Complete the square so that the left side of x2 + 8x − 3 = 0 becomes a binomial squared. (x +___)2 = ___

The vertex of the graph for the function g(x) = (x- 3)^2 + 9 is located 3 units to the right and 9 units upwards compared to the vertex of the function f(x) = x^2.

Answer:

P-value = 0.0455

Step-by-step explanation:

This inquiry focuses on calculating the P-value in a test.

Mathematically, we establish that;

P-value = 2 * P(Z > |z|)

Please refer to the attached document for a comprehensive resolution and step-by-step explanation

Answer:

To summarize the answer:

Step-by-step explanation:

Given:

Here is the graph associated with this question:

The second function, denoted as , does not qualify as a function.

Keep in mind that the g(x) function is the inversion of the f(x) function. Recognizing this pattern indicates a reflection on the Y-axis.

Reflection on the axes:

In the x-axis:

Enhance the function by -1 to illustrate an exponential curve around the x-axis.

In the y-axis:

Decrease the input of the function by -1 to depict the exponential function around the y-axis.

Let
denote the length of the pond and <span> signify its width. It's recognized that the pond's volume equals the area of its base multiplied by its depth. In this case, the base area can be computed as volume divided by depth, equating to 72000 in³ divided by 24 in, resulting in an area of 3000 in². Given that the area is expressed as x multiplied by y, we come to equation 1, 3000 = x * y. If we have x = 2y, we substitute this into equation 1, leading to 3000 = (2y) * y, simplifying to 2y² = 3000 and consequently y² = 1500, giving y = 38.7 in. Thus, x = 2y yields x = 2 * 38.7 = 77.4 in. The conclusion is that the pond's length is 77.4 in while its width is 38.7 in. </span>

Respuesta:

(a) 4.98x10⁻⁵

(b) 7.89x10⁻⁶

(c) 1.89x10⁻⁴

(d) 0.5

(e) 2.9x10⁻²

Explicación paso a paso:

La probabilidad (P) de encontrar la partícula está dada por:

 

    (1)

La solución de la integral de la ecuación (1) es:

 

(a) La probabilidad de encontrar la partícula entre x = 4.95 nm y 5.05 nm es:

   

(b) La probabilidad de encontrar la partícula entre x = 1.95 nm y 2.05 nm es:

 

(c) La probabilidad de encontrar la partícula entre x = 9.90 nm y 10.00 nm es:

   

(d) La probabilidad de encontrar la partícula en la mitad derecha de la caja, es decir, entre x = 0 nm y 50 nm es:

(e) La probabilidad de encontrar la partícula en el tercio central de la caja, es decir, entre x = 0 nm y 100/6 nm es:

Espero que te ayude.