Basic Math Questions and Answers

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)

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

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

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

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?

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.

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 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 + ...

Use the distributive property to remove the parentheses. 2+14+26+...+ (12k-10)+(12(k+1)-10) = k(6k-4) + 12(k+1)-10 =6k²-4k+.... Then we simplify the right side of the formula. 2+14+26+...+ (12k-10)+(12(k+1)-10) = 6k²-4k+ 12k+12-10 = .... Factor the right side. 2+14+26+...+(12k-10)+(12(k+1)-10) = 6k² +8k+2=...

A statement S, about the positive integers is given below. Write statements Sk and Sk+ 1. Sn: 4+10+16+...+(6n-2) = n(3n+1) Sk: 4+10+16+...+(6k-2)= Sk+1:4+10+16+...+ [6(k+ 1)-2] =

The selling price of a refrigerator, is $537.90. If the markup is 10% of the dealer's cost, what is the dealer's cost of the refrigerator?

What is the missing factor? 6 x ? = 264 50 44 40 30

A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The four walls and one additional vertical segment (to separate the regions) are made up of fencing, as shown below. If the farmer has 234 feet of fencing, what are the dimensions of the region which enclose the maximal area?

Find the middle term in the expansion of (8/x+x/8)^10.

Find the sum of the first 25 terms of the sequence. 5, 8, 11, 14,..

Find the sum of the odd integers between 20 and 48.

A company claims that the mean monthly residential electricity consumption in a certain region is more than 860 kilowatt-hours (kWh). You want to test this claim. You find that a random sample of 60 residential customers has a mean monthly consumption of 900 kWh. Assume the population standard deviation is 129 kWh. At α = 0.01, can you support the claim? Complete parts (a) through (e) (d) Decide whether to reject or fail to reject the null hypothesis. A. Fail to reject Ho because the standardized test statistic is in the rejection region. B. Reject Ho because the standardized test statistic is not in the rejection region. C. Fail to reject Ho because the standardized test statistic is not in the rejection region. D. Reject Ho because the standardized test statistic is in the rejection region. (e) Interpret the decision in the context of the original claim. At the1% significance level, there enough evidence to the claim that the mean monthly residential electricity consumption in a certain kWh.

Solve the following inequality. ⎮9x + 10⎮≤9 Choose the correct answer below and fill in the values. Round to three decimal places if needed. ≤x≤ x≤ OR x ≥ All real numbers. There is no solution.

Momentum is mass times velocity. Suppose the momentum of a 275 g object is kg m measured to be 219 kg*m/s. Calculate the object's velocity. Be sure your answer has a unit symbol and the correct number of significant digits.

Find the fourth term in the expansion of (x-2)^8. (Simplify your answer.) The fourth term is

Use technology to help you test the claim about the population mean, μ, at the given level of significance, a, using the given sample statistics. Assume the population is normally distributed. Claim: μ> 1300; α= 0.01; σ = 200.81. Sample statistics: x= 1317.94, n=275 Calculate the standardized test statistic. The standardized test statistic is (Round to two decimal places as needed.) Determine the P-value. (Round to three decimal places as needed.) Determine the outcome and conclusion of the test. Ho. At the 1% significance level, thereenough evidence to the claim.

Consider a function that describes how a particular car's gas mileage depends on its speed. What would an appropriate domain for this function be? Choose the correct answer below. A. An appropriate domain would be 0 to 50 miles per gallon because the gas mileage is the independent variable of the function, and the domain consists of all reasonable values of the independent variable. B. An appropriate domain would be times from 0 to 10 minutes because the time is the dependent variable of the function, and the domain consists of all reasonable values of the dependent variable. C. An appropriate domain would be 0 to 100 miles per hour because the speed is the independent variable of the function, and the domain consists of all reasonable values of the independent variable. D. An appropriate domain would be 0 to 100 miles per hour because the speed is the dependent variable of the function, and the domain consists of all reasonable values of the dependent variable. E. An appropriate domain would be 0 to 50 miles per gallon because the gas mileage is the dependent variable of the function, and the domain consists of all reasonable values of the dependent variable.

Describe the basic differences between linear growth and exponential growth. Choose the correct answer below. A. Linear growth occurs when a quantity grows by the same absolute amount in each unit of time, and exponential growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time. B. Linear growth occurs when a quantity grows by random amounts in each unit of time, and exponential growth occurs when a quantity grows by different, but proportional amounts, in each unit of time. C. Linear growth occurs when a quantity grows by different, but proportional amounts, in each unit of time, and exponential growth occurs when a quantity grows by random amounts in each unit of time. D. Linear growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time, and exponential growth occurs when a quantity grows by the same absolute amount in each unit of time.

Choose the best answer to the following question. Explain your reasoning with one or more complete sentences. Which of the following is necessary if you want to make monthly contributions to savings? Choose the correct answer below. A. You must be spending less than 20% of your income on food and clothing. Spending less on food and clothing will increase cash flow exponentially every month. B. You must not owe money on any loans. This means that you are not spending any money toward interest. If you are not paying interest, you have money to save. C. You must be spending less than 20% of your income on food and clothing. As long as you don't increase your spending in any other category, you should be able to find money to save. D. You must have a positive monthly cash flow. If you have a positive monthly cash flow, you can pay more towards your credit card balance. Once the balance is zero, you should start putting that extra money in the bank. E. You must have a positive monthly cash flow. If your cash flow is positive, you will have money left over at the end of each month, which you can use for savings. F. You must not owe money on any loans. If you do not owe any money on loans, you will have many Ieft overe at the end of each month, which you can use for savings.

Summarize how average spending patterns change with age. How can comparing your own spending to average spending patterns help you evaluate your budget? Summarize how average spending patterns change with age. Choose the correct answer below. A. As people get older, they tend to spend more on food and entertainment than younger people. They also tend to spend less on housing than younger people. B. As people get older, they tend to spend more on health care and donations to charity than younger people. They also tend to spend less on personal insurance, pensions, clothing, and services than younger people. C. As people get older, they tend to spend more on transportation and housing than younger people. They also tend to spend less on health care. D. As people get older, they tend to spend more on clothing and services than younger people. They also tend to spend less on food and housing than younger people. How can comparing your own spending to average spending patterns help you evaluate your budget? A. It can be useful to check how you compare to the rest of the population. If you notice that most people donate less than you do to charity, it might be time to stop giving away so much. B. If you are spending a higher percentage of your money on an item in your budget than the average person, you might want to consider finding lower-cost options or adjusting your budget. C. It is a good idea to check how you compare to the rest of the population. If you find that people spend more than you on gas, you can give others advice on how to spend less. D. If you are spending a higher percentage of your money on entertainment than the average person, you might be able to find cheaper ticket prices if you ask around.

Briefly summarize the story of the bacteria in the bottle. Explain the answers to the four questions in the text. Briefly summarize the story of the bacteria in a bottle. Choose the correct answer below. A. The number of bacteria in a bottle increases by 1 every minute. There is one bacteria at 11:00 and the bottle is full at 12:00, so the colony is doomed. B. The number of bacteria in a bottle triples every minute. There is one bacteria at 11:00 and the bottle is full at 12:00, so the colony is doomed. C. The number of bacteria in a bottle doubles every minute. There is one bacteria at 11:00 and the bottle is full at 12:00, so the colony is doomed. D. The number of bacteria in a bottle increases by 2 every minute. There is one bacteria at 11:00 and the bottle is full at 12:00, so the colony is doomed.

What does the fact that the Dow Jones Industrial Average (DJIA) changes from day to day say? Choose the correct answer below. A. Time is a function of the DJIA because the DJIA, the dependent variable, changes with respect to time, the independent variable. B. The DJIA and time are both functions because the DJIA, the dependent variable changes with respect to time, the independent variable. C. The DJIA is a function of time because time, the dependent variable changes with respect to the DJIA, the independent variable. D. The DJIA is a function of time because the DJIA, the dependent variable, changes with respect to time, the independent variable. E. The DJIA and time are both functions because both the DJIA and time describe how one variable depends on another. F. Time is a function of the DJIA because time, the dependent variable, changes with respect to the DJIA, the independent variable.

All of the following are functions of time. Which one would you expect to be closest to being a periodic function of time? Choose the correct answer below. A. The price of gasoline is closest to a periodic function of time because the price of gasoline repeats over and over with time. B. The volume of traffic on an urban freeway is closest to a periodic function of time because the volume of traffic becomes larger with time. C. The price of gasoline is closest to a periodic function of time because the price of gasoline gets larger over time. D. The population of a given country is closest to a periodic function of time because the population decays exponentially over time. E. The population of a given country is closest to a periodic function of time because the population grows exponentially over time. F. The volume of traffic on an urban freeway is closest to a periodic function of time because the volume of traffic repeats over and over with time.

In mathematics, what is the purpose of a function? Choose the correct answer below. A. A function describes an operation, such as multiplication or division. B. A function describes how one variable depends on another. C. A function describes how a domain and a range interact with one another. D. A function describes how inputs and outputs are affected by machines.

Write and solve an equation for the following problem: How many liters of pure acid should be added to 10 liters of 40% concentrate to raise the concentration to 55%?

The general population has been scared of HIV/AIDS for more than twenty years. The Center for Disease Control (CDC) warns of other infectious diseases that the public should be fearful of as well. You don't have to be a germophobe to be leery of the H7N9 flu which is one of the newer forms of bird flu. Research has identified some alarming details which note that the infectious disease can be passed from animals to humans without making the infected animals sick. As such, identifying and containing infected animals is difficult at best. At the present, there is no vaccine for the H7N9 flu. Most human cases to date have been found from exposure to infected poultry. The one item that has prevented the H7N9 from turning into a global pandemic is the saving grace that the flu is not passed from person to person. Click the icon to view the graph. ..... From the information given in the graph above, determine which decade saw the largest decrease in volume of reported flues from the past 100 years of reported cases. A. 1910-1920 B. 1980-1990 C. 1990-2010 D. 1920-1930

What is a mathematical model? Explain this statement: A model's predictions can only be as good as the data and the assumptions from which the model is built. Choose the correct answer below. ***** A. Mathematical models are based on relationships between quantities that remain constant and are described by mathematical tools called functions. B. Mathematical models are based on relationships between quantities that change and are described by very complicated functions that can only be understood using supercomputers. C. Mathematical models are based on relatickships between quantities that remain constant and can only be described by a graph. D. Mathematical models are based on relationships between quantities that change and are described by mathematical tools called functions.

At 11:00 you place a single bacterium in a bottle, and at 11:01 it divides into 2 bacteria, which at 11:02 divide into 4 bacteria, and so on. If the bacteria occupy a volume of 1 cubic meter at 12:02 and conti their exponential growth, when will they occupy a volume of 2 cubic meters? The bacteria will occupy a volume of 2 cubic meters at

Mathematical modeling abounds with algebraic applications such as quadratic graphs representing maximum and minimum cost equations. The mathematical principles involved are explored in typical high school algebra classes. In the past 30 years, computer modeling has catapulted our ability to mathematically model complex items in our world such as weather prediction, unemployment, and how buildings behave under stress such as those imposed by extreme weather. Computer mathematical modeling not only opens the door for evaluating these more complex models that are tedious to evaluate by hand but also saves time and financial resources. Car manufacturers no longer need to build prototypes of proposed car design changes to perform tests such as wind resistance, roll-over, and initial crash tests. The use of computer modeling has shortened the time from seeing a car move from a drawing to the assembly line. Computer modeling can be found in which of the following arenas? Choose the correct answer below. A. Unemployment models B. Earthquake strength of skyscrapers C. Weather D. All of the above

The impact of the recession of 2009 was widely felt across America. One response that continues well into 2013 is an effort to build local economies by thinking and spending locally. This decry has been heard in both large cities and small towns and has colored the shopping habits of a growing number of individuals even as some relief from the recession is felt. The results can be noteworthy. A national newspaper reported that if residents of New Orleans were to reallocate 10% of their spending to locally owned businesses and services, more than $200 million would be remain in the local economy. To meaningfully build local economies for the long haul, consumers as well as business owners must take the next step and produce more of what the community has imported over the years. Source: Christian Science Monitor, volume 101 Which of the following would not be an example of thinking and spending locally? A. Holiday shopping at a craft fair featuring community vendors. B. Contracting with a nationally known music group to provide entertainment for a town's centennial celebration. C. Selling jams made from area berry farms to surrounding communities. D. Using locally grown ingredients in country restaurants.

Mr. Montoya instructs the students in his math class to draw a rectangle with a certain area. Catlynn draws a rectangle with a length of 18 centimeters and a width of 6 centimeters. This proportional situation represents variation. The constant of variation, k, is equal to If Sergio draws a rectangle with a length of 27 centimeters, the width of the rectangle must be centimeters.

The variable fvaries inversely as the square root of g. When f= 4, g = 4. Jordan's work finding the value of fwhen g = 100 is shown: f√g = k 4(4) = k 16 = k f√g = 16 f√100 = 16 10f=16 f= 1.6 What is the first error, if any, in Jordan's work? A.He used an equation that models direct variation instead of inverse variation. B.He substituted incorrectly when calculating the constant of variation. C.He took the square root of the wrong variable. D.He did not make any errors.

Decide whether the following statement makes sense or does not make sense. Explain your reasoning. Scientists at an atmospheric research center use mathematical models to learn about the climate of a given planet. ne Choose the correct answer below. A. The statement does not make sense because a research center has no need to use mathematical models. Weather is a branch of science that does not use mathematics, B. The statement makes sense because the research center can use mathematical models to predict future trends of the planet's climate and determine the trends of the planet's climate before data was available. C. The statement makes sense because a research center can use mathematical models to collect data from the atmosphere. D. The statement does not make sense because mathematical models are unreliable in regards to climate and weather.

What are the three basic ways to represent a function? Choose the correct answer below. A. The three basic ways to represent a function are an ordered pair, a graph, and an expression. B. The three basic ways to represent a function are a table, a graph, and an equation. C. The three basic ways to represent a function are a table, a graph, and an expression. D. The three basic ways to represent a function are a table, an ordered pair, and an equation.

65% of a Carbon-14 sample has decayed and 56 grams remain. What was the mass of the original sample? Round your answer to the nearest whole number.

A car company says that the mean gas mileage for its luxury sedan is at least 23 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 6 cars has a mean gas mileage of 20 mpg and a standard deviation of 3 mpg. At a= 0.05, test the company's claim. Assume the population is normally distributed. Which sampling distribution should be used and why? A. Use a normal sampling distribution because n > 30. B. Use a normal sampling distribution because the population is normal, and a is unknown. C. Use a normal sampling distribution because the population is normal, and o is known. D. Use a t-sampling distribution because the population is normal, and a is unknown. E. Use a t-sampling distribution because the population is normal, and o is known. F. Use a t-sampling distribution because n< 30. State the appropriate hypotheses to test.

Find the number of edges on this polyhedron. First count the number of faces Fand vertices V. Then use Euler's formula: F+ V= E + 2. Solve for E. Type your answer and then click or tap Done. The number of edges on this octahedron is