1. What is the units digit of the product of all of the odd integers between 0 and 12?
2. The side length of a square is 16 cm long. The midpoints of each side are joined to form a second square. The process of joining the midpoints of the sides of the innermost square is repeated. What is the number of centimeters in the perimeter of the fifth square?
3. A British television program shows homes that are for sale. One home is listed as costing 500,000 pounds, or $850,000. The ratio of pounds to dollars used in this TV program can be written in the form “1 pound : x dollars.'' What is the value of x? Express your answer as a decimal to the nearest tenth.
4. A dose of a shrinking potion makes a person 50% smaller than they were before they drank it, and eating a growth cake makes a person 50% larger than they were before they ate it. After drinking 2 doses of shrinking potion and eating 1 growth cake, what is the ratio of Alice's final size to her original size? Express your answer as a common fraction.
5. A right isosceles triangle has a hypotenuse with measure 18 centimeters. What is the length, in centimeters, of one leg of the triangle? Express your answer in simplest radical form.
6. How many even positive divisors does the number 180 have?
1. 5 2. 16cm 3. 1.7 4. 1/2 I know she is 50% less of her original size, but I am not sure whether or not the fraction is right. 5. 3 cm 6. 12 divisors:2,4,6,10,12,18,20,30,36,60,90,180
Neha, try problems 4 and 5 again. Also, try to think of another way to solve problem 6. Your way is fine, but it would be long and tedious if there was a bigger number to work with. It would be easy to miss some factors along the way.
Here are the size ratios from final to original for each sip she takes of each potion/growth cake:
x → x/2 → x/4 → x/4 + x/8 → 3x/8
Therefore, the answer is 3/8.
5. Call the one leg of the isosceles right triangle x. By the Pythagoras Theorem, you can say that:
2x² = 18²
Solving for x, we have x = √162 = 9√2
6. 180 = 3² ∙ 2² ∙ 5
To make a number even, we must have at least one power of two. Therefore, there are 3 choices for the power of 3 (0, 1, 2), 2 choices for 2 (1 or 2), and 2 choices for the 5 (0 or 1).
Problems
ReplyDelete1. What is the units digit of the product of all of the odd integers between 0 and 12?
2. The side length of a square is 16 cm long. The midpoints of each side are joined to form a second square. The process of joining the midpoints of the sides of the innermost square is repeated. What is the number of centimeters in the perimeter of the fifth square?
3. A British television program shows homes that are for sale. One home is listed as costing 500,000 pounds, or $850,000. The ratio of pounds to dollars used in this TV program can be written in the form “1 pound : x dollars.'' What is the value of x? Express your answer as a decimal to the nearest tenth.
4. A dose of a shrinking potion makes a person 50% smaller than they were before they drank it, and eating a growth cake makes a person 50% larger than they were before they ate it. After drinking 2 doses of shrinking potion and eating 1 growth cake, what is the ratio of Alice's final size to her original size? Express your answer as a common fraction.
5. A right isosceles triangle has a hypotenuse with measure 18 centimeters. What is the length, in centimeters, of one leg of the triangle? Express your answer in simplest radical form.
6. How many even positive divisors does the number 180 have?
Have fun!!
I am not sure if all of them are right but here they are:
ReplyDelete1) 5
2) Perimeter=4, Side Length=1
3) 1.7
4) I am working on it
5) 3
6) 5
1. 5
ReplyDelete2. 16cm
3. 1.7
4. 1/2 I know she is 50% less of her original size, but I am not sure whether or not the fraction is right.
5. 3 cm
6. 12 divisors:2,4,6,10,12,18,20,30,36,60,90,180
P.S.- I also got a prize last week! :)
I just checked my work and for #6 I got 12 divisors.
ReplyDelete1)5
ReplyDelete2)perimeter=2
3)1.7
4)1:2
5)6
6)12
I still doubt i got #4 right.
You guys are so prompt about posting your answers! Keep up the good work.
ReplyDelete--------------------------------------------------
Nidhi, check problems 2 and 5. For problem 2, try drawing the diagram again.
For problem 5, assign a variable to represent the side length of one leg of the triangle and then make an equation using the Pythagorean Theorem.
Keep trying problem 4. Take any number for Alice's size and then follow the directions in the problem.
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Neha, try problems 4 and 5 again. Also, try to think of another way to solve problem 6. Your way is fine, but it would be long and tedious if there was a bigger number to work with. It would be easy to miss some factors along the way.
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Vishal, look over your work for problems 2, 4, and 5. Use the hints provided above.
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Everyone, please post your answer, along with your solution, to problem 2.
Neha, I was referring to the treat for Week 12/6. Other than that, you did earn a prize. :) You're doing great!
ReplyDelete2)a=square 1, b=square 2(etc.)
ReplyDeletea=2b
b=2c
c=2d
d=2e
a=16
b=8
c=4
d=2
e=1
1+1+1+1=4
perimeter=4
4)For example 16 is the original height
16 - 1/2 x 16 = 16 - 8 = 8
8 - 1/2 x 8 = 8 - 4 = 4
4 + 1/2 x 4 = 4 + 2 = 6
6 : 16
Answer 3 : 8
I am working on 5
Vishal, check problem 2. The area of the square is not halved each time.
ReplyDeleteFor problem 4 - Your answer is correct.
When dealing with percents, use a number that is easy to work with, like 100.
Neha, please provide your solution for problem 2.
ReplyDeleteFor the ratio on problem 4, is it 3:8 ?
ReplyDeleteSolutions
ReplyDelete1. The set contains a 5, and any odd number times a number with units digit 5 ends in 5.
2. Sides: 16, 8√2, 8, 4√2, and 4
Perimeter: 4 × 4 = 16
3. 500,000 pounds : 850,000 dollars
1 pound : 850,000/500,000 dollars
1 pound : 1.7 dollars
4. Think of Alice's original size as x:
Here are the size ratios from final to original for each sip she takes of each potion/growth cake:
x → x/2 → x/4 → x/4 + x/8 → 3x/8
Therefore, the answer is 3/8.
5. Call the one leg of the isosceles right triangle x. By the Pythagoras Theorem, you can say that:
2x² = 18²
Solving for x, we have x = √162 = 9√2
6. 180 = 3² ∙ 2² ∙ 5
To make a number even, we must have at least one power of two. Therefore, there are 3 choices for the power of 3 (0, 1, 2), 2 choices for 2 (1 or 2), and 2 choices for the 5 (0 or 1).
There are 3 ∙ 2 ∙ 2 = 12 even factors.
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Nidhi, Neha, and Vishal, great work done! Keep it up!!
1. 5
ReplyDelete2. don't know
3. 1.7
4. 3/8
5. 12.73
6. 12
I'm sorry I'm late, I didn't look at the answers.
1.5
ReplyDelete2. 16
3.1.7
4. 3/8
5. 9 (square root)2
6. 12