1. Of the eggs produced by salmon, 80% hatch, and of those, 25% survive to migrate to the ocean. How many eggs are needed to produce 100 salmon that migrate to the ocean?
2. The sequence 2, 7, 12, a, b, 27 is arithmetic. What is the value of a + b?
3. Define a $ b to be a(b + 1) + ab. What is the value of (-2) $ 3?
4. The ants in a colony of African ants average one centimeter in body length. The ants in this colony, lined up end to end, stretch one kilometer. How many ants are there in the colony? Express your answer in scientific notation.
Agni- you were going to teach us how to do #3 on Monday (11-29) but you never got around to it. We have never seen this notation before. I just guessed we were supposed to be plugging -2 in for a and 3 in for b. What is the deal with the dollar signs, though? My answers are:
I would like to let you know that the use of calculators on these types of problems are not permitted.
For example, for problem 5, leave the answer in lowest fractional form. Don't bother to convert your answer to a decimal. Think about cancelling common factors in the numerator and denominator.
2. Clearly the common difference is 5 so we keep on adding 5 to get a and b. We find that a = 17 and b = 22 and their sum is 17 + 22 = 39
3. First, we go back to the equation with the variable. We can distribute, and get: ab + a + ab
Combining like terms, you get: 2ab + a
Then, we can plug in our numbers and get: 2 × (-2) × 3 + (-2) = -12 – 2 = -14
4. There are 100 centimeters in a meter, and 1000 meters in a kilometer, so there are 100000 centimeters in a kilometer. In scientific notation, this is 1 ∙ 10^5
5. Factor out 8! from the top and bottom. You get:
Problems
ReplyDelete1. Of the eggs produced by salmon, 80% hatch, and of those, 25% survive to migrate to the ocean. How many eggs are needed to produce 100 salmon that migrate to the ocean?
2. The sequence 2, 7, 12, a, b, 27 is arithmetic. What is the value of a + b?
3. Define a $ b to be a(b + 1) + ab. What is the value of (-2) $ 3?
4. The ants in a colony of African ants average one centimeter in body length. The ants in this colony, lined up end to end, stretch one kilometer. How many ants are there in the colony? Express your answer in scientific notation.
5. Calculate:
(10!-8!)/(10!+8!)
Express your answer as a common fraction.
Have fun working out the problems!
Auryan,
ReplyDeleteTo be able to make a comment, click the link Follow on the right hand side of this page. Then, sign in with your yahoo or google email account.
Hope this helps!
Agni
Actually, I tried all of them, but I can't get #3 or #5.
ReplyDeleteMy answers:
1) 168
2) 39
3) No idea
4) 1*10^5
5) I don't know how to do factorials.
Actually Agni, I figured out #5. Is the answer 0.97802198 ?
ReplyDeleteWell done, Nidhi! Problems 2 and 4 are correct. Check over your work for problems 1 and 3.
ReplyDeleteI will explain factorials soon.
You deserve a treat! :)
Agni
Practicing math problems is the only way to get better at math!
ReplyDeleteEveryone, keep working! I'll be available for help if you need any.
Factorials
ReplyDeleten! = 1 × 2 × 3 × ... × n
Example: Evaluate 6!.
1 × 2 × 3 × 4 × 5 × 6 = 720
We'll discuss more factorial problems in the meetings.
1)500 eggs
ReplyDelete2)39
4)1 x 10^5
5)89/91
I will keep trying to solve #3
But, is my answer to #5 correct?
ReplyDeleteOh, and I tried #1 again and I got 502. Is that correct?
ReplyDeleteNidhi, your answer to number 5 is correct. Well done! I will show you an easier way to do it without using a calculator.
ReplyDeleteKeep trying problem 1.
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Vishal, great job!
Hint (Problem 3): Look for the numbers that you can substitute for a and b; then solve.
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Anyone who would like to earn a treat, please post your answers before 10 P.M. today!
This comment has been removed by the author.
ReplyDeleteHere are my answers:
ReplyDeleteI didn't get #3. The wording messed with my brain.
1) 500 eggs
2) 39
3)?!?!?!
4)1 x 10^5
5) 89/91 or 0.978021978
Neha, great work!
ReplyDelete--------------------------------------------------
Everyone, work on number 3 - it's not hard! Reread the hint.
I actually got 500 (for #1).
ReplyDelete1) 500 eggs'
ReplyDelete2) 39
3. ? ( can u discuss this)
4. 1 x 10^5
5) 0.97802198
This comment has been removed by the author.
ReplyDeleteI tried #3 one more time and is it -8?
ReplyDeleteAgni- you were going to teach us how to do #3 on Monday (11-29) but you never got around to it. We have never seen this notation before. I just guessed we were supposed to be plugging -2 in for a and 3 in for b. What is the deal with the dollar signs, though? My answers are:
ReplyDelete1. 500 eggs
2.39
3. -14
4.10^6
5. 0.978021 repeating
1. 500
ReplyDelete2. 39
3. $-8 (not sure)
4. 1*10^5
5. 89/91 or 0.978021978
I found out the answer to #3,
ReplyDeleteIt is -14
This comment has been removed by the author.
ReplyDeletea $ b = a(b+1) + ab
ReplyDeletesubstitute....
(-2) $ 3 = -2 (3+1) + (-2)(3)
= -8 - 6
= -14
This comment has been removed by the author.
ReplyDeleteAgni,
ReplyDeleteHere are my answers:
1)500 eggs
2)39
3)-14
4)1*10^5
5)0.97802198
Great participation, everyone!
ReplyDeleteNMS Math Team ROCKS!
Good solutions for problem 3, Avanthika and Grace! I'm sure you guys all got it now. The final solutions will be posted at 10 P.M.
Grace, if I ever miss out on explaining anything, remind me at the meeting.
I'm proud of you all! :)
I would like to let you know that the use of calculators on these types of problems are not permitted.
ReplyDeleteFor example, for problem 5, leave the answer in lowest fractional form. Don't bother to convert your answer to a decimal. Think about cancelling common factors in the numerator and denominator.
Solutions
ReplyDelete1. 100 ÷ 0.25 = 400
400 ÷ 0.8 = 500
2. Clearly the common difference is 5 so we keep on adding 5 to get a and b. We find that a = 17 and b = 22 and their sum is 17 + 22 = 39
3. First, we go back to the equation with the variable. We can distribute, and get: ab + a + ab
Combining like terms, you get: 2ab + a
Then, we can plug in our numbers and get:
2 × (-2) × 3 + (-2) = -12 – 2 = -14
4. There are 100 centimeters in a meter, and 1000 meters in a kilometer, so there are 100000 centimeters in a kilometer. In scientific notation, this is 1 ∙ 10^5
5. Factor out 8! from the top and bottom. You get:
(8!(10×9-1))/(8!(10×9+1))= 89/91
Where are the problems for next week?
ReplyDelete