Solve the recurrence relation with the given initial conditions.

b₀ = 0, b₁ = 4, b_n = 2b_{n ? 1} + 2b_{n ? 2} for n ? 2

Check whether the following families of functions of t are linearly independent or not

(a) t^2 + 1, 2t, 4(t + 1)^2

(b) sin(t) cos(t), sin(2t) + cos(2t), cos(2t)

(c) e^2t , e^-2t , 2e^t

(d) 2e^t , 3 cosh(t), 13 sinh(t)

(e) 1/((t^2)-1) , 1/(t + 1), 1/(t-1)

The parking authority in downtown Halifax reported the following information for a sample of 240 customers on the number of hours cars are parked and the amount they are charged: Number of Hours Frequency Amount Charged 1 23 $2 2 41 4 3 54 6 4 41 8 5 38 10 6 11 14 7 6 18 8 26 20 Total 240 a-1. Convert the information on the number of hours parked to a probability distribution. (Round the final answers to 3 decimal places.) Hours Probability 1 2 3 4 5 6 7 8 a-2. Is this a discrete or a continuous probability distribution? b-1. Find the mean and the standard deviation of the number of hours parked. (Round the final answers to 3 decimal places.) Mean Standard deviation b-2. How would you answer the question, how long is a typical customer parked? (Round the final answer to 3 decimal places.) The typical customer is parked for hours. c. Find the mean and standard deviation of the amount charged. (Round the final answers to 2 decimal places.) Mean Standard deviation

Correlations

1. A correlation is a:

2. A perfect positive correlation of +1.00 means that:

3. A correlation of .00 means that:

4. A correlation of -1.00 means that:

5. The frequencies on a communication task are listed below. The hypothesis being tested is also provided. Fill out the chart below and follow the 12 steps on page 348 to compute the correlation coefficient (r), test r against its critical value at the .05 significance level, answer the hypothesis, and interpret your findings.

H_alt:      When people are giving directions, the number of hand movements will be positively correlated to the number of facial expressions.

1. Step 6:
2. Step 7:
3. Step 8:
4. r =
5. df =
6. Critical r =
7. Interpretation:

Suppose that the denomination of the coins in a country are c1 > c2 > . . . cn (e.g. 25, 10, 5, 1 for the United States). The problem to consider is: Given an integer a, find the minimum number of coins needed to make a-cents change. (We assume c1 = 1 and we have unlimited supply of each of the coin types, so that it is always possible to make change for any amount a.) For example, let c3 = 4, c2 = 2, c1 = 1 and a = 6. Then there are 6 distinct ways to make 6-cents change: (6 = 6 × 1, 6 = 4 × 1 + 2, 6 = 1 + 1 + 2 + 2, 6 = 2 + 2 + 2, 6 = 1 + 1 + 4, 6 = 2 + 4). So the answer for this problem instance is 2 coins. (a) A simple heuristic strategy for solving this problem is the following: Always pick the coins with the largest value. For example, for US coins, c1 = 1, c2 = 5, c3 = 10, c4 = 25 and a = 63. We will pick: two 25 coins, one 10 coin, three 1 coin. So we use a total of 6 coins. This strategy does not always work. Describe a counter example. Note: this strategy works for US coins (although the proof is not trivial). So your counter example must use a different coin denominations. (b) Describe a dynamic programming formulation for finding the minimum number of coins needed to make the change, as follows: Define an array A[0..n; 0..a]. The entry A[i, j] is the minimum number of coins needed to make j-cents change, using only the coins with the values c1, c2, . . . , ci . Derive a recursive formula for the entry A[i, j]. The entry A[n, a] will be the answer to the problem. (c) Describe a dynamic programming algorithm for calculating A[∗, ∗] in proper order. The runtime of the algorithm should be at most O(na). (d) Describe an algorithm, that uses A[∗, ∗] and any additional information, to output the optimal solution of the problem. (Namely, output the actual coins needed to make the a cents change).

2. Consider the following demand schedule for widgets:

What is the price elasticity of demand for widgets between $8 and $10?______ What is the elasticity of demand between $2 and $4? ______ As price decreases, demand becomes more / less elastic. What is total revenue per month at a price of $4?______ A reduction in price from $4 to $2 causes total revenue to rise / fall because demand is elastic / inelastic. If price is currently $2, then a 1% increase in price will cause a______ percent increase / decrease in quantity demanded.

Find a closed formula for each of the following sequences. Show all work and explain your answers.

(a) {1, 6, 17, 34, 57, 86, 121, . . .}, where a₀ = 1.

(b) a_n = 5a_n−1 + 4, a₀ = 2

(c) a_n = 10a_n−1 − 21a_n−2, a₀ = 6, a₁ = 26.

QUESTION 1

Studd Enterprises sells big-screen televisions. A concern of management is the number of televisions sold each day. A recent study revealed the number of days that a given number of televisions were sold.

# of TV units sold      # of days

0                             2

1.                         4

2.                       18

3.                       12

4.                       10

5.                         4

Answer the questions below. For each part, show your calculations and/or explain briefly how you arrived at your answer, as appropriate or needed.

Required:

1. Convert the frequency distribution above into a probability distribution (or relative frequency distribution) showing the proportion of days (rather than the number of days) that the number of televisions sold was 0, 1, 2, 3, 4, and 5 respectively. ( 3 marks)
2. Compute the mean of this general discrete probability distribution. ( 3 marks)
3. Compute the standard deviation of this general discrete probability distribution. ( 5 marks)
4. What is the probability that exactly 4 televisions will be sold on any given day? What is the probability that 2 or more televisions will be sold on any given day? What is the probability that less than 2 televisions will be sold on any given day? What is the probability that between 1 and 4 televisions inclusive will be sold on any given day? (4 mark)

I need the full Explanation and calculation of the answer

The following information regarding a dependent variable (y) and an independent variable (x) is provided.

                        y          x

                        2         9

4 7

5 6

                        5         4

7 5

8 1

Determine the least squares estimate of the y-intercept, slope, and coefficient of determination (?²).

Given the following cash flows, what is the project's payback for an initial investment of $100,000?

Year 1 - $25,000

Year 2 - $40,000

Year 3 - $45,000

Year 4 - $50,000

a. 2.8 years

b. 2 years

c. Answer cannot be determined.

d. 4 years