1) Let A be nxn matrix and Ax=b, if we need change A to Upper triangular matrix using Gaussian Elimination, how many additions/subtraction operations are involved? how many multiplication/division operations are involved?

2) Once we got the upper triangular matrix, now we need to apply back-substitution, how many additions/subtraction operations are involved? how many multiplication/division operations are involved?

1)The doctor has determined that the reason you and your child fell ill is that you have a protein deficiency. Therefore, you determine to increase the amount of protein that you and your child consume. To begin this process, you have to figure out how much protein you should consume in a day. Assume that you are 30 years old and weigh 158 pounds and that your child is 2 years old and weighs 35 pounds. Try doing a Google search for the answer. List your results for the 158 pound female and the 2 year old 35 pound child. Child’s amount of daily protein _______ and your amount of daily protein________

Which item is the best purchase in terms of price per gram of protein?

Were you surprised with any of your results? Answer in complete sentences.

3)While still in the hospital, the doctor writes an order for an antibiotic at 250mg/kg/day. You are nervous now because the nurse was wrong before. Assuming that you weigh 158 lb, determine how many milligrams should you be given. What is the equivalent number of grams? (Hint: 1000 mg = 1 g and mg/kg/day = )

The Snowplow Problem

To apply the techniques discussed in this chapter to real-world problems, it is neces-

sary to translate these problems into questions that can be answered mathematically.

The process of reformulating a real-world problem as a mathematical one often requires

making certain simplifying assumptions. To illustrate this, consider the following snow-

plow problem:

One morning it began to snow very hard and continued snowing steadily

throughout the day. A snowplow set out at 9:00 am to clear a road,

clearing 2 mi by 11:00 am and an additional mile by 1:00 pm. At what

time did it start snowing?

To solve this problem, you can make two physical assumptions concerning the rate

at which it is snowing and the rate at which the snowplow can clear the road. Because

it is snowing steadily, it is reasonable to assume it is snowing at a constant rate. From

the data given (and from our experience), the deeper the snow, the slower the snowplow

moves. With this in mind, assume that the rate (in mph) at which a snowplow can clear

a road is inversely proportional to the depth of the snow.

please show all work

Two Snowplows: One day it began to snow exactly at noon at a heavy and steady rate. A snow plow left its garage at 1:00 pm, and another followed in its tracks at 2:00 pm. (a) At what time did the second snowplow crash into the first? To answer this questions, assume as in Project D that the rate (in mph) at which a snowplow can clear the road is inversely proportional to the depth fo the snow (and hence to the time elapsed since the road was clear of snow). [Hint: Begin by writing dierential equations for x(t) and y(t), the distances traveled by the first and second snowplows, respectively, at t hours past noon. To solve the dierential equation involving y, let t rather than y be the dependent variable!]

(b) Could the crash have been avoided by dispatching the second snowplow at 3:00 pm instead?

please show all work

Discuss the following terms giving their definitions and clarifying the definitions by giving suitable examples.

1-subset

2-proper subset

3-improper subset

4-emtpy set

5-power set

can you please write the question using the keypoard to be able to copy and paste the answer not picture . Thanks

It is estimated by experts on agriculture that one-third of an acre of land is needed to provide food for one person on a continuing basis. It is also estimated that there are 10 billion acres of arable land on earth, and that therefore a maximum population of 30 billion people can be sustained if no other sources of food are known. The total world population at the beginning of 1970 was 3.6 billion. Assuming that the population continues to increase at the rate of 2 percent per year, when will the earth be full? What will be the population in the year 2000?

prove that the square of the product of 3 consecutive integers is always divisible by 12

Show that any open subset of R (w std. topology) is a countable union of open intervals.

What is the objective of this problem and enough to show ?

Minimum 320 words and unique content please. In your opinion, what is the most important aspect of starting a business? What passion or interests led you to the decision to create your business?
Thank you!

Show that, for each natural number n, (x − 1)(x − 2)(x − 3). . .(x − n) − 1 is irreducible over Q, the rationals.

Using the SATGPA data set in Stat2Data package. Test by using α= .05.

1) Create the following three variables and then print out all the six variables.

Create a new variable “SAT”, which is the sum of MathSAT and VerbalSAT.

Create second new variable “SATLevel”, and assign the value of “SATLevel” as 1 when

SAT<=1100, 2 when 1100<SAT<=1200, 3 when 1200<SAT<=1300, and 4 when

SAT>1300.

Create third new variable “GPALevel” and assign the value of “GPALevel” as 1 when

GPA<=2.8, 2 when 2.8<GPA<=3.3, 3 when 3.3<GPA<=3.5, and 4 when GPA>3.5

Print out all the data in the descending order of their GPALevel and the ascending order of

their SAT when GPALevel is the same.

2) Use the Chi-Square test to conclude if the SATLevel and GPALevel are independent.
3) Compute the mean and variance of “GPA” for each level of “GPALevel”, and compute the

correlation matrices for the four variables: MathSAT, VerbalSAT, GPA and SAT.
4) Do the data provide sufficient evidence to indicate that the mean of MathSAT is significantly greater

than the mean of VerbalSAT.
5) Test if the proportion of MathSAT greater than VerbalSAT is 0.6.

(2) PQRS is a quadrilateral and M is the midpoint of PS.
PQ = a, QR = b and SQ = a – 2b.
(a) Show that PS = 2b.
Answer(a)
[1]
(b) Write down the mathematical name for the quadrilateral PQRM, giving reasons for your answer.
Answer(b) .............................................................. because ...............................................................
............................................................................................................................................................. [2]
__________

A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 metres per second.
It continues at this speed for 1 minute.
It then decelerates for 3 minutes until it stops at the next station.
The diagram shows the speed-time graph for this journey.
Calculate the distance, in metres, between the two stations

Carry out a numerical experiment to compare the accu- racy of Formulas (5) and (19) on a function f whose derivative can be computed precisely. Take a sequence of valuesforh,suchas4−n with0≦n≦12.

hint: For CE 4.3.4, use f(x) = sin x and x = 0.25, for example. Then the exact derivative is cos 0.25, so you can compare your results to it, compute errors, and study how they behave as h decreases. You may want to format your outputs so that for each n you print, on the same row, the values of h, approximate f 0 (0.25), error of the approximation, and the theoretically estimated error term (h 2/6 for formula (5) and h 4/30 for formula (19)—here we are using the fact that the derivatives of sin x are at most 1 in absolute value). Don’t forget to discuss your findings!

f′(x)≈ 1 [f(x+h)− f(x−h)] (5)

f′(x)≈ 1 [f(x+h)− f(x−h)] /2h − 1 /12h(f(x +2h)−2[f(x +h)− f(x −h)]− f(x −2h)) (19)

Describe in detail a Queueing Theory. Include in your discussion general examples of particular industries that might employ Queueing Theory and why? Finally, present a specific example showing in detail where Queueing Theory can be employed and show a stepwise solution using this theory.