The percentage of U.S. college freshmen claiming no religious affiliation has risen in recent decades. The bar graph shows the

Given parameters:

  Equation:

          (x-4)²=9

Problem: Solve the equation by both factoring and extracting the square root.

Solution:

    Starting equation:

                  (x-4)²=9

         Subtracting 9 from both sides brings us to zero;

                (x-4)² - 9 = 0

                (x -4)² - 3² = 0

  This fits the concept of the difference of squares;

          x² - y² = (x + y)(x-y)

Let x  = x-4 and y = -3

  Then input and solve;

              (x - 4 -3)(x - 4 -(-3)) = 0

              (x - 7)(x - 1) = 0

S thus,

             x - 7 = 0 or x-1 = 0

             x = 7 or 1

          (x-4)² = 9

         √(x-4)² = √9

              x - 4 = 3

              x  = 4 + 3 = 7; however, this is not the sole solution

Thus, direct extraction of the square root is not the method for complete solutions.

Answer:

a. La ganancia total es de $ 4,060,000.00

b. 31 vehículos fabricados

Step-by-step explanation:

(a) Los datos suministrados son;

Cantidad de autos tipo sedán producidos = 24

Cantidad de SUV ensamblados = 16

Cantidad de vehículos tipo VAN producidos = 12

Cantidad de pick-ups fabricadas = 8

Cantidad de autos deportivos producidos = 2

Ganancia de los autos sedán vendidos = $ 185,000 - $ 140,000 = $ 40,000

Ganancia por las SUV vendidas = $ 320,000 - $ 250,000 = $ 70,000

Ganancia de los vehículos tipo VAN = $ 400,000 - $ 310,000 = $ 90,000

Ganancia de las pick-ups = $ 285,000 - $ 210,000 = $ 75,000

Ganancia de los autos deportivos vendidos = $ 550,000 - $ 400,000 = $ 150,000

La ganancia total se calcula de la siguiente manera: 24 * $ 40,000 + 16 * $ 70,000 + 12 * $ 90,000 + 8 * $ 75,000 + 2 * $ 150,000 = $ 4,060,000

(b) Debido a que hay una producción constante, solo se completará la mitad del total de automóviles en un lapso de 12 horas

Por lo tanto, se fabrican

12 sedanes, 8 SUV, 6 VAN, 4 pick-ups y 1 deportivo, alcanzando así un total de 31 vehículos.

Reducing

9x + -31 = 43

Rearranging the components:

-31 + 9x = 43

Finding the solution

-31 + 9x = 43

Isolating the variable 'x'.

Shift all terms with x to one side,

Add '31' to both sides of the equation.

0 + 31 + 9x = 43 + 31

Summing up similar items:

-31 + 31 = 0

0 + 9x = 43 + 31

9x = 43 + 31

Summing similar items:

43 + 31 = 74

9x = 74

Split each side by '9'

x = 8.222222222

Simplifying

x = 8.222222222

Answer:

FV(n)=42,000(1.04)^n

Step-by-step explanation:

FV represents future value.

PV is present value.

r indicates the interest rate.

n is the number of periods.

t represents time (in years).

Here, PV=42,000

r=4%=0.04

n=1

t=n

Finding FV(n) gives us p(1+r/n)^nt.

=42,000(1+0.04/1)^1*n

=420000(1+0.04)^n

=42,000(1.04)^n

Answer:

a) 11,880

b) 495

c) 0.00202

Step-by-step explanation:

Given:

Here is the full question:

"A corporation needs to select a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It also needs to form a planning committee comprising four distinct members. There are 12

qualified candidates, and the officers can also serve on the committee.

Find:

a. Determine the number of ways to appoint the officers.

Solution:

- Total qualified candidates = 12

 - Number of officers to appoint = 4 (President, Chief Executive Officer, Chief Operating Officer, Chief Financial Officer)

- Since the order matters, we use permutations:

- The number of different arrangements to appoint officers = 12P4 = 11,880

b. Determine the number of ways to select the committee members.

   Total qualified candidates = 12

  The number of planning committee members = 4  

  Here, order doesn't matter, so we use combinations:

  The number of different ways to form a committee = 12C4 = 495

c. What is the likelihood of randomly choosing the committee members being the four youngest qualified candidates?

  P ( 4 youngest officers ) =  Chances of selecting 4 youngest / Total number of committees

                                           = 1 / 495

                                           = 0.00202