Answer:
where is the picture?
Step-by-step explanation:
Answer:
Please check explanations for answer
Step-by-step explanation:
Here, we want to check the given list and state the true values;
1. This is true
Compound interest has the exponent nt; simple interest has no exponent
2. This is false
Simple interest is only earned on the principal which is the amount deposited
3. True
Due to its multiplication chain, it earns more money as we can compound more than once within the given time frame
4. This is false; check explanations above
5. This is true
Its value is only based on the amount invested originally
6. This is false
simple interest earns the same amount annually based on rate
7. This is false
Both considers the time factor t in their formulas
8. This is true
The interest and principal forms the principal for another compounding time
Let's start by solving this problem when there are only two positive numbers involved, and then see whether we can apply the same technique when there are three positive integers.
Let the two positive integers be x and y.
Then x + y = 100, and xy = the product.
Let's eliminate x. Solve x + y = 100 for x: x = 100 - y. Now subst. this last result into P = xy: P = product = (100 - y)(y) = 100y - y^2
Differentiating, dP/dy = 100 - 2y. Set this = to 0 and solve for y: -2y = -100, and y = 50. Since x + y = 100, x is thus also = to 50.
Solution set: (50,50).
Now suppose that three positive integers add up to 100, and that we want to maximize their product.
Then x + y + z = 100. Let's maximize f(x,y,z) = xyz (the product of x, y and z).
Since x + y + z = 100, we can eliminate z by solving x + y + z = 100 for z and subst. the result back into f(x,y,z) = xyz:
We get f(x,y) =xy(100-x-y), a function of two variables instead of three.
I won't go through the entire procedure of maximizing a function in three variables, but will get you started:
Find the 'partial of f with respect to x' and then the 'partial of f with respect to y'. Set each of these partial derivatives = to 0:
f = 0 = (partial of xy(100-x-y) with respect to x
x
= xy(partial of 100-x-y with respect to x) + (100-x-y)(partial of xy with respect to x)
= xy(-1) + (100-x-y)(y)
We must set this partial = to 0: -xy+100y-xy-y^2 = 0
-2xy + 100y - y^2 = 0
or y(-2x + 100 - y) = 0
of which y=0 is one solution and in which -2x + 100 - y = 0
You must now go through the same procedure with respect to the partials with respect to y.
If you'd like to continue this discussion, please respond with questions and comments.
Answer: 0.0637
Step-by-step explanation:
There are 13 hearts. The chance of drawing a heart in your first draw is 13/52, or in other words 1/4
There are 13 diamonds. The chance of drawing a heart on your second draw after removing the heart is 13/51
The chance of drawing a heart, and then, drawing an orange, are 1/4*13/51=13/204.