Expert Help with Multivariable Function Questions

${\displaystyle Letf\left(x\right)=x^5+5x^4+6x+3.}$
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""

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?

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.)

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?
$$\begin{array}{|ccc|}\hline & & Roundness\\ & & Conforms& Doesnot\\ & & & Conforms\\ Surface& Conform& 345& 5\\ Finish& Doesnot& 1& 8\\ & Conform\\ \hline\end{array}$$

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:
${\displaystyle \theta =\frac{\pi }{3},-1\le r\le 3}$

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

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)

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?

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?

T-Shirts The Physics Club sells ${\displaystyle E=m{c}^2}$.
T-shirts at the local flea market. Unfortunately, the club’s previous
administration has been losing money for years, so you decide to do an
analysis of the sales. A quadratic
regression based on old sales data reveals the following demand equation for the T-shirts:
${\displaystyle q=-2p+33p(9\le p\le 15)2}$
 Here, p is the price the club charges per T-shirt and q is the
number it can sell each day at the flea market. a. Obtain a formula for
the price elasticity of demand for ${\displaystyle E=m{c}^2}$ T-shirts. b. Compute the
elasticity of demand if the price is set at $10 per shirt. Interpret the
result. c. How much should the Physics Club charge for the T-shirts to
obtain the maximum daily revenue? What will this revenue be?"

Discuss the continuity of function ${\displaystyle f\left(x\right)=\frac{1}{x^3+1}}$ on ${\displaystyle \mathbb{R}}$

Consider the integral ${\displaystyle {\int }_0^{3}3x^{2}dx}$. Use Riemann sums with right endpoints to compute the exact value of the integral.

Bob wanted to reach the peak of a mountain.He started at te the base and started driving a car towards the peak of the mountain.
The car started at 0 mph and the speed increased over time to 40 mph.Halfway towards the peak of the mountain,the terrain became too rugged and Bob instantly stopped his car to analyze the terrain.After spending time observing the terrain, Bob decided to instantly climb the rocky terrain at a slov pase.OnceBob passed the rocky terrain he realized his shins were cut up so he immediately travelled back to the car at thesame slov pace as before. After spending time putting on bandages, he realized there was a side path to thepeak of the mountain. He immediately started running to the peak of the mountain and eventually reached the peak.
Graph the relationship between Bob's (a) distance and time and (b) position and time.
For the graph,make it clear what part of your function corresponds with his different parts of his travels,
(Label each segment of your graph)

A large number N of people are subjected to a blood investigation. This investigation can be organized in two ways.
(1) The blood of each person is investigated separately. In this case N analyses are needed.
(2) The blood of k people are mixed and the mixture is analysed. If the result is negative, then this single analysis is sufficient for k persons. But if it is positive, then the blood of each one must be subsequently investigated separately, and in toto for k people, k+1 analysis are needed. It is assumed that the probability of a positive result (p) is the same for all people and that the results of the analysis are independent in the probabilistic sense.
For what k is the minimum expected number of necessary analysis attained?