In how many ways can you put seven marbles in different colors into two jars? Note that the jars may be empty.

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

<pBy extracting the square roots;

          (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:

Step-by-step explanation:

It has been established that the count of drivers traveling between a specific origin and destination in a certain time frame follows a Poisson distribution with a mean μ = 20 (as indicated in the article "Dynamic Ride Sharing: Theory and Practice"†).

a)

b)

c)

d) 2 standard deviations = 2(20) = 40

Thus, this means the range for 2 standard deviations is

20-40, 20+40

which equates to (0,60)

The question clearly seeks the highest values from both functions, meaning the vertices of each.

<span>The graph depicting the path of Ed’s football indicates the vertex's coordinates (the peak of the graph).
</span>
Specifically,

(h,k) = (1.5, 7.5)

Where (h,k) represents the vertex's location.

Conversely,<span>the trajectory of Steve's football is defined by the equation:
y = - 2x
²</span> + 5x + 4<span>To find the axis of symmetry, we use the formula:x = - b
÷ 2a
Where:

a = -2</span>
b = 5

Consequently,

x = - 5 ÷ - 4

x = 5 / 4




x = 1.25
Now substituting this x-value back into the main equation to determine y.
y = - 2x² + 5x + 4
y = - 2(1.25)² + 5(1.25) + 4

y = - 3.125 + 6.25 + 4


y = 7.125


Thus, the vertex (h,k) = (1.25, 7.125)
As observed from the calculations
Ed’s

<span>football attains a higher height.</span>