, and his wife ½ per hour. Together, they clean ¼ + ½ = ¾ per hour. Thus, it will take 1 / (3/4) = 4/3 hours = 1.3 hrs

  26. The mean, sum, and product of three integers are all the same. If one of the numbers is 3, what are the other 2?

  27. The mean, sum, and product of three integers are all the same. If one of the numbers is 3, what are the other 2? Yes, there is enough information!

  28. The mean, sum, and product of three integers are all the same. If one of the numbers is 3, what are the other 2? Mean = average = sum / 3 And we know that sum = sum / 3 Subtract sum /3 to give 2/3 sum = 0 Sum = 0 = product, as well… Thus, the other two numbers must be 0 and -3

  29. What is it that we heat, then make cold; sweeten, then make sour?

  30. Riddle: Two boys were sent by their mothers to sell an equal amount of cupcakes each, worth one dollar per cupcake.They were told not to eat the cupcakes they are selling, and that they should sell all of the cupcakes.At the end of the day, all cupcakes were sold, yet neither boy gained nor lost a dollar.What happened?

  31. If | x + 5 | + 3 = 11, then x = • -13 II. 3 III 19 • I only B) II only C) I and II only • D) II and III only E) I , II, and III

  32. If | x + 5 | + 3 = 11, then x = • -13 II. 3 III 19 • I only B) II only C) I and II only • D) II and III only E) I , II, and III • Try answers? • |-13 + 5|+ 3 = 11 yep • |3 + 5|+ 3 = 11 yep • |19 + 5| + 3 ≠ 11 C)

  33. If | x + 5 | + 3 = 11, then x = • -13 II. 3 III 19 • I only B) II only C) I and II only • D) II and III only E) I , II, and III • Or solve: • x + 5 = 8 or x + 5 = -8

  34. Bonus: Can you arrange 4 pennies so they’re all touching each other?

  35. If (x) = 3x + 7, then ((1)) has what value?

  36. If (x) = 3x + 7, then ((1)) has what value? • = 3(1) + 7= 10 • (10) = 3(10) + 7 = 37 3 7 3 7

  37. Bonus Riddle: John’s wife shot him, drowned him, and then hung him. Yet she won an award for this. Why?

  38. If 25% of x = 50, what is 50% of 4x? • 25 B) 50 C) 200 D) 400 E) 500 • (Yes, it’s been awhile!)

  39. If 25% of x = 50, what is 50% of 4x? • 25 B) 50 C) 200 D) 400 E) 500 • Without finding x: • 50% doubles it, and 4x multiplies it by 4 • 8 * 50 = 400 • D) 400

  40. If 25% of x = 50, what is 50% of 4x? • 25 B) 50 C) 200 D) 400 E) 500 • Or, if you insist on finding x: • .25x = 50  x = 200 • 4x = 800 • .5(800) = 400 (D) still

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