What is the rule: 36 --> 60, 12 --> 20, 6 --> 10, 15 --> 25
2 answers:
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Answer:
See below
Step-by-step explanation:
To find the values of a and b, we use the intersection point P.
Since the graph of f is intersected by P=(-2,2), f(-2)=2, that is, a(2)^(-2)=2. Then a=2(2)²=8.
Since the graph of g is intersected by P=(-2,2), g(-2)=2, that is, -2+b=2. Then b=2+2=4.
Hence a=8, b=4.
To find the other point of intersection Q, we need to find a number x such that f(x)=g(x), that is, 8(2)^(x)=x+4. Rewrite this equation as follows:
It is not easy to solve this equation analitically. Instead, you can apply a quantitative method. First, the left hand side is an exponential function, so it is always positive. Then the solution will be a number in which the right side (x+4) is positive, that is, x > -4. The solution is an integer, then the possible values are x=-3,-2,-1,0,1,2,...
Now, the RHS must be a power of two, so the possible integers are x=-3,-2,0,4,12,28,... However, the LHS grows very quickly, while the LHS grows slowly. Then, it is only necessary to test small integer values (we already know that x=-2 is a solution).
If we test with x=-1, we get 2²=4=3, then x=-1 is not a solution. Any x>-1 will not be a solution, because f increases much faster than g, and then they won't intersect. So our possibilities reduce to x=-3,-2. Taking x=-3, we get f(-3)=2⁰=1=-3+4=g(-3). Thus, (-3,0) is the other point of intersection Q. (r=-3, s=0).
Answer:
a) Figure attached
b)
c) The correlation coefficient would be r =0.47719
d)
Step-by-step explanation:
(a) Draw a scatter diagram for the data.
See the figure attached
(b) Find x, y, b, and the equation of the least-squares line. (Round your answers to three decimal places.) x =__ y =__ b =__ y =__ + __x
Where:
With these we can find the sums:
And the slope would be:
Nowe we can find the means for x and y like this:
And we can find the intercept using this:
So the line would be given by:
(c) Find the sample correlation coefficient r and the coefficient of determination r?2. (Round your answers to three decimal places.)
n=14
And in order to calculate the correlation coefficient we can use this formula:
So then the correlation coefficient would be r =0.47719
What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)
The % of variation is given by the determination coefficient given by and on this case
, so then the % of variation explaines is 22.8%.
(d) If a female baby weighs 21 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) ___ lb
So we can replace in the linear model like this:
