1. is sin(pi/4) causal?

2. is sin(pi/4) stable?

3. is delta(n+1) causal?

4.  = ?

5. If function w [ n ] is convolved with , what will the result be?

6. if a system with signal length 4 is convolved with its own system response, what will the length of that signal be?

7. In an LTI system, x[n] * h[n]= y[n]. What is x[n-3] * h[n-2] =?

Time (hours) spent on social media per day

2 5 4 6 3 2 4 1 0 1 3 2 5 4 2 6 3 7 4 3 5 2 4 1 3 4 2 4 3 5 3 6 3 2 4

1. For the above data set, give the minimum and maximum score and calculate the range.

2. Calculate the standard deviation (show your work).

3. Choosing the appropriate format, draw a bar chart or histogram of the scores. Does the data appear to be normally distributed? From this picture, give what you think the category of skew and kurtosis is, and why.

4. Regardless of your answer to 3 above, assume a normal distribution and compute the z score of 5. Based on the z score, what percentage of people spent 5 or fewer hours on social media? Be sure to draw the appropriate picture!

5. Assuming a normal distribution, compute the z score for a score of 3. Based on the z score, what percentage of the people spent 3 or more hours on social media? Be sure to draw the appropriate picture!

6. Based on z score calculations, what percentage of people spent between 4 and 6 hours on social media?   Be sure to draw the appropriate picture!

7. Based on the z score, how much time did a person at the 61^st percentile spend on social media? Be sure to draw the appropriate picture!

(a) use the data n the table to construct a standardized p-chart,

(b) interpret your chart, and

(c) give reasons for out-of-control conditions

1. Show that the function above satisfies the probabilities of a joint probability mass function.
2. Find E(X), E(Y), V(X), V(Y)
3. Find marginal probability distribution of X
4. Find the covariance and correlation.

On January 1, 2021, Gless Textiles issued $21 million of 10%, 10-year convertible bonds at 101. The bonds pay interest on June 30 and December 31. Each $1,000 bond is convertible into 40 shares of Gless’s no par common stock. Bonds that are similar in all respects, except that they are nonconvertible, currently are selling at 99 (that is, 99% of face amount). Century Services purchased 15% of the issue as an investment.

Required:
1. Prepare the journal entries for the issuance of the bonds by Gless and the purchase of the bond investment by Century.
2. Prepare the journal entries for the June 30, 2025, interest payment by both Gless and Century assuming both use the straight-line method.
3. On July 1, 2026, when Gless’s common stock had a market price of $33 per share, Century converted the bonds it held. Prepare the journal entries by both Gless and Century for the conversion of the bonds (book value method).

On January 1, 2021, Gless Textiles issued $29 million of 8%, 20-year convertible bonds at 101. The bonds pay interest on June 30 and December 31. Each $1,000 bond is convertible into 40 shares of Gless’s no par common stock. Bonds that are similar in all respects, except that they are nonconvertible, currently are selling at 99 (that is, 99% of face amount). Century Services purchased 10% of the issue as an investment.

Required:
1. Prepare the journal entries for the issuance of the bonds by Gless and the purchase of the bond investment by Century.
2. Prepare the journal entries for the June 30, 2025, interest payment by both Gless and Century assuming both use the straight-line method.
3. On July 1, 2026, when Gless’s common stock had a market price of $33 per share, Century converted the bonds it held. Prepare the journal entries by both Gless and Century for the conversion of the bonds (book value method).

On January 1, 2021, Gless Textiles issued $12 million of 9%, 10-year convertible bonds at 101. The bonds pay interest on June 30 and December 31. Each $1,000 bond is convertible into 40 shares of Gless’s no par common stock. Bonds that are similar in all respects, except that they are nonconvertible, currently are selling at 99 (that is, 99% of face amount). Century Services purchased 10% of the issue as an investment. Required: 1. Prepare the journal entries for the issuance of the bonds by Gless and the purchase of the bond investment by Century. 2. Prepare the journal entries for the June 30, 2025, interest payment by both Gless and Century assuming both use the straight-line method. 3. On July 1, 2026, when Gless’s common stock had a market price of $33 per share, Century converted the bonds it held. Prepare the journal entries by both Gless and Century for the conversion of the bonds (book value method).

On January 1, 2021, Gless Textiles issued $28 million of 7%, 10-year convertible bonds at 101. The bonds pay interest on June 30 and December 31. Each $1,000 bond is convertible into 40 shares of Gless’s no par common stock. Bonds that are similar in all respects, except that they are nonconvertible, currently are selling at 99 (that is, 99% of face amount). Century Services purchased 20% of the issue as an investment.

Required: 1. Prepare the journal entries for the issuance of the bonds by Gless and the purchase of the bond investment by Century. 2. Prepare the journal entries for the June 30, 2025, interest payment by both Gless and Century assuming both use the straight-line method. 3. On July 1, 2026, when Gless’s common stock had a market price of $33 per share, Century converted the bonds it held. Prepare the journal entries by both Gless and Century for the conversion of the bonds (book value method).

1) Determine the angle between vectors:

U = <2, -3, 4> and V= <-1, 3, -2>

2) determine the distance between line and point

P: -2x+3y-4z =2

L: 3x – 5y+z =1

3) Determine the distance between the line L and the point A given by

L; (x-1)/2 = (y+2)/5 = (z-3)/4 and A (1, -1,1)

4) Find an equation of the line given by the points A, B and C.

A (2, -1,0), B (-2,4,-1) and C ( 3,-4,1)

5) Determine whether the lines are parallel, perpendicular or neither.

(x-1)/2 = (y+2)/5 = (z-3)/4 and (x-2)/4 = (y-1)/3 = (z-2)/6

6) A) Find the line intersection of vector planes given by the equations

-2x+3y-z+4=0 and 3x-2y+z=-2

B) Given U = <2, -3, 4> and V= <-1, 3, -2>

Find

a. U . V

b. U x V

7) Find the angle between the planes:

3x -5y+7z -4=0 and 3x -2y+5z +3 =0

4. A firm has the following production function:y = L 1/3 K 1/2 .
2
(a) Does this production function exhibit increasing, decreasing, or
constant returns to scale? Prove.
(b) Suppose in the short run, capital is fixed at K = 100. Assuming
that the output and factor prices are p, w, and r respectively, find
firm’s factor demand for labor. What will the effects be when w,
r, and p increase? Explain your results intuitively.
(c) Now, suppose the government decides to impose a payroll tax of
$t per worker employed. What will the effect be on L ∗ ? Why?
(d) Alternatively, if the government decides to impose a lum-sum tax
of $T, what will the effect be on L ∗ ? Why?