Exercises 53-56: Use the midpoint formula for the following. 53. Nintendo Wii Six months after Nintendo Wii was introduced it had sold 10 million units, and after 24 months it had sold 44 million units. Estimate the number of units sold 15 months after the Nintendo Wii was introduced. The actual value was 25 million units. (Source: Company Reports.) 54. World Population In 1874 the world population was 1.24 billion. By 2050 this number is expected to be 9 billion. Estimate the world population in 1962. The actual value was 3.14 billion. (Source: United Nations Data.) 55. Olympic Times In the Olympic Games, the 200-meter dash is run in approximately 19 seconds. Estimate the time to run the 100-meter dash. 56. Real Numbers Between any two real numbers a and b there is always another real number. How could such a number be found?

Q: A function is given. Determine (a) the net change and (b) the average rate of change between the giv...

A: Now, to find the net change the substitute t=a and t=a+h in the function ft=2t and subtract the seco...

Q: How many years will it take for an initial investment of $25,000 to grow to $80,000? Assume a rate o...

A: Given : Initial investment = $25,000  Future value = $80,000 Rate of interest = 7 % Time ( years ) =...

Q: write the equation of each circle. Express the final equation in the form x2 + y2 + Dx + Ey + F = 0....

A: Known fact: The equation of circle centered at x1, y1 and radius r is given by x-x12+y-y12=r2.  

Q: True or False If f and g are inverse functions, then the domain of f is the same as the range of g.

A: If the statement is true or false.

Q: Show that loga(M/N) = loga M - loga N, where a, M, and N are positive real numbers and a ≠ 1.

A: Here given equation loga(M/N) = loga M - loga N

Q: Solve. If v varies directly as w and  v = 7  when  w = 1/2,   find the equation that relates v and w...

A: Given,            v varies directly as w and  v=7  when  w=12 .

Q: Exercises 5 and 6: Use the graph of the quadratic function f to write it as f(x) = a(x – h)² + k. 5....

A: (5) The horizontal transformation will result in shifting of the graph of the parent function to eit...

Q: find the intercepts and the equations for the asymptotes.4x2 - 9y2 = 16

A: GIVEN 4X2-9Y2=16 We need to find the intercepts and the equation for the  asymptotes .    

Q: Water in a Tank The graph shows the amount of water in a 100-gallon tank after x minutes have elapse...

A: A graph

Q: A function f is given. (a) Use a graphing calculator to draw the graph of f. (b) Find the domain and...

A: fx=x25 a). The graph is,

Q: If y varies inversely with x and  y = 3  when  x = 5,  find the equation that relates x and y.

A: Given:  y varies inversely with x i.e..,                                   y ∝ 1xy=k1x -------------...

Q: Explain how the graph of g is obtained from the graph of f.

A: Given: a  fx=x, gx=x+2-2b  fx=x ,gx=x-2+2 Concept Used: f(x)+a shifts graph a unit upward f(x)-a shi...

Q: perform the indicated operations and express the answers in simplified form. (y3 - 7y2 + 16y - 12)/(...

A: The equation given to us is  y3-7y2+16y-12y-2

Q: If the graph of y = f(x) undergoes a horizontal stretch or shrink to become the graph of y = g(x), d...

A: Given that, y= f(x) is a function. f(x) will undergo a horizontal compression when the scale factor ...

Q: Describe the translation in f(x)= 2*² +5 as it relates to the parent function f(x)=2^

A: Given,          The translation in fx=2x-2+5 as it relates to the parent function fx=2x.

Q: find the center and the length of a radius of each circle. x2 + y2 = 12

A: Given equation of circle is x2+y2=12. To find the center and the length of a radius of each circle. ...

Q: In Problems 23–30, use the given zero to find the remaining zeros of each function.

A: " Since you have asked multiple question, we will solve the first question for you. If you want any ...

Q: EXAMPLE 6 Making Linear Models Involving Speed John and Mary are driving westward along I-76 at cons...

A: A graph

Q: Find the sum and the product of the complex numbers 3 - 2i and - 3 + 5i.

A: Given complex numbers are: 3-2i and -3+5i       ……1

Q: For each of the following equations, (1) predict the type and location of the graph, and (2) use you...

A: (a) First simplify the equation to form the general equation of the conic y2=x2+16y2-x2=16y216-x216=...

Q: In the problem you are asked to find a function that models a real life situation. Use the principle...

A: Given, Equilateral triangle of area A sides of triangle are x we know area of triangle is A=34a2 whe...

Q: Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded ...

A: Given that, lnx-3lnx+2=0

Q: The graph of a function is given. Determine (a) the net change and (b) the average rate of change be...

A: Points (-1,0),(5,4)

Q: Sketch the graph of the polar equation.r = 5

A: Given polar equation is: r = 5 Its cartesian form is: x2+y2=5⇒x2+y2=25 Thus the graph of the given e...

Q: Critical Thinking Graph y = 1000x + 1000 in the standard window. (a) Is the graph a vertical line? (...

A: Given equation is: y = 1000x + 1000 Rearranging the terms we get, 1000x-y=-1000⇒1000x-1000+-y-1000=1...

Q: find the vertex of each parabola. y = x2 - 6x + 9

A: Given equation of parabola is y=x2-6x+9. To find the vertex of given parabola. Solution: We know tha...

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

A: A function is a relation between an input variable and an output variable wherein each input variabl...

Q: Every polynomial function of odd degree with real coefficients has at least real zero(s).

A: The given statement is, Every polynomial function of odd degree with real coefficients has at least ...

Q: The points (x, y) and (y, x) are mirror images of each other across the line y = x. Therefore, by in...

A: (a) x=y2  mirror image across the line y=x is y=x2

Q: A function is given. Determine (a) the net change and (b) the average rate of change between the giv...

A: A net change of a function is the difference between the function values at two points . The net cha...

Q: Exercises 47-50: Write a formula for a linear function f whose graph satisfies the conditions. 47. S...

A: A linear function in  variable x  is a function of the form f(x)=ax+b. So that f(x) is linear in x. ...

Q: Describe the part of a hyperbola given by the equation.

A: The standard form of equation of hyperbola having center at (0,0) and major axis on x axis is given ...

Q: Sketch a graph of the function. Use transformations of functions whenever possible. f(x) = 2x2 - 1

A:      Given :             The graph of a function is                             f(x) = 2x2 - 1      ...

Q: Use the set builder notation in describing the given set.7. {5, 10, 15}8. {1, 4, 9, 16, 25, 36, 49, ...

A: 7. Given set: S1=5, 10, 15  ……1

Q: Brian invests $11,500, at 6% interest, compounded semiannually for 2 years. Manually calculate the c...

A: Given problem is : Brian invests $11,500, at 6% interest, compounded semiannually for 2 years. Manua...

Q: Why do we distribute exponents in cases like (x/y)^2 = x^(2)/y^(2) but not distrute in cases like (x...

A: Because the power rule is different for division and addition.

Q: Solve the inequality: (x + 1)/(x - 2) ≥ 1

A: the given inequality is: x+1x-2≥1 we have to solve the given inequality.

Q: graph each circle. x2 + y2 + 6x - 2y + 6 = 0

A: To graph the circle:x2+y2+6x-2y+6=0 Solution: We know, the equation of a circle in general form is g...

Q: Describe the following sets using Listing method.1. P= {n | n is a natural number less than 8}2. S= ...

A: Part (1) - P = n|n is a natural number less than 8Here, n is a natural number which is less than 8.N...

Q: How would you convince someone that y = (x + 3)2 is the basic parabola moved 3 units to the left but...

A: we have to tell how would we convince someone that y = (x + 3)2 is the basic parabola moved 3 units ...

Q: If f is an exponential function of the form f(x) = Cax with growth factor 3, and if f(6) = 12, what ...

A: In the exponential function y=Cax is called the growth factor.       Thus, if the growth factor is 3...

Q: Q-4 Solve the boundary value problem (D² + 36)y = sin 6x ,given thatY(0) = 1 and Y (0) = 2

A: The given differential equation is D2+36y=sin6xy(0)=1 and y'(0)=2

Q: No cursive  need to be neat and able to see it clear  thank you  need help

A:

Q: The population of a midwestern city follows the exponential law.(a) If N is the population of the ci...

A: (A) If N is the population of the city and t is the time in years, express N as a function of t. Nt=...

Q: Construction A box is being constructed by cutting 2-inch squares from the corners of a square sheet...

A: given: A box is being constructed by cutting 2-inch squares from the corners of a square sheet of me...

Q: Use SUESS method

A: Parallelogram PQRS represents the wreck site with P(9,2) , Q(-8, 2), R(-7, 7) and S is not mapped a)...

Q: Find the sum, if it existsof the Infinite geometric series S=21+9+3.86+...

A: solution:- its geometric series because the common ration is same between the digits 

Q: Exercises 1-20: Simplify by using the imaginary unit i. 1. V-4 2. V-16 3. V-100 4. V-49 5. V-23 6. V...

A: The given number is -4

Q: Critical Thinking If your salary is $35,000 per year and increases by 200%, what is your new salary?

A: The salary is $35000 

Q: A quadratic function f is given. (a) Express f in standard form. (b) Sketch a graph of f. (c) Find t...

A: The standard form of quadratic function is given as f(x)=a(x-h)2+k,where a is the coefficient of x2 ...