Hey there! :)
Answer:
a) 32 sticks.
b) 5n + 2 sticks.
Step-by-step explanation:
Solve this by finding the pattern.
Pattern # 1 = 7 sticks.
Pattern #2 = 12 sticks
Pattern #3 = 17 sticks.
We can see an increase of 5 sticks within each. We can use this to write an equation:
f(n) = 7 + 5(n-1)
***Where n is the term number
You can simplify the equation to become:
f(n) = 7 + 5n - 5
f(n) = 5n + 2.
Use this equation to solve for pattern # 6:
f(6) = 7 + 5(n-1)
f(6) = 7 + 5(5)
f(6) = 7 + 25
f(6) = 32.
If the mean is 20.8, one standard deviation each way is adding and subtracting 3.1, so 17.7 and 23.9 (68% of values)
Two standard deviations adding and subtracting 3.1*2 = 6.2, or 14.6 and 27.
Three standard deviations is 11.5 and 30.1
So we have
11.5 - 14.6 - 17.7 - 20.8 - 23.9 - 27 - 30.1
Going left to 11.5 is 3 standard deviations out, so 99.7/2 = 49.85%
Going right to 27 is 2 standard deviations out, so 95/2 = 47.5%
Add those two % to get 97.32%
This is hard to do without a picture so I hope that helps!
A linear function is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. For example, a common equation,
y
=
m
x
+
b
, (namely the slope-intercept form, which we will learn more about later) is a linear function because it meets both criteria with
x
and
y
as variables and
m
and
b
as constants. It is linear: the exponent of the
x
term is a one (first power), and it follows the definition of a function: for each input (
x
) there is exactly one output (
y
). Also, its graph is a straight line.
Start by finding the area of each smaller right triangle.
Right triangle area = (1/2)hb -> h = height & b = base
b = 4 & h = 3
(1/2)(4)(3) = 6
6*2 = 12 (there are two right triangles)
The area of the entire triangle is 12yd^2
With the number being x, we have 3x^2>6(x/9). Expanding, we get 3x^2>6x/9 and 3x^2>2x/3. Dividing by x, we get 3x>2/3 and dividing by 3 we get x>2/9
