If 75% of a class answered the 1st question on a certain test correctly, 55% answered the 2nd question on the test correctly and
1 answer:
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Answer: The required fourth term of the geometric sequence is
Step-by-step explanation: We are given to find the value of the fourth term in a geometric sequence with first term and common ratio as follows :
We know that
the n-th term of a geometric sequence with first term a1 and common ratio r given by
Therefore, the fourth term of the given geometric sequence will be
Thus, the required fourth term of the geometric sequence is
The quadratic model and the linear model of the table of values are the same
<h3>The linear model of the data</h3>To do this, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
- Sum of X = 0
- Sum of Y = 113
- Mean X = 0
- Mean Y = 22.6
- Sum of squares (SSX) = 10
- Sum of products (SP) = 28
The regression equation is
y = mx + b
Where
m = SP/SSX = 28/10 = 2.8
b = MY - bMX = 22.6 - (2.8*0) = 22.6
So, we have:
y = 2.8x + 22.6
See attachment for graph (1)
<h3>The quadratic model of the data</h3>To do this, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
- a = 0
- b = 2.8
- c = 22.6
0 X^2 +2.8 X +22.6
The regression equation is
y = ax^2 + bx + c
So, we have:
y = 0x^2 + 2.8x + 22.6
See attachment for graph (1)
<h3>Why both graphs look the same</h3>The graphs look the same because when the quadratic model is simplified, it gives the linear model.
This in other words mean that:
The quadratic model and the linear model of the table of values are the same
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