A study conducted by the Metro Housing Agency in a midwestern city revealed the following information concerning the age distribution of renters within the city. (Round your answers to four decimal places.)

(a) What is the probability that an adult selected at random from this population is a renter?


(b) If a renter is selected at random, what is the probability that he or she is in the 21-44 age bracket?


(c) If a renter is selected at random, what is the probability that he or she is 45 years old or older?

Solve the following differentioal equation by undetermined coefficients:

1- yⁿ - 4y = (x² - 3 ) sin 2x

2- y⁴ - yⁿ = 4x + 2xe^-x

3- yⁿ + 3y = -48x²e^3x

6.3

. The DVM has a 200 kHz clock, and the integrator control waveform frequency is 45 Hz. Calculate the number of clock pulses that occur during tl and determine a suitable time duration for t2 when the input is 1V. Recalculate t1, t2 and the measured voltage if the clock frequency drifts by -5%.

Initial Value Problem. Use Laplace transform.

m''(t) - m'(t) - 6*m(t) = e^(4t)

where m(0) = 1 and m'(0) = 1

Let f left parenthesis x comma y right parenthesis equals cos left parenthesis pi space x right parenthesis plus 3 y squared minus 6 y. Which of the following are TRUE? Select ALL that apply. a. f has a saddle point at left parenthesis k comma 1 right parenthesis whenever k is an odd integer b. f has a saddle point at left parenthesis k comma 1 right parenthesis whenever k is an even integer c. f has a local minimum at left parenthesis k comma 1 right parenthesis whenever k is an odd integer d. f has a local maximum at left parenthesis k comma 1 right parenthesis whenever k is an even integer

An invasive species from maize crops comes into contact with a population. It has been measured that 200,000 plants remain on the second day and 90,000 plants remain on the fifth day.

a) What was the number of plants when the invasive species entered?

b) Crop insurance will pay for total losses when only 5% of the amount of plants remains. How long should it take for farmers to claim their insurance?

Give an isomorphism that proves the two vector spaces M3,2 and P5 are isometric to each other.

plz solve in detail

Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use

h = 0.1

and then use

h = 0.05

y' = y − y², y(0) = 0.8;    y(0.5)

A company manufactures and sells scientific calculators. The function P=7.87.8x2plus+59705970xminus−290 comma 000290,000​, x≤​150, gives the profit if x thousand calculators are manufactured and sold. Use the table feature of a graphing calculator or use a spreadsheet to make a table of values for the profit function with x=​0, 5, 10,​ ..., 150. Use the table to answer the following question.

Approximately how many calculators must be sold in order for the company to make a​ profit?

For matrices, a mulitplicative identity is a square matrix X such XA = AX = A for any square matrix A. Prove that X must be the identity matrix.

Prove that for any invertible matrix A, the inverse matrix must be unique. Hint: Assume that there are two inverses and then show that they much in fact be the same matrix.

Prove Theorem which shows that Gauss-Jordan Elimination produces the inverse matrix for any invertible matrix A. Your proof cannot use elementary matrices (like the book’s proof does).

Prove that null(A) is a vector space.

Prove that col(A) is a vector space.

Linear Algebra

we know that x ∈ R^n is a nonzero vector and C is a real number.

find all values of C such that ( In − Cxx^T ) is nonsingular and find its inverse

knowing that its inverse is of the same form

Section 5.3: Find the equilibrium values of a general quadratic population model:

dx/dt=a1x+b1x^2+c1xy

dy/dt=a2y+b2y^2+c2xy

Don’t forget to show this for all four cases:

• Case 1: ? = 0, ? = 0
• Case 2: ? ≠ 0, ? = 0
• Case 3: ? = 0, ? ≠ 0
• Case 4: ? ≠ 0, ? ≠ 0 (Use Cramer’s Rule to set up the solution for this case.)

(A) Find the general solution for the displacement x = x(t) of the forced mechanical system x´´ + 6x´ + 8x = 35 sin t. (B) Identify the steady-periodic part

Suppose G is a connected cubic graph (regular of degree 3) and e is an edge such that G − e has two connected components G1 and G2

(a) Explain what connected means.

(b) We say that e is a____________ of G

(c) show that G1 has an odd number of vertices.

(d) draw a connected cubic graph G with an edge e as above.