We are to solve the total area of the pyramid and this can be done through area addition. We first determine the area of the base using the Heron's formula.
A = √(s)(s - a)(s - b)(s - c)
where s is the semi-perimeter
s = (a + b + c) / 2
Substituting for the base,
s = (12 + 12 + 12)/ 2 = 18
A = (√(18)(18 - 12)(18 - 12)(18 - 12) = 62.35
Then, we note that the faces are just the same, so one of these will have an area of,
s = (10 + 10 + 12) / 2 = 16
A = √(16)(16 - 12)(16 - 10)(16 - 10) = 48
Multiplying this by 3 (because there are 3 faces with these dimensions, we get 144. Finally, adding the area of the base,
total area = 144 + 62.35 = 206.35
Given:
Uniform distribution of length of classes between 45.0 to 55.0 minutes.
To determine the probability of selecting a class that runs between 51.5 to 51.75 minutes, find the median of the given upper and lower limit first:
45+55/2 = 50
So the highest number of instances is 50-minute class. If the probability of 50 is 0.5, then the probability of length of class between 51.5 to 51.75 minutes is near 0.5, approximately 0.45. <span />
-5x-10=10 x= -4
Work:
-5x-10=10
+10 +10
______________
-5x=20
_______
-5 -5
x=-4
Answer:
y = -1x + 6 or y = -x + 6
Step-by-step explanation:
First, let's identify what slope-intercept form is.
y = mx + b
m is the slope. b is the y-intercept.
We know the slope is -1, so m = -1. Plug this into our standard equation.
y = -1x + b
To find b, we want to plug in a value that we know is on this line: (2, 4). Plug in the x and y values into the x and y of the standard equation.
4 = -1(2) + b
To find b, multiply the slope and the input of x(2)
4 = -2 + b
Now, add 2 from both sides to isolate b.
6 = b
Plug this into your standard equation.
y = -1x + 6
This is your equation.
Check this by plugging in the point again.
y = -1x + 6
4 = -1(2) + 6
4 = -2 + 6
4 = 4
Your equation is correct.
Hope this helps!
