Linear Algebra -- Vector Spaces -- another proof

Let S denote the set of all infinite sequences of real numbers with scalar multiplication and addition defined by: alpha*{an} = {alpha*an} {an} + {bn} = {an + bn} Show that S is a vector space. What do these special brackets mean? And how do I go through the vector space axioms and the closure properties to show that this ...continues

Finding the Volume of a Fish Tank (filling the fish tank with sand)

I need an equation or equations to help me find out how many pounds of sand I will need to fill my fish tank and so I can determine how much it will cost me. The tank measures 71 inches in length and 18 inches in width. I want to know how much sand I will need for a 3, 4, 5, and 6 inch base.

Linear Algebra -- Subspaces

Determine whether the given sets form subspaces of R-square. What does the T stand for in these equations?

Linear Algebra -- Spanning Sets

Proving X as an element of the spanning set (see attachment)

Linear Algebra -- More Spanning Sets

Solving problems on spanning sets

Probability and Statistics College Project

We were supposed to find all these stats on colleges such as # who applied and # who got accepted, then it says to find the mean mode and median for all the info and I don't know what it means...of all five colleges...of just one...can someone help me find these averages please...I'm desperate.

Determining the total number of solutions (including complex and repeated)

Determine the total number of solutions (including complex and repeated) of the following equations. 1.) 4x^3 - 7x^2 + 5x - 9 = 0 2.) 8x^6 - 3x^4 - 11x^3 - 2x^2 + 4 = 0 3.) x^5 + 2x^3 - 4x^2 + 7x = 12 4.) -3x^4 + 2x^3 + 15x^2 - x + 1 = 8

Determining measurements for perimeter maximization.

An architect is designing an office building that is 120 feet by 72 feet. The architect wishes to use prefabricated rectangular panels to construct the outside walls. If the same size panels are to be used on all sides of the building what is the widest panel that can be used? Explain your reasoning.

Understanding an example about economic life of capital assets. Attachments in Word.

The attached file contains a worked example from a textbook. Explain it.

Formulating and cross tabulating distinct hypotheses concerning relations between variables.

Formulate two distinct hypotheses concerning relations between variables. Cross tabulate the two pairs of variables corresponding to each hypotheses.