Express in a simplified exponential notation 18a^3b^2/2ab
2 answers:
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Answer:
Step-by-step explanation:
The table shows a set of x and y values, thus showing a set of points we can use to find the equation.
1) First, find the slope by using two points and substituting their x and y values into the slope formula, . I chose (-3, 13) and (0,17), but any two points from the table will work. Use them for the formula like so:
Thus, the slope is .
2) Next, identify the y-intercept. The y-intercept is where the line hits the y-axis. All points on the y-axis have a x value of 0. Thus, (0,17) must be the y-intercept of the line.
3) Finally, write an equation in slope-intercept form, or format. Substitute the
and
for real values.
The represents the slope of the equation, so substitute it for
. The
represents the y-value of the y-intercept, so substitute it for 17. This will give the following answer and equation:
Answer:
165 different teams of 3 students can be formed for competitions
Step-by-step explanation:
Combinations of m elements taken from n in n (m≥n) are called all possible groupings that can be made with the m elements so that:
- Not all items fit
- No matter the order
- Elements are not repeated
That is, a combination is an arrangement of elements where the place or position they occupy within the arrangement does not matter. In a combination it is interesting to form groups and their content.
To calculate the number of combinations, the following expression is applied:
It indicates the combinations of m objects taken from among n objects, where the term "n!" is called "factorial of n" and is the multiplication of all the numbers that go from "n" to 1.
In this case:
- n: 3
- m: 11
Replacing:
Solving:
being:
- 3!=3*2*1=6
- 8!=8*7*6*5*4*3*2*1=40,320
- 11!=39,916,800
So:
C= 165
<u><em>165 different teams of 3 students can be formed for competitions</em></u>