Algebra

give me 20 ex of special products of algebra

In how many ways can 4 girls and 4 boys be seated in a row containing 8 seats if boys and girls must sit in alternate seats?
The answer in my notes is 1,152..
I need a solution please.
Thanks in advance.

A committee of 3 is to be selected from a group of 5 girls and 3 boys. What is the probability that two boys are selected?

The answer in my notes is: 15/56.
I need a solutions on how it came up to 15/56.
Please help..thank you..

Let $x$ be a real number that satisfy the equation

$4^x + 6^x = 9^x$

What is the value of $\left(\dfrac{2}{3}\right)^x$ ?

Hello. I'm having a hard time with this problem. Please help. Thank you.

When a certain polynomial p(x) is divided by (x-1), remainder is 12. When the same polynomial is divided by (x-4), the remainder is 3. Find the remainder when the polynomial is divided by (x-1)(x-4).

Hello mga Engrs/ Sirs,

Pwede po ba patulong ng correct answer and solution for this question:

A series of square figures are made with match sticks. If the first three figures are the following, how many matchsticks will be needed to form the 6th figure? see link po, thank you in advance po.

Let A be a square matrix of order n. Then (A - kI)X = 0, where k is called eigen value and I is called Identity matrix of order n, X is called eigen vector, is called characterstic equation. The equation A - kI = 0 gives n values of k and for each value of k, n column vectors. P be the square matrix of order n formed by the n column vectors.

The diagonal matrix of A = (inverse of P)AP.

Hello,
I want to calculate the liquid level of a horizontal cylindrical tank. Consider the equation :

V=L{(Pi)R^2-R^2ArcCos[(R-h)/R]+(R-h)Sqrt(2Rh-h^2)}

V=Tank volume
L= Tank length
R= Tank radius
h= Distance from top of tank to surface of liquid

What I want to do is to rearrange the above equation so that h is the subject. can this be done?

among 10000 random digits, find the probabilty that the 3 appers at most 950 times.
please help, thank you.