2. For the following question, we will be considering the permutations of the digits in the number 77,422. a) How many different 5 digit numbers can be formed with the digits of the number 77,422? b) How many different odd 5 digit numbers can be formed with these digits? / 3. Alice, Bob, Charlie, David, Emily, and Francis are the finalists in a race. What is the probability that Alice. Bob and Charlie will be the three to win medals (Gold, silver, bronze)?

Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 O B.…

A:

Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 O B.…

A:

Q: If a, b and c are three non-coplanar vectors, then find the value of a.(bxc) b.(cxa) c.(bxa) +…

A: Use the properties of vector box product as follows: a→.(b→×c→)=[a→ b→ c→]=[b→ c→ a→]=[c→ a→…

Q: Graph each system of Inequalities below. Name the coordinates of the vertices of the polygon formed.…

A:

Q: Find the standard equation Asymptotes y 4x 3 71 3 17 3 - 4 -x and y 3 ‚ vertex at (17,9)

A: Given information Asymptotes:  y = -43x + 713    and     y = 43x - 173 Vertex: 17, 9.

Q: Provide the exact algebraic models, in factored form, for the following functions. Show your work in…

A:

Q: Show that -p-->(q-->r) and q-->(pVr) are logically equivalent by completing the table below: P F F F…

A:

Q: 12. Sketch the interval (a,b) on the x-axis with the point c inside. Then find the largest value of…

A: We have to sketch the interval and find the largest value of delta.

Q: Question: Consider the following standard topology, please define the sets below are closed, open,…

A:

Q: Determine if logical notation is tautology, contradiction, or contingency a. (pVq)A (pr)^(q →r) → r…

A:

Q: Determine if logical notation is tautology, contradiction, or contingency a. (pVq)^(pr)^(q →r) → r…

A:

Q: Give the center, foci, vertices & asymptotes. Sketch the graph y - x = 1 y + x

A: Given that        y-x=1y+x(y-x)(y+x)=1y2-x2=1-x2+y2=1-x21+y21=1 Compare to (x-h)2a2+(y-k)2b2=1 Here…

Q: (a) Let the integers 1 to 23 be written on a straight line. Can you insert “+” and “−“ signs between…

A:

Q: There are only 12 such shapes that can be formed in the plane by joining five squares along their…

A:

Q: a dß + B da + aß(3 da + dB) =0

A:

Q: Graph the feasible region for the given system of inequalities. x + 3y ≤ 12 3x + y ≤ 12 x ≥ 0 y 20

A:

Q: where product is over all primes which divides n.

A:

Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 OA. OB. ey eLny ALT OD.y

A: Given : yx+y+1dx+xx+3y+2dy=0 To Find : IF of Given equation

Q: For all x 1 we have

A:

Q: 6. In a sample of a certain type of bacteria, there are 500 initially. It is known that the amount…

A:

Q: Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1 O A. 1/4 O B. 1/2 O C.…

A: The given differential equation dy-y+xy5dx=0 We have to find the value of arbitrary constant C when…

Q: Find Vz. z = sin(5y² - 5xy) NOTE: Give your answer in unit vector notation; that is, in terms of i…

A: For any scalar valued function: z=f(x, y), it can be written that ∇z=∂f(x, y)∂xi^+∂f(x, y)∂yj^.

Q: Suppose a 3 x 3 real matrix A has only two (real) distinct eigenvalues. Suppose that tr(A) = -1 and…

A:

Q: Similar matrices have the same determinant.

A: Suppose A and B are similar matrices.

Q: 3. Consider the canonical basis {₁,2,3} of R³ and let F = {f₁, f2, fs} be defined by =(1,0,-1), 72…

A:

Q: Solve for the value of C in the equation: dy - (y + xy5)dx = 0 when y(0) = 1 O A. 1/4 OB. 1/2 O C.…

A:

Q: -4 -2 20 10- 0 -10- -20- -30- X Write the factored form of the equation of the most appropriate…

A: In this question, the concept of polynomials is applied. Polynomial The term "polynomial" refers to…

Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 –…

A:

Q: Consider the following matrices: A = V₁ = V₂= 7377 V3 2 For each of the following matrices,…

A: Given matrices are ,  A=   2   3-2   1   , B=-2-1  3-4  , C=-6-5   9-6  a matrix  'v' can be written…

Q: x² - y² lim (x,y) →(a,a) x² - y² Here a is a constant. (Find the limit assuming x + y) Find the…

A: Given,            limx, y→a, ax4-y4x2-y2=

Q: -6 im f(x) 11 MA 2 im f(x) = di ↑ -4 Her the graph of y = f(x) above. State the value of each of the…

A: According to our guidelines, we have to answer the first three subparts if question with multiple…

Q: The integrating factor (IF) of the equation y' - 2ycot2x O A. sin2x O B. cot2x O C. Lnsin2x…

A: Solution:  To find the integrating factor of the given differential equations

Q: A simplified economy involves just three commodity categories agriculture, manufacturing, and…

A: Given: Economy involves just three commodity categories - agriculture, manufacturing and…

Q: p = F, q = T, and r = T. Select the expression that evaluates to true. O-(qvr) O (-par)vq O (-qvr)^p…

A:

Q: Problem 10.6_2 Use Cauchy's integral formula to evaluate the following integral. $₁21-1 -dz sino (z)…

A: By using Cauchy's integral formula we have to evaluate the following integral :…

Q: When air expands adiabatically (without gaining or losing heat), its pressure PP and volume VV are…

A:

Q: Solve the following differential equations by separation of variables.  Show complete solutions

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: Consider the function f(x) = cos and its graph shown in the figure. (a) What is the domain of the…

A:

Q: m = b If a = OA and b OB, prove that OP P = n na +mb m+n B

A:

Q: 4. Does 3 divide (3k + 1)(3k + 2)(3k + 3)?

A: We will show by induction, put the value of k = 0 we find, (3x0+1)(3x0+2)(3x0+3) = 6  Which is…

Q: If a an and b are two vectors, then prove that (a x b)² = a.a →→ a.b →→ ba b.b

A:

Q: 2. (a) What is the negation of [Por Q]? (b) What is the negation of [P &-Q]? (c) Using the rules of…

A: Note-  Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: (-∞0,4) U {5} in E₁

A:

Q: Let A be similar to B and B be similar to C. Then to prove that A is similar to C.

A:

Q: Sahara arranges 2n + 2 different objects taken n at a time and Casey arranges 2n different objects…

A:

Q: 2. Let S = - [x³ − 2xy² − y³ +1 ysin(x)+1 = 0 = 0 (a) Using Newton's method, approximate two roots…

A: Using calculator:

Q: D. The computation from part C above shows that between any two unequal real numbers is another real…

A: There can be any number of critical approaches to the pard D of this question . But we will refer to…

Q: 1. Consider the parallelepiped with adjacent edges u = −2ï° + 3j* + k”, v² = −í* + 3j* + 3k* and w*…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Draw a Venn diagram and shade the area corresponding to each of the expressions below using the…

A:

Q: Show that there is no simple group of order pqr, where p, q, and rare primes ( p, q, and r need not…

A: We know the definition of simple group, A simple group is a group whose only normal subgroups are…