Become a Multivariable Calculus Pro!

Find the solution set for the system
${\displaystyle x^2+y^2=25}$
${\displaystyle 25x^2+y^2=25}$
by graphing both of the system’s equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

Explain about Correlation test for Scale/ Ordinal Variables in terms of
a. Analysis background - a brief introduction on the objective of the analysis, hypothesis statements, and the variables.
b. Analysis procedures - the flow chart of the analysis procedures or the step-by - step procedure in performing the analysis.

Forest Fires and Acres Burned Numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned for 7 recent years are shown.
$$\begin{array}{cccccccc}Numberoffiresx& 62& 57& 72& 69& 58& 47& 84\\ Numberofacresburnedy& 61& 56& 71& 68& 57& 46& 83\end{array}$$
The correlation coefficient for the data is r=1 and a=0.05, Should regression analysis be done?
Find the equation of the regression line.
${\displaystyle y^{{}^{\prime }}=a+bx}$
Find ${\displaystyle y^{{}^{\prime }}}$ when x = 60.

Graph the sets of points whose polar coordinates satisfy the given polar equation. The given polar equation is written as follows:
${\displaystyle \theta =\frac{\pi }{2},r\le 0}$

What is the difference between a relative maximum and an absolute maximum on an interval |?

It has been reported that many university students are increasingly stressed out as a result of the pandemic and current online learning environment. To respond to the situation, a mental health center at a university is offering online meditation sessions for students. They are planning to investigate if attendance in the sessions can help students reduce their stress levels.
a) What type of experimentation and statistical analysis among the following: ANOVA (one-way, two-way), hypothesis testing (t-test, chi-squared test, F-test, ...), regression analysis, is needed to conduct such investigation?
b) If your answer to part (a) is hypothesis testing, specify the type of the test (e.g. t-test, chi squared test, F-test, ...) that is needed and then write the null and alternative hypothesis for your test.
If your answer to part (a) is one-way or two-way ANOVA, define the factor(s) and their level(s).
If your answer to part (a) is regression analysis, define your random variables.

${\displaystyle Letf\left(x\right)=x^5+5x^4+6x+3.}$
a. Conduct a sign analysis of f"". That is, determine the sign off"" on each interval. Make sure to show how you found the boundaries (endpoints) of the intervals and how you computed the sign in each interval.
b. indicate the intervals, if any, on which fis concave up and the intervals, if any, on which fis concave down.
c. Find the x-coordinates of any inflection points of f. If there are more than one, enter them as a comma- separated list. If there are none, enter ""DNE""

The analysis of shafts for a compressor is summarized by conformance to specifications. Suppose that a shaft is selected at random. What is the probability that the selected shaft conforms to surface finish requirements or to roundness requirements?
$$\begin{array}{|ccc|}\hline & & Roundness\\ & & Conforms& Doesnot\\ & & & Conforms\\ Surface& Conform& 345& 5\\ Finish& Doesnot& 1& 8\\ & Conform\\ \hline\end{array}$$

Question: Do laying hens have a comparable average weight depending on the food they eat ?
Find the type of analysis and the studied population used to answer the question above
information provided to help:
type of analysis: choose the right type of analysis to answer the questions
studied population: describe which population is concerned in each question (Ex: cows of all regions, or cows in X region, etc.)

Contract analysis. A contractor's financial outlay X and labor force Y are random variables with bivariate pdf given by: ${\displaystyle f_{X,Y}(x,y)=kxy}$ for ${\displaystyle 10,000<x<100,000}$ and ${\displaystyle 10<y<20}$ and ${\displaystyle =0}$, elsewhere. (a) Evaluate constant k.
(b) Detemine the marginal pdf of X and Y.

(a) In a regression analysis, the sum of squares for the predicted scores is 100 and the sum of squares error is 200, what is ${\displaystyle R^2}$?
(b) In a different regression analysis, 40% of the variance was explained. The sum of squares total is 1000. What is the sum of squares of the predicted values?

From 0-2 ${\displaystyle \sin \left(x^2\right)dx}$ using trapezoidal rule with n=4 as well as midpoint rule with n=4

Graph the sets of points whose polar coordinates satisfy the given polar equation.
The given polar equation is written as follows:
${\displaystyle -\frac{\pi }{4}\le \theta \le \frac{\pi }{4},-1\le r\le 1}$

Graph the sets of points whose polar coordinates satisfy the given polar equation.
The given polar equation is written as follows:
${\displaystyle \theta =\frac{\pi }{3},-1\le r\le 3}$

Here is partial output from a simple regression analysis.
The regression equation is
EAFE = 4.76 + 0.663 S&P
Analysis of Variance
$$\begin{array}{cccccc}Source& DF& SS& MS& F& P\\ Regression& 1& 3445.9& 3445.9& 9.50& 0.005\\ ResidualError& & & & & \\ Total& 29& 13598.3& & & \end{array}$$
Calculate the values of the following:
The regression standard error, ${\displaystyle s_e}$ (Round to 3 decimal places)
The coefficient of determination, ${\displaystyle r^2}$ (Round to 4 decimal places)
The correlation coefficient, r (Round to 4 decimal places)

What is the advantage of saying that to multiply a number by 100, we shift the digits two places to the left, instead of saying move the decimal places to the right?

Quick decision analysis Please pick the best outcome after calculation,
a) Council would accept ${\displaystyle (P_2=0.6)}$ and the mayor would not veto ${\displaystyle (P_3=0.8)}$, The probability of the compound event is
b) Council would accept ${\displaystyle (P_2=0.6)}$ and the mayor would veto ${\displaystyle (1-P_3=0.2)}$. The probability of the compound event is
c) Council would reject ${\displaystyle (1-P_2=0.4)}$ and the council would retum the same budget ${\displaystyle (P_4=0.6)}$. The probability of this compound event is

In the given equation as follows, use Taylor’s Theorem to obtain an upper bound for the error of the approximation. Then calculate the exact value of the error|:-
see the equation as attached here:-
${\displaystyle \cos \left(0.3\right)\approx 1-\frac{{\left(0.3\right)}^2}{2!}+\frac{{\left(0.3\right)}^4}{4!}}$

Why is it very easy to conclude that ${\displaystyle {\int }_1^{\propto }{x}^{2}dx}$ diverges without making any integration calculations?