Answer:
1.9 miles.
Step-by-step explanation:
John jogs 2 7/10 miles to the park. Marsha jogs 4/5 miles to the park.
Convert the fractions into decimals:
2 7/10 = 2.7
4/5 = 0.8
Subtract '0.8' from '2.7':
John should jog 1.9 miles farther than Marsha.
Hope this helps.
Earlier today I set you ten questions from this year’s International Singapore Maths Competition. Here are the questions and the answers. On the whole you did very well - smarter than a 10-year-old Singaporean! (With the caveat that they didn’t have multiple choice answers to choose from, and they are only ten). The only questions where your most popular answer the wrong one were 6 and 8. (C in Q6, and B in Q8). Thanks for taking part - now look through your workings...
For Year 5 pupils:
1. Mary cut off 2/5 of a piece of string. Later, she cut off another 14 m. The ratio of the length of string remaining to the total length cut off is 1 : 3. What is the length of the remaining string?
A. 5 m
B. 7 m
C. 10 m
D. 14 m
Solution is C. [73 per cent of readers got it right]
Oh Mary! This is how I would have solved it, using equations. Let L be the original length of the string, and R be what is remaining once you have cut the string twice. We know that R = (L x 3/5) – 14m, and that ((L x 2/5) +14) /R = 3, or 2L/5 + 14 = 3R. By substituting the first equation in the second we have 2L/5 + 14 = 9L/5 –42. Which rearranges to:7L/5 = 56, or L = 40. So R = 10m.
Interestingly, the Singapore method of solution is different. It requires us to think more visually about the string: We cut 2/5 of it. Then 14m, and are left with a piece that is a third of the size of what was cut. In other words, we are left with 1/4 of the original length. In order to compare the fractions 2/5 and then 1/4, lets change them to the lowest common denominator, which is 20. So, we cut off 8/20, subtract 14m and are left with 5/20. Let’s now draw the string divided into twentieths:
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The 14m must be 7/20 of the string, which mean each twentieth is 2m. The remaining piece of string is 5/20, i.e 10m
2. The areas of the faces of a rectangular box are 84 cm2, 70 cm2 and 30 cm2. What is the volume of the box?
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Photograph: ISMC
A. 300 cm3
B. 420 cm3
C. 490 cm3
D. 504 cm3
Solution is B. [85 per cent of readers got it right]
First we need to work out the possible side lengths, by seeing which two numbers multiply to be the area of each face. The 84 face could be 1 x 84, 2 x 42, 3 x 28, 4 x 21, 6 x 14 or 7 x 12. The 70 face could be 1 x 70, 2 x 35, 5 x 14 or 7 x 10. The 30 face could be 1 x 30, 2 x 15, 3 x 10 or 5 x 6.
The common factors between 84 and 70 are 1, 2, 7 and 14.
The common factors between 84 and 30 are 1, 2, 3 and 6.
The only way to make 84 with one each of these common factors are 14 from the top line and 6 from the bottom. So the edge bordering the 84 and 70 faces has length 14, and the edge bordering the 84 and 30 edges has length 6. Which means the height must be 30/6, or 70/14 = 5. Thus the volume is 14 x 6 x 5 = 420cm.
3. There are four numbers. If we leave out any one number, the average of the remaining three numbers will be 45, 60, 65 or 70. What is the average of all four numbers?
A. 50
B. 55
C. 60
D. 65
Solution is C. [82 per cent of readers got it right]
If the four numbers are A, B, C and D, then we know that
A + B + C = 45 × 3
A + B + D = 60 × 3
A + C + D = 65 × 3
B + C + D = 70 × 3
Now add them up to get 3A + 3B + 3C + 3D = (45 + 60 + 65 + 70) × 3
Which is A + B + C + D = (45 + 60 + 65 + 70) = 240. So their average is 240/4 = 60
Answer:
<u>After four games, a player can lose up to $ 16 to win up to $ 26. These are the probabilities for every game:</u>
<u>1/8 or 12.5% of landing three "heads"</u>
<u>3/8 or 37.5% of landing two "heads"</u>
<u>4/8 or 50% of landing no or only one "head".</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
If three coins land "heads" the player wins $ 10
If two coins land "heads" the player wins $ 5
Cost of playing = $ 4
2. What is the player's expected outcome after four games?
Probability of two coins out of three lands "heads" = 3/8
Probability of three coins out of three lands "heads" = 1/8
Now, let's calculate the player's expected outcome, as follows:
Four games:
Cost = 4 * 4 = $ 16
Worst-case scenario: No wins
Best-case scenario: 4 out of 4 of $ 10 win
Worst-case scenario profit or loss = 0 - 16 = Loss of $ 16
Best-case scenario profit or loss = 40 - 16 = Profit of $ 24
After four games, a player can lose up to $ 16 to win up to $ 26. These are the probabilities for every game:
1/8 or 12.5% of landing three "heads"
3/8 or 37.5% of landing two "heads"
4/8 or 50% of landing no or only one "head".
Answer:
18
Step-by-step explanation:
Substitute 9 as y. 6(9-6). Subtract: 6(3). Multiply: 18
