Use y=mx+b to find EOL.
if two lines are perpendicular it means their slopes are negative reciprocals of one another. So, if the slope of the given line is 2, the slope of the line we are trying to find is -1/2.
To find “b” (the y-intercept) we have to plug in the given point into y=mx+b with the slope we just found;
y = mx+b
-2 = (-1/2)(-1) + b
-2 = 1/2 + b
-2 - 1/2 = b
-5/2 = b
the EOL is y = -1/2x - 5/2
For the first scenario, you’re looking at a compound interest problem. You’re given all the information you need, so just input it into the compound interest equation.
A = P(1 + r/n)^nt
P is your principal, aka starting amount. That’s the 12000 people you start with.
R is your rate of interest, aka how much your principal is expanding by. That’s the 5% growth rate each year, or 0.05.
N is the number of times your principal grows each year. That’s only once here.
T is however long the change lasts. In this scenario, its from 2006 to 2020, so 14 years.
Input all this in and solve for A, which is your total amount.
A = 12,000(1 x 0.05/1)^(1 x 14) = 23,759.18
Since I doubt you can have 1/5 of a person, you round this down to 23,759, which is your answer.
I’d like to help with your second problem, but it’s cut off on the edge of the image, I can’t see all the numbers.
Answer:
It is given that the volume of a cone = 
cubic units
Volume of cone with radius 'r' and height 'h' = 
Equating the given volumes, we get
× 
It is given that the height is 'x' units.
Therefore, 
Therefore, 
So, the expression '
' represents the radius of the cone's base in units.
Answer:
To calculate the relative frequency, first we need to know what exactly is and how to calculate it.
Relative frequency is the ratio between the absolute frequency (how many repetitions have a specific outcome) and the total outcomes. Also, this type of frequency is used to show the representation that some data have over the whole distribution.
So, in this case, we need to just divide 13, which belongs to red marble's results, to 60 which is the total outcomes, as it's presented:
13redmarble Fr = -------------------------
60 totalmarbles
Normally, relative frequency is shown as a percentage multiplying this result by 100. Therefore, 22% is the approximate percentage of the relative frequency, which means that 22% is the representation of red marbles outcomes of the whole distribution, or we can say it as a probability: there's 22% of chances when someone extract a marble, it will be red.
