Given the conditional relative frequency table below which was generated by
column using frequency table data comparing the number of calories in a meal to
whether the meal was prepared at home or at a restaurant.
Number of Calories and Location of Meal Preparation.
Home Restaurant Total
≥ 500 calories 0.15 0.55 0.28
< 500 calories 0.85 0.45 0.72
Total 1.0 1.0 1.0
To determine whether there is an association between where food is prepared and the number of carories the food contain, we recall that an "association" exists between two categorical variables if the column conditional relative frequencies are different
for the columns of the table. The bigger the differences in
the conditional relative frequencies, the stronger the association
between the variables. If the conditional relative frequencies are
nearly equal for all categories, there may be no association between the
variables. Such variables are said to be <span>independent.
For the given conditional relative freduency, we can see that there is a significant difference between the columns of the table.
i.e. 0.15 is significantly different from 0.55 and 0.85 is significantly different from 0.45
Therefore, we can conclude from the given answer options that t</span><span>here is an association because the value 0.15 is not similar to the value 0.55</span>
Given the function f (x) = 3x, find the value of f-1 (81).
For this case, the first thing you should do is rewrite the function.
We have then:
y = 3 ^ x
From here, we clear the value of x:
log3 (y) = log3 (3 ^ x)
log3 (y) = x
Then, we rewrite the function again:
f (x) ^ - 1 = log3 (x)
Now, we evaluate the inverse function for x = 81:
f (81) ^ - 1 = log3 (81)
f (x) ^ - 1 = 4
Answer:
the value of f-1 (81) is:
f (x) ^ - 1 = 4
Answer:
x=27
Step-by-step explanation:
The mean is add all the numbers and divide by the number of points
(2+7+x)/3 =12
Multiply each side by 3
(2+7+x)/3 *3 =12*3
2+7+x = 36
Combine like terms
9+x = 36
Subtract 9 from each side
9+x-9 = 36-9
x = 27
The equation will be y=4/x. u can make the table of variables by inserting the values of x in the equation. for suppose here, if x=1 then y=4 , x=2 then y=2 and so on.
Answer:
<h2>It must be shown that both j(k(x)) and k(j(x)) equal x</h2>
Step-by-step explanation:
Given the function j(x) = 11.6
and k(x) = 
, to show that both equality functions are true, all we need to show is that both j(k(x)) and k(j(x)) equal x,
For j(k(x));
j(k(x)) = j[(ln x/11.6)]
j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}
j[(ln x/11.6)] = 11.6(x/11.6) (exponential function will cancel out the natural logarithm)
j[(ln x/11.6)] = 11.6 * x/11.6
j[(ln x/11.6)] = x
Hence j[k(x)] = x
Similarly for k[j(x)];
k[j(x)] = k[11.6e^x]
k[11.6e^x] = ln (11.6e^x/11.6)
k[11.6e^x] = ln(e^x)
exponential function will cancel out the natural logarithm leaving x
k[11.6e^x] = x
Hence k[j(x)] = x
From the calculations above, it can be seen that j[k(x)] = k[j(x)] = x, this shows that the functions j(x) = 11.6 and k(x) = are inverse functions.
