Complex numbers Questions and Answers

The distribution of the number of occurrences of the letter "a" on the pages of a book is found to be a normal distribution with a mean of 60 and a standard deviation of 15. If there are 600 pages in the book, what percentage of the time is "a" found 45 times or more on a page? Select one: a. 34% of the time b. 84% of the time c. 50% of the time d. 68% of the time

Find the expected value in % of an insurance bet if you have removed 6 small cards from a single deck (and the dealer has an ace up)

Suppose m and n vary inversely and n = 17 when m = -4. Inverse variation Formula: y = k/x a) Write an equation that models the variation. b) Find n when m = -136. a) m = -68/n; n = 1/2 b) m = - 68/n; n = 2

Your shirt drawer contains 6 different colored shirts that you will wear over the next 6 days. What is the probability that you will randomly choose the green shirt to wear today and the red shirt to wear tomorrow? a.) 1/6 b.) 1/30 C.) 1/3 d.) 12

Solve and check the equation. x/5=x/6-9 What is the solution? A. The solution set is {____}. B. The solution set is {x|x is a real number}. C. The solution set is Ø.

C and D are sets of real numbers defined as follows: C= {z|z=>4} D={z|z<5} Write CUD and CND using interval notation. If the set is empty, write Ø

The points (6, -1) and (3, 2) fall on a particular line. What is its equation in slope-intercept form? Write your answer using integers, proper fractions, and improper fractions in simplest form. y = _______ x + _______.

Out of 10 possible points, a class of 20 students made the following test scores: 0,9,4,2,4,4,5,6,6,6,7,8,8,8,8,9,9,9,10,10 What is the median score? What is the mode? What is the mean test score? Calculate the variance and range (to the nearest hundredth)? What is the standard deviation (to the nearest hundredth?" What percent of the scores lie within 1 standard deviation from the mean? What percent of the scores lie within 2 standard deviation from the mean?

A plane heads S 10° E at 150 mi/h. It experiences a 30 mi/h crosswind blowing N 50° E. What is the ground speed of the plane? What is the plane's direction of movement relative to the ground? (Round all values to 2 decimal places.)

Find equations in Cartesian, cylindrical, and spherical coordinates for the following surfaces: (a) A sphere of radius 2 centered at x = 2, y = 0, z = 0. (b) A cylinder of radius 3. (c) A cone represented by the Cartesian equation x² + y² - z² = 0.

For the function, determine whether y varies directly with x. If so, find the constant of variation and write the function rule. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. Yes, y varies directly with x. The constant of variation is k = and the function rule is (Simplify your answers. Use integers or fractions for any numbers in the expression.) B. No, y does not vary directly with x.

Every year, the Rock and Roll Hall of Fame and Museum inducts legendary musicians and musical acts to the Hall. The table shows the number of inductees for each year. (upload a picture of your work from a separate piece of paper) Rock and Roll Hall of Fame Inductees Year Number of Year Number of Inductees Inductees 2001 11 2004 8 2002 8 2005 7 2003 9 2006 6 a. Represent the data using a mapping diagram b. Represent the data as a graph on the coordinate plane c. Represent the data as a list of ordered pairs d. Identify the domain and range of the relation

Find the amount in a continuously compounded account for the given conditions. 16. principal: $500; annual interest rate: 4.9%; time: 2.5 years 17. principal: $6000; annual interest rate: 6.8%; time: 10 years

Plot the product of the complex numbers on the plane below. (2e^315'i) (2e^210i)

Solve the system by using the addition method. 4x + 5y =-11 3x - 4y= 46 Do not enter any spaces in the answers. The solution is

2. A contestant on a game show spins a wheel that is located on a plane perpendicular to the floor. He grabs the only red peg on the circumference of the wheel, which is 2.0m above the floor, and pushes it downward. The red peg reaches a minimum height of 0.5m above the floor and a maximum height of 3.5 m above the floor. Determine the equation of the sine function that represents the height of the red peg above the floor, as a function of the total distance moved.

Convert the following point from polar to Cartesian coordinates. Write the exact answer as an ordered pair. Do not round. (5, 5π/3)

Convert the point from Cartesian to polar coordinates. Write your answer in radians. Round to the nearest hundredth. (-11, 12)

Show, using the definition of uniform continuity, the function f(x) =*₁ is uniformly continuous on [0,3].

A surveyor needs to find the distance AC and BC on this picture. She has the given measurements (all are in feet). Find the two missing sides. [Hint: Use Laws of Sines and Cosines.] This is not to scale - I am not that good!!

Find all zeros of the function. f(x) = 4x³. 24x² + 48x - 36 Entry tip: Enter the zeros (exact values, not decimal approximations) separated by commas.

Select all sets that √16 belong to. natural numbers whole numbers integers rational numbers irrational numbers real numbers

Solve the equation (1+i)2³ = -1+√3i and list all possible solutions in Euler form with principal arguments.

Given the following functions, find each: f(x) = x² − 8x + 15 g(x)=x 3 (f+g) (c) = (f = g)(x) = (g-f)(x) Preview Preview Preview

Given the following functions, find (f 9) (-2) f(x) = 11x + 28 g(x) = x + 7 Preview Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity

Prove that the Galois group of x5 - 1 E Q[x] is is a cyclic group of order 4.

Outside temperature over a day can be modelled using a sine or cosine function. Suppose you know the high temperature for the day is 57 degrees and the low temperature of 43 degrees occurs at 2 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

Given the functions below, evaluate the expressions. Round answers to 3 decimal places as needed p(r)=7r/(4r²-3) (q o h)(4)= (p o h)(3)= (h o q)(3) (p o q)(4) =

Express in terms of i. √-98 √-98 =[] (Simplify your answer. Type your answer in the form a + bi.)

Add and simplify. (9-4i) + (2-2i) (9-4i)+(2-2i) = (Type your answer in the form a + bi.)

Consider the function f(θ) = 3 sin(θ/2 - 45)+1 (a) Determine the amplitude of the function. (b) Determine the period of the function. (c) Determine the phase shift of the function. (d) Determine the vertical shift of the function. (e) Graph the function above using transformations. (f) Describe the transformations that would need to take place with in order to achieve the same function as above.

The surface area of a sphere is 4πr². Find the percentage increase in its diameter when the surface area increases by 21%. a. 30.2% b. 33.1 % c. 34.5 % d. 30.9 %

Find the normalization constant A ∫sin⁵ (θ)dθ=-5 cos(θ)/8 +5cos (3θ)/48-cos(5θ)/80

Find the x- and y-intercepts of the graph of the function f(x) = -4|x-7| +4. Enter your answers as points, (a, b). Enter the z-intercepts in order of increasing x-value. If there are no x-intercepts, enter NA in both answer areas. z-intercepts: y-intercept:

You want to buy a new pair of Kickin' sneakers and you see the following ads: Store A Store B All Sneakers 25% Off! All Sneakers 20% Offl Kickin' Brand priced at $80 Kickin' Brand priced at $80 Coupon for Store A Coupon for Store B Good for an additional 10% Good for an additional 15% off on any sneaker purchase. off on any sneaker purchase. Which store would you go to in order to get the best deal on your sneakers? Explain your reasoning.

Solve the radical equation. Check all proposed solutions. √(2x+5)-1=x Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is { (Use a comma to separate answers as needed. Simplify your answer.) B. The solution set is Ø.

Solve the following formula for the specified variable. B = πt²s for s s=[] (Type an exact answer, using π as needed.)

Solve the equation in the interval 0 ≤ θ < 2π 3 sin (2θ) 4 sinθ + 2 = 3 cos θ

Use Green theorem to evaluate ∮[7y-e^sinx]dx + [15x-sin(y³ +8y)] dy Where (c) is a positively oriented circle radius 3 centered at the origin.

Let w=(-4, 12,-7), v₁ = (1, 3,-2), v₂ = (3, 1,-1). Then w is a linear combination of the other two vectors, and W= ____V₁+ _____V₂. All answers are numeric.

Find the x-intercepts of the graph of the equation. Use the x-intercepts to match the equation with its graph. y=√(x+6)+√(x-2)-4 The set of x-intercepts is

Write the sentence as an equation. The sum of - 56 and 19 is -37. "The sum of -56 and 19 is - 37" written as an equation is

Solve the initial value problem 4y" - 12y' +9y = 0, y(0) = 3, y'(0) = 5. y(t) = How does the solution behave as t → ∞?

You would like to have $950,000 when you retire in 40 years. How much should you invest each quarter if you can earn a rate of 4.5% compounded quarterly? a) How much should you deposit each quarter? b) How much total money will you put into the account? c) How much total interest will you earn?

Write the following sentence as an equation. Use x to represent "a number." The product of 2 and the sum of -4 and a number is -30. The equation is

Write using exponential notation. 8.7.7.9.9.9=

If a mortgage is 185,000. calculate the monthly payment and closing cost for each. 20 yr fixed rate at 5.5% with closing cost of 2200 and 1 point. 20 yr fixed rate at 5.25% with closing cost of 2200 and 5 points

Find the x- and y-coordinates of point B. The coordinates of B are (Type an ordered pair.)

Suppose you wanted to use a trigonometric function to model the height of a passenger (with respect to time) on a Ferris wheel. Explain why you could use a reflected sine curve (with no phase shift) if the passenger boards at point (1,0) and the wheel moves clockwise.

Solve the inequality. 6(3z + 1) <6 The solution set is