Permutations and Combinations Questions and Answers

Consider the system of equations x₁ + x₂ + x₂ = 2 2x₁ + x₂ - x₂ = 5 x₁ - x₂-3x₂ = 2 Using the inverse of A or otherwise, find the solution x =

Suppose that and B are acute angles such that cos (a) = 4/5 and tan (B) = 15/8 Compute the following. Enter exact answers; decimal approximations will be marked incorrect. (a) sin(a + B) (b) cos(a + B) (c) sin(2a)

You choose 1000 ordered pairs where x and y are both randomly chosen between 0 and 1. How many of those ordered pairs would you expect to satisfy y>x^3?

In how many ways can the letters of CALCULATOR be arranged? a)453,600 b) 3,628,800 c) 100,000,000 d) 24

The amount of caffeine remaining in a person's system t hours after drinking an energy drink can be modeled by the function y = yoe -0.12160477t. If a person's system initially contains 175 mg of caffeine from consuming an energy drink, how long will it take for the amount of caffeine to decay to 10mg? Setup an equation and solve. Label your answer and round it to one decimal place.

Simplify the radical expression. It may be helpful to change the expression to the exponential form first. (√x/z2)6 When simplified, what is the power of x in numerator? When simplified, what is the power of z in denominator?

Find all solutions to each congruence. (a) 7x ≡ 3 (mod 15) (b) 6x ≡ 5 (mod 15) (c) x² ≡ 1 (mod 8)

6. It is determined that an artifact has 30 grams of its original 40 grams of carbon-14 remaining. How old is the artifact? Label your answer and round it to the nearest year. Recall: =yoe-0.00012097t

Solve the equation. Give the exact value and approximate the solution to the nearest thousandth. Use ^ to enter exponents, as in 2^5-1 means 25 – 1. log(m - 8) = 1.9

Rewrite the rectangular equation in polar form. y = 16

You are a landlord and one of your tenants complained that the refrigerator was not working properly. You plan to sell this property in three years, so you are only concerned with the least expensive solution that results in the refrigerator working for the next three years. To address this issue you can purchase a new refrigerator for $400 and it will last for 3 years. You can repair the current refrigerator for $150, but estimate there is only a t 30% chance it will last a full 3 years. If the repaired refrigerator does not last a full 3 years, you will end up purchasing a new refrigerator, but it will cost you $500 if you wait. You can buy a used refrigerator for $200, and there is a 60% chance it will last for 3 years. If it breaks down within the three years, you estimate a 40% probability that you will repair the used refrigerator for $150, otherwise, you will end up purchasing a new refrigerator for $500. If the used refrigerator is repaired, there is only a 30% chance it will last the remainder of the 3 years. If the repaired used refrigerator breaks down within three years from today, you will end up purchasing a new refrigerator for $500.

Solve the equation. x/2x+2 = -2x/4x+4 + 2x-3/x+1

Determine whether there is a minimum or a maximum value to each quadratic function. Find the value and the axis of symmetry. f(x) = 2x² - 8x - 9

Consider the graph and identify the Amplitude and Period. Choose the correct answer to fill in the blanks below.

Evaluate the following expression. Write the exact answer. Do not round. If the value does not exist, write DNE for your answer.

Determine the exact value of the following expression. cos615

Val belongs to a Netflix-lovers group with a total of n people, We say that between two members of the group there where n is a Netflix-party relationship if the two have Netflix-partied together, and we know that each person in the group has Netflix-partied with p or more other members of the group. Prove that if p > 2, then the group is connected (i.e. any two members are connected by a path of Netflix-party relationships).

Given a function f with its inverse function, f1, which of the following must be true?

Above is a graph of the sinusoidal function. State the function's formula in terms of x. Be sure to PREVIEW your answer before submitting!

Prove that the dihedral group Dn, n ≥ 3, is not simple.

Find the equation of the line passing through the given points: (-2, 9) and (-2,8).

A common style of counting problem involves drawing from a deck of playing cards. In a standard deck of playing cards, there are 52 different cards. Each card is one of 13 different values, and one of 4 different suits (of which there are 2 red suits and 2 black suits). A hand of cards is a selection of cards from the deck, where the order they are selected in does not matter. How many 11-card hands contain cards of only one suit? b) How many 5-card hands contain four cards of the same value? c) How many 10-card hands contain four cards of the same value? d) A hand of 15 cards is sellected from a standard deck of playing cards. At least one sult is guaranteed to appear at least how many times?

Find the domain and range of the relation: {(-7, 9), (-7, 8), (-7, 7), (-7, 6)}. Then determine whether the relation is a function.

y = 2/5x - 3 a. Write the equation of a line parallel to the given line b. Write the equation of a line perpendicular and passing to the given line and passing through (1, -1). Show your work. through (1, -1). Show your work.

Solve the following formula for the specified variable. C = 4πw for w w=(Type an exact answer, using as needed.)

How can sales tax alter the size of the tip you leave at a restaurant? a. A tip of a given percentage (such as a 20% tip) will be larger if calculated after tax than if calculated before tax. b. The tip becomes part of the bill as a whole, so you have to increase the sales tax by a corresponding amount. c. You do not have to double-calculate a percentage on any purchases, so you should pay for tax or a tip but not both. d. A standard tip is 15% to 20% of the sales tax. Please select the best answer from the choices provided

the table shows the numbering system used in the United States (x) and Europe (y) for shoe sizes. Shoe Sizes U.S. Size 1 3 5 7 9 11 European Size 31 34 36 39 41 44 a). Make a scatter plot by hand. b). Describe the correlation. Give a reason for your answer. c). Write the equation of a trend line. Show your work.

Solve the following formula for the specified variable. C=(1/4)e .p for e e=

Solve the following formula for the specified variable. V = Ghc for G G=[]

Let V be an inner product space with an orthonormal basis B {V₁, V2,..., Vn}. Let v = a₁v₁ + a₂V₂+...+anVn and w = b₁V₁+b₂V2+...+bnVn. Prove (v, w) = a₁b₁+a₂b2+...+anbn.

Show that if an n-vertex graph G contains at least [n²/4]+1 edges, then G contains at least [n/2] triangles.

Write a polynomial in standard form with zeros at 3, 2, -1. Choose all that apply to the polynomial. Select one or more: a. There are three positive terms and one negative term. b. There are four terms in the polynomial. c. There are two coefficients that are even numbers. d. There are two positive terms and two negative terms. e. All the coefficients are odd numbers.

Evaluate x-y for the given replacement values. x = 2 and y = -25 x-y=

Find a third-degree polynomial equation with rational coefficients that has roots -4 and 2 + i. Select one: a. x³ - 11x + 20 = 0 b. x³ - 11x = 0 c. x³ - 4x² + 5x = 0 d. x³ - 4x + 5 = 0

If a baseball is projected upward from ground level with an initial velocity of 32 feet per second, then its height is a function of time, given by s=-16t² +32t . What is the maximum height reached by the ball? The maximum height reached by the ball is _____

Although rare, tied swimming races occur with some frequency. In fact, at the 2016 Olympics there was a three-way tie for second position in the men's 100 m butterfly event. Find the number of different ways four swimmers can finish a race if (a) there are no ties (b) we include the possibility of ties.

Use the Rational Root Theorem to list all the possible rational roots of the polynomial equation. Do not find the actual roots. x³ - 4x² + 7x-8=0 Select one: a. 1, 2, 4, 8 b. ±1, ±8 c. ±1, ±2, ±4, ±8 d. no possible roots

Evaluate the following expression for x = -3, y = 2, and z = -1. 2x-3y-6z 2x-3y-6z=

Evaluate 4x + y for x=2 and y = -1. The result is

Solve the system of equations by the addition method. 3x-3y = 7 2x+6y= 10 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution is (Simplify your answer. Type an ordered pair.) O B. There are infinitely many solutions; {(x,y)|3x - 3y = 7} or {(x,y) |2x+6y=10}. O c. There is no solution; } or Ø.

Graph the linear equation. x= -8 Use the graphing tool to graph the linear equation.

Solve the following second order ODE. xy"- cos x y' + sin x y = 0, x>0

Solve the system of linear equations by graphing. y = - 2x 2x-y = -4 Use the graphing tool to graph the system.

Solve the system of linear equations by graphing. y+x= -1 (3x)+3y=-3 Use the graphing tool to graph the system.

Find the domain of the rational expression. f(x) = 2/ x^2 + 2x - 24

Solve the inequality. 18x-81-x<0

Find the chromatic polynomials of (i) the complete bipartite graph K2,5; (ii) the cycle graph C5.

You currently have $8,900 (Present Value) in an account that has an interest rate of 8% per year compounded continuously. You want to withdraw all your money when it reaches $16,910 (Future Value). In how many years will you be able to withdraw all your money?

Give the domain for m(x) =x-6/x² + 16x + 63 in interval notation.

If you place a 23-foot ladder against the top of a building and the bottom of the ladder is 11 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.