Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = (x - h)² + k (h, k) are the coordinates of the vertex
Given y = x² + 7x - 5
To express in vertex form use the method of completing the square
add/subtract ( half the coefficient of the x- term )²
y = x² + 2( )x +
-
- 5
y = (x + )² -
-
y = (x + )² -
Hence
a = and b = -
Answer:
The percentage of people should be seen by the doctor between 13 and
17 minutes is 68% ⇒ 2nd term
Step-by-step explanation:
* Lets explain how to solve the problem
- Wait times at a doctor's office are typically 15 minutes, with a standard
deviation of 2 minutes
- We want to find the percentage of people should be seen by the
doctor between 13 and 17 minutes
* To find the percentage we will find z-score
∵ The rule the z-score is z = (x - μ)/σ , where
# x is the score
# μ is the mean
# σ is the standard deviation
∵ The mean is 15 minutes and standard deviation is 2 minutes
∴ μ = 15 , σ = 2
∵ The people should be seen by the doctor between 13 and
17 minutes
∵ x = 13 and 17
∴ z =
∴ z =
- Lets use the standard normal distribution table
∵ P(z > -1) = 0.15866
∵ P(z < 1) = 0.84134
∴ P(-1 < z < 1) = 0.84134 - 0.15866 = 0.68268 ≅ 0.68
∵ P(13 < x < 17) = P(-1 < z < 1)
∴ P(13 < x < 17) = 0.68 × 100% = 68%
* The percentage of people should be seen by the doctor between
13 and 17 minutes is 68%