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mathematics
precalculus

Questions and Answers of Precalculus

Problems 113–122. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
The binomial coefficientequals
Find a rectangular equation of the plane curve with parametric equations x(t) = t + 5 and y(t) = √t for t ≥ 0.
Find the function g whose graph is the graph of y = √x but is stretched vertically by a factor of 7 and shifted left 5 units.
Problems 113–122. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Solve: 3x2 − 2x = −1
The_________ of A and B consists of all elements in either A or B or both.
In Problems 4 – 9, use the information supplied in the figure.How many are in A ? 20 A 1 2 6 4 С 0 B 5 20 U
A(n)_______ is an ordered arrangement of r objects chosen from n objects.
Find the complex zeros of f(x) = 5x49x37x2 - 31x6
Solve the each equation C(n,r) =
Solve the each equation P(n,r) =
Determine whether the following is a probability model. Outcome Shanice Destiny Jordan Xavier Probability 0.3 0.2 0.1 0.3
The Counting Formula states that if A and B are finite sets, then n(A ∪ B) = _______. (a) n(A) + n(B) (c) n(A) n(B) . (b) n(A) + n(B) - n(ANB) (d) n(A) n(B)
Solve: |x − 4|≤ 0.01
In Problems 5–7, compute the value of the given expression.7!
Determine whether the following is a probability model. Outcome Kwamie Joanne Laura Donna Angela Probability 0.3 0.2 0.1 0.5 -0.1
If each element of a set A is also an element of a set B, we say that A is a______ of B and write A________ B .
Solve the system: x - 2y + z = 15 3x + y - 3z = -8 -2x + 4y z = -27
In Problems 5–7, compute the value of the given expression.P(10, 6)
In Problems 5–7, compute the value of the given expression.C(11, 5)
In Problems 7 – 14, find the value of each permutation.P(6, 2)
Solve: log2 (3x − 2) + log2 x = 4
In Problems 7 – 14, find the value of each permutation.P(7, 2)
The following data represent the marital status of males 15 years old and older in the U.S. in 2020.(a) Determine the number of males 15 years old and older who are widowed or divorced.(b) Determine
How many distinct 8-letter words (meaningful or not) can be formed from the letters in the word REDEEMED?
In Problems 7 – 14, find the value of each permutation.P (4, 4)
The following data represent the marital status of females 15 years old and older in the U.S. in 2020.(a) Determine the number of females 15 years old and older who are divorced or separated.(b)
In Problems 7 – 14, find the value of each permutation.P(8, 8)
Graph: y = 3 sin(2x +π)
In Problems 7 – 14, find the value of each permutation.P (7, 0)
In Problems 7 – 14, find the value of each permutation.P(9, 0)
In Problems 7 – 14, find the value of each permutation.P (8, 4)
In Problems 7 – 14, find the value of each permutation.P(8, 3)
For this problem, assume that a year has 365 days.(a) In how many ways can 18 people have different birthdays?(b) What is the probability that no 2 people in a group of 18 people have the same
According to the U.S. Bureau of Labor Statistics, 3.8% of the U.S. labor force was unemployed in February 2022.(a) What is the probability that a randomly selected member of the U.S. labor force was
Determine whether the infinite series converges or diverges. If it converges, find the sum. 12 36 108 4 + + + 5 25 125 + ..
Problems 36 – 45. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.
How many three-digit numbers can be formed using the digits 0 and 1? Repeated digits are allowed.
In how many ways can 4 people be lined up?
Problems 36 – 45. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 36 – 45. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
If the sides of a triangle are a = 2, b = 2, and c = 3, find the measures of the three angles. Round to the nearest tenth.
Find all the real zeros of the function:f (x) = (x − 2)(x2 − 3x − 10)
Problems 36 – 45. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.
Problems 36 – 45. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Companies whose stocks are listed on the New York Stock Exchange (NYSE) have their company name represented by 1, 2, or 3 letters (repetition of letters is allowed). What is the maximum number of
Problems 36 – 45. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
For Problems 41–44, two fair dice are rolled.Determine the probability that the sum of the faces is 7.
Problems 36 – 45. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
True/False Test How many arrangements of answers are possible for a true/false test with 10 questions?
If P(A) = 0.60, P(A ∪ B) = 0.85, and P(A ∩ B) = 0.05, find P(B).
If P(B) = 0.30, P(A ∪ B) = 0.65, and P(A ∩ B) = 0.15, find P(A).
According to the Federal Bureau of Investigation, there was a 74.5% probability that a motor vehicle theft in 2019 was an automobile. If a motor vehicle theft from 2019 is randomly selected, what is
According to Omnicore, there is an 81% probability that an adult in the United States uses YouTube. If a U.S. adult is randomly selected, what is the probability that he or she does not use YouTube?
Problems 63–66 are based on a survey of annual incomes in 100 households. The following table gives the data.What is the probability that a household has an annual income of $50,000 or more?
Problems 63–66 are based on a survey of annual incomes in 100 households. The following table gives the data.What is the probability that a household has an annual income of $75,000 or more?
According to the National Center for Education Statistics, there was a 56% probability that a doctoral degree in Science, Technology, Engineering, or Mathematics (STEM) fields was earned by a
According to outerboxdesign.com, 79% of smartphone users have made a purchase online using their mobile device in the last 6 months. If a smartphone user is randomly selected, what is the probability
According to the Girl Scouts of America, 19% of all Girl Scout cookies sold are Samoas/Caramel deLites. If a box of Girl Scout cookies is selected at random, what is the probability that it does not
Baseball In Major League Baseball a designated hitter may be used to hit for the pitcher. How many batting orders is it possible for a manager to use?
Problems 68 – 77. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Suppose a baseball league exists where the pitcher must bat. The pitcher usually bats ninth. If this is the case, how many batting orders is it possible for a manager to use?
Problems 68 – 77. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Suppose a password must have at least 8 characters, but no more than 12 characters, made up of letters (without distinction for case) and digits. If the password must contain at least one letter and
Problems 75–84. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.To
Problems 68 – 77. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Find the rectangular coordinates of the point whose polar coordinates are 6, 2п 3
Problems 68 – 77. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 68 – 77. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Find the partial fraction decomposition: 5x2 + 3x + 14 x4 + 4x² + 4
Problems 68 – 77. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 68 – 77. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
If 3 six-sided dice are tossed, find the probability that exactly 2 dice have the same reading.
Problems 68 – 77. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 75–84. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 68 – 77. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
In Problems 9–42, find each limit algebraically. lim 5 x-1
True or False 5√-32 = -2
Ifthen f is_______ at ________. lim f(x) = f(c), X-C
In Problems 9–42, find each limit algebraically. lim (-3) x-1
True or False To check division, the divisor should equal (Quotient )(Dividend) + Remainder .
True or False The product of a complex number and its conjugate is a nonnegative real number.
True or False The surface area of a sphere of radius r is 4/3 πr2.
Which of the following is the principal square root of − 4?(a) −2i(b) 2i(c) −2(d) 2
In Problems 8–12, use the graph of y = f (x). -4 у -4 4 X
In Problems 1 – 11, find the limit. -: 1 x2 lim x--1x3 - 1
In Problems 8–12, use the graph of y = f (x). -4 у -4 4 X
In Problems 8 – 11, determine whether the statement is True or False if a < b and c < 0.a − c < b − c
In Problems 9 – 18, factor each polynomial by removing the common monomial factor.3x + 6
In Problems 1 – 11, find the limit. x³ - 8 3 x-2x32x2 2x² + 4x - 8 lim-
In Problems 8 – 11, determine whether the statement is True or False if a < b and c < 0.a c > bc
In Problems 1 – 11, find the limit. x4 lim- x-3x3 - 3x3 + x - 3 3x² + 2x 6 -
In Problems 8–12, use the graph of y = f (x). -4 у -4 4 X
In Problems 7–16, use a table to investigate the indicated limit. 2- x lim x 0x² + 4 2
Which operation involving complex numbers requires the use of a conjugate?(a) Division(b) Multiplication(c) Subtraction(d) Addition
True or False t √(-3)4 -3
In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.f (x) = −2x + 1 at (−1, 3)
In Problems 9–42, find each limit algebraically. lim x x-4
In Problems 8–12, use the graph of y = f (x).Does the graph suggest thatexists? If so, what is it? If not, explain why not. -4 у -4 4 X

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