An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the probability of round seeds: 4 3 .
Calculate the probability of yellow seeds: 4 3 .
Multiply the probabilities to find the probability of round and yellow seeds: 4 3 × 4 3 = 16 9 .
The ratio of offspring with round and yellow seeds is 16 9 .
Explanation
Analyze the problem Let's analyze the problem. We have two plants with genotypes RrYy crossed together. We want to find the ratio of offspring that have round and yellow seeds. Round seeds occur if the genotype is RR or Rr. Yellow seeds occur if the genotype is YY or Yy.
Plan the solution To solve this, we can use a Punnett square. However, since we only care about the ratio of round and yellow seeds, we can calculate the probabilities separately and then multiply them.
Calculate probability of round seeds First, let's consider the R gene. We have Rr x Rr. The possible offspring genotypes are RR, Rr, rR, and rr. The probabilities are:
P(RR) = 4 1
P(Rr) = 4 1
P(rR) = 4 1
P(rr) = 4 1
The probability of round seeds (RR or Rr) is P(RR) + P(Rr) + P(rR) = 4 1 + 4 1 + 4 1 = 4 3 .
Calculate probability of yellow seeds Next, let's consider the Y gene. We have Yy x Yy. The possible offspring genotypes are YY, Yy, yY, and yy. The probabilities are:
P(YY) = 4 1
P(Yy) = 4 1
P(yY) = 4 1
P(yy) = 4 1
The probability of yellow seeds (YY or Yy) is P(YY) + P(Yy) + P(yY) = 4 1 + 4 1 + 4 1 = 4 3 .
Calculate probability of round and yellow seeds Now, we multiply the probabilities of round and yellow seeds to get the probability of offspring with round and yellow seeds:
P(round and yellow) = P(round) * P(yellow) = 4 3 ∗ 4 3 = 16 9 .
State the final answer Therefore, the ratio of offspring with round and yellow seeds is 9:16.
Examples
In agriculture, understanding the probabilities of different traits appearing in offspring is crucial for selective breeding. For example, a farmer might want to breed plants that produce high yields and are resistant to disease. By understanding the genetic ratios, they can predict the likelihood of obtaining offspring with the desired traits, optimizing their breeding strategies to improve crop production. This problem demonstrates a simplified version of how genetic traits are inherited and can be used to predict outcomes in plant breeding programs.
To find the number of electrons flowing through a device with a current of 15.0 A for 30 seconds, we first calculate the total charge using the formula Q = I × t which gives us 450 C . Then, by dividing this charge by the charge of one electron ( 1.6 × 1 0 − 19 C ), we find that approximately 2.81 × 1 0 21 electrons flow through the device.
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