The image presents three biology-related math problems. Problem VII: a. Calculate the total length of DNA molecules in human cells, given that each cell contains $6 \times 10^9$ nucleotide pairs. b. Explain how the DNA molecules, with such a length, can fit within the nucleus of a cell, which has a diameter of only 2-3 thousandths of a millimeter. Problem VIII: Given that a single strand of DNA contains $3 \times 10^4$ nucleotides: a. Determine the number of free nucleotides needed when the DNA molecule replicates twice. b. If Cytosine constitutes 14% of the nucleotides in a DNA molecule, calculate the number of each type of nucleotide in the molecule. c. Assuming this DNA molecule is used as a template, determine how many mRNA molecules are needed if each mRNA molecule contains an average of $10^4$ nucleotides.

1. Problem Description

The image presents three biology-related math problems.

Problem VII:

a. Calculate the total length of DNA molecules in human cells, given that each cell contains $6 \times 10^9$ nucleotide pairs.

b. Explain how the DNA molecules, with such a length, can fit within the nucleus of a cell, which has a diameter of only 2-3 thousandths of a millimeter.

Problem VIII:

Given that a single strand of DNA contains $3 \times 10^4$ nucleotides:

a. Determine the number of free nucleotides needed when the DNA molecule replicates twice.

b. If Cytosine constitutes 14% of the nucleotides in a DNA molecule, calculate the number of each type of nucleotide in the molecule.

c. Assuming this DNA molecule is used as a template, determine how many mRNA molecules are needed if each mRNA molecule contains an average of $10^4$ nucleotides.

2. Solution Steps

Problem VII a:

We need to find out the total length of the DNA molecules. We are given the number of base pairs as $6 \times 10^9$. We need to know the length of a base pair to compute the total length. However, the length per base pair is not provided. Thus, we cannot proceed with the calculation without this information.

Problem VII b:

This is a conceptual question and does not involve math. The reason the DNA can fit inside the cell nucleus is because of its highly condensed and folded structure. The DNA wraps around histone proteins to form nucleosomes. These nucleosomes are further coiled into chromatin fibers, which are then further condensed into chromosomes. This hierarchical packaging allows a long DNA molecule to fit within the tiny nucleus.

Problem VIII a:

Each single strand has $3 \times 10^4$ nucleotides. A DNA molecule is double-stranded, so each molecule has $2 \times 3 \times 10^4 = 6 \times 10^4$ nucleotides.

For each replication, the DNA molecule needs $6 \times 10^4$ nucleotides from free nucleotides. If it happens twice, we would require $2 \times 6 \times 10^4 = 12 \times 10^4 = 1.2 \times 10^5$ free nucleotides.

Problem VIII b:

If Cytosine (C) constitutes 14% of the nucleotides, then Guanine (G) also constitutes 14%. Thus, C + G = 28%. The remaining percentage is for Adenine (A) and Thymine (T).

A + T = 100% - 28% = 72%. Since A = T, each constitutes 36%.

The total number of nucleotides in the double-stranded DNA is $6 \times 10^4$.

Number of Cytosine = 0.14 * $6 \times 10^4 = 0.84 \times 10^4 = 8.4 \times 10^3 = 8400$

Number of Guanine = 0.14 * $6 \times 10^4 = 0.84 \times 10^4 = 8.4 \times 10^3 = 8400$

Number of Adenine = 0.36 * $6 \times 10^4 = 2.16 \times 10^4 = 21.6 \times 10^3 = 21600$

Number of Thymine = 0.36 * $6 \times 10^4 = 2.16 \times 10^4 = 21.6 \times 10^3 = 21600$

Problem VIII c:

The double-stranded DNA has $6 \times 10^4$ nucleotides.

Each mRNA has $10^4$ nucleotides.

Number of mRNA molecules needed = ($6 \times 10^4$) / ($10^4$) = 6

3. Final Answer

Problem VII a: Cannot be solved without the length of a base pair.

Problem VII b: DNA is highly condensed and folded.

Problem VIII a: $1.2 \times 10^5$

Problem VIII b: Cytosine = 8400, Guanine = 8400, Adenine = 21600, Thymine = 21600

Problem VIII c: 6