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timama [110]
3 years ago
6

You cross two true-breeding parents (one with purple flowers and one with white flowers). All of the F1 progeny (offspring) have

purple flowers. You grow and self-pollinate this F1 generation and collect 500 F2 progeny. How many purple flowers should be produced?
Mathematics
1 answer:
kogti [31]3 years ago
7 0

Answer:

The correct answer is 375 purple flowers.

Step-by-step explanation:

If all the F1 generation from true-breeding parents are purple than the genotype would be heterozygous i.e., Pp and Pp. Here P indicates the dominant allele which produces purple flower and p indicates the recessive allele of white flower.

So if we will cross the F 1 generation than the genotype would be PP, Pp, Pp, pp. That means 3 out of 4 offspring would be purple because three genotypes out of four have dominant purple allele(P).

So if out of 4 flower 3 is purple than according to calculation out of 500 flower 375 offspring would be purple(3/4*500= 375). Therefore the correct answer is 375 purple flowers should be produced.

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The length of a rectangle is 6 more than twice the width. if the area is 40 cm^2, find the length and breadth of the rectangle
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Answer: 3.217 & 12.434

Step-by-step explanation:

If we use <em>w</em> to represent the width, the length will be 6 more than 2 times w.

Hence, the length is 2w+6.

The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.

A=w(2w+6)

We can also substitute 40 in for A as it's given in the question.

40 = w(2w+6)

Distributing <em>w</em> by multiplying it by both terms in the parentheses, we get

40 = 2w^2+6w

We can make the equation simpler by dividing both sides by 2.

20 = w^2+3w

Subtracting both sides by 20 will make the left-hand side 0.

0=w^2+3w-20

Now that we have put this <em>quadratic equation</em> into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.

For reference, the quadratic formula is

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

In this case, a is 1, b is 3, and c is -20.

Substituting, we get

w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}

w= \frac{-3\pm\sqrt{9+80}}{2}

w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}

Since the second solution results in a negative number, it cannot be the length of w.

w=\frac{-3+\sqrt{89}}{2}\approx3.217

The width/breadth of the rectangle is 3.217 cm.

To calculate the length, let's substitute the width into the expression for the length:

l=2(3.217)+6

l=12.434

The length of this rectangle is 12.434 cm.

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