Question: simplify and express answers using positive
simplify and express answers using positive exponents only. Variables are restricted to avoid division by 0.
> multiply, and express answers using positive exponents only.
> Simplify each expression using properties of radicals. All variables represent positive real numbers.
> Simplify each expression using properties of radicals. All variables represent positive real numbers.
> Simplify each expression using properties of radicals. All variables represent positive real numbers.
> simplify each expression and write answers using positive exponents only. All variables represent positive real numbers.
> simplify each expression and write answers using positive exponents only. All variables represent positive real numbers.
> simplify each expression and write answers using positive exponents only. All variables represent positive real numbers.
> simplify each expression and write answers using positive exponents only. All variables represent positive real numbers.
> simplify each expression and write answers using positive exponents only. All variables represent positive real numbers.
> perform the indicated operations and simplify.
> find rational number representations for each, if they exist. 8-2/3
> find rational number representations for each, if they exist.
> find rational number representations for each, if they exist.
> find rational number representations for each, if they exist.
> find rational number representations for each, if they exist. 163/4
> find rational number representations for each, if they exist. 641/3
> Change each expression to rational exponent form. Do not simplify.
> Change each expression to rational exponent form. Do not simplify.
> simplify and express answers using positive exponents only. Variables are restricted to avoid division by 0.
> simplify and express answers using positive exponents only. Variables are restricted to avoid division by 0.
> factor by grouping.
> The United States had a 2016 population of 323 million people and a land area of 3,539,000 square miles. What was the population density? Compute the answer using scientific notation and convert the answer to standard decimal form (to one decimal place).
> express the given standard: (A) In scientific notation (B) In standard decimal notation (C) As a percent 0.03 ppm, the standard for sulfur oxides, when averaged over a year
> Carry out the following computations using scientific notation, and write final answers in standard decimal form. (A) What was the per capita debt in 2000 (to the nearest dollar)? (B) What was the per capita interest paid on the debt in 2000 (to the ne
> Write the fractions in Problem as simple fractions reduced to lowest terms.
> Write the fractions in Problem as simple fractions reduced to lowest terms.
> If m = -n, then property 1 in Theorem 1 implies that a-n an = a0 = 1. Explain how this helps motivate the definition of a-n
> Refer to Problem 51. What is the difference between 2132 2 and 1232 2 ? Which agrees with the value of 232 obtained with a calculator? Data from Problem 51: What is the result of entering 232 on a calculator?
> convert each number to scientific notation and simplify. Express the answer in both scientific notation and in standard decimal form.
> convert each number to scientific notation and simplify. Express the answer in both scientific notation and in standard decimal form.
> Write each expression in Problem with positive exponents only, and as a single fraction reduced to lowest terms.
> perform the indicated operations and simplify.
> Write each expression in Problem with positive exponents only, and as a single fraction reduced to lowest terms.
> write each expression in the form axp + bxq or axp + bxq + cxr , where a, b, and c are real numbers and p, q, and r are integers. For example,
> write each expression in the form axp + bxq or axp + bxq + cxr , where a, b, and c are real numbers and p, q, and r are integers. For example,
> simplify and express answers using positive exponents only. Assume that variables are nonzero.
> simplify and express answers using positive exponents only. Assume that variables are nonzero.
> simplify and express answers using positive exponents only. Assume that variables are nonzero.
> simplify and express answers using positive exponents only. Assume that variables are nonzero.
> simplify and express answers using positive exponents only. Assume that variables are nonzero.
> write each number in standard decimal notation. 1.13 x 10-2
> write each number in standard decimal notation. 3.044 x 103
> factor out all factors common to all terms.
> write each number in standard decimal notation. 2 x 10-5
> write each number in standard decimal notation. 9 x 106
> write each number in scientific notation. 0.000 000 007 832
> write each number in scientific notation. 0.019
> write each number in scientific notation. 5,380,000
> simplify and express answers using positive exponents only. Variables are restricted to avoid division by 0.
> simplify and express answers using positive exponents only. Variables are restricted to avoid division by 0.
> simplify and express answers using positive exponents only. Variables are restricted to avoid division by 0.
> simplify and express answers using positive exponents only. Variables are restricted to avoid division by 0.
> perform the indicated operations and simplify.
> Replace each question mark with an appropriate expression that will illustrate the use of the indicated real number property. Commutative property 1 + 2: x + 7 = ?
> find each indefinite integral
> Find each indefinite integral and check the result by differentiating.
> Find the equation of the curve that passes through (1, 3) if its slope is given by for each x.
> Find each indefinite integral and check the result by differentiating.
> find the particular antiderivative of each derivative that satisfies the given condition.
> Find each indefinite integral and check the result by differentiating.
> find the particular antiderivative of each derivative that satisfies the given condition.
> Is F(x) = ln 1ln x2 an antiderivative of ? Explain.
> find the particular antiderivative of each derivative that satisfies the given condition.
> Is F(x) = 1 - 0.2e-5x an antiderivative of (x) = e-5x Explain.
> find a standard form for the absorbing Markov chain with the indicated transition matrix.
> find the particular antiderivative of each derivative that satisfies the given condition.
> Is F(x) = (x2 – 1)100 an antiderivative of (x) = 200x (x2 – 1)99? Explain.
> Find each indefinite integral. (Check by differentiation.)
> Is F(x) = 1/x an antiderivative of (x) = ln x? Explain.
> Find each indefinite integral. (Check by differentiation.)
> the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent.
> Find each indefinite integral. (Check by differentiation.)
> The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent.
> Find each indefinite integral. (Check by differentiation.)
> the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent.
> find a standard form for the absorbing Markov chain with the indicated transition diagram.
> Find each indefinite integral. (Check by differentiation.)
> Find each indefinite integral and check the result by differentiating.
> Find each indefinite integral. (Check by differentiation.)
> Find each indefinite integral and check the result by differentiating.
> Could the three graphs in each figure be anti-derivatives of the same function? Explain
> Find each indefinite integral and check the result by differentiating.
> could the given matrix be the transition matrix of a regular Markov chain?
> could the given matrix be the transition matrix of a regular Markov chain?
> Could the three graphs in each figure be anti-derivatives of the same function? Explain
> without using a calculator, find P100. [Hint: First find P2 .]
> without using a calculator, find P100. [Hint: First find P2.]
> without using a calculator, find P100. [Hint: First find P2 .]
> without using a calculator, find P100. [Hint: First find P2 .]
> Table 4 gives the percentage of the U.S. population living in the northeast region during the indicated years. The following transition matrix P is proposed as a model for the data, where N represents the population that lives in the northeast region:
> The Senate is in the middle of a floor debate, and a filibuster is threatened. Senator Hanks, who is still vacillating, has a probability of .1 of changing his mind during the next 5 minutes. If this pattern continues for each 5 minutes that the debate c
> Suppose that a gene in a chromosome is of type A or type B. Assume that the probability that a gene of type A will mutate to type B in one generation is 10-4 and that a gene of type B will mutate to type A is 10-6 . (A) What is the transition matrix? (
> Refer to Problem 63. The chemists at Acme Soap Company have developed a second new soap, called brand Y. Test-marketing this soap against the three established brands produces the following transition matrix: Proceed as in Proble
> Repeat Problems 61 if 40% of preferred customers are moved to the satisfactory category each year, and all other information remains the same. Data from Problem 61: An auto insurance company classifies its customers in three categories: poor, satisfacto
> Consumers in a certain area can choose between three package delivery services: APS, GX, and WWP. Each week, APS loses 10% of its customers to GX and 20% to WWP, GX loses 15% of its customers to APS and 10% to WWP, and WWP loses 5% of its customers to AP
> Find each indefinite integral and check the result by differentiating.
> The U.S. Census Bureau published the home ownership rates given in Table 2. The following transition matrix P is proposed as a model for the data, where H represents the households that own their home. (A) Let S0 = 3.654 .3464 and find S1, S2, and S3
> The railroad in Problem 55 also has a fleet of tank cars. If 14% of the tank cars on the home tracks enter the national pool each month, and 26% of the tank cars in the national pool are returned to the home tracks each month, what percentage of its tank
> The transition matrix for a Markov chain is Let mk denote the minimum entry in the third column of Pk . Note that m1 = .3. (A) Find m2, m3, m4, and m5 to three decimal places. (B) Explain why mk … mk + 1 for all positive integers
> require the use of a graphing calculator. Refer to the transition matrix P in Problem 50. What matrix P do the powers of P appear to be approaching? Are the rows of P stationary matrices for P?
