A mixture of 4-methylphenol and 4-methylcyclohexanol was run on a TLC plate using 3:1 hexane:ethyl acetate as the eluent. Only one spot was seen using a UV lamp. Does this mean that both spots have the same R_f or is there another explanation? How might you solve this problem?

4. [5 marks] Suppose that Best Buy sells 4 TVs per day on average.

a) [1 marks] What is the probability that 8 TVs will be sold in a day?

b) [2 marks] What is the probability that fewer than 3 TVs (inclusive) will be sold in a day?

c) [2 marks] Suppose 5 customers enter Best Buy independently. The probability that a single customer will buy a TV is 0.1. What is the probability that at least one of these 5 customers buys a TV? Do not round your answer.

POS 220

Answer 4 of the following questions in approximately 4-6 sentences

1)Identify and explain the three indicators of power.

2)Identify and explain four ways the Corporate Community is powerful outside formal politics.

3)Identify and define the three components of the Policy Planning Network.

4)Identify the three organizations involved in the Opinion Molding Process and explain what each does.

5)Identify and define the 4 aspects of Hamilton's ''energetic executive.”

6)What Supreme Court case established judicial review? Identify two court cases where judicial review led to an increase in corporate power.

7)Identify and explain four ways in which Congress is restrained in its lawmaking power.

nCalculate a 95% confidence interval for the mean mileage of make 2. Use the method for single meanswhen σ is not known, but use the Error Mean Square as the estimate of the variance. The degrees of freedom will be the Error DF, not n‑1!

Reminders:

Confidence Interval = mean ± margin of error

Margin of error = critical value * standard error

Use critical value for T at a/2 = 0.025 and df = error df  (t table or EXCEL T.INV function)

Use standard error = Ö(error mean square/number of observations of that make of car)

                                                                                                                                      {Example 24}

nConduct a test of hypothesis that the mean mileage of makes 2 and 3 do not differ. Use the method for single means when σ is not knownwith the Error MS serving as the pooled variance.

Reminders:

            Test statistic t = difference of means / standard error of difference of means.

The standard error of the difference equals square root of the sumof variances of the two means. The variance of each mean is estimated by the error mean square/number of observations in that mean.

1 20.8 1 20.4 1 25.1 1 27.4 1 15.4 1 15.3 1 13.9 2 16.3 2 14.5 2 10.4 2 12.2 2 12.5 2 9.5 2 15.3 3 16.8 3 20.9 3 28.4 3 22.5 3 17.5 3 14.9 3 22.4 3 17.5 3 25.4 3 22.4 4 16.7 4 14.5 4 13.7 4 15.4 4 12.4 4 16 4 7.5 4 12.9 4 18.3  Calculate a 95% confidence interval for the mean mileage of make 2. Use the method for single means when σ is not known, but use the Error Mean Square as the estimate of the variance. The degrees of freedom will be the Error DF, not n 1! Reminders: Confidence Interval = mean ± margin of error Margin of error = critical value * standard error Use critical value for T at /2 = 0.025 and df = error df (t table or EXCEL T.INV function) Use standard error = (error mean square/number of observations of that make of car) 10. What was the margin of error for the confidence interval for gasoline mileage of make 2?

11. What was the lower 95% confidence limit for make 2 mileage?

12. What was the upper 95% confidence limit for make 2 mileage?

 Conduct a test of hypothesis that the mean mileage of makes 2 and 3 do not differ. Use the method for single means when σ is not known with the Error MS serving as the pooled variance. Reminders: Test statistic t = difference of means / standard error of difference of means. The standard error of the difference equals square root of the sum of variances of the two means. The variance of each mean is estimated by the error mean square/number of observations in that mean.

13. What is the value of the t test statistic for testing the hypothesis that makes 2 and 3 do not differ in mileage?

Convert the following pieces of code in just a single line of code. In all cases, A and B are arrays of size 5 x 5. Important: The expression "single line of code" implies a single command or equality. In other words, the code: X=A+1; X=X+B; is considered to be TWO lines.

(a) (4%) for i=1:5,

for j=1:5

A(i,j)=B(i,j)+1;

end

end

_________________________________

(b) (4%) for i=1:3

for j=2:4

A(i,j)=B(i,j);

end

end

_________________________

(c) (5%) for i=1:3

for j=2:4

A(i,j)=B(i+2,j+1);

end

end

_________________________________

(d) (4%) for i=1:5

for j=1:5

A(i,j)=1/(B(i,j))^2;

end

end

_________________________________

(e) (5%) for i=1:5

for j=1:5

A(i,j)=B(6-i,j);

end

end

_________________________________

Q 6-14 Multiple Choice In the space provided after the question #, record A if 1, 2, 3 are all correct B if 1 & 3 are correct C if 2 & 4 are correct D if 4 is only correct E if all are correct 6 During glucose tolerance testing: 1 The patient starts in a fasting state 2 Collection of blood is done at timed intervals 3 Used to detect hypo and hyper glycemia 4 Glucose is administered at timed intervals 7 Blood glucose: 1 Is low in hyperglycemia 2 Is elevated by insulin 3 Is not influenced by diet or exercise 4 Determinations are demonstrated most specifically by enzyme methods 8 The glucose renal threshold 1 Is the blood glucose concentration above which glucose is excreted in the urine 2 May differ slightly amongst individuals 3 Is a regulating effect that the kidney controls 4 Is most commonly exceeded in diabetes mellitus 9 Glucose determinations can be done on 1 Whole blood 2 Serum 3 Plasma 4 Cerebrospinal fluid 10 Normally blood sugar not oxidized at once for energy is: 1 Stored in the liver as glycogen 2 Stored in the muscles as glycogen 3 Converted to fat and stored in the adipose tissue of the body 4 Excreted by the kidneys 11 Hormones that have the effect of raising blood glucose concentrations is(are) 1 Growth hormone (GH) 2 Adrenocorticotropic hormone (ACTH) 3 Thyroxin 4 Insulin 12 Capillary blood specimens for glucose determination 1 Are used for point of care (POCT) home monitoring 2 Is thought of as venous rather than arterial blood 3 Is 5 mg/dL higher than venipuncture glucose 4 Must have anticoagulant added prior to testing 13 Blood obtained by venipuncture may show falsely decreased glucose concentration 1 Due to glycolysis 2 Due to enzymes present in blood cells 3 And may be avoided by storing as cell-free plasma 4 By using sodium fluoride anticoagulant 14 Sources of error when using blood glucose reflectance meters are 1 Variations in the amount of blood used 2 Washing and wiping of strips 3 Calibration of the meter 4 Using capillary blood rather than venous blood

The Monet Company produces four types of picture frames, which are labeled types 1, 2, 3, and 4. The four types of frames differ in size, shape, and materials used. Each type requires a certain amount of skilled labor, metal, and glass. These requirements, along with the profit for each one are shown in the table below:

During the coming week Monet has 4000 hours of labor, 6000 ounces of metal, and 10,000 ounces of glass. Also, due to market constraints, it is impossible to sell more than 1000 type 1 frames, 2000 type 2 frames, 500 type 3 frames, and 1000 type 4 frames. The company wants to maximize profits.

Formulate a linear program to determine how many of each type of frame should Monet build. Include an objective function and all constraints.

A Scrabble game has identical copies of each letter tile numbering as follows: A-9, B-2, C-2, D-4, E-12, F-2, G-3, H-2, I-9, J-1, K-1, L-4, M-2, N-6, O-8, P-2, Q-1, R-6, S-4, T-6, U-4, V-2, W-2, X-1, Y-2, Z-1 and Blanks-2. Seven tiles are randomly sampled without replacement from the above 100 tiles.If a letter appears exactly once in this seven-tile sample, we call it a singleton in this problem.

a. Consider a letter that has n copies in total (e.g., for the letter E, n=12). What is the probability that this letter is a singleton?

b. What is the expected value of the number of singletons? (Count “blank” as a letter.)

1-Prove the identity.

cosh(x) + sinh(x) = e^x

2-Prove the identity.

sinh(x + y) = sinh(x) cosh(y) + cosh(x) sinh(y)

3-Prove the identity.

sinh(2x) = 2 sinh(x) cosh(x)

4-Prove the identity.

= e^2x

5-If

tanh(x) =

,

find the values of the other hyperbolic functions at x.