2. In 2016, the Centers for Disease Control and Prevention reported that 36.5% of adults in the United
States are obese. A county health service planning a new awareness campaign polls a random sample
of 750 adults living there. In this sample, 228 people were found to be obese based on their answers
to a health questionnaire. Do these responses provide strong evidence that the 36.5% figure is not
accurate for this region? Use a significance level of 5% to test your hypothesis.
a) Define the parameter of interest.
b) State the hypotheses statements.
c) Check that the conditions have been met and name the significance test to be used.
d) Perform the test and show all work.
e) Interpret the P-value and state your conclusion.
f) Calculate and interpret a 95% confidence interval.
g) Describe what a Type I and Type II error would be in the

The PFK1 enzyme is regulated by a number of factors in the cell, including the level of ATP. ATP is not only

involved in the reaction the enzyme catalyses but also binds to an allosteric site leading to a reduction in

activity.

The binding of ATP can be measured using a fluorescently labelled derivative of ATP – TNP-ATP. The data

presented below represents the determination of the binding of ATP to PFK. The change in fluorescence (?

fluor.) represents the concentration of PFK1 with TNP-ATP bound. This value was determined at 5

different concentrations of TNP-ATP, and the experiment was carried out in triplicate.

a) Create a double reciprocal plot of this data (1/[TNP-ATP] vs. 1/ ? fluor.). Plot the data from

each experiment as a separate dataset on the same graph. Only plot the data points – do

not join data points with lines. Ensure that each dataset is distinct from the others (use

alternate colours and/or shapes for the data points).

b) Fit an equation to each dataset separately. Do not show these on your plots. For each

experiment give the fitted equation and the value of Kd. Show these in a table. Ensure you

include the units of this value. Show your working for the Experiment 1 data.

c) Determine the mean and standard deviation of the data for each concentration of TNPATP.

Show these in a table. Transform this data as you have done in (a). Fit an equation to

the transformed data. Give the fitted equation and the calculated Kd for the averaged

data. Add a trendline defined by this equation to your graph.

d) With reference the data you plotted and Kd values you determined, explain the positive

and negative aspects of using a double reciprocal plot.

Let V = {P(x) ∈ P10(R) : P'(−4) = 0 and P''(2) = 0}. If V= M_3×n(R), find n.

Ed's utility from vacations (V) and meals (M) is given by the function
U(V,M) = V2M. Last year, the price of vacations was $200 and the price of meals
was $50. This year, the price of meals rose to $75, the price of vacations remained
the same. Both years, Ed had an income of $1500.
a. Set up a Lagrangian to solve utility maximization problem with initial
price and find equilibrium.
b. When price of meals increased repeat the a and find equilibrium.
c. Show both equilibrium in the graph. Place vacation on the vertical axis
and meals on the horizontal axis.
d. show the compensating variation for price change in meals in the graph.
e. Calculate compensating variation as numeric number for the price
change in meals. (Hint: Use expenditure function)
f. Calculatethe equivalent variation as numeric number for the price
change in meals.

Calculate the vibrational energy difference, in cm-1, between the v=0 and v=1 energy level in a hydrogen chloride-35 molecule. Isotope masses to three decimal places are taken from NIST and force constants from hyperphysics. Use the isotope mass, not the average mass.

For the following unbalanced 3Φ voltages V_a = 240/15° V, V_b = 340/-65° V, V_c = 400/105°V calculate:   

1. the positive sequence component V_a1

[Insert answer here]

2. the negative sequence component V_a2

[Insert answer here]

3. the zero sequence component V_a0

[Insert answer here]

4. show V_a1 + V_a2 +V_a0 = V_a

[Insert answer here]

4.11)The equivalent circuit parameters of a 150 kVA, 2400 V/ 240 V, 60 Hz transformer are as follows:

RHV = 0.21Ω, RLV = 2mΩ, XlHV = 0.45Ω, XlLV = 4.6mΩ, XmHV = 1.6kΩ, and RcHV = 12kΩ.

The transformer delivers to a load, rated current at a power factor of 0.85 lagging at rated voltage. Determine the input voltage, current, apparent power and power factor, (a) using the approximate equivalent circuit, and (b) not using the approximate equivalent circuit.

Problem 4.12 For the transformer in problem (4.11), determine the efficiency when operating with, 1. rated current, rated voltage and lagging power factor of 0.8, 2. 80% of rated current, rated voltage, and unity power factor. Problem

4.13 Calculate the voltage regulation of the transformer in problem (4.11) when delivering,

1. rated current at 0.9 lagging power factor,

2. rated current at unity power factor, and

Ed's utility from vacations (V) and meals (M) is given by the function U(V,M) = V2M. Last year, the price of vacations was $200 and the price of meals was $50. This year, the price of meals rose to $75, the price of vacations remained the same. In both years, Ed had an income of $1500. Calculate the ΔCS, CV, and EV from the change in meal prices.

(1) Run Prim's algorithm and Kruskal's algorithm for the following graph:

G(V, E)
where V = {A, B, C, D, E}
E = { {A,B}, {B,C}, {C, A}. {B, D}, {B, E}, {D, E}}
use edge weights: w({A, B} = 1), w({B, C}) = 2, w({C, A}) = 3, w({B, D}) = 4, w({B, E}) = 5, w({D, E}) = 6.

(2) Can the maximum weight edge be in every minimum spanning tree of a graph?