<h3>
Answer: y = 12/(x^2)</h3>
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Explanation:
"y varies inversely as x^2" means y = k/(x^2) for some constant k.
Plug in (x,y) = (2,3) and solve for k
y = k/(x^2)
3 = k/(2^2)
3 = k/4
3*4 = k
12 = k
k = 12
The original equation updates to y = 12/(x^2)
As a check, plugging in x = 2 should lead to y = 3
y = 12/(x^2)
y = 12/(2^2)
y = 12/4
y = 3 ... we get the proper y value, so the answer is confirmed.
Piecewise functions have different definitions, depending on when you evaluate them.
Given an input x, your function returns:
- 2x if the input is negative
- 1 if the input lies between 0 (included) and 2 (excluded)
- the square root of x if the input is greater than 2 (included)
You want to know what f(0) is. In other words, you want to know what happens if we give 0 as input.
The piecewise definition tells us that, if the input is 0, the function outputs 1.
So, you have f(0) = 1.
Answer:
Step-by-step explanation:
We can do this a couple of ways. We can graph it -- see below. Or we can do the math.
Math
y = x^2 - 2x - 15
This trinomial factors into
y = (x - 5)(x + 3)
from which
x - 5= 0
x = 5
and
x + 3 = 0
x = - 3
The y intercept is the value obtained when all the xs on the right = 0
y = 0^2 - 2*0 - 15
y = - 15
<em>Answer</em>
- x intercepts: (-3,0),(5,0)
- y intercept: (0,-15)
The graph is below.
Answer:
B. There is an association because the value 0.15 is not similar to the value 0.55
Step-by-step explanation:
Based on the above picture, for the nutritionist to determine whether there is an association between where food is prepared and the number of calories the food contains, there must be an association between two categorical variables.
The conditions that satisfy whether there exists an association between conditional relative frequencies are:
1. When there is a bigger difference in the conditional relative frequencies, the stronger the association between the variables.
2. When the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables.
For the given conditional relative frequency, we can see that there exists a significant difference between the columns of the table in the picture because 0.15 is significantly different from 0.55 and 0.85 is significantly different from 0.45
We can conclude that there is an association because the value 0.15 is not similar to the value 0.55
