zestymathblog

Empirical Rule:  There is no objective Empirical Rule Example: When using the empirical rule the problem has to call for normal distribution or else you can  not use the empirical rule. There are three numbers you have to remember for empirical rule those numbers are; 68%, 95%, and 99.7%. These numbers represent the intervals of information that is included in these margins. The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives  16 1 6  years; the standard deviation is  1.7 1 . 7  years. Use empirical rule to estimate the probability of a gorilla living longer than 14.3 years?  In order to find   the probability I would need to make a normal distribution table and place 16 years as the mean and add and subtract 1.7 as intervals. The numbers I would use would be 9.2, 10.9, 12.6, 14.3, 16, 17.7, 19.4, 21.1, 22.8. Now that I know the numbers I can figure out the percentage. The number 14.3 ...

Recursive and Explicit forms: There is no objective Recursive Example:  Find the fifth term of a recursive define sequence a(1)=1 a(n)=a(n-1)+2n+1 where n is greater than or equal to two. a(1)=1 a(2)=a(2-1)+2(2)+1=a(1)+4+1=1+5=6 a(3)=a(3-1)+2(3)+1=6/a(2)+6+1=13 a(4)=a(4-1)+2(4)+1=13/a(3)+8+1=22 a(5)=a(5-1)+2(5)+1=22/a(4)+10+1=33 33 is the fifth term Explicit Example: Find the first four terms of the sequence given by a(n)=2n(-1)^n         ______            _______            _______           _______                  a1                     a2                       a3                     a4 a1=2(1)(-1)^1= -2           ...

Arithmetic and Geometric Sequences: I will be able to understand arithmetic series and sequence. I will be able to understand geometric series and sequence. Example of arithmetic sequence: -9,-2,5,12,___,___,___,___                        a(n)=a(1) + (n-1)d I do not know what my end term[a(1)] is so that is what I am looking for. I do know what my first term [a(1)] is, it is -9, I have 8 terms [n] and I can find my common difference by subtracting -2 from -9. which is 7. To solve all I need to do is add 7 to 12 then to that number and so on until I have all the terms I need.12+7=19, 19+7=26, 26+7= 3, and 33+7= 40. Now that I have my four terms I can add them to my series. Solution: -9,-2,5,12, 19,26,33,40 Example of geometric sequence: Find two geometric means between -2 and 54 -2, __, __, 54 a(n)=a(1)*r^(n-1) I do know what my end term is, it is 54, my first term is -2, I do not know what the common ratio is I h...

Piecewise Word Problems: I will be able to be able to write piecewise functions Piecewise word problem example: The admission rates at an amusement park are as follows:                 Children 5 years old and under: Free                 Children between 5 years and 12 years ,inclusive: $10                 Children between 12 years and 18 years, inclusive: $25                 Adults: $35 To solve this this first thing I would do is to write down the ages. The ages will serve as the x because they change. So for the first I say 0 less or than equal to x less than or equal to 5, because you can not just say less than or equal to 5 because that would include negative numbers and no one's age is a negative number. So 0 would have to be the lowest number. For the second I  say 5 less than x less than or equal to 12. Th...

Writing Piecewise Functions: I will be able to write piecewise functions. An example of writing piecewise functions: In order to write a piecewise function the first thing I look at the higher function and figure out if the function goes on forever or has a ending point. The top line does have a ending point with a closed circle. This means that this is a real point and not a placeholder so the equation x if x is greater than or equal to 2 would work for the top line. The bottom line has an open circle so this mean it is not a real point it is just a placeholder. This line is pointing upward toward the second quadrant with an arrow. The equation -.5x+-.5 if x is less than 1 (not equal to because the circle is open) . One misconception I had was with when two points were at the same coordinate but from different functions and had different end points. For example lets say two graphs have converge on the same point but one graph has a closed circle and the other has a open...

The Law of Sine and Cosine: I will be able to use law of Cosine and law of Sine.                                                          Example of law of Cosine:                                                                                                                       Solve for C: a=2 b=3 C=60 degrees        I n order to solve I need to figure out whether the equation is sine or cosine. The triangle is cosine  has Side Angle Side . Because it is a cosine problem I will use the cosine ...