First of all, observe that the graphed function is .

Now, if we want to shift the graph 4 units up, it means that we want each point on the graph enlarge its y coordinate by 4: we no longer want to associate

but

And since , we want to map

And in our case, , so the answer is

In paraller connection you can calculate the equivlant resistqnce from the relation :

1/R(equi) = 1/R1 + 1/R2 + 1/R3

1/R(equi) = 1/20 +1/20 + 1/10

1/R(equi) = 0.05+0.05+0.1 = 0.2

so, R(equi) = 5 ohms

The answer is 256 ,

explanation- 6+2 is 8 and 36-4 is 32. 8 times 32= 256

3. The original sequence

TAC - CGC - TTA - CGT - CTG - ATC - GCT

codes for

tyr - arg - leu - arg - leu - ile - ala

while the mutated sequence codes for

TAC - CGC - TTA - **TTA **- **TTA **- CGT - **G**<u>**CT**</u> - <u>**G**</u>**CT** - ATC - GCT

tyr - arg - leu - **leu** - **leu** - arg - <u>**ala**</u> - **ala** - ile - ala

There are several **frameshift mutations** involved here:

• the first inserts 6 bases (TTA - TTA)

• the second inserts 1 base (G) before the CTG triplet (underlined)

• the third inserts 2 bases (CT) after the CTG triplet

4. The original sequence is the same as before. The mutated sequence

TAC - CGC - **TAA** - TTA - **TTA** - CGT - **G**<u>**CT**</u>** - **<u>**G**</u>**CT** - ATC - GCT

codes for

tyr - arg - **STOP** - leu - **leu** - arg - **ala** - **ala** - ile - ala

Then

• there is a **(nonsense) point mutation** that swaps T for A in the original TTA triplet (nonsense since it produces a stop codon that would halt replication/expression)

• there is a **frameshift mutation** that inserts 3 bases (TTA)

as well as two other frameshift mutations that also occurred in the previous part.