A population, obeying the logistic equation, begins with 1000 bacteria, then doubles itself in 10 hours. The population is observed eventually to stabilize at 20,000 bacteria. Find the number of bacteria present after 25 hours and the time it takes the population to reach one-half of its carrying capacity.

Please show all work and steps clearly so I can follow your logic and learn to solve similar ones myself. I will rate your answer for you and provide positive feedback. Thank you kindly!

You have 10 friends: 3 couples and 4 singles. How many ways can you invite 7 of them to your house, such that the two people of every couple are either both invited or not?

Use Matlab to find a subset of the set of vectors that forms a basis for the span of the vectors.

(a) {(1, 2, −1, 0), (−3, −6, 3, 0), (1, 0, 0, 1), (−2, −2, 1, −1)}

The zoo is building a new polar bear exhibit, and wants to put a semi-circular window in the concrete wall of the swimming tank. (Note: picture is not to scale)



If the semi-circle has diameter 80 centimeters, and the bottom of the window is at a depth of 3 meters, find the hydrostatic force on the window.



   Newtons

A=[ 7 8 -2 -6 7 4 1 ; 2 4 -4 -13 9 9 -12 ; 6 6 0 -9 8 9 -4 ; 1 8 -14 -22 5 8 -1 ; 4 9 -10 -14 7 4 -1]

B=[ 19 4 4 14 -3 -7 -5 ; 21 -6 -5 10 14 -2 4 ; 22 -4 5 13 5 -6 4 ; 41 20 0 26 11 -1 -27 ; 29 14 -2 20 3 -4 -19]

Remark: You may only use rref , or commands that are covered in our MATLAB guides, and no other special MATLAB functions for this problem.

(a) (3 points) Find a basis for Col(A) and determine its dimension.

(b) (5 points) Find a basis for Nul(A) and determine its dimension.

(c) (3 points) Find a basis for Row(A) and determine its dimension.

(d) (5 points) Find a basis for the left nullspace of A and determine its dimension.

(e) (2 points) Find a basis for Col(B) and determine its dimension.

(f) (6 points) Determine whether Col(A) = Col(B), i.e. determine whether the two given subspaces of R 5 are the same or not. If not, find a vector v

that belongs in one of the subspaces and not the other.

(g) (6 points) Determine whether Nul(A) = Nul(B). If not, find a vector v that belongs in one of the subspaces and not the other.

Use generating functions to solve the following recurrence relation: an = 2an−1 + 3n , n ≥ 1 a0 = 2

Assume you have been given $400,000 CAD with access to all listed stocks, bonds, futures, and options worldwide. You can trade in options and futures, in combination with the underlying asset. Assume today is Feb 1, 2020 and you have been given $400,000 CAD fake money to trade until April 20, 2020.

Perform a bear spread (either call or put) strategy.

Describe the trade and provide the reason for such trade.

Please provide table and or/ graph.

Kolkmeyer Manufacturing Company is considering adding two machines to its manufacturing operation. This addition will bring the number of machines to ten. The president of Kolkmeyer asked for a study of the need to add a second employee to the repair operation. The arrival rate is 0.05 machines per hour for each machine, and the service rate for each individual assigned to the repair operation is 0.4 machines per hour.

Compute the operating characteristics if the company retains the single-employee repair operation. If required, round your answers to four decimal places. P0 = Lq = L = Wq = hours W = hours

Compute the operating characteristics if a second employee is added to the machine repair operation. If required, round your answers to four decimal places. P0 = Lq = L = Wq = hours W = hours

Each employee is paid $20 per hour. Machine downtime is valued at $70 per hour. From an economic point of view, should one or two employees handle the machine repair operation? Explain. If required, round your answers to two decimal places. Cost of one employee system: $ Cost of two employees system: $ From an economic point of view, should handle the machine repair operation.

Can anyone help?

Given n ∈N and p prime number and consider the polynomial f (x) = xn  (xn-2)+1-p

1)Prove that f (x) is irreducible in Q [x]

2) If n = 1 and p = 3, find Q [x] / f (x))

3) Show that indeed Q [x] / (f (x)) is a field in the previous paragraph

PLEASE answer all subsections

Let P be an external point of a circle. Given two distinct secants PAB and PCD such that AB
and CD are chords of the circle. We know that PA x PB = PC x PD.
(a) Alternatively, if the point P lies on the circle, i.e., P moves from being an external point
to become concurrent with A and C, state why PA x PB = PC x PD is still obtained.
(b) It can be shown that PA x PB = PC x PD even if P is an internal point of a circle. The
power of a point P with respect to a circle is defined as ?2 − ?2 where d is the distance
from P to the centre of the circle and R is the radius of the circle. Using the results above,
determine the three possible locations of P when its power is zero, positive and negative,
respectively.

why is understanding quantities and units
important

The temperature T at a point (x,y,z) in space is inversely proportional to the square of the distance from (x,y,z) to the origin. It is known that T(0,0,1) = 500. a. [2] Compute T(2,0,0). b. [3] Find the rate of change of T at the point (2,3,3) in the direction of the point (3,1,1). c. [3] What is the maximal rate of change of T at the point (2,3,3)?

1a. An ATM requires a four-digit PIN, using the digits 0-9. How many PINs have no repeated digits?

1b. How many ways can president and vice president be determined in a club with twelve members?

1c. A security team visits 12 offices each night. How many different ways can the team order its visits?

1d. In a certain lottery you select seven distinct numbers from 1 through 39, where order makes no difference. How many different ways can you make your selection?

1e. First, second, and third prizes are to be awarded to three different people. If there are ten eligible candidates, how many outcomes are possible?

1f. Three identical “Outstanding Teacher” awards are to awarded to three different people. If there are ten eligible candidates, how many outcomes are possible?