Answer:
6y - 13
Step-by-step explanation:
5 - 3(6 - 2y)
Distribute;
5 - 18 + 6y
-13 + 6y <em>OR</em> 6y - 13
3 = 4 - 4^0 * 4/4
4 = 4^0 + 4^0 + 4^0 + 4^0
5 = 4^2 / (4^0 * 4) + 4^0
6 = 4^2 / 4 + 4^0 + 4^0
Answer:
Step-by-step explanation:
Recall that the notion of the derivative of a function is the rate of change of it. So it kind of tells us how much the value of functioin changes as the independt variable increases or decreases. If it is positive, this means that the function will increase as the indepent variable increases, and if it is negative, that means that the function will decrease as the indepent variable increases.
a) Since f(x) is the number of units you can make out of x units of raw material, it is natural to think that the more material you have, the more units you can make, so we expect f'(x) to be positive.
b) The company buys each unit of raw material at the price w. So the product wx represents the total cost of the raw material used to produce f(x) units. Since each produced unit is sell at the price of p, then the product pf(x) represents the total income for selling all f(x) units.Recall that the profit is the difference between the total income and the total cost of production. Hence, the profit in this case is represented by the formula pf(x)-wx.
c) Recall that a function h(x) that is differentiable attains it's maximum when it's derivative is 0 and it's second derivative is negative.
In this case, we know that the derivative of the profit function, evaluated at x* must be 0, since it is a maximum. So, using the rules of derivation, we know that the derivative of the profit function is pf'(x)-w. Hence,
pf'(x*)-w =0. From where we know that f'(x*)=w/p.
A) x^2 +x -30 = 0 is factored by looking for two factors of 30 that differ by 1. We know ... 30 = 1*30 = 2*15 = 3*10 = 5*6The last two factors differ by 1, so we can factor the trinomial as (x +6)(x -5) = 0
b) The solutions are found by finding values of x that make these factors zero. The only way the product will be zero is if one or more of the factors is zero. x + 6 = 0 x = -6 . . . . . subtract 6
x - 5 = 0 x = 5 . . . . . add 5
The solutions are x = -6 or x = 5These are the values of x that will satisfy the equation (make it true). What they mean depends on the meaning of the variable and the situation the equation is a model of.
Answer:
Step-by-step explanation:
GIVEN: A bag contain 
red marbles,
green marbles and 
blue marble. A marble is chosen at random from the bag and not replaced, then a second marble is chose.
TO FIND: What is the probability both marbles are green.
SOLUTION:
Total marbles in bag 
total number of green marbles 
Probability that first marble will be green 
Probability that second marble will be green 
As both events are disjoint
probability both marbles are green 
Hence the probability both marbles are green is
