Answer: 14,515,200
Note: this is a single number (not an ordered triple or a collection of three different numbers) roughly equal to about 14.5 million if you round to the nearest hundred thousand.
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Explanation:
There are 13 people. Let's call them person A, person B, person C, ... all the way up to person M. The first four people are given who we'll call A through D. The rest (E through M) aren't really important since they aren't named.
A = Monsier Thenardier
B = Madame Thenardier
C = Cosette
D = Marius
Peron's E through M = remaining 9 people
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A and B must stick together. Because of this, we can consider "AB" as one "person".
So we go from 13 people to 13-2+1 = 12 "people".
Likewise, C and D must stick together. We can consider "CD" as one "person". So we go from 12 "people" to 12-2+1 = 11 "people"
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The question is now: how many ways can we arrange these 11 "people" around a circular table? The answer is (n-1)! ways where n = 11 in this case
So, (n-1)! = (11-1)! = 10! = 10*9*8*7*6*5*4*3*2*1 = 3,628,800
We're almost at the answer. We need to do two adjustments.
First off, for any single permutation, there are two ways to arrange "AB". The first is "AB" itself and the second is the reverse of that "BA". So we will multiply 3,628,800 by 2 to get 2*3,628,800 = 7,257,600
Using similar logic for "CD", we double 7,257,600 to get 2*7,257,600 = 14,515,200
The final answer is 14,515,200
Answer:
0.08x = $5400-0.1x Add 0.1x to both sides of the equation.
0.18x = $5400 Divide both sides by 0.18
x = $3000 and $54000-$3000 = $24000
$3,000 is invested at 8%
$2,400 is invested at 10%
Step-by-step explanation:
Answer:
B) -2
Step-by-step explanation:
I got the slope by using two points on the line (0,7) and (4,-1)
Slope=y2-y1/x2-x1
(7--1)/(0-4)
=
8/-4
I then simplified 8/-4 to -2
You could also solve by finding the rise over run for two points on the line.
The rise is 2 and the run is -1, making it 2/-1 or -2
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Answer:</h2><h3>
A. Domain </h3>
The domain of a function is the x-values that the graph applies to. This means that the domain is whatever x-values the graph crosses. All vertical parabolas (like the one pictured) have a domain of all reals. This is because any x-value could be plugged into the function and provide a y-value. while it may not seem like it, that graph will cover every single x-value in existence.
<h3>
B. Range</h3>
The range is similar to the domain but is for y-values. So, the range is whatever y-values the graph applies to and crosses. As you can see from the graph, there are no y-values above 1. This means the range is y≤1.
<h3>
C. Increasing Interval</h3>
A graph is increasing when the y-values are increasing. So, on the parent function of a parabola, the graph increases to the right and decreases to the left. However, this graph is inverted and shifted to the left, so the interval will also be flipped and shifted. In this case, the graph increases from -∞ to 2.
- Increasing Interval = [-∞, 2]
<h3>
D. Decreasing Interval</h3>
The decreasing interval is very similar to the increasing interval. This interval applies when the y-values are decreasing as the x-values increase. For a parabola, the increasing and decreasing intervals always meet at the x-value of the vertex, which is 2 on this graph. The y-values decrease during the interval 2 to ∞.
- Decreasing Interval = [2, ∞]
<h3>
E. Opening</h3>
The direction of a parabola is decided by the sign (+ or -) of the leading coefficient. Positive coefficients open up and negative opens down. As you can see from the graph, the sides of the parabola point downwards. This means that the leading coefficient must be negative.
<h3>
F. Min and Max</h3>
A parabola will always only have a min or a max, never both. If a graph opens up it has a min because there is one y-value which is the minimum possible y-value. Graphs that open downwards have a maximum because there is one y-value that is the largest possible. So, this graph has a maximum of 1 because that is the largest possible y-value.
