Answer:
- A relationship modeled by the function f(x) = 4x³ - 72x² + 320x is the volume of a right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
Explanation:
To find a relationship modeled by the given function it is recommendable to factor it.
The function is:
The first step to factor it is to extract common factor 4x:
The second step is to factor the quadratic trinomial.
That is made by writting it as a product of two binomials, for which the two constant terms add up - 18 and their product is 80. Those terms are -10 and - 8; so the two factors are (x - 10) and (x - 8), and the factored form is:
Then, a relationship modeled by that polynomial is the volume of right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
- x is the desired (unknown) length
- 4x is 4 times the desired length
- x - 10 is 10 less than the desired length
- x - 8 is 8 less than the desired length
Thus, the volume of the prism is the product of the three factors:
Parallel:
y
=
2
3
x
−
11
3
y=
3
2
x−
3
11
perpendicular:
y
=
−
3
2
x
+
5
y=−
2
3
x+5
Answer:
The correct options are;
B) The mean and median for the security company are both lower than the mean and the median for the collections performed by other companies
B) Since the security company appear to have collected lower revenue than other companies, there is some evidence of stealing by the security company's employees
Step-by-step explanation:
We use the acronym SC for the security company and OC for the other company
SC OC
1.6 1.5
1.8 2.1
1.6 1.9
1.8 2.2
1.7 1.9
1.2 1.7
1.1 2.1
1.2 2.2
1.2 2.2
1.5 1.8
∑x 14.7 19.6
The mean is given by ∑x/n
n = 10
SC OC
∴ Mean 1.47 1.96
The median is the
Hence
SC OC
Median 1.55 2
Therefore, the mean and median for the security company are both lower than the mean and the median for the collections performed by other companies.
b) Since the security company appear to have collected lower revenue than other companies, there is some evidence of stealing by the security company's employees.
Answer:
$52
Step-by-step explanation:
Using the equation
y=mx+c
82=7x+c
122=11x+c
11x-7x=122-82
4x=40
x=10
To get c
82=7(10)+c
82-70=c
c=12
For 4 lessons
y=10(4)+12=52