Question 11 [10 marks / 10 minutes]
For the mutations in the 5’ UTR of the trp operon given below, explain the effect on expression of the trp operon relative to wildtype (increased, decreased, or unchanged).
Assume medium levels of tryptophan, such that TrpR (repressor) is inactive and attenuation is active.
a) A mutation in region 2 such that it cannot bind with region 3. [4 marks]
b) A mutation in region 4 such that it cannot bind with region 3. [4 marks]
c) Insertion of T-A basepairs immediately after region 3, such that uracils are transcribed. This insertion does not change the stem-loop formation properties of regions 1, 2, 3 or 4. [2 marks]

Journalize each of the following transactions assuming a perpetual inventory system. (If no entry is required for a transaction/event, select "No journal entry required" in the first account field.) Feb. 1 Sold merchandise with a cost of $1,900 for $2,900; terms 2/10, n/30, FOB destination. 2 Paid $265 to ship the merchandise sold on February 1. 3 The customer of February 1 returned half of the amount purchased because it was the incorrect product; it was returned to inventory. 4 Sold merchandise to a customer for $4,600 (cost of sales $3,080); terms 2/10, n/30, FOB destination. 11 Collected the amount owing from the customer of February 1. 23 Sold merchandise to a customer for cash of $1,280 (cost of sales $800). 28 The customer of February 4 paid the amount owing.

1. a) Prove that if n is an odd number then 3n + 1is an even number. Use direct proof.

b) Prove that if n is an odd number then n^2+ 3 is divisible by 4. Use direct proof.

2. a) Prove that sum of an even number and an odd number is an odd number. Use direct proof.

b) Prove that product of two rational numbers is a rational number. Use direct proof.

3. a) Prove that if n2is an even number then n is an even number. Use indirect proof.

b) Prove that if n3is an odd number then n is an odd number. Use indirect proof

4. Prove that n2is an even number if and only if 3n + 1 is an odd number by proving

a) If n2is even then 3n + 1 is odd.

b) If 3n + 1 is odd then n^2 is even.

5. For each piecewise linear function, graph the function and find:      2 lim x f x      2 lim x f x (a) { ? + 3 ?? ? < 2 2? + 1 ?? ? ≥ 2 (b) ?(?) = { ? − 2 ?? ? < 2 ? + 1 ?? ? ≥ 2 6. For each piecewise linear function, graph the function and find:    x  0 lim f x    x  0 lim f x   x 0 lim f x   (a) ?(?) = −|?| + 4 (b) ?(?) = − 2|?| �

Using PYTHON. Implement the stooge sort algorithm3to sort an array/vector of integers.

Your program should be able to read inputs from a file called “data.txt” where the first value of each line is the number of integers that need to be sorted, followed by the integers

The output will be written to a file called “stooge.txt”.

Stooge sort is a “bad” recursive sorting algorithm. Given an array A, the algorithm can be defined as follows:

Step 1:

If the value at the leftmost position of the array is larger than the value at the rightmost position then swap values.

Step 2: If there are 3 or more elements in the array, then:

 Recursively call Stooge sort with the initial 2/3 of the array

 Recursively call Stooge sort with the last 2/3 of the array.

 Recursively call Stooge sort with the initial 2/3 of the array again.

Examplevalues for data.txt :

4 19 2 5 11

8 1 2 3 4 5 6 1 2

A study by Staub, 1970, was concerned with the effects of instructions to young children and their subsequent attempts to help another child (apparently) in distress. Twenty-four first-grade students were randomly assigned to one of three groups. The first group was labeled as indirect responsibility (IR). Students in the IR group were informed that another child was alone in an adjoining room and had been warned not to climb up on a chair. The second group was labeled direct responsibility one (DR1). Students in the DR1 group were told the same story as in the IR condition, but was also told that they were left in charge and to take care of anything that happened. The students were given a simple task, and the researcher left the room. The students then heard a loud crash in the adjoining room followed by a minute of sobbing and crying. Students in the third group, direct responsibility two (DR2), had the same instructions as the DR1 group, but the sounds of distress also included calls for help. Ratings from 1 (no help) to 5 (went to the adjoining room) were given to each student by an observer sitting behind a one-way mirror. The ratings are given below. Perform a one-way ANOVA in SPSS with α = .05 and answer the following questions:

PART A: Perform ANOVA analysis using SPSS and present the results in a tabular format (do not copy and paste SPSS’s output).

PART B: Calculate the effect size (w2) and interpret (in words) its meaning.

Consider a study involving turbulent water jets. Shape factor was determined for five different nozzle designs at six levels of jet efflux velocity. Researchers were particularly interested in potential differences in shape factor between nozzle designs, with jet efflux velocity considered a nuisance factor. The data for this experiment are provided below. The first column provides the nozzle design number, the second column provides the jet efflux velocity (in m/s), and the third column provides the shape factor measurement. Note that the run order is not provided. 1. Use SAS to perform ANOVA for a randomized complete block design to test for differences in the population mean shape factor among the five different designs. Use α = 0.05. Be sure to state the null and alternative hypotheses, identify the test statistic, identify the p-value for the test, determine whether to reject or fail to reject the null hypothesis, and state a conclusion within the context of the problem. 2. By hand, calculate the critical value for comparing pairs of mean using both the LSD and Tukey methods. In other words, determine Tα and LSD using the results of this experiment. HINT: Use the MSE from the SAS output to perform your calculations. 3. Determine which pairs of nozzle designs have significantly different treatment means using both the LSD and Tukey methods. NOTE: You may use the lsmeans or means statement in PROC GLM to make this determination. You do not need to perform calculations by hand. 4. Which method (LSD or Tukey’s) would you recommend using to determine significant differences among pairs of treatment means for this experiment? Clearly explain your choice. 5. Determine if the model assumptions are reasonably met. Be sure to state the assumptions of the test and identify which plot/test can be used to evaluate each assumption.