Unlock the Secrets of Upper Level Math with Expert Guidance and Real-World Applications

Find a transformation from u,v space to x,y,z space that takes the triangle ${\displaystyle U=\left[\begin{array}{cc}0& 0\\ 1& 0\\ 0& 1\end{array}\right]}$ to the triangle
${\displaystyle T=[(1,0),-2),(-1,2,0),(1,1,2)]}$

The rate of change of the volume of a snowball that is melting is proportional to the surface area of the snowball. Suppose the snowball is perfectly spherical. Then the volume (in centimeters cubed) of a ball of radius r centimeters is ${\displaystyle \frac{4}{3}\pi r^3}$. The surface area is ${\displaystyle 4\pi r^2}$.Set up the differential equation for how r is changing. Then, suppose that at time $t=0$ minutes, the radius is 10 centimeters. After 5 minutes, the radius is 8 centimeters. At what time t will the snowball be completely melted.

Advanced Math
Find the final form of the median and range for uniform distribution (0,1) for order statistics.

Find the curvature K of the curve at the point $r(t)=e^t\cos t\cdot i+e^t\sin t\cdot j+e^{t}k,P(1,0,1)$

Find the present value of$5436.22 due in four years and three months at 4% compounded annually.
a:$4601.56
b:$4592.55
c:$4646.90
d:$6422.27

Advanced Math
If the height of a pyramid is increased by 60% and the length of an arm of a square is reduced by 35%, how much will the size of the pyramid increase or decrease?

At a certain university 523 of the seniors are history majors or math majors(or both).There are 100 senior math majors, and 33 seniors are majoring in both history and math. How many seniors are majoring in history?

The equation above gives the monthly cost C, in dollars, to take care of k kittens and b bunnies. John has 3 kittens and 5 bunnies, and Jenny has 2 kittens and 3 bunnies. How much greater, in dollars, is Johns

in Advanced Math
New Covid-19 patients arrive at the emergency room in Sultan Qaboos Hospital at a mean arrival rate of 18.8 patients per hour. Use Poisson distribution to compute the probability that at least three new patients will arrive at the emergency room within a 15-minute interval?

In fall 2014, 38% of applicants with a Math SAT of 700 or more were admitted by a certain university, while 12% with a Math SAT of less than 700 were admitted. Further, 32% of all applicants had a Math SAT score of 700 or more. What percentage of admitted applicants had a Math SAT of 700 or more? (Round your answer to the nearest percentage point.)

Advanced Math
A bipolar alkaline water electrolyzer stack module comprises 160 electrolytic cells that have an effective cell area of ${\displaystyle 2m^2}$. At nominal operation, the current density for a single cell of the electrolyzer stack is 0.40 ${\displaystyle \frac{A}{c}{m}^2}$. The nominal operating temperature of the water electrolyzer stack is ${\displaystyle {70}^{\circ }}$ C and pressure 1 bar. The voltage over a single electrolytic cell is 1.96 V at nominal load and 1.78 V at 50% of nominal load. The Faraday efficiency of the water electrolyzer stack is 95% at nominal current density, but at 50% of nominal load, the Faraday efficiency decreases to 80%.
(Give your answer to at least three significant digits.)
Calculate the nominal stack voltage:
Answer in V
Calculate the nominal stack current:
Answer in A
Calculate the nominal power on the water electrolyzer stack:
Answer in kW

What is the future of $2200 invested for nine months at 4.25% compounded semiannually?
Select one:
a:$2270
b:$2341.73
c:$2234>97
d:$2269.76

A bakery owner offered a 20% discount on a dozen cupcakes. The amount of the discount is 4.25$.
What is the regular price of a dozen cupcakes?

At a High school, 70% of the seniors have taken an advance calculus course. Of those who have taken Advanced Calculus, 60% will apply for a Pre-Health science major when they apply for college admission. Of those who have not taken advanced calculus, 40% will apply for a Pre-Health science major when they apply for college admission. A senior is selected at random. What is the probability that the senior have taken advanced calculus, given that the senior will apply for a pre-health science major?

The first four term of sequeces A,B,C,D are shown
Sequence A $(1/3),(2/4),(3/5),(4/6)$