Answer: It is equivalent to a reflection over the y-axis.
Step-by-step explanation:
We start with the function:
f(x) = m*x + b
where the slope is m.
If we only multiply the slope by -1, the function becomes:
f(x) = -m*x + b
There is a transformation called a reflection over the y-axis.
This works as follows, if we have a function f(x), a reflection over the y-axis is written as:
g(x) = f(-x)
If we apply this to our function, we get:
g(x) = f(-x) = m*(-x) + b
g(x) = -m*x + b
Then we can conclude that:
"When the slope m is multiplied by -1 in f(x)=mx+b, it is equivalent to a reflection over the y-axis"
Answer:
E(X) = 1.5
Var(X) = 2.325
Step-by-step explanation:
X - the number of pairs of cats (out of the 5 cats) to choose the same type of treat, can take values of:
X = (0, 1, 2, 3, 4, 5)
Also probability of choosing a treat, since they are all equally likely is: f(x) = 1/10
E(X) - expectation of x, is given by:
E(X) = Summation [X*f(x)]
E(X) = 0x(1/10) + 1x(1/10) + 2x(1/10) + 3x(1/10) + 4x(1/10) + 5x(1/10)
= (1/10) x (1+2+3+4+5)
E(X) = 3/2 = 1.5
Also, variance is:
Var(X) = Summation f(x)*[X - E(X)]^2
= (1/10)x(0-1.5)^2 + (1/10)x(1-1.5)^2 +(1/10)x(2-1.5)^2 +(1/10)x(3-1.5)^2 +(1/10)x(4-1.5)^2 +(1/10)x(5-1.5)^2
= (1/10)x[2.25 + 0.25 + 2.25 + 6.25 + 12.25]
Var(X) = 2.325
Answer:
(-0.75, 3.5)
Step-by-step explanation:
See below for graph, please!
Hope this helped!
Answer:
Break-even price is the amount of money, or change in value, for which an asset must be sold to cover the costs of acquiring and owning it. It can also refer to the amount of money for which a product or service must be sold to cover the costs of manufacturing or providing it.
Step-by-step explanation:
Answer:
1065 cubic mm
Step-by-step explanation:
split the shape into two cuboids
V = L x W x H
17 - 10 = 7
19 X 5 X 7 = 665
19 - 11 = 8
8 X 5 X 10 = 400
add together
655 + 400 = 1065 cubic mm