F(x) is continuous for all x.
Pick a point and show that f(x) is either negative or positive. Pick another point and show that f(x) is negative, if positive, or positive, if negative.
At x = 30, f(30) - 1000 = 900 + 10sin(30) - 1000 ≤ 0
Now, show at another point f(x) - 1000 is positive, and hence, there would be root between 30 and such point.
Let's pick 40.
At x = 40, f(40) - 1000 = 1600 + 10sin(40) - 1000 ≥ 0
Since f(x) - 1000 is continuous, there lies a root between 30 and 40, and hence, 30 ≤ c ≤ 40
From the problem, the vertex = (0, 0) and the focus = (0, 3)
From the attached graphic, the equation can be expressed as:
(x -h)^2 = 4p (y -k)
where (h, k) are the (x, y) values of the vertex (0, 0)
The "p" value is the difference between the "y" value of the focus and the "y" value of the vertex.
p = 3 -0
p = 3
So, we form the equation
(x -0)^2 = 4 * 3 (y -0)
x^2 = 12y
To put this in proper quadratic equation form, we divide both sides by 12
y = x^2 / 12
Source:
http://www.1728.org/quadr4.htm
<span>The Federal Insurance Contributions Act (FICA) requires employers to withhold a certain percentage of an employee's income as tax. The categories are:
6.2% as social security tax
1.45% as Medicare tax
0.9% as Medicare surtax for employees earning more than $200,000
In this case, the percentage of tax applied will be 6.2 + 1.45 = 7.65%
The FICA tax will be 110,330 * 0.0765
FICA tax = $8,440.24</span>
Answer:
Lewie Survey produces less valid result.
Step-by-step explanation:
Given:
1. Kelvin surveys every other person leaving the food area.
2. Lewie surveys every fifth person leaving the mall's main entrance.
Therefore,
Kelvin will able to produce valid result as he is surveying every person who is leaving food court.
Means,
There are high chances that would have bought food from the court.
Whereas,
Lewie is surveying every fifth person leaving the the mall's entrance.
Therefore,
Here probability to produce valid result is less as they may have not buy food or they may visited other shops.
So, Lewie survey will produce less valid result.