The inverse is y = x/2 - 4
Steps involved are -
- replace f(x) with y: y = 2(x + 4)
- Then switch y and x: x = 2(y + 4)
- Finally make y the subject:
- x = 2(y + 4)
- x/2 = y + 4 (divide by 2)
- x/2 - 4 = y (subtract 4)
- So, the inverse is y = x/2 - 4
<h3>What is the formula for inverse function?</h3>
- In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f.
- The inverse of f exists if and only if f is bijective.
- f-1(y) = y/2 = x, is the inverse of f(x).
To learn more about inverse functions from the given link
brainly.com/question/3831584
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Answer:
a) The value of a= 0.59
b) The probability that there are at-least 3 cars passing through the stop sign
P(x>3) = 0.03
c)
The Expected value of X = 0.62
d)
The variance of X is σ² = 0.9556
e)
The standard deviation of X
σ = 0.9775
Step-by-step explanation:
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Given data
X : 0 1 2 3 4 5
P(x) : a 0.30 0.05 0.03 0.02 0.01
a)
∑
= 1
a + 0.30+ 0.05+ 0.03+ 0.02+0.01 = 1
a + 0.41 = 1
a = 1 - 0.41
<em> a = 0.59</em>
b)
<em> The probability that there are at-least 3 cars passing through the stop sign</em>
<em>P(x >3) = P( x=4) + P( x=5)</em>
= 0.02 +0.01
= 0.03
c)
X : 0 1 2 3 4 5
P(x) : 0.59 0.30 0.05 0.03 0.02 0.01
The Expected value of X
E(X) = ∑ x P(X= x)
= 0 + 1 ×0.30 + 2×0.05 + 3×0.03 + 4×0.02 + 5×0.01
= 0.30 + 0.1 + 0.09 +0.08 +0.05
= 0.62
<em>The Expected value of X </em>
<em> E(X) = 0.62</em>
<em>d) </em>
The variance of the discrete distribution
σ² = ∑ x²p(x) -μ²
σ² = 0 + 1² ×0.30 + 2² ×0.05 + 3² ×0.03 + 4² ×0.02 + 5²× 0.01 - (0.62)²
= 1.34 - 0.3844
= 0.9556
σ² = √0.9556
<em>e) The standard deviation of the discrete distribution</em>
<em> σ = 0.9775</em>
<em></em>
Answer:
Ulthwé was caught in the pull of the Eye of Terror, where the Immaterium intersects with realspace. It is a breeding ground for Chaos and a gateway into the Warp. Due to this baleful proximity to the Eye, Ulthwé must be on constant high alert in case of attacks by the Forces of Chaos. Constant risk and warfare has hardened this Craftworld's citizens to hardship. Due to the lack of Aspect Warriors on the Craftworld, Ulthwé maintains a standing militia known as the Black Guardians, who are more skilled and better-trained than the Guardians of other Craftworlds.Step-by-step explanation:
Well i dont think that 20 hundredths is equal to 2 thousands
Let numbers of books be 'b' and numbers of CDs be 'c'
We can set up two equations:
Equation [1] ⇒

Equation [2] ⇒

We are solving for the number of books and the number of CDs bought
When we have two equations in terms of two different variables;

and

, that we need to solve, then this becomes a simultaneous equation problem.
First, rearrange Equation [1] to make either

or

the subject:


Then we substitute

into Equation [2]






Now we know the value of

which is

, substitute this value into

we have

Answer:
Numbers of books = 13
Numbers of CDs = 7