Hardy-weinberg Principle - Ques from Topscore 2

[thakdha]

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According to the Hardy-Weinberg principle, if there are only two eye colors: brown and blue
and 25% of the population have recessive blue eyes, what percentage of the population is
heterozygous for brown eyes?
A. 50%, B. 100%, C. 12.5 %, D. 75% E. 25%

Solution:

brown eyes:
p - BB Homozygous dominant
Bb Heterozygous

blue eyes:
q - bb Homozygous recessive = 0.25

p = 1-q = 0.75

p^2 = 0.75 * 0.75 = 0.56
2pq = 2 * 0.75 * 0.25 = 0.375
q^2 = 0.25 * 0.25 = 0.0625

The correct answer for the above question is 50%. I don't understand how did they get that answer. Am I doing something wrong in my calculations?

Also, one more question from QR section
2.
A roof is 45 feet wide and 35 feet long. Each shingle covers an area that is 16 inches wide and 8 inches long. Each 5 gallon pail of tar covers 102 square feet of roof. How many shingles
and pails of tar should you purchase to roof the house?
A. 15 pails, 1771 shingles
B. 16 pails, 1772 shingles
C. 17 pails, 1772 shingles
D. 1 pails, 1821 shingles
E. 17 pails, 1821 shingles

Does anyone know the quickest way to solve these kind of problems?

Please help. Thanks.

 

[mobius]

25% is homo zyqous leaving 50% as hetero 1:2:1 ratio

for the second one i calculated the first part leaving only two answer it could be and guessed the second.... ot the best way but i got it right. actually i first tried to do it and got frustrated and guessed...

 

[Sk8aBull]

For the math problem... I believe the answer is B. This is how i figured it out.

First, I found the area of the rooftop: 45 x 35 = 1575 square feet

Then, one 5 gallon can of tar covers 102 sq ft. So, to find how many cans I'd need, I divided total sq. ft of the house by 102. That gives 15.4 since you need more than 15 cans, I rounded it up to 16. There is only one answer choice with 16, so I would go with that.

But, I wanted to make sure. Finding the area of a shingle (16 x 8), it is 128 square inches. One sq ft is 144 sq inches. dividing 128/144 tells you that one shingle is .8888 of a square foot. Dividing the Total area of the roof by how many sq ft a shingle covers (1575/.8888) yields 1772 shingles for the roof.

So, it fits B. 16 cans, 1772 shingles.


If I'm wrong, please let me know....

 

[thakdha]

B is the correct answer. I didn't think I would get reply this quick. Thanks for the instant response.

 

[drat]

According to the Hardy-Weinberg principle, if there are only two eye colors: brown and blue
and 25% of the population have recessive blue eyes, what percentage of the population is
heterozygous for brown eyes?
A. 50%, B. 100%, C. 12.5 %, D. 75% E. 25%

Solution:

brown eyes:
p - BB Homozygous dominant
Bb Heterozygous

blue eyes:
q - bb Homozygous recessive = 0.25

p = 1-q = 0.75

p^2 = 0.75 * 0.75 = 0.56
2pq = 2 * 0.75 * 0.25 = 0.375
q^2 = 0.25 * 0.25 = 0.0625

The correct answer for the above question is 50%. I don't understand how did they get that answer. Am I doing something wrong in my calculations?

It's been awhile since I did this principle, but I think q^2 = 0.25, therefore q = 0.5. Then your equation, p = 1 - q would make p = .5 and p^2 = 0.25

p^2 + 2pq + q^2 = 1
0.25 + 2pq + 0.25 = 1
2pq = .5 or 50%

Someone double check me. Don't have my book here to look it up. 😉

 

[drusier]

I found that u can pick up some xtra time on math problems like this. Basically this is two problems, so look at the answers and find that one that is different from the others. Just as Sk8aBul did, work out the tar section first then return if you have more time to varify by working the other problem # of shingles...

 

[BigRed12]

drat I believe you are right on that...p^2=.25, not p=.25

 

[gabrielmeraz]

Yeah thadka the question is already telling us that the population is homozygous recesive for blue eyes (i.e. bb) hence the expresion has already been squared q^2. And that's the only trick so you just have to square the percentage to get q and then subtract that to 1. p=1-q and then its simple. 🙄

 

[x-linked]

A roof is 45 feet wide and 35 feet long. Each shingle covers an area that is 16 inches wide and 8 inches long. Each 5 gallon pail of tar covers 102 square feet of roof. How many shingles
and pails of tar should you purchase to roof the house?
A. 15 pails, 1771 shingles
B. 16 pails, 1772 shingles
C. 17 pails, 1772 shingles
D. 1 pails, 1821 shingles
E. 17 pails, 1821 shingles

Does anyone know the quickest way to solve these kind of problems?

Please help. Thanks.

i think this question is totally wrong. i am not sure though. it asks How many shingles and pails of tar should you purchase to roof the house, so what i do is 45*35(total area) divided by 102, then it is 15.4 something, so i think it should be 15 pails, then 45*35-102*15==45 sq ft. then i multiply this by 144 then divied by 128, which is the area of shingle. apparently no choice here!!

but if it was B, the question should ask how many pails or shingles 😕 😕

 

[gabrielmeraz]

I think this problem involves looking at the answer choices. If the choices give the amount of pails of tar as the first part of the answer, then its is imperative we go and solve for the number of cans we need to cover the roof. If you try and go solve for the number of shingles, you will be faced with a lengthy and tedious division. I know, its tricky tricky tricky

 

[joy2dmd]

I think this problem involves looking at the answer choices. If the choices give the amount of pails of tar as the first part of the answer, then its is imperative we go and solve for the number of cans we need to cover the roof. If you try and go solve for the number of shingles, you will be faced with a lengthy and tedious division. I know, its tricky tricky tricky

I agree here. I did quick "guess" math on this one.
45x35=1575. Divide by 102 gives me 15 but less than 16. I can't buy a 1/2 pail so it's 16. Now there are two choices left. I know it's 128 sq inches per shingle. 128/144 is .88 so 1575 div by .88 is 17..., so it's B.

I think the key here is the pails first. Know that you can't buy a partial pail at HomeDepot. Then a quick two digit division (note it was a repeating). Since the shingles were relative close in number, I figured a .81 would be different than .89. I was right.