Expert Help with Multivariable Function Questions

Find the GPA of a student if he gives average hours to study by using regression alysis. A random sample of ten students is selected from a class of 60 students, find regression line and also find the GPA of a student if he gives average hours to study by using this regression analysis. Their GPA and the hours to study are given below:
$$\begin{array}{|ccccccccccc|}\hline GPA& 2.5& 3.1& 3.6& 3.2& 2.9& 3.7& 2.9& 2.4& 3.3& 3.5\\ Hourstostudy& 3& 5& 7& 5& 3& 8& 4& 2& 5& 7\\ \hline\end{array}$$
Also interpret the regression coefficient.

In a university examination, which was indeed very tough, ${\displaystyle 50\mathrm{\%}}$ at jeast failed in "Statistics",${\displaystyle 75\mathrm{\%}}$ at least in Topology, ${\displaystyle 82\mathrm{\%}}$ at least in "Functional Analysis" and ${\displaystyle 96\mathrm{\%}}$ at least in "Applied Mathematics". How many at least failed in all the four? (Ans.${\displaystyle 3\mathrm{\%}}$)

Javier earned $8.50 per hour for 32 hours and $12.75 per hour for 8 hour. What was his average hourly wage for those 40 hours?

Loring Brace and colleagues at the University of Michigan Museum of Anthropology indicate that the size of human teeth continues to grow. Decrease, and that the evolutionary process is not yet stop. In northern Europeans, for example, tooth size the reduction is now 1% in 1000 years. What size will the teeth of our descendants be in 20,000 years? Now (as a percentage of our current tooth size)?
The analysis of tooth shrinkage by

A researcher calculates the variance of her sample to be ${\displaystyle s^2=-6.}$
What would you tell the researcher about her analysis?

Find the variance/covariance matriz for the following data set
$$\begin{array}{|cccc|}\hline Student& Algebra& Combinatorics& Analysis\\ 1& 90& 80& 90\\ 2& 30& 60& 30\\ 3& 60& 60& 50\\ 4& 90& 60& 30\\ 5& 40& 70& 40\\ \hline\end{array}$$

Based on the design of the antennas, the Standard Absorption Rate (SAR) of RF power by the patient tissue is expected to be as follows:
${\displaystyle SAR\left(t\right)=\sqrt{2t+e^{0.1t+2}}}$ where, t is time in seconds.
1. Fonnulate a mathematical model for the dosage of exposure, D(t). Hint: the dosage is the area under the SAR curve.
2. Plot the dosage function for the first 80 seconds.

The response area during an analysis of compound A in river water samples for five replications using HPLC-DAD were tabulated below.
$$\begin{array}{|cccccc|}\hline \text{No. of trial}& 1& 2& 3& 4& 5\\ \text{Area of metoprolol}& 424& 540& 428& 431& 532\\ \hline\end{array}$$
(I) Based on the tabulated data, calculate the % RSD
(II) Comment on the precision obtained from the analysis.

Mus. Spring Analysis I Suppose that ${\displaystyle x\left(t\right)=4\cos 4t-3\sin 4t+5t\sin 4t}$ I is the solution of a mass-spring system mi ${\displaystyle +bi+kx=F\left(t\right),x\left(O\right)=xo,.i\left(O\right)=fo}$ Assume that the homogeneous solution is not identically
(a) Determine the pan of the solution associaaed with the homogeneous DE.
(b) Calculate the amplitude of the oscillation of the homogeneous solution.
(c) Determine the amplitude of the panicular solution.
(d) Which part of the solution will be unchanged if the conditions are changed?
(e) If the mass is 1 kg, what is the spring constant?
(f) Describe the motion of the mass according to the solution.

Break-Even Analysis You are setting up a part-time business with an
initial investment of $21,000. The unit cost of the product is $11.50, and the selling price is $19.90.
a) Find equations for the total cost C (in dollars) and total revenue R (in dollars) for x units.
b) Find the break-even point by finding the point of intersection of the cost and revenue equations.
c) How many units would yield a profit of $1000?

A company charges ${\displaystyle \mathrm{\$}2.50}$ per bottle when a certain beverage is bought in lots of 120 bottles or less, with a price per bottle of ${\displaystyle \mathrm{\$}2.25}$ if more than 120 bottles are purchased. Let ${\displaystyle C\left(x\right)}$ represent the cost of x bottles. Find the cost for the following numbers of bottles.
a) 90
b) 120
c) 150

What is one way of expressing the special number e as a limit? What is an approximate numerical value of e correct to 7 decimal places?

State and prove the linearity property of the Laplace transform by using the definition of Laplace transform. Give an example by selecting different types of function, from, trigonometric, polynomial, exponential that shows the application of this property while solving the Laplace transform by using direct rules.Does such property hold for the inverse Laplace transform as well? Prove by giving a suitable example.

a) A low voltage transformer manufacturing line has a purchase order of 1700 piece, If the manufacturing line production rate is 22 piece per minute use dimensional analysis techniques to determine the time taken to produce the requested transformers tothe nearest minut in hours and minutes.
b) Assume that the production time of a transformer can be given by the following formals:
${\displaystyle t=G{m}^{\frac{1}{3}}{v}^{-3}{l}^2}$
Where m is the mass of the transformer in kg, v is the velocity of the manufacturing line in ${\displaystyle \frac{m}{s}}$ and l is the length of the production line in meters. Find the diamensions of G.
c) In b, if ${\displaystyle m=220}$ grams, ${\displaystyle l=10.2m,v=2.3\frac{m}{s}}$ and time is 30.1 ms. Find G?

In a certain city, the temperature (in ${\displaystyle F^{\circ }}$) at t hours after 9 AM is modeled by the function ${\displaystyle T\left(t\right)=50+14\sin \left(\frac{\pi t}{12}\right)}$. Find the average temperature during the period from 9 AM to 9 PM.

The reason to find points of intersection of polar graph which may require further analysis beyond solving two equations simultaneously
Take examples of two polar equations ${\displaystyle r=1-2\cos \theta }$ and ${\displaystyle r=1}$.

Stock analysis. The price-earning ratios of 100 randomly selected stocks from the New York Stock
$$\overline{)\begin{array}{cc}Interval& Frequency\\ -0.5-4.5& 7\\ 4.5-9.5& 54\\ 9.5-14.5& 22\\ 14.5-19.5& 10\\ 19.5-24.5& 2\\ 24.5-29.5& 3\\ 29.5-34.5& 2\end{array}}$$
a. Find the mean of the price-earning ratios.

To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one or two separate steps, and the second procedure requires either one, two, or three steps.
(a)
List the experimental outcomes associated with performing the blood analysis. (Select all that apply.)
(1)(2)(3)(1, 1)(1, 2)(1, 3)(2, 1)(2, 2)(2, 3)(3, 1)(3, 2)(3, 3)
(b)
If the random variable of interest is the total number of steps required to do the complete analysis (both procedures), show what value the random variable will assume for each of the experimental outcomes. (If an experimental outcome does not occur, enter NONE.)
Experimental Number of Steps
Outcome Required
(1)
(2)
(3)
(1, 1)
(1, 2)
(1, 3)
Experimental Number of Steps
Outcome Required
(2, 1)
(2, 2)
(2, 3)
(3, 1)
(3, 2)
(3, 3)

Determine whether the function is continuous at the given point. Show your solution.
${\displaystyle k\left(x\right)=\frac{x^2}{x^3+1}atx=-1}$"

Evaluate the given limits by using table of values. Use table of values to evaluate the given limit, show your Complete Solutions (This is all about Basic Calculus: Evaluating limits using Table of Values).
a) ${\displaystyle \underset{t\to 0}{lim}\left(\frac{\sin t(\cos t-1)}{t^2}\right)}$
b) ${\displaystyle \underset{t\to 0}{lim}(e^{2t}\times \frac{e^t-1}{t})}$