Answer:
The first option
Step-by-step explanation:
Given a quadratic function in standard form : ax² + bx + c : a ≠ 0, then
The equation of the axis of symmetry which is also the x- coordinate of the vertex is found using
x = -
f(x) = - 2x² - 2x - 1 ← is in standard form
with a = - 2, b = - 2, so
x = - = - 0.5
Equation of axis of symmetry is x = - 0.5
Substitute x = - 0.5 into f(x)
f(- 0.5) = - 2(- 0.5)² - 2(- 0.5) - 1 = - 0.5 + 1 - 1 = - 0.5
Vertex = (- 0.5, - 0.5 )
Answer:
16% of its popular porcelain tile will have breaking strengths greater than 412.5 pounds per square inch.
Step-by-step explanation:
We are given that the breaking strength of its most popular porcelain tile is normally distributed with a mean of 400 pounds per square inch and a the standard deviation of 12.5 pounds per square inch.
Let X = <u><em>the breaking strength of its most popular porcelain tile</em></u>
SO, X ~ Normal()
The z score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = mean breaking strength of porcelain tile = 400 pounds per square inch
= standard deviation = 12.5 pounds per square inch
Now, probability that the popular porcelain tile will have breaking strengths greater than 412.5 pounds per square inch is given by = P(X > 412.5)
P(X > 412.5) = P( >
) = P(Z > 1) = 1 - P(Z
1)
= 1 - 0.84 = <u>0.16</u>
Therefore, 16% of its popular porcelain tile will have breaking strengths greater than 412.5 pounds per square inch.