Permutations and Combinations Questions and Answers

Let the region R be the area enclosed by the function f(z) = In (z) and g(z) = 3x/4-2. Write an integral in terms of z and also an integral in terms of y that would represent the area of the region R. If necessary, round limit values to the nearest thousandth.

A given perceptron network has a weight matrix: [0.49 0.71 0.681 0.45 0.75 0.66 0.65 0.28 0.16] and given the following training point: 1 with its desired Assume threshold theta=0.8 and learning rate eta=0.2 Apply perceptron training for 2 iterations.

Given the lines: a)L₁(x, y, z)=(1,2,-2)+t1 (1,2,1) b)L₂(x, y, z) =(2,1,3)+t2(1,2,3) c)L₃(x, y, z)=(1,1,1) +t₃(2,7,3) where t1,t2,t₃ Find the equation of the line which is parallel to L3 and which intersects both L₁ and L2.

Solve the inequality (x - 5)(x-6)² <0 Select all the intervals below that are included in the solution. a) x<5 b) x>5 c) x<6 d) 5<x<6 e) x>6

Computing conditional probability using a sample space Eight balls numbered from 1 to 8 are placed in a bag. Some are white and some are grey, as shown below. Answer the following questions. Write each answer as a fraction. A ball will be randomly selected. (a) What is the probability that the selected ball is grey? (b) What is the probability that the selected ball is grey, given that an even numbered ball is selected?

The profit function for a firm making widgets is P(x) = 132x - x² 1200. Find the number of units at which maximum profit is achieved. X = [ ] units . Find the maximum profit.

The amount of money in an investment is modeled by the function A(t) = 800(1.0185)t.The variable A represents the investment balance in dollars, and t the number of years. What is the doubling time for the investment? Round answer to 1 decimal place.

tanA + tanB = 1.2 , cosB -cosA - 0.7cosAcosB = 0 What is A and B angle, with detailed steps?

The random variables x and θ are independent and θ is uniform in the interval (-π, π). Show that if z = x cos(w t + θ), then -|z| ∞ fz(z) = (1/π) ∫ {fx(y) / √(y² - z²)}dy + (1/π) ∫ {fx(y) / √(y² - z²)}dy -∞ |z|

An equation of the function y(t) is shown. y (t) = −t² + 14t - 40 Select all of the statements below that are true about the graph of y(t) for 6 ≤ t ≤ 8 O The average rate of change over the interval 6 ≤ t ≤7 is the same as the average rate of change over the interval 7 <t<8 O The value of y(t) is constant over the interval 6 ≤ t ≤8 O The value of y(t) increases over the interval 6 ≤ t ≤7 O The value of y(t) increases over the interval 7 ≤ t ≤ 8 O The average rate of change over the interval 6 ≤ t ≤8 is 0

The Venn diagram below shows the number of students in a class who read any of 3 popular magazines A, B and C. One of these students is selected at random. (a) Show that the probability that the student reads more than one magazine is (b) Find the probability that the student reads A or B or both. (c)Write down two events that are: (i) mutually exclusive (ii) NOT mutually exclusive (d) Determine whether or not reading magazine B and reading magazine C are statistically independent

A helicopter travels 240 miles every 2 hours, how far does it travel in 3 hours?

The national average price per gallon for gasoline is normally distributed with a mean (currently) of $2.34 per gallon with a standard deviation of $0.26 per gallon. Which of the following represents the proportion of the gas prices that lie between $2.00 and $3.00? (1) 56% (3) 84% (2) 72% (4) 90%

Fill in the missing values to make the equations true. (a) log₂ 3-log₂ 5 = log₂_ (b) log₉7+log₉_ = log₉56 (c) log₇25 =log₇ 5

Find the equation of a line passing through (3,4) and (1,-4). Enter your answer in the slope-intercept form (namely, type your answer exactly in the form of y = mx + b).

Sketch the set of complex numbers such that z(i - z) — z(i + z) = 2|z|² and justify your answer. Hint: Use (a).

Perform the operations and simplify. Leave your answer in exponential form. 3a⅘.2a^3/2

An analyst researches the relationship between different energy sources in each state for 2014. The data in the table show the number of states that use coal as an energy source. Given that a state does not use nuclear power, what percentage of those states use coal? Type in the number as a percentage but do NOT include a % sign. For example, if the answer was 35.6%, just type in 35.6. Round to the nearest tenth.

A grasshopper jumps off of a tree stump. The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function shown. h(t) = -t²+ (4/3)t +1/4 After how many seconds will the grasshopper land on the ground? Express your answer as a decimal, rounded to the nearest tenths place.

A scientist is studying wildlife. She estimates the population of bats in her state to be 270,000. She predicts the population to grow at an average annual rate of 2.9 percent. Using the scientist's prediction, which of the following is an equation that models the population of bats, y, after x years? y= 0.29x + 270,000 y= 2.9x + 270,000 y=270,000 (1.029)^x y=270,000 (2.9)^x y = 0.29(270, 000)^x

An equation is shown y = (1/2)x + (3/4) Select which of the given points are contained in the graph of the equation. A) (0, 1/2) B) (3/4, 1/2) C) (3/4, 0) D) (1/2, 1) E) (0, 3/4)

2. Use the Fourier transform to solve this transport equation for u = u(x, t), defined on the whole real line: 2ut- 3uz =0 u(x,0) =exp(-x²) (You should be able to write your solution u(x, t) entirely in terms of the variable with no integrals.)

A photo is printed on a 20-inch by 24-inch piece of paper. The photo covers 320 square inches and has a uniform border. What is the width of the border?

1.What is the value of Log 8 32768? 2.What is the value of Log the cube root of 15625? 3. What is the value of Ln e^₅? 4. Evaluate Log 16 1/8?

Find the minimum or maximum value of y = -x² + 4x + 4. The function has a _________ value of __________ .

Given events A and B, such that P(A) = 0.6, P(B) = 0.5, and P(A U B) = 0.8, determine whether A and B are independent or dependent.

Which of the following functions have a range of all Real numbers? Quadratic Functions. Square Root Functions Cube Root Functions Polynomial Functions with even power of n Polynomial Functions with odd power of n Rational Functions

You buy two icecream cones, one for you, and one for your friend. The probability that both both icecream cones are chocolate is 10%. If you choose chocolate, the probability that your friend also chooses chocolate is 20%. What is the probability that you choose chocolate?

Identify the graph of g(x) = 5 sin(1/4)x.

Consider the end behavior of the function g(x) =4|x-2|-3 As x approaches negative infinity ,g(x) approaches. . . infinity As x approaches positive infinity, 9(x) approaches . . . infinity

What is the value of x in the equation log4(x-1)³ = 9. (a)x=49 (b)x = 65 (c)x=64 (d)x=81

In Quadrant I, sin A = x. In Quadrant I, cos B = x. What is true about tan A and tan B? (a)Their product is always 1. (b)Their sum is always 1. (c)Their product is always 0. (d) Their sum is always 0.

Find all solutions to (x + 5)(2x-3) = 0. Explain or show your reasoning.

the number of the cycle made by mass per unit time means c) frequency b) amplitude a) constant spring a and b When the load and the spring constant are directly proportional, the relationship is called non one of them b) linear relation a) non-linear relation a and b

Give the best estimate for the following value for "x", given 2^x = 12. A. Between 3 and 4 B. Between -3 and 6 C. Between -3 and -4 D. Exactly 6

Sara has a deck of ten cards that are of equal size and shape. What is the probability that Sara will draw a triangle, not replace the card, and then draw a circle?

A block of wood has the shape of a triangular prism. The bases are right triangles. Find its surface area. The surface area is ____ in.².

Shane and John goes to a restaurant for Lunch. If there are 20 items on the menu and Shane orders 11 items and John orders 7 items, What expression represents the total number of choices between them?

A bag contains eight yellow jerseys numbered one to eight. The bag also contains ten purple jerseys numbered one to ten. You randomly pick a jersey. Fill out the following chart. What is the probability that it is purple or has a number greater than five ?

Liliana used 4 dark power crystals to raise 14 zombie soldiers. She wants to know how many zombie soldiers (z) she can raise with 10 dark power crystals. How many zombie soldiers can Liliana raise with 10 power crystals?

About of a town's population has black hair. About 2/7 of the population has blonde hair. What is the probability that a person chosen at random from this town will have either bleak hair or blonde hair?

What is the value of this logarithmic expression? log₂ 16-log₂4 A). 0.60 B). 2 C). 6 D). 3.58

Given below are descriptions of two lines. Line 1: Goes through (8,-3) and (0,3) Line 2: Goes through (4,3) and (0,6) The slope of Line 1 is m =____________________ The slope of Line 2 is m =____________________ Finally, which of the following is true? Line 1 is parallel to Line 2. Line 1 is perpendicular to Line 2 Line 1 is neither parallel nor perpendicular to Line 2

The linear function g is defined by g(x) = 4x. a. Show that g(3) and g(2) have a difference of 4. b. Show that when the input value increases from x to x +1, the output values g(x + 1) and g(x) have a difference of 4. The exponential function h is defined by h(x) = 4^x. a. Show that h(3) and h(2) have a quotient of 4. b. Show that when the input value increases from x to x + 1, the output values h(x + 1) and h(x) have a quotient of 4.

Let f = (17) (264) (39) (5 8) and g = (2 946) (3 8) (57) be permutations in S9, written in cycle notation. What is the second line of f in two-line notation? Enter it as a list of numbers separated by single spaces. ____________ Let h=f.g-¹. What is h in cycle notation? Enter single spaces between the numbers in each cycle. Do not type spaces anywhere else in your answer. ____________

The crime rate of a certain city is increasing by exactly 7% each year. If there were 600 crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2018.

If a = (-4, -8) and b= (-2, -6), find |2.5a - 3b| A) 20 B) 2√5 C) -6 D) 4√2

Use Pascal's triangle to expand the binomial. (m+n)⁷ (m+n)⁷ =

Shawn has a bank account with $3,069. He decides to invest the money at 3.25% interest, compounded annually. How much will the investment be worth after 5 years? Round to the nearest dollar. Type your numerical answer below. $____________

Find a normal vector to the plane 5(x - z) = 6(x + y) +6j + 5k