sapphiredog393

In the diagram, points P, Q, R, and S are at intersections of gridlines in a 6 × 6 grid. What is the perimeter of parallelogram P QRS?
(A) 14     (B) 15     (C) 16    (D) 17    (E) 18

Aqueous solutions of caffeine, C8H10O2N4

Molality:

Mass Percent Solvent:

Ppm solute:

Mole fraction solvent: 0.900

Create a good one-liner comic that is going to promote the laughter for April fools day. Keep it original and keep it appropriate. Some of the best comics ever were very simple. Keep it clean and have some fun. Thank you.

Go online and explore a variety of subjects and photographic styles and genres including historical, contemporary, commercial, and fine art. Create two concise sentences for each genre/style listed that you examine: one that succinctly captures the main idea behind the style and one that expresses how you feel about the style or what you like/dislike about it.

Given the following short-run production function (x = variable input, Q = output):

Q = 3x² - 0.1x³

(a) Determine the marginal product function (MP_x) and the average product function (AP_x ).

(b) Find the value of x that maximizes Q.

(c) Find the value of x for which MP_x is maximum.

(d) Find the value of x for which AP_x is maximum.

(e) Determine the boundaries of the three stages of production.

Let
v⃗ 1=[1,2,1,−1]
v⃗ 2=[−2,3,8,−3]
v⃗ 3=[−8,5,22,2]
v⃗ 4=[1,2,3,0]
v⃗ 5=[2,3,0,−1]

be row vectors in ℝ4

a)(3 points) Are row vectors v⃗ 1,v⃗ 2,v⃗ 3

linearly dependent?

b)(1 point) Are row vectors v⃗ 1,v⃗ 2,v⃗ 3,v⃗ 4,v⃗ 5

linearly dependent?

. Suppose a particular consumer has 8 birr to be spent on two goods, A and B. The unit price of good A is 2 birr and the unit price of B is 1 birr. The marginal utility (MU) she gets from consumption of the goods is given below.

Quantity

MUA

MUB

1

36

30

2

24

22

3

20

16

4

18

12

5

16

10

6

10

4

1. A) Based on the cardinal analysis, what is the combination of the two goods that gives maximum utility to the consumer?
2. B) What is the total utility at the utility maximization level?
3. Suppose the production function is given by Q(L, K) = L 4 K 4 . Assuming capital is fixed,

find APL and MPL.

1. Consider the following short run production function:

Q=6L2 -0.4L3

1. a)  Find the value of L that maximizes output
2. b)  Find the value of L that maximizes marginal product
3. c)  Find the value of L that maximizes average product

A hexagonal prism has a height of 165 cm. Its two hexagonal faces are regular hexagons with sides of length 30 cm. Its other six faces are rectangles. A fly and an ant start at point X on the bottom face and travel to point Y on the top face. The fly flies directly along the shortest route through the prism. The ant crawls around the outside of the prism along a path of constant slope so that it winds around the prism exactly n + 1/2 times, for some positive integer n. The distance crawled by the ant is more than 20 times the distance flown by the fly.
What is the smallest possible value of n?

Raoul works with a food stylist and together they are working on a shoot for a fast food burger establishment. His food stylist just called to let Raoul know they can’t make it and he has no one to use as a back-up. Raoul will have to rely on his own creativity to make the burger, fries, and milkshake look perfect. He is going to send his assistant out to get whatever supplies he needs to do this. Create a list of items that Raoul could use to make sure that the food looks amazing in terms of color, texture, and all other aesthetics (e.g., paint? glue?). Write several sentences explaining your plan of action.

Five balls, numbered 1 to 5, are placed in order on a table. A sequence of steps is performed on the balls. In step 1, the rightmost ball is picked up and put in the middle of the four remaining balls. (The remaining balls are shifted to make room for the inserted ball.) Then in step 2, the leftmost ball is picked up and put in the middle of the four remaining balls. These steps repeat, with the rightmost and leftmost balls alternately picked up and put in the middle of the four remaining balls. Immediately after step N, the balls are in the reverse of their original order. Which of the following is a possible value of N?