7th Graders  Here's a link to our online curriculum: https://im.kendallhunt.com/MS/students/2/index.html Here's a link to our online glossary: https://im.kendallhunt.com/MS/students/2/glossary.html Problem of the Week Engine Failure
An aircraft is equipped with three engines that operate independently. The probability of an engine failure is .01. What is the probability of a successful flight if only one engine is needed for the successful operation of the aircraft?
Milk or Bread or Both?
A customer enters a supermarket. The probability that the customer buys bread is 0.6, the probability that he buys milk is 0.5, and that he buys both bread and milk is 0.3. What is the probability that the customer would buy either bread or milk or both?
Solution .8, or 4/5. Let Brepresent the event that the customer buys bread, Mthe event that the customer buys milk. Then, according to the rule of addition, we have P(B∪M) = P(B) + P(M) − P(B∩ M) = .60 + .50 − .30 = .80
Alternate solution.A Venn diagram offers a visual approach. If we first show the probability that the customer buys mile andbread—P(M∩ B)—then we can complete the diagram by subtraction: P(M∪B) = .2 + .3 + .3 = .8 Rectangular Solids
How many rectangular solids are possible with a volume of 100 cubic meters and sides of only whole numbers? Solution 8. The solutions by dimension are (1, 1, 100), (1, 2, 50), (1, 4, 25), (1, 5, 20), (1, 10, 10), (2, 2, 25), (2, 5, 10), and (4, 5, 5).
10 Digit Number
Write a tendigit number so that the first digit indicates how many 0s are in the number, the second digit indicates how many 1s are in the number, the third digit indicates the number of 2s, etc. Solution 6,210,001,000
Flat Tire
After a cyclist has gone 2/3 of his route, he gets a flat tire. Finishing on foot, he spends twice as long walking as he did riding. If his walking and riding rates are both constant, how much faster does he ride than walk? Solution 4 times as fast. He walks onethird of the way, or half as far as he rides, but it takes him twice as long. Therefore, he rides four times as fast as he walks.
Pluto Math
Pluto's inhabitants use the same mathematical operators that we do (+, −, etc.). They also use an operator, @, that we do not know. The following are true for any real numbers x and y. x@ 0 = x x@ y= y@ x x @ y = ((y–1) @ x) + (x+1) = (y2) @ x + 2(x+1) = ((y–3) @ x) + 3(x+1)…. What is the value of 12 @ 5? Solution 77. We have 12 @ 5 = 5 @ 12 = (4 @ 12) + 13 = (3 @ 12) + 13 + 13 = (3 @ 12) + 26. Continuing, (3 @ 12) + 26 = (2 @ 12 + 39) = (1 @ 12) + 52 = (0 @ 12) + 65 = (12 @ 0) + 65 = 77 Path Distance
Jeremy walks along a spiral path (as shown). If the path is 2 meters wide, how far does he walk? Solution 97 meters. By superimposing a grid of 2X2 squares, one can see that the path Jeremy travels can be broken into 13 sections of lengths 13, 12, 12, 10, 10, 8, 8, 6, 6, 4, 4, 2, and 2 meters. Chicken Nuggets
Chicken nuggets come in packets of 6, 9, or 20. What is the largest number of nuggets that you cannot buy when combining various packets?
Solution 43. Any multiple of 3 that is greater than 3 can be obtained from packets of 6 and 9 nuggets. Since 36 = 9 + 9 + 9 + 9, 38 = 20 + 9 + 9, and 40 = 20 + 20, any even number ≥ 36 can be achieved by adding 6s to each of these. Similarly, by adding another 9, any odd number ≥ 45 can be achieved. But 43 is not yet guaranteed, so we need to examine the possibility of combinations that yield 43 nuggets. Since 43 is not a multiple of 3, likewise, 43 – 20 = 23 is not a multiple of 3, and 43 – 2 • 20 = 3 is too small to achieve. Consequently, 43 cannot be obtained.
