Answer:
56
Step-by-step explanation:
Given data:
{1 ,2 ,4, 6, 8, 9}
Formula for combinations is used since the order does not matter and repetition is allowed.
nCr = (n + r -1) /(r! * (n-1)!) where n is the total number of items and r is the items to be picked
6C3 = (6 + 3 - 1)! /(3! * (6 -1)!
6C3 = 8!/(3! *5!) Simplifying the factorials)
6C3 = 40320/(6*120)
6C3 = 40320/720
6C3 = 56
Answer:
7. f(x) = 4x+1
8. g(x) = 3^x
9. g(x)
Step-by-step explanation:
<h3>7.</h3>
The graph of f(x) is a straight line that crosses the y-axis at y=1, and passes through another grid intersection at (1, 5). This grid intersection is 1 unit right and 4 units up from the y-intercept. This means the slope of the line is ...
slope = rise/run = 4/1 = 4
In slope-intercept form, the function f(x) is ...
f(x) = mx +b . . . . . . where the slope is m and the y-intercept is b
f(x) = 4x +1
__
<h3>8.</h3>
The horizontal asymptote and the rapid rate of rise of g(x) tells us this is an exponential function. The generic exponential function is of the form ...
g(x) = a·b^x
The value of 'a' is the y-intercept, which is the same as for f(x). That is, a=1. The value when x=1 is ...
g(1) = a·b^1 = ab
We observe from the graph that g(1) is 3, so ...
g(1) = 3 = ab = 1b ⇒ b = 3
Using the values of 'a' and 'b', we have ...
g(x) = 3^x
__
<h3>9.</h3>
We observe that g(x) is already greater than f(x) for x > 2, so g(x) will be greater in the long run.
(In the long run, an exponential function will exceed <em>any</em> polynomial function.)
Answer:
1 and 3
Step-by-step explanation:
Answer:
Length = x^2 = 0.835^2 = 0.698 m = 69.8cm
Breadth = x = 0.835 m = 83.5cm
Step-by-step explanation:
Given;
Length of the rectangular plot l = x^2 m
Breadth b = x m
Area A = 5832 cm^2 = 0.5832 m^2
(They should be converted to the same units before solving: length in metres and area in square metres)
The area of a rectangular plot can be calculated using the formula;
Area = length × breadth
A = l × b
Substituting the values of l and b;
A = x^2 × x
A = x^3
Substituting the value of A;
0.5832 = x^3
solving for x;
x = (0.5832)^(1/3)
x = 0.835 m
Length = x^2 = 0.835^2 = 0.698 m = 69.8cm
Breadth = x = 0.835 m = 83.5cm
Try shutting of things that could distract you. (Television, phone, computer etc.)
Get away from noise; go somewhere quiet.
