### Graph Each System of Inequalities

Consider the following: y>x and x>3. Now, knowing this, graph y>x and x>3.

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Consider the following: y>x and x>3. Now, knowing this, graph y>x and x>3.

The following tables form part of a database held in a relational DBMS: Hotel (hotelNo, hotelName, city) Room (roomNo, hotelNo, type, price) Booking (hotelNo, guestNo, dateFrom, dateTo, roomNo) Guest (guestNo, guestName, guestAddress) where Hotel contains hotel details and hotelNo is the primary key; Room contains room d

Please see the attached file for the fully formatted problems. A. i) Find the natural logarithms of the values given as Items 8 and 9 on the worksheet. (Give your answer to 3d.p. where appropriate). ii) Refer to Item 10 on your worksheet. Using common logarithms find the value of 'x' and check your answer by numerical subst

1. Find all zeros for f(x)=x^4-15x^3+70x-156 2. Solve 3^x+2=65 Round your answer 3 decimal places. 3. Solve 6^4x+5=3^7x-1 Round your answer 3 decimal places. 4. Solve logx=4.952 Round your answer to 3 decimal places. 5. Solve 2^3x=3^4x-2 Round your answer to 3 decimal places. Please

Write recursion formula for series an = 1/2n

Sometimes a slight change in a problem can significantly alter the form of its solution. For example, find a simple algorithm for solving the following problem and classify it using big-theta notation: Divide a group of people into two disjoint subgroups (of arbitrary size) such that the difference in the total ages of the m

Category: Statistics Subject: Brownian Bridge Details: Let B(t) denote a process of Brownian motion. Let Q(t) be a Brownian Bridge process. Then, B(t)=(1+t) Q(t/(t+1)). Using the fact that P(max((b+B(t))/(1+t))>a)=exp(-2a(a-b)) show that for a Brownian Bridge Q(t) P(max(Q(u)>a)=exp(-2 a^2) where 0<=u<=1

Alice chooses two large prime numbers p and q. She finds their product, m=pq which is public. She also finds n= (p-1)(q-1) which is private. She chooses e which is a number relatively prime to n and finds d= the inverse of e (mod n). The number e is public and the number d is private. When Bob wants to send a message x (a number

Consider the differnetial equation y'(x) + xy(x) = 0 with y(0) = 0 Look for a solution of this problem of the form y(x) = A + B + Ce^-x + De^-1/2x^2 Use the fact that y must satisfy the equation and the initial conditions to identify the constants A,B,C and D. By setting u = -x^2/2 in the power series for f(u) = exp{u},

Let g(x)=integral from 1 to x sin t ln t dt. Find g'(x)

Eight small cubes are put together to form one large cube. All six sides of the larger cube are painted, the paint is allowed to dry, and then the cube is taken apart. a) How many of the small cubes will have paint on just one side? On two sides, On three sides? On no sides? b) Complete the following table, assuming in turn

Please see the attached file for the fully formatted problems. Can you please assist me with the problems listed below? P. 237 1. a) #6, b) #18 2. a) #22, b) #24 3. a) #32, b) #46 P.253 4. a) #1, b) #2, c) #3. d_ #4 5. a) #10, b) #12 6. a) # 28, b) #30 7. P.260, Matched Problem 1 P.271 8. # 2 - 22 (Eve

Find the solutions of (1) 153x is congruent to 6 (mod 12) (2) x + 1 is congruent to 3 (mod 7) (3) 8x is congruent to 6 (mod 422) (4) 363x is congruent to 345 (mod 624).

Find the solutions of (a) 4x is congruent to 3(mod 7) (b) 9x is congruent to 11(mod 26) (c) 3x + 1 is congruent to 4(mod 5) (d) 8x is congruent to 6(mod 14).

I have two sets of 64 numbers (1.1 to 7.4). Both number sets are created using the same equation for values of i from 0 to 63. m = 1.1 + ( i * 0.1 ) n = 1.1 + ( i * 0.1 ) I am trying to understand if the following equality is false in all cases except when the terms in each expression are equal (e.g. m^-12 = n^-12 and

Logarithms and exponents. See attached file for full problem description. Q1: Express in log form 82=64 Q2: express in exponential form log4256=4 Q3: find unknown log327=x Q4: express as sum diff or multiple logarithm a. log314 b. log2 5/10 c. log5 (n3) Q5: express as log of single quantity a. long23 + log22

Sketch the graph of each function. Be sure to label three points on the graph. If f(x) = integral (2x), find: (a) f(1.2) (b) f(1.6) (c) f(-1.8)

What is the additive principle? Please provide simple examples.

Show by induction that: a) Sum(n^2/[(2n-1)*(2n+1)],n=1..) = n(n+1)/[2*(2n+1)] b) Sum( r/(r-1)!, r=1..n) = 1-1/(n+1)! c) n^3+3n^2-10n is divisible by 3 d) 4^(2n+1) + 3^(n+2) is divisible by 13 See attached file for full problem description.

Prove by induction where n is a positive integer. (The questions are attached).

If the perimeter of a rectangle is 10 inches, and one side is one inch longer than the other, how long are the sides? Can you show me the steps to take to work out this and similar problems.

Diagonals in a Rectangle. In the case of a 2 X 2 rectangle, or a 3 X 5 rectangle, we can simply count. However, can we make a decision about a 100 X 167 or a 3600 X 288 rectangle? In general, given an N X K rectangle, how many grid squares are crossed by its diagonal?

The endpoints of the diameter of a circle are P=(-3,2) and Q=(5,-6) Find: (i) the center of the circle (ii) The radius of the circle (iii) the equation of the circle.

Application of Mathematical Induction It is an application of Mathematical Induction in proving the relations of Fibonacci Numbers. To prove: F 2n+1 - Fn Fn+2 = (-1) n for n > or, = 3.

Logarithmic and Exponential Equations. See attached file for full problem description.

Solve the integral using partial fraction decomposition. This example has a denominator that is the product of quadratics. Example 1) S (x2 + x +1)/[(x2 + 3x +1)(x2 +4x +2)] dx

A 5000 gallon aquarium is maintained with a pumping system that circulates 100 gallons of water per minute through the tank. To treat a certain fish malady, a soluble antibiotic is introduced into the inflow system. Assume that the inflow concentration of medicine is 10te-t/50 oz/gal, where t is measured in minutes. The well-

I will use the ^ sign for the squared sign. Write the following algebraic expression in its simplest form: x^ + 2x + 3x^ + 2 + 4x + 7

Simplify the following algebraic expression: 3X - (2 - X). Could you please explain the steps that I take when simplifying algebraic expressions such as this one? Thanks.

Can you provide me with the basic steps for solving problems in algebra? Please provide an example (e.g., a problem solving for the variable x) using these steps.