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Complete Question:
The container of a breakfast cereal usually lists the number of calories and the amounts of protein, carbohydrate, and fat contained in one serving of the cereal. The amounts for two common cereals are given below. Suppose a mixture of these two cereals is to be prepared that contains exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat. a. Set up a vector equation for this problem. Include a statement of what the variables in your equation represent. b. Write an equivalent matrix equation, and then determine if the desired mixture of the two cereals can be prepared.
Nutrient General mills cheerios Quaker 100% Natural cereal
Calories 110 130
Protein (g) 4 3
Carbohydrate (g) 20 18
Fat (g) 2 5
Solution:
Representation of data in equation.
x1 is the number of servings of Cheerios and
x2 is the number of servings of Natural Cereal
110
+ 130
= 295
4 + 3 = 9
20 + 18 = 48
2 + 5 = 8
Representation of data in vector equation,
![\left[\begin{array}{ccc}110\\4\\20\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D110%5C%5C4%5C%5C20%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
+ ![\left[\begin{array}{ccc}130\\3\\18\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D130%5C%5C3%5C%5C18%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D295%5C%5C9%5C%5C48%5C%5C8%5Cend%7Barray%7D%5Cright%5D)
Equivalent matrix equation of data
![\left[\begin{array}{ccc}110&130&295\\4&3&9\\20&18&48\\2&5&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D110%26130%26295%5C%5C4%263%269%5C%5C20%2618%2648%5C%5C2%265%268%5Cend%7Barray%7D%5Cright%5D)
Row reduce the matrix
≅ ![\left[\begin{array}{ccc}1&0&1.5\\0&1&1\\0&0&0\\0&0&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%261.5%5C%5C0%261%261%5C%5C0%260%260%5C%5C0%260%260%5Cend%7Barray%7D%5Cright%5D)
1.5 serving of cherrios with 1 serving of natural cereal requried to make desired mixture.
= 1.5 , = 1
a) + =
b) = 1.5 , = 1
The ionosphere<span> can reflect radio waves directed into the sky back toward the Earth. </span>
Answer:
Option (d).
Explanation:
Mutation may be defined as the sudden, heritable change in the nucleotide sequence of the organism. Mutation may occur due to the errors in DNA replication or may occurs due to the mutagens.
Joshua and Lederberg experiment explains that mutation is the non adaptive and random process that occur in the organism. He used the replica plating of E.coli and grows them on streptomycin drug. The bacteria was grown on the the primary plate and they are transferred to the secondary plate with streptomycin drug in the growth environment. The resistant strain of bacteria grows in the streptomycin environment.The pattern of bacteria growth on the plate explained that mutation occurs randomly and it is a non adaptive process.
Thus, the correct answer is option (d).
Answer:
Since there is no distinction in the measure of the RNA polymerases yet rather their movement, the distinction lies in their structure and not their grouping. Adjustments are made to widen the states of endurance. Thus E. coli would not constrain it's endurance by restricting its development to hotter temperatures. Thus the appropriate response is "the RNA polymerase sub-units of the P. syringe strain most likely have additional adaptability with the goal that they can move all the more openly in colder temperatures".
