Math Questions

Which of the following represents the rectangular equation x² + y² + 5x - 3y = 0 in polar form? r= -5sin θ + 3cos θ r= -3sin θ+ 5cos θ r=3sin θ- 5cos θ r= 5sin θ- 3cos θ

Find the inverse function of y = g(x) = 5x³ + 1 g-¹(y) =

Given point Q=(-6√3,-6) in rectangular coordinates, what are the corresponding polar coordinates? 6, 5π/6 12, 5π/6 6, 7π/6 12, 7π/6

Check that the functions f(x) = e2x and g(x)=In(x)/2 are inverses using algebra.

A polar curve is represented by the equation r₁ = 2 + 3cosθ. Part A: What type of limaçon is this curve? Justify your answer using the constants in the equation. Part B: Is the curve symmetrical to the polar axis or the line θ = π/2? Justify your answer algebraically.

Decompose the function y = 2x+1 into u(v(x)). If we assume u(x) = 2x, what is v(x)?

Suppose f(q) = C = 200+ 0.1q gives the cost, C, in dollars to manufacture q kg of a chemical. Find and interpret f-¹(C).

There is a 25% chance the high school lacrosse team will win its game this week and a 56% chance the high school gymnastics team will win its meet this week. If the events are independent, what is the probability that the lacrosse team and the gymnastics team both win this week? A 81% B 52% C 22% D 14%

A company, which manufactures lawn mowers, estimates its daily profit, p(n) in dollars, to be given by p(n) = -n²+ 100n, where n is the number of mowers produced. The company can manufacture at most 45 lawn mowers a day. a) How many mowers should this company produced daily to maximize the profit? b) What will its daily profit be?

(a) From the 13 albums released by a musician, the recording company wishes to release 10 in a boxed set. How many different boxed sets are possible? (b) 71 athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the 3 medals be distributed?

Suppose Chris places $7000 in an account that pays 16% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding. (a) Find the amount in the account at the end of 1 year. (b) Find the amount in the account at the end of 2 years.

You invest $1134 in a special savings account that earns 1.2 % interest, compounded continuously. The money will be invested for t years. Write the equation that represents the situation.

The half-life of radium-223 is approximately 11.43 days. Step 3 of 3: How much of an 8 gram sample of radium-223 would remain after 9 days? Round to three decimal places. Answer

True or False. The samples in sampling distribution must come from the same population. True False

A museum gift shop sells hats with embroidered logos of the museum. The hats are available in small, medium, and large sizes. They are available in the colors red and green. Make a tree diagram to represent all possible varieties of hats sold at the museum

About what percent of the data in a data set falls between the median value and the maximum value? Explain. About___% of the data falls in this range because the minimum, first quartile, median, third quartile, and maximum divide a data set into___equal parts and the given range comprises___of these parts.

A state makes auto license plates that have two letters (excluding I, O, and Q) followed by four digits of which the first digit is not zero. How many different license plates are possible? 3,085,128 3,470,769 O4,761,000

Compute the simple interest. If the time is given in months, let one month be 1/12 of a year. Round the answer to the nearest cent. Principal, Rate, and Time Interest $1,500 at 8% for 2 years Interest: $120.00 Interest: $220.00 Interest: $140.00 Interest: $240.00

In one town, 68% of adults have health insurance. a. What is the probability that 6 adults selected at random from the town all have health insurance? (Assume the population is large enough that we can consider events to be independent.) A) 0.68 B) 0.099 C) 0.088 D) 4.08 b. What is the probability that 3 of the 6 adults have health insurance. (use binomial)

Directions: Simplify each of the following expressions. Partial credit will be given if enough work is shown to indicate some understanding of the process. You are highly encouraged to show every step so that you can earn as many points as possible even if your final answers are not correct, and so that I can help you figure out what exactly you do not understand if you do not simplify an expression correctly. 1. (3x-6) + 2xy + 4(x -3xy)-x 2. 8+(-7x+4)-(3x + y) 3. -(3x-5x + 7) + 4(-x-1) 4. 3(x-6) + (-2+4x)-2x 5. 3(xy)-5(x + y)-(- xy + x)

The blue catfish (Ictalurus Furcatus) is the largest species of North American catfish. The current world record stands at 143 pounds, which was caught in the John H. Kerr Reservoir (Bugg's Island Lake) located in Virginia. According to American Expedition, the average weight of a blue catfish is between 20 to 40 pounds. Given that the largest blue catfish ever caught was at the John H. Kerr Reservoir, you believe that the mean weight of the fish in this reservoir is greater than 40 pounds. Use the data below, which represents the summary statistics for 42 blue catfish caught at this reservoir, and a 0.05 significance level to test the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds. n = 42; = 40.71 pounds; s = 3.89 pounds a) Identify the null and alternative hypotheses? Ho: HA: b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)? left-tailed right-tailed two-tailed c) Identify the appropriate significance level. d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places. e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.

Find the interval I and radius of convergence R for the given power series. (Enter your answer for interval of convergence using interval notation.) Σ k = 0 to ∝ k! (x - 3)k

What is the maximum vertical distance between the line y = x + 12 and the parabola y = x² for -3 ≤ x ≤ 4?

a) Find and classify the critical point(s). b) Find the interval(s) where f(x) is increasing. c) Find the interval(s) where f(x) is decreasing. 1. f(x)=x²-x-1 2. f(x)=2x^4 - 4x² +1 3. f(x)=xe^1/x

Find all zeros of the following polynomial. Be sure to find the appropriate number of solutions (counting multiplicity) using the Linear Factors Theorem. f(x) = x^5 + 4x^4+21x³ +66x² + 80x + 32

Three different bacteria are cultured in one environment and feed on three nutrients. Each individual of species I consumes 1 unit of each of the first and second nutrients and 2 units of the third nutrient. Each individual of species II consumes 2 units of the first nutrient and 2 units of the third nutrient. Each individual of species III consumes 2 units of the first nutrient, 3 units of the second nutrient, and 5 units of the third nutrient. If the culture is given 5100 units of the first nutrient, 7200 units of the second nutrient, and 12,300 units of the third nutrient, how many of each species can be supported such that all of the nutrients are consumed? (Let x = species I, y = species II, and z = species III. If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (x, y, z) =____ where 2100 ≤ z ≤ 2400

Consider the following equation. -4x+2y-26 = 0 Step 3 of 3: Plot the point on the line with the x-coordinate x = -4.

Your pet groomer charges according to how much your dog weighs. For a dog that weighs 20 pounds or less, the groomer charges $25. For a dog that weighs more than 20 pounds and less than 50 pounds, the groomer charges $45. For any dog that weighs 50 pounds or more, the groomer charges $45 plus an additional $1 for each pound over 50. Using this situation, match each piece of the piecewise function with the corresponding domain restriction. f(x)=25 f(x)=45 f(x)=45+1(x-50)

Yum Yum Sandwich Shop has a lunch special. Customers can choose one sandwich, one bag of chips, and one drink. The options are below. Sandwich Chips Drinks Ham Potato Chips Water Egg Salad Corn Chips Tea Tuna Salad Coke BLT Sprite Root Beer Power Aid

Let f(x) = x² - 4x - 21 and g(x) = x² − 9x + 14. Find f.g and f/g respective domains. Simplify your answers. 1. f. g = 2. What is the domain of f. g ? Answer (in interval notation): 3. f/g = Answer (in interval notation): 4. What is the domain of f/g? Answer (in interval notation):

Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation. x² + y² +6x-4y - 12 = 0 The equation of the circle in standard form is

Find the vector w w of length 6 6 in the direction of v = 8 i +7j. v=8i+7j. (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.)

Roper Through their Roper Reports Worldwide, GfK Roper conducts a global consumer survey to help mul- tinational companies understand different consumer attitudes throughout the world. Within 30 countries, the researchers interview 1000 people aged 13-65. Their samples are designed so that they get 500 males and 500 females in each country. (www.gfkamerica.com) a) Are they using a simple random sample? Explain. b) What kind of design do you think they are using?

A company found that new employees prefer training sessions of moderate length, shorter training sessions provided too little instruction to complete a task, while longer training sessions contain too much instruction to remember. For a training session on a particular task, the company determined that the ratings new employees gave for the training session could be approximated by R(t)=32t/t²+256 where t is the length of the training session in minutes. Find the training session length that received the highest rating The training session length that received the highest rating is____minutes (Simplify your answer.)

Historical data show that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every two hours. Assume that the patient arrivals are distributed according to a Poisson distribution. Determine the probability of 6 patients arriving in a five-hour period. 136 .109 .246 .001

Discussion Board Topic: In this discussion board you will: Part 1: Use a real life application to come up with a QUESTION utilizing the Law of Sines and Law of Cosines in Trigonometry. Post the question on the discussion board. Please use proper directions and equation editor for any mathematical notation. You may post this as a pdf file. Part 2: Solve one of your classmate's questions. Part 3: Once someone has answered your question, provide feedback.

A golf ball is selected at random from a golf bag. The golf bag contains the following golf ball brands: 9 Titleists, 8 Maxflis, and 3 Top-Flites. Find the probability that the golf ball is: A Titleist or Maxfli

Consider the equation and the following ordered pairs: (-4, y) and (x, 2). y = 2x + 8 Step 1 of 2: Compute the missing x and y values so that each ordered pair will satisfy the given equation.

Heather drove 268 miles using 12 gallons of gas. At this rate, how many miles would she drive using 9 gallons of gas?

Write a rule for g described by the transformations the vertex. of the graph off. Then identify 2 f(x) = x²; vertical stretch by a factor of 4 and a reflection in the x-axis, followed by a translation 1 unit left. a. g(x) = -4(x + 1)²; (-1,0) b. g(x) = 4x² + 1; (0,1) c. g(x)=-1/4 (x + 1)² ; (-1,0) d. g(x) = 4(x + 1)²; (-1,0)

The population in a certain town is increasing linearly each year. The population at time t = 3 is 1285 and at time t = 8 is 2460, where t is the number of years after 1990. If P(t) is the population at time t, write the equation below that correctly represents this situation.

Find all relative extrema and saddle points of the function. Use the Second Partials Test where applicable. (If an answer does not exist, enter DNE.) f(x, y) = -8x² - 5y^2 + 8x - 10y + 8 relative minimum. relative maximum saddle point

Write the first five terms of the geometric sequence. an = -6a(n-1), a₁ = 12

1. Which of the following rules correctly represents the translation from ABC to MNP? A (x,y) → (x + 5,y - 2) B (x,y) → (x-2, y + 5) C (x,y) → (x-5,y + 2) D (x,y) → (x+2, y-5)

The radius r of a sphere is increasing at a rate of 2 inches per minute. (a) Find the rate of change of the volume when r = 11 inches. in.3/min (b) Find the rate of change of the volume when r = 36 inches. in.3/min

A town's population increases at a constant rate. In 2012 the population was 50,903. By 2019 the population had increased to 103,753. Assume this trend continues. Predict the population in 2022. Identify the year in which the population will reach 191,000.

The rate R that a certain disease spreads is proportional to the number of infected individuals and is also proportional to the number of uninfected individuals. The total population is P and the number of infected individuals is D. Express the rate that the disease spreads in terms of this information. Use C as your proportionality constant.

A truck costs $80,000. It depreciates in value $6,000 per year. Write a linear model in the form v(t) = mt + b where v(t) represents the current value of the truck after t years of ownership.

Internetlivestats.com reported in December 2017 around 38% of the world population has an Internet connection today. If there are 3,074,488,191 users, what is the world population? (Round your answer to the nearest whole number.)

Express the repeating decimal as a fraction in lowest terms. 0.97= 97/100 + 97/10,000 + 97/1,000,000 + ...