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mathematics
precalculus

Questions and Answers of Precalculus

Find the value of the permutation. P(8, 4)
Find the value of the permutation. P(9, 0)
Find the value of the permutation. P(7, 0)
Find the value of the permutation. P(8, 8)
Find the value of the permutation. P(4, 4)
Find the value of the permutation. P(7, 2)
Find the value of the permutation. P(6, 2)
C(n , r) = _______.
P(n , r) = ______.
A(n)_______is an arrangement of r objects chosen from n distinct objects, without repetition and without regard to order.
A(n)________is an ordered arrangement of r objects chosen from n objects.
True or False. (п + 1)! п! п
As a financial planner, you are asked to select one stock each from the following groups: 8 DOW stocks, 15 NASDAQ stocks, and 4 global stocks. How many different portfolios are possible?
The following data represent the marital status of females 18 years old and older in 2007. (a) Determine the number of females 18 years old and older who are widowed or divorced. (b)
The following data represent the marital status of males 18 years old and older in 2007. (a) Determine the number of males 18 years old and older who are widowed or divorced. (b) Determine
Human blood is classified as either Rh+ or Rh-. Blood is also classified by type: A, if it contains an A antigen but not a B antigen; B, if it contains a B antigen but not an A antigen; AB, if it
In a survey of 100 investors in the stock market.50 owned shares in IBM40 owned shares in AT&T45 owned shares in GE20 owned shares in both IBM and GE15 owned shares in both AT&T and GE20
In a student survey, 200 indicated that they would attend Summer Session I and 150 indicated Summer Session II. If 75 students plan to attend both summer sessions and 275 indicated that they would
In a consumer survey of 500 people, 200 indicated that they would be buying a major appliance within the next month, 150 indicated that they would buy a car, and 25 said that they would purchase both
How many five-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0 or 1? Repeated digits are allowed.
How many four-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0? Repeated digits are allowed.
A woman has 5 blouses and 8 skirts. How many different outfits can she wear?
A man has 5 shirts and 3 ties. How many different shirt and tie arrangements can he wear?
Use the information given in the figure.How many are in A or B or C? U A B 3 15 5. 2 10 2 4 15 C
Use the information given in the figure.How many are in A and B and C? U A B 3 15 5. 2 10 2 4 15 C
Use the information given in the figure.How many are not in A? U A B 3 15 5. 2 10 2 4 15 C
Use the information given in the figure.How many are in A but not C? U A B 3 15 5. 2 10 2 4 15 C
Use the information given in the figure.How many are in A and B? U A B 3 15 5. 2 10 2 4 15 C
Use the information given in the figure.How many are in A or B? U A B 3 15 5 2 10 15 C
Use the information given in the figure.How many are in set B? U A B 3 15 5 2 10 15 C
Use the information given in the figure.How many are in set A? 3 15 10 5. 4 15
If n(A ∪ B) = 60, n(A ∩ B) = 40, and n(A) = n(A), find n(A).
If n(A ∪ B) = 50, n(A ∩ B) = 10, and n(B) = 20, find n(A).
If n(A) = 30, n(B) = 40, and n(A ∪ B) = 45 find n(A ∩ B).
If n(A) = 15, n(B) = 20, and n(A ∩ B) = 10 find n(A ∪ B).
Write down all the subsets of {a, b, c, d, e}.
Write down all the subsets of {a, b, c, d}.
True or False.If a task consists of a sequence of three choices in which there are p selections for the first choice, q selections for the second choice, and r selections for the third choice, the
If A and B are finite sets, the Counting Formula states that n(A ∪ B) = ________ .
If the number of elements in a set is a nonnegative integer, we say that the set is ______.
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.
True or False.If A is a set, the complement of A is the set of all the elements in the universal set that are not in A.
True or False.The intersection of two sets is always a subset of their union.
The ________ of A with B consists of all elements in both A and B.
The ________ of A and B consists of all elements in either A or B or both.
If θ = 1/4 and θ is in the second quadrant, find:(a) cos θ(b) tan θ(c) sin (2θ) (d) cos (2θ) (e) sin (1/2 θ)
Find the exact value of cos-1 (-0.5).
Solve the equation2sin2x – sinx – 3 = 0 ≤ x < 2π
Find the polar equation of a circle with center (0, 4) at that passes through the pole. What is the rectangular equation?
Find the equation of a parabola with vertex at (-1, 2) and focus at (-1, 3).
Find the equation of an ellipse with center at the origin, a focus at (0, 3) and a vertex at (0, 4).
Find: (a) (f º g)(2)(b) (g º f)(4)(c) (f º g)(x) (d) The domain of (f º g)(x)(e) (g º f)(x) (f) The domain of (g º f)(x)(g) The function g-1 and its domain.(h) The function f-1
Find the standard equation of the circle whose center is the point (-1, 2) if (3, 5) is a point on the circle.
Find an equation of the line with slope 5 and x-intercept 2.
Solve the equation 2ex = 5.
(a) Graph the circle x2 + y2 = 100 and the the para y = 3x2(b) Solve the system of equations: (c) Where do the circle and the parabola intersect? + y? = 100 у %3 Зx?
Find all the solutions, real and complex, of the equation |x2| = 9.
A weightlifter begins his routine by benching 100 pounds and increases the weight by 30 pounds for each set. If he does 10 repetitions in each set, what is the total weight lifted after 5 sets?
A new car sold for $31,000. If the vehicle loses 15% of its value each year, how much will it be worth after 10 years?
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers. = n + 1 3 п
Expand (3m + 2)5 using the Binomial Theorem.
Determine whether the infinite geometric series 256 - 64 + 16 - 4 + ... converges or diverges. If it converges, find its sum.
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric,
Write out each sum. Evaluate the sum. 4 k k 3 k=1
Write out each sum. Evaluate the sum. k + 1 1)* Σ-1. k? k=1
Write down the first five terms of the sequence. a1 = 4, an = 3an-1 + 2
Write down the first five terms of the sequence. nt n? – 1 {S,} n + 8
Your friend has just been hired at an annual salary of $20,000. If she expects to receive annual increases of 4%, what will be her salary as she begins her fifth year?
Jacky contributes $500 every quarter to an IRA. If Jacky plans on retiring in 30 years, what will be the value of the IRA if the per annum rate of return of the IRA is 8% compounded quarterly?
Chris gets paid once a month and contributes $200 each pay period into his 401(k). If Chris plans on retiring in 20 years, what will be the value of his 401(k) if the per annum rate of return of the
A ball is dropped from a height of 20 feet. Each time it strikes the ground, it bounces up to threequarters of the previous height. (a) What height will the ball bounce up to after it strikes
A mosaic tile floor is designed in the shape of a trapezoid 30 feet wide at the base and 15 feet wide at the top. The tiles, 12 inches by 12 inches, are to be placed so that each successive row
A brick staircase has a total of 25 steps. The bottom step requires 80 bricks. Each successive step requires three less bricks than the prior step. (a) How many bricks are required for the top
Find the coefficient of x6 in the expansion of (2x + 1)8.
Find the coefficient of x2 in the expansion of (2x + 1)7.
Find the coefficient of x3 in the expansion of (x – 3)8.
Find the coefficient of x3 in the expansion of (x + 2)9.
Find the coefficient of x7 in the expansion of (3x + 4)4.
Expand the expression using the Binomial Theorem.(2x + 3)5
Expand the expression using the Binomial Theorem. (x – 3)4
Expand the expression using the Binomial Theorem. (x + 2)5
Evaluate each binomial coefficient.
Evaluate each binomial coefficient. 2,
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers. 1•3 + 2•4 + 3•5 + … + n(n + 2) = n/6 (n + 1)(2n + 7)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers. 12 + 42 + 72 + … + (3n – 2)2 = ½ n(6n2 – 3n – 1)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers. 2 + 6 + 18 + … + 2•3n-1 = 3(2n – 1)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers. 2 + 6 + 18 + … + 2.3n-1 = 3n – 1
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers. 2 + 6 + 10 + … + (4n – 2) = 2n2
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers. Зп (п + 1) 2 3 + 6 + 9 +...+ 3n
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 3\k-1 30 4 (-) k=1
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. k-1 Σ (2, k=1
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 5 k-1 Σ5. 5• 4 k=1
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 9. 3 4
Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. 16 8. 6 – 4 + 3

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