\text { Let } U=\{1,2,3,4,5\} \text { and } A=\{1,2,3\} . \text { Find } A^{\prime} \text { . }

Q: Find two numbers whose sum is 50 such that the square of one number plus six times the other number ...

A: Let 'x' be the one number and the other number is (50-x).  

Q: 11. Consider the following rational functions: x³ + 6x? + 9x x³ + 27 s(x) 2x - 1 x - 9x x? + x - 6 r...

A: Functions

Q: determine if the following relations determine a function. Specify the domain and range. {(0, 8), (1...

A: Given relation is: 0,8,1,8,2,8,3,8 We have to determine whether the above relation is a function. We...

Q: An investment of $7000 is deposited into an account in which interest is compounded continuously. Co...

A:

Q: (a) To obtain the graph of g(x) = 2* - 1, we start with the graph of f(x) = 2* and shift it (upward/...

A: Given- (a) To obtain the graph of gx=2x-1,we start the graph of fx=2xand shift it .........(upward/d...

Q: - DISCUSS: The Googolplex A googol is 10100, and a googolplex is 10%00gol Find log(log(googol)) and ...

A: Consider that a googol=10100 and googolplex=10googol Implies 10googol=1010100. a) Calculate log log ...

Q: 51-52 - Difference Quotients These exercises involve a differ- ence quotient for an exponential func...

A: 51). Given function is fx=10x. To show that: fx+h-fxh=10x10h-1h Solution: We have fx=10x. Simplifyin...

Q: Use the Laws of Logarithms to expand the expression.

A: log32xy

Q: Determine whether the function is one-to-one.

A: Given function, f(x)=1x2

Q: Evaluate the expression.

A: Evaluate the expressions

Q: The order of

A: We have to find the order of the element 3 in ℤ24.

Q: Q2: Graph the following function:- 1) f(x) = \x + 31 – 1

A: To graph the function,  f(x) = |x + 3| - 1 We draw the above graph using transformations from the ba...

Q: Use the Laws of Logarithms to expand the expression.

A: lnr3s

Q: Use the Change of Base Formula and a calculator to evaluate the logarithm, rounded to six decimal pl...

A: To evaluate: log4125 Solution: We know, base change formula is given by: logba=logxalogxb      (base...

Q: 3. (a) 5 = 125, so log (b) log, 25 = 2, so

A: a. 53=125 b. log525=2

Q: Consider the function y = 2×. Complete the table of points for x = -2, -1, 0, 1, 2. Find the exact y...

A:

Q: 61-62 Present Value The present value of a sum of money is the amount that must be invested now, at ...

A: Given:         Principal P=$100,000         Rate R=8%          Time T=5 years     Monthly compound i...

Q: "Matrix"

A: Solving the given equation by using Cramer's rule.

Q: EXAMPLE 14 a Time Required to Grow an Investment A sum of $1000 is invested at an interest rate of 4...

A: Formula for calculating amount of compount interest at a given principal is - A = P1+R100t          ...

Q: Solve the following system of equations by graphing. If the system is inconsistent or the equations ...

A: The given system of equation is, x−2y=8x+2y=0

Q: ALWAYS true, SOMETIMES true, or NEVER true x+1 2* 42>24 1+1<2! Sometimes true X'< (x - 1)"*1 if xis ...

A:

Q: Solve each of the following problems. If y is inversely proportional to the square root of x, and if...

A: Given- y is inversely proportional to the square root of x  and if y=0.08 when x=225. To Find- The v...

Q: It's given that A,B are invertible matrices and A is also symmetric. If C =BA , D=AB and F=(D-'A"BC)...

A:

Q: Sketch the graph of the glven function. Check your sketch using technology. x3 g(x) = (x2 + 12) (a) ...

A: Since you have posted a question with multiple sub- parts, we will solve first three subparts for yo...

Q: Rates of Growth Compare the rates of growth of the func- tions f(x) = In x and g(x) = Vx by drawing ...

A: First draw the graph of both the functions . For this first draw x and y axes . Choose some arbitrar...

Q: Let U = 51, 2, 3, 4, 5, 6, 76, A = 51, 3, 5, 76, and B = 53, 4, 66. Find each set. U^{\prime}

A: Given sets - U = 51, 2, 3, 4, 5, 6, 76A = 51, 3, 5, 76B = 53, 4, 66We need to find the prime or comp...

Q: - Magnitude of Stars The magnitude M of a star is a measure of how bright a star appears to the huma...

A: Part (a) - Given relation - M =-2.5logBB0M =-2.5logB-logB0                                          ...

Q: Iodine-131 is a radioactive element that decays at a rate of 8.3% per day. You have a 12 gram sample...

A:

Q: Determine the x-intercept of the line passing through the points (−3,−1) and (−3,2). If the line has...

A: This question is related to coordinate geometry.

Q: Find the distance find find the distance between each pair of points round your answer to the neares...

A:

Q: Algebra Question

A:

Q: Graph the function, not by plotting points, but by starting from the graphs in the figure. State the...

A: Explanation: Given that,  h(x)  = 6 - 3x   Graph of the given function is:

Q: Solve each of the following problems. The period (the time required for one complete oscillation) of...

A: For a given variation problem, the variation equation can be written keeping following things in min...

Q: Complete the table shown to the right for the population growth model for a certain country. 2006 Po...

A: Topic-  population growth

Q: Find all rational, irrational, and complex zeros (and state their multiplicities). Use Descartes' Ru...

A: To find zeroes of : P(x)=x4+15x2+54 Solution: For finding zeroes, substituting,P(x)=0 ⇒x4+15x2+54=0 ...

Q: Express the equation in logarithmic form.

A: We know that if an=x then logax=n. (a). Given equation is 62=36. On comparing, we get  a=6, n=2 and ...

Q: If there were 60 grams of carbon-14 initially, how many grams would be remaining after 12 half-lives...

A:

Q: The perception of the loudness B (in decibels, dB) of a sound with physical intensity I (in W/m²) is...

A: The decibel level of sound is to be found when the physical intensity is 100 times that of I0. Subs...

Q: Find the quotient and remainder using synthetic division.

A: Given:  x3-8x+2x+3 Now we solve it by using the synthetic division. Now we take the constant term of...

Q: question 2,3,4 and 5

A: Since you have asked multiple questions in single request so we will be answering only first questio...

Q: Use the Laws of Logarithms to expand the expression.

A: The given logarithm expression can be expanded using following properties of logarithms. The exponen...

Q: graph each of the functions. f (x) = -2x + 5

A: We have a  linear equation of the form y=mx+b . A linear equation is a straight line equation and it...

Q: What is 7 + 5

A: Given  =7+5

Q: 2 -3 -5] 9. Show that A =-1 4 5 is an idempotent matrix. 1 -3 -4

A: A matrix is idempotent if A2=A 

Q: The composition idea can also be used to find the inverse of a function. For example, to find the in...

A: Given the composition idea for finding the inverse of a function. If fx=5x+3 then ff-1x=5f-1x+3 and ...

Q: translate each statement of variation into an equation, and use k as the constant of variation. The ...

A: Intensity of Illumination = IDistance from source = dConstant of proportionality = k

Q: Find the domain of the function. f(x) = log10(x + 3)

A: Domain is set of values for which the function is defined. Or it is the set of values for which the ...

Q: Find the domain of the function. g(x) = log3(x2 - 1)

A: Given function - g(x) = log3x2-1For a logarithmic function to be defined, the input to logarithm sho...

Q: Find the least common denominator for the set of rational expressions. a + 6 a + 5 (a - 2)(a - 7) (a...

A:

Q: Find the present value of the following future amount. $200.000 at 11% compounded quarterly for 25 y...

A: Use the formula relating the future value and present value and simplify.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.