If there is such a scalar function <em>f</em>, then



Integrate both sides of the first equation with respect to <em>x</em> :

Differentiate both sides with respect to <em>y</em> :


Integrate both sides with respect to <em>y</em> :

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :



Integrate both sides with respect to <em>z</em> :

So we end up with

Answer:
The Answer is B) Hope it helps!
Step-by-step explanation:
Hey there! Welcome to Brainly!
Let's see how many marbles we have in total.
12+11+17+5=45
We want to find the probability of selecting a marble that is not blue. Let's see how many marbles aren't blue.
12+11+5=28
We have this probability out of 48.
28/48
We simplify, giving us 7/12 or about 58.33%.
I hope this helps!
<span>Find
the number of columns and rows of the cupcake in a rectangle shape with 120
pieces.
=> The row must ne even and the column must be add
=> 120 = 2 x 2 x 2 x 15
=> 120 = 8 x 15
=> 120 = 120
Thus, the glee club will need to arrange the row of the rectangle shaped
cupcake as 8 rows and the column as 15
columns.
That gets the total of 120 cupcakes in all.
</span>
Answer:
Step-by-step explanation:
Hello!
Given the linear regression of Y: "Annual salary" as a function of X: "Mean score on teaching evaluation" of a population of university professors. It is desired to study whether student evaluations are related to salaries.
The population equation line is
E(Y)= β₀ + β₁X
Using the information of a n= 100 sample, the following data was calculated:
R²= 0.23
Coefficient Standard Error
Intercept 25675.5 11393
x 5321 2119
The estimated equation is
^Y= 25675.5 + 5321X
Now if the interest is to test if the teaching evaluation affects the proffesor's annual salary, the hypotheses are:
H₀: β = 0
H₁: β ≠ 0
There are two statistic you can use to make this test, a Student's t or an ANOVA F.
Since you have information about the estimation of β you can calculate the two tailed t test using the formula:
~
= 25.1109
The p-value is two-tailed, and is the probability of getting a value as extreme as the calculated
under the distribution 
p-value < 0.00001
I hope it helps!