Dr. Beadle conducted an experiment to determine how many genes control the differences between maize and teosinte. He crossed teosinte with maize (the two parental plants) to produce F1 hybirds, and then crossed the F1 plants to produce an F2 generation (offspring). He then looked at the appearance, or phenotype of the offspring. Based on classical genetics, he predicted if just one gene was responsible for all the differences between maize and teosinte, a parental phenotype was expected in one of every four offspring—in other words ¼ of the offspring would look like maize and ¼ would look like teosinte. If two genes are involved, one out of every 16 offspring would look like maize and one out of 16 like teosinte.
This relationship can be summarized by this equation: X = (¼)n
a. In the equation above, X represents the proportion of offspring expected to have a parental phenotype.
What does n represent?
b. Dr. Beadle planted 50,000 plants and discovered that 1 out of 500 offspring had the phenotype of one
parent and 1 out of 500 of the other parent. Approximately how many plants had a teosinte phenotype?
A maize phenotype? What phenotype(s) did the rest of the plants have?
c. Use the equation X = (¼)n to explain how Dr. Beadle came to conclude that four or five genes are
responsible for the differences between maize and teosinte.
d. Explain how changes in a small number of genes can result in very different-looking plants.

Step-by-step explanation:

A. In the equation, the n represents the no. of genes involved. If n =1, a single gene is responsible, then X= (1/4)^1= 1/4 offsprings will be of one parental type.

B. Out of 50,000 plants, 1 out of 500 had maize phenotype and another 1 out of 500 terosinte phenotype.

So 1 in 500 so how much in 50000?

1*50000/500 = 100.

100 plants are of terosinte and 100 are of maize phenotype. The rest plants have recombinant phenotype. The exact phenotypes cannot be told from the given information.

C. According to formula, if 2 genes are involved, then 1 in 16 will be of one parental type. If genes 4 are involved, then 1 in 4^4= 1 in 256 will be of one parental type. If 5 genes are involved then it will be 1 in 512 plants will be of parental type. On the question, every 1 in 500 plants have one parental type. Hence Dr.Beadle concluded that 4 or 5 genes are involved in the phenotypic difference.

D. Genes code for all physical characteristics of an organism. Changes to genetic material can result in far reaching consequences in one or more particular metabolic pathways, this results in different phenotype compared to parents. Genes can mask other genes effect, complement it, or supplement it resulting in diverse response. The genes can also act in additive manner called quantitative genetics. Certain gene upon expression can block other genes expression, called epistasis. Such diverse mechanism can result in very different looking plants even with changes in small number of genes.

256π units²   (answer b)

step-by-step explanation:

the formula for the surface area of a sphere of radius r

is             a = 4πr²

and so, if r = 8 units, then the surface area is:

a = 4π(8 units)² = 256π units²   (answer b)

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363