Homework Nest – Get Help with Math – Statistics, Advanced Math, Algebra, Permutations, and Calculus Engineering Questions

STATISTICS

*Question: *Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.29 ounces and a standard deviation of 0.04 ounces. Find the probability that the bottle contains between 12.19 and 12.25 ounces. Give your answer correct to four decimals.

*Question*: The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 4.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 4.0 minutes. Give your answer correct to four decimals.

*Question*: Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $40,000 and a standard deviation of $4000. What is the cutoff salary for teachers in the bottom 10%? Give your answer in dollars and include the dollar sign in your answer.

*Question*: Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.29 ounces and a standard deviation of 0.04 ounces. Find the probability that the bottle contains between 12.19 and 12.25 ounces. Give your answer correct to four decimals.

*Question*: Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $40,000 and a standard deviation of $4000. What is the cutoff salary for teachers in the bottom 10%? Give your answer in dollars and include the dollar sign in your answer.

CALCULUS

*Question*: A. Prove that in a tree with at least 2 vertices, there exists at least one leaf (in a tree, a le…

- Prove that in a tree with at least 2 vertices, there exists at least one leaf (in a tree, a leaf is any vertex of degree 1).
- Prove that in a tree with at least 2 vertices there exist at least two leaves.
- Prove that in a tree the number of leaves is greater or equal to the degree of the tree.

*Question*: A. Write down all the automorphisms of a 4–cycle. b. Prove that in each graph the number of verti…

- Write down all the automorphisms of a 4–cycle.
- Prove that in each graph the number of vertices of odd degree is even.
- Some pairs of the people at a party shake their hands. Prove that at least two persons shook the same number of hands. 9. Is it true that the complement of a connected graph is connected? Prove or disprove it. Is it true that the complement of a connected graph is not connected? Prove or disprove it.

*Question*: 10. Fix a path in a connected graph G. Then prove that there exists a spanning tree of G containi…

- Fix a path in a connected graph G. Then prove that there exists a spanning tree of G containing that path. More generally: given a subtree of G, then there exists a spanning tree containing it.
- (Uniqueness of paths in a tree) Prove that in a forest, given any tow vertices x and y, there exists at most one path between x and y (hence, in a tree, there exists exactly one path between them).

*Question*: 3. Determine the vertical and horizontal asymptotes (if any) of the graph of y- r2 +5x +6 4. Usin…

*Question*: 5. Determine the following limits. a) lim 3a2-2+1. 2+1 b) lim 3-6 c) lim In r. d) lim 3

*Question*: 6. Solve 73rtı = 11 for z. 7. a) Suppose we invest $3000 at a 5% annual rate compounded monthly. …

*Question*: 9. A company that makes office chairs has fixed costs of $7,000 per month plus a cost of $35 per …

*Question*: 10. Let f(x)-2 a) Draw the graph of y- f(x). b) Draw the graph of y-f(2)-1. e) What is the msxinm…

*Question*: 9. A company that makess office chairs has fixed costs of $7,000 per mouth plus a cost of $35 per…

What is the break even point?

*Question*: Calculate the integral from 1 to infinity of (sin t/t^2) dt

*Question*: 44. A cart is sliding along a straight track. Its position s as a function of time can modeled by…

*Question*: More practice problems: SET 1 I. For f(x)-I, state the domain, classify any discontinuities, and …

*Question*: A truck gets 10 miles per gallon (mpg) of diesel fuel traveling along an interstate highway at 50 mph. This mileage decreases by 0.15 mpg for each mile per hour increase above 50 mph. If the truck driver is paid $41/h and diesel fuel costs *P* = $3/gal, which speed *v* between 50 and 70 mph will minimize the cost of a trip along the highway? Notice that the actual cost depends on the length of the trip, but the optimal speed does not. (Round your answer to four decimal places.)

*Question*: Naltul/Student Basic Calculus-Math 1100-005 FS2018 – Homework: SECTION R.1 Score

*Question*: Chloe and Bao are in motorboats at the center of a lake. At time t = 0, Chloe begins traveling south at a speed of 55 km/h. One minute later, Bao takes off, heading east at a speed of 45 km/h. At what rate is the distance between them increasing at t = 13 min? (Round your answer to three decimal places.)

*Question*: 1. Find the derivative. a. f()sin1x b. f(x) tan 1(sin 2x) 2. Evaluate the integral. CoS x a. V9-s…

*Question*: Naltul/Student Basic Calculus-Math 1100-005 FS2018-Hussen Homework: SECTION R.

*Question*: Week Four Assignments- MA1xCoursework 3.pdf e i Need These Three Please ! C × x С Es seguro https…

ALGEBRA

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*Question*: The sum of two consecutive integers is between 20 and 24. Give all possible pairs of values that satisfy the inequality.

Question: Graph polynomial function f(x) = x^2-1, then state the domain and range.

*Question*: 1. Algebra: Consider the system of equations 2r2 + 2r3 C1 2×1 + x2 + 2×3 = -1. (a) Write the syst…

*Question*: Find the matrix A for each linear transformation T, given its action on the standard basis. Then …

*Question*: Unit Conversion Example: Determine the following unit conversions to SI units: 1 kamde 이000 (mol…

*Question*: Unit Conversion Example: A machine automatically fills cases of canned corn at the rate of one

*Question*: Given that g(x)-2x -2x+1, find each of the following a) g(0) b) g(-2) c) g(2) d) g(-x) e) g(1-t) …

*Question*: City Cabs charges a $1.25 pickup fee and $1.75 per mile traveled. Diego’s fare for a cross-town cab ride is $17.00 How far did he travel in the cab?

ADVANCED MATH

*Question*: 2. Let X be a set, and P(X) its powerset. Define a function f : P(X) P(X) by (a) (b) Consider the…

*Question*: Algebra Let F: R3 → R2 be a linear transformation satisfying (a) Find F (b) Find ker(F) In both

*Question*: Question 5. (4 marks.) D is the region in the first quadrant that lies between the circles 2 y 9 …

*Question*: 1.28 Geometric interpretations of integrals. (Sections 2.0). Complete the missing analytical stat…

*Question*: 1.27 Integrals of commonly-encountered functions. (Section 2.9). Calculate the following indefini…

*Question*: 1 0 0 (12) If A01 0 0 0 1. find projc(alo for b-(1,2,3,4). Find P the matrix of projection for C(A)

*Question*: (16) Consider the points (0,0), (1,8), (3,8),(4,20). Fit the best straight line through the point…

*Question*: (16) Consider the points (0,0), (1,8), (3,8),(4,20). Fit the best straight line through the point…

*Question*: (24) Let A-2-1 -2 4 {q1, 72^ span C(A a) Find orthonormal vectors q1, q2, q3 such that (b) In wha…

*Question*: X1, X2, X3, X4 X1 + X2 + X3-X4 a F1nd a basis for the subspace S (b) Find a basis for the subspac…

*Question*: ( ) r or e slog e mu e s such that ol T- (r, r, r, r) (28) Let A = | 2 1 | . Apply QR decompositi…

DISCRETE MATH

*Question*: **How many of the following curves are characteristic curves of the equation**

**(i) **

**(ii) **

**(iii) **

**(iv) **

**v)**

**vi)**

*Question*: a) How many of the following lines are admissible side condition lines for the equation in the domain ,

** **

*Question*: The Cone tank has a dipstick to measure the level of water W in the tank. The dipstick measures the vertical height (h) of the water level in the tank.

Assume the Cone holds 1000 litres of water, and its height is 100 cm.

Complete the table below for the volume and height of water level in the 1000 litre Cone tank.

Height of water level (h cm) |
0 cm |
10 cm |
20 cm |
30 cm |
40 cm |

Radius (cm) of water surface |
|||||

Volume of water (W litres) |

Complete the table below to show where the 100 litre marks should be placed on the gauge.

Volume ofwater (W) |
100 L |
200 L |
300 L |
400 L |
500 L |
600 L |
700 L |
800 L |
900 L |
1000 L |

Depth ofwater (h) |
100 cm |

*Question*: 10 marks Consider the curve y x3-5×2 7x-2 (a) Find all stationary points of the curve. (b) Determ…

*Question*: a) **A plane curve **** is such that**** and **** .Find the two-norm of the image of the tangent vector **** under the map **

**given by. **

*Question*: 2.Medication Z is prescribed for a 50 kg woman and is to be given in enteric-coated pills of 125 …

*Question*: 1. Consider the joint density

f(x ,x )=2e−x1 ,x >0,0<x <1.12 x21 2

- a) Compute fX2 (x2) and fX1|X2 (x1|x2).
- b) Give the best approximation g∗(X2) in mean square sense for X1 (i.e. find explic- itly g∗(X2) that minimizes E[X1 − g(X2)]2 over all possible choices of g(X2) such thatE[g(X2)2] < ∞).
- c) For a given realization x2, calculate the mean square error of the best approximation (that is, calculate E{[X1 − g∗(X2)]2|X2 = x2}.)

MECHANICAL ENGINEERING

A heat engine operates between two reservoirs at 1000°C and 20°C. The heat engine is used to driv…

*Question*: Air enters an adiabatic nozzle steadily at 300 kPa, 200°C, and 30 m/s and leaves at 100 kPa and 1…

*Question*: QUESTION 1 (Basic Principles: Dixon and Hall) Derive the governing equations for work input requi…

*Question*: QUESTION 2 (Axial flow Turbines: Dixon and Hall ) Air is expanded in a multi-stage axial flow tur…

*Question*: A system contains 0.2 m3 of air at a pressure of 400 kPa and 200°C It is expanded polytropically …

*Question*: QUESTION 4 (Axial Flow Compressors: Dixon and Hall) In a jet engine rotor the high pressure axial…

* **Question*: Problem 3 (25pts.): Water flows over a flat plate with free-stream velocity uo – 0.1m/s. The temp…