The value of k is (A) 20/3.
<h3>
What is a parabola?</h3>
- A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics.
- It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves.
- A point and a line are two ways to describe a parabola.
To find the value of k:
Where (a, b) is the vertex and c is the constant.
- (a, b) = (-4, k)
- y - k = c (x - (- 4))²
- y - k = c (x + 4)²
So,
- x = 0, y = 12
- 12 - k = 16c
- k = 12 - 16c ...... (1)
Then,
- (-3, 7) = (x, y)
- 7 - k = c (1)²
- k = 7 - c ...... (2)
Now,
- 12 - 16c = 7 - c
- 12 - 7 = 16c - c
- 5 = 15c
- c = 5/15 = 1/3
So, the value of k:
- k = 12 - 16 (1/3) = 12 - 16/3 = 36-16/3 = 20/3
Therefore, the value of k is (A) 20/3.
Know more about a parabola here:
brainly.com/question/4061870
#SPJ4
The complete question is given below:
The coordinates of the vertex of a parabola in the XY plane are (-4,k). If the y-intercept of the parabola is 12 and the parabola passes through the point (-3,7), then what is the value of k?
(A) 20/3
(B) 16/5
(C) 14/3
(D) 12/5
Answer:
0.26684
Step-by-step explanation:
Given that :
Mean, μ = 62.5
Standard deviation, σ = 1.96
P(Z ≥ 63.72)
The Zscore = (x - μ) / σ
P(Z ≥ (x - μ) / σ)
P(Z ≥ (63.72 - 62.5) / 1. 96) = P(Z ≥ 0.6224)
P(Z ≥ 0.6224) = 1 - P(Z < 0.6224)
1 - P(Z < 0.6224) = 1 - 0.73316 = 0.26684
Answer:
The difference between these cut-offs is of $1.9.
Step-by-step explanation:
In this question, we have to find the 90% confidence interval, using the t-distribution.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 41 - 1 = 40
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 40 degrees of freedom(y-axis) and a confidence level of 
. So we have T = 1.684
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 9.03 - 0.95 = $8.08.
The upper end of the interval is the sample mean added to M. So it is 9.03 + 0.95 = $9.98.
What will be the difference between the upper and lower spending cut-offs which define the middle 90% of the customers if the sample contains 41 customers
$9.98 - $8.08 = $1.9
The difference between these cut-offs is of $1.9.
Answer:
Step-by-step explanation:
A = (3.14)(8)2
= 200.96
