You have a set of building-blocks which contains blocks of heights 1, 3 and 4 centimeters. (Other dimensions irrelevant.) You are constructing towers by piling blocks directly on top of one another. (A tower of height 7 cm could be obtained using seven blocks of height 1; one block of height 3 and one block of height 4; 2 blocks of height 3 and one block of height 1; etc.) Let bn be the number of ways to construct a tower of height n cm using blocks from the set. Assume that there is an unlimited supply of blocks of each size. Find a recurrence relation for bn. (You are not required to solve the recurrence relation.)

I am stuck on this question and don't really know where to start. I've seen examples done but they don't give a final result and I'm not sure how to get there.

Find the charge on the capacitor in an LRC-series circuit at t = 0.05 s when P = 0.05 h, R = 3 Ω, C = 0.008 f, E(t) = 0 V, q(0) = 4 C, and i(0) = 0 A.

(Round your answer to four decimal places.)

Determine the first time at which the charge on the capacitor is equal to zero.

(Round your answer to four decimal places.)

Consider a pyramid with height h and a rectangular base with dimensions b and 2b.

(a) Cross-sections that are parallel to the base are rectangles. Find a formula for the area A(z) of the cross-section parallel to the base and z units above it.

(b) Find the volume of the pyramid by integrating the function A(z).

Check if (A x B) x C = A x (B x C) using half-precision format.

Let

• A = 3.41796875x10 ^-3 = 1.1100000000 x 2 ^-9
• B = 4.150390625 x10^-3 = 1.0001000000 x 2^-8
• C = 1.05625x10² = 1.1010011010 x2⁶

Calculate (A x B) x C by hand, assuming each of the values are stored in the 16-bit half precision format described in Exercise 3.27 (and also described in the text).

Assume 1 guard, 1 round bit, and 1 sticky bit, and round to the nearest even.

First, we calculate AxB = 1.M x 2^N  

M =_______ (10-bit binary)

N = _________(a negative (decimal) integer)

The product of A and B is an underflow. That is, the result of A*B cannot be represented in the normal 16-bit half precision format.

However, it could be represented as a denorm number. What is the encoding of the this denorm number? (a 4-digit hexadecimal number with uppercase letter digit.)

Matlab Code
Illustrate the fact that the average of a large number of independent random variables will approximate a Gaussian by the following:
a) to generate n random integers from a uniform distribution U(xl , xu).
b) to choose xl and xu randomly, in the range −100 ≤ xl < xu ≤ 100 and the number of samples n randomly in the range 0 < n ≤ 1000.
c) Generate and plot a histogram of the accumulation of 10⁴ points sampled as just described.
d) Calculate the mean and standard deviation of your histogram, and plot it.
e) Repeat the above for 10⁵ and 10⁶ points. Discuss your results.

Given the vectors d = [−3, 6, 7] e = [8, −5, 3] and f = [3, −1, 4]
a. Let x1(t) be the equation between d and f, express x1(t) in vector and parametric form. Then find x1(3); x1(-2); x1(1)
b. Let x2(t) be the equation through f and parallel to x1(t), express x2(t) in vector and parametric form
c. Let g = 4d – 2f, express the equation of the line containing g and e

Q1. The normal distribution is a bell-shaped curve defined by: y=e^(〖-x〗^2 ) Use the golden-section search to determine the location of the inflection point of this curve for positive x.

PLEASE do the iterations on excel and show the written text in the cells. Thank you!

Office One Super Store sells office furniture, equipment, supplies and business technology for small businesses and home offices. The company sells 5600 file cabinets per year, 60% of which are imported from Canada. All the imported file cabinets are purchased from a single supplier at a cost of $40 each. The shop calculates annual holding cost as 20% of unit cost per year. The set up cost for placing an order is estimated to be $350.

a) Determine the optimal number of file cabinets to order (EOQ) each time an order is placed. When EOQ is implemented, determine the time between placement of orders and the annual total cost incurred by the store for the imported cabinets.

b) If store has to order the imported file cabinets in multiples of 40, what order size should it choose? What is the percentage increase in the annual total cost from using this new order quantity compared to the original EOQ?

c) If the replenishment lead time for the imported file cabinets is three weeks, what is the reorder point based on the level of on-hand inventory?

d) The current reorder policy is to buy the imported file cabinets only once every four months. What is the additional annual total cost incurred by this policy compared to using the original EOQ?

SIGNS = 'ARI:03,21--04,19;TAU:04,20--05,20;GEM:05,21--06,21;CAN:06,22--07,22;' + \
'LEO:07,23--08,22;VIR:08,23--09,22;LIB:09,23--10,23;SCO:10,24--11,20;' + \
'SAG:11,21--12,21;CAP:12,22--01,20;AQU:01,21--02,21;PIS:02,22--03,20;'

def find_astrological_sign(month: int, date: int) -> str:
'''
Given two int values representing a month and a date, return a
3-character string that gives us what star sign a person born in that
month and on that date belongs to. Use the SIGNS string (already
defined for you at the top of this file) to figure this out.

NOTE: A lot of string slicing to do here. It looks like the
information for each sign is exactly 17 characters long.
We can probably use that.

>>> find_astrological_sign(8, 24)
'VIR'

>>> find_astrological_sign(12, 31)
'CAP'
'''

Here is my attempt, I don't know what's wrong

def find_astrological_sign(month, date):
sign_list = SIGNS.split(";")
for s in sign_list:
if s != "":
start_m = int(s[4:6])
start_d = int(s[7:9])
end_m = int(s[11:13])
end_d = int(s[14:16])
if (start_m == month and end_d <= date) or (end_m == month and end_d >= date):
return s[12:]
  

Consider the following catastrophic reasoning:

If I don't get an A on this test, I will fail the class. If I fail the class, I will never get a real job.

I'll either study and get an A on the test, or I'll go to work and not study.

So If I go to work, I'll never get a real job.

A) Translate this argument into the language of propositional logic. (Provide a key. E.g. C = The cat is on the mat)

B) Draw a truth table for the argument.

C) Using the truth tables determine whether the argument is valid. (This should only take one or two sentences)

5. Consider the earth to be a sphere of radius 6370 km. (a) Express the coordinates of Jacksonville and Los Angeles in spherical coordinates if the z-axis points from the center of the earth towards the north pole and the x-axis crosses the 0-deg longitude. (b) Find the straight line distance between these two cities and (c) the distance between the two cities along the surface of the earth 'as the crow flies'.

Let {v1, v2, v3} be a basis for a vector space V , and suppose that w = 3v1 − 5v2 + 0v3. For each of the following sets, indicate if it is: a basis for V , a linearly independent set, or a linearly dependent set. (a) {w, v2, v3} (b) {v1, w} (c) {v1, v2, w} (d) {v1, w, v3} (e) {v1, v2, v3, w}

Let A = {1, 2, 3, 4, 5}. Find the inverse of the following functions f: A→ A.

1. 1. ? = {(1,1),(2,3),(3,2),(4,4),(5,5)    
2. 2. ? = {(1,5),(2,4),(3,2),(4,1),(5, 4)}
3. 3. ? = {(2,1),(3,4),(1,3),(4,1),(5, 2)}

Solve each IVP using Laplace transform method:

1. y''+0.04y=0.02t^2 y(0)=-25 y'(0)= 0

2. y''+2y'+5y=50t-100 y(2)= -4 y'(2)= 14