Sequence and Series
Find the 13th term
33,48,63,78
48-33=15 63-48=15 78-63=15
d=15 n=13 a=33
Tn=33+(13-1)(15)
Tn=33+(12)(15)
Tn=33+180
Tn=213 213 is the 13th term for this sequence
A science teacher wanted to see the correlation between 3 student's homework grade and test grades, where x is the homework grades and y is their test grades. Write a linear regression equation that represents the data rounding all coefficients to the nearest tenth.
96 84
88 79
90 88
y=0.3x+53.8
What is a scatter-plot?
A data set that is plotted on a graph showing the correlation between two variables.
Solve.
x/100 =2 /20
x/100 *100 = 2/20 *100
x=200/20
x=10
A high school student wanted to find the correlation between female teens shoe sizes and their grade where x is their grade and y is their shoe sizes. Looking at this table, find the equation for the scatter-plot rounding all coefficients to the nearest tenth.
10 9.5
7 8
8 7.5
7 8
8 10
10 9
11 7
9 6.5
10 5
11 9
7 10
12 9.5
y=0.1x+8.8
Find the 30th term
8,17,26,35,44
17-8=9 26-17=9 35-26=9 44-35=9
d=9 a=8 n=30
Tn=8+(30-1)(9)
Tn=8+(29)(9)
Tn=8+261
Tn=269 269 is the 30th term
The number of newly reported cases of robberies in a city in New York is shown in the table where x is the years since 2012 and y is the number of of new cases of robberies. Write a linear regression equation that represents the set of data rounding all coefficients to the nearest tenth.
0
1 237
2 289
3 309
4 377
5 401
y= 41.6x+197.8
What is the definition of correlation? Give an example.
Correlation is the relationship between a dependent and independent variable.
Ex: Correlation of a high school student's height vs their shoe size.
Answer may vary
Solve for x
7/63 = x/98
7/63 = x/98
7/63 *63 = x/98 * 63
7*98=686
63*x=63x
686/63=63x/63
x=10.9
What is the slope of the line of best fit based on this table showing the monthly heating bill in Dallas where x is the average temperature and y is the heating bill.Round to the nearest hundredth.
21 258
29 255
36 246
33 250
46 203
59 168
66 100
73 98
slope= -3.50
Find the 8th term.
35,245,1715,12005,...
245/35=7 1715/245=7 12005/1715=7
a=35 r=7 n=8
Tn=(35)(7)^(8-1)
Tn=(35)(7)^7
Tn=(35)(823,543)
Tn=28,824,005
A history teacher wanted to see the correlation between his student's classwork and test grades, where x is the classwork grades and y is the homework grades. Write a linear regression equation that represents this set of data rounding all coefficients to the nearest tenth. Using the equation, find the projected test grade for a student with a classwork grade of 78 rounding to the nearest whole number.
82 89
74 80
98 81
96 88
86 90
78 77
90 87
68 78
79 85
y= 0.2x+ 63.1
y=0.2(78)+63.1
y=78.7
y=78
What is a positive and negative correlation and how do you know when there is a positive or negative correlation to the data?
A positive correlation is the relationship between two variables that move in the same direction and as x increases, y increases.A negative correlation is the relationship between two variable when one increases, the other decreases where as x increases, y decreases.
When r is closer to -1 there is a negative correlation and when r is closer to 1 there is a positive correlation.
Solve for x on both equations and find the difference of the equations.
2256/2 = 564/x
282/8 = 752/x
2256/2 *2 = 564/x *2
2256*x=2256x
564*2=1128
2256x/2256x = 1128/2256
x=2
282/8=752/x
282/8*8 = 752/x*8
282*x=282x
752*8=6016
6016/282 = 282x/282x
x=21.3
21.3-2= 19.3
difference is 19.3
Graph f(x)= 5 sin(2(x-3))+24 and name the amplitude, the vertical translation, the period, and the phase shift. How would you change the vertical translation to make the line shift vertically down?
a=5
vertical translation= up 24
period=2
phase shift= left 3
To change the vertical translation of the line you would make d a negative number so that it would shift down vertically.