Which of the following statements is equivalent to p(z < –2.1)?
a. p(z > –2.1)
b. 1–p(z < 2.1)
c. 1–p(z > 2.1)

Thus, The correct answer is B. 1 - P(z < 2.1)

Step-by-step explanation:

We are given that : P(z < –2.1)

And we need to find an equivalent statement for this.

The given statement needs to find the area under the curve when the z-score is less than -2.1

As the sum is equivalent to 1 , so to find the area under the given value we subtract the positive value of the given z-score from 1.

Hence, The given expression P(z < –2.1) is equal to 1 - P(z < 2.1)

Therefore, The statement equivalent to the given P(z < –2.1) is 1 - P(z < 2.1)

Thus, The correct answer is B. 1 - P(z < 2.1)

Part B: x = -5/2, and x = 1/2,

Part C: f(x)→ + ∞, as x→ − ∞, f(x)→ + ∞, as x→ + ∞ ,

Part D: I would start with determining the vertex. Knowing it's properties ( f(x)→ + ∞, as x→ − ∞ etc. ) we would determine the type of graph, and provided it's x - intercepts we can plot two points on either side and connect them to this vertex and extend beyond infinitely

Step-by-step explanation:

Part B: It would be easier to factor the expression 4x^2 + 8x - 5, firstly;

( 4x^2 - 2x ) + ( 10x - 5 ),

2x ( 2x - 1 ) + 5 ( 2x - 1 ),

Factored Expression: ( 2x + 5 )( 2x - 1 ) ⇒ f ( x ) = ( 2x + 5 )( 2x - 1 )

Now this equation isn't in standard form, but to determine the x - intercept the y - value must still be 0;

0 = ( 2x + 5 )( 2x - 1 ),

2x + 5 = 0, and 2x - 1 = 0,

x = -5/2, and x = 1/2

Part C: Knowing that this graph extends upwards ( an upward facing parabola ), the end behavior would be such;

f(x)→ + ∞, as x→ − ∞,          ⇒        demonstrated by the above

f(x)→ + ∞, as x→ + ∞        

Part D: I would start with determining the vertex. Knowing it's properties ( f(x)→ + ∞, as x→ − ∞ etc. ) we would determine the type of graph, and provided it's x - intercepts we can plot two points on either side and connect them to this vertex and extend beyond infinitely