Math Answers

List the first 10 terms of each of these sequences.

a) the sequence that begins with 2 and in which each

successive term is 3 more than the preceding term

b) the sequence that lists each positive integer three

times, in increasing order

c) the sequence that lists the odd positive integers in in-

creasing order, listing each odd integer twice

d) the sequence whose nth term is n! − 2n

e) the sequence that begins with 3, where each succeed-

ing term is twice the preceding term

f ) the sequence whose first term is 2, second term is 4,

and each succeeding term is the sum of the two pre-

ceding terms

g) the sequence whose nth term is the number of bits

in the binary expansion of the number n (defined in

Section 4.2)

h) the sequence where the nth term is the number of let-

ters in the English word for the index n

from the top of the building 256 ft high an object is thrown vertically upward with an initial velocity of 96 ft/sec. when will it strike the ground?

an agricultural scientist is comparing maize yields per acre for which a nitrate based fertilizer has been used to those from plots having a Sulphur based fertilizer. A sample of 100 acres using nitrate has yielded an average of 56.2 bags per acre with a standard deviation of 12.5 bags. The sample of 150 acres with sulphur fertilizer has yielded an average of 52.6 bags per acre with a standard

deviation of 13.8 bags. Test the relevant hypothesis to validate or invalidate whether

nitrate based fertilizer is superior at 10 percent significance level

A retired employee wants to invest no more than ₱1,500,000 by buying a stock from a well-known bank and of a university. The stock from the bank offers 7% interest while the stock of a university pays a 5% return. He decided to invest no more than ₱800,000 in the stock from the bank and at least ₱300,000 in the stock of the university. Also, he wants his investment in the stock from the bank to be smaller than his investment in the stock of the university. How much stock should he buy for each investment to maximize his profit? Given that x and y are non-negative, what are some of the constraints? Check whether each constraint is the correct expression for the problem. *

show that when a body is dropped from a height h ft above the ground, its velocity v (neglecting air resistance) when it strikes the ground will be v=√2gh where g=32ft/sec^2.

On the moon the acceleration of gravity is 1.6 m/sec2. If a rock is dropped into a crevasse, how fast will it be going just before it hits the bottom 30 seconds later.

The following data represent a random sample of 9 marks (out of 10) on a statistics quiz. The marks are normally distributed with a standard deviation of 2. Estimate the population mean with 90% confidence.

7 9 7 5 4 8 3 10 9

With what velocity must an object. Be thrown vertically upward or authority in the maximum height of 900ft from its starting point.

The raw data has been organised in the frequency table below.

games frequency

6 2

7 5

8 n

9 4

10 4

11 2

12 2

13 2

(a) Write down the value of n.

(b) Calculate the mean number of games played per set.

(c) What percentage of the sets had more than 10 games?

(d) What is the modal number of games?

Find the surface integral of the vector field 𝑭(𝑥,𝑦,𝑧)=(𝑥,𝑦,𝑧) over the part of the paraboloid 𝑧=1−𝑥^2−𝑦^2 with 𝑧≥0 and having normal pointing upwards.

Hint: take 𝑥 and 𝑦 as independent parameters.