Which statements represent the relationship between y=2x and y=log2x ? Select each correct answer. The functions are inverses of each other. The graphs of the functions are symmetric about the line y = 0. The graphs of the functions are symmetric to each other over the line y = x. The equation y=log2x is the logarithmic form of y=2x .

The given function are inverse of each other.

The graphs of the functions are symmetric to each other over the line y = x.

Given function are,   and  

Therefore, both given function are inverse of each other.

The graphs of the functions are symmetric to each other over the line y = x.

Here, graph is attached below.

From attached graph, it is observed that ,the graphs of the functions are not symmetric about the line y = 0.

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The correct options are;

1) The functions are inverse of each other and

3) The graphs of the functions are symmetric to each other over the line y = x

Step-by-step explanation:

Here we have

y = 2ˣ and y = log₂x

We are to analyze each of the options as follows;

1) The functions are inverse of each other

The above statement is correct as the inverse of y = 2ˣ is x = therefore  y = log₂x is inverse of y = 2ˣ

2) The graphs of the functions are symmetric about the line y = 0

The above statement is not correct as the line y = 0 is the x axis whereby  y = 1 and y = -1 give x = 5 and x = 0.5 respectively

3) The graphs of the functions are symmetric to each other over the line y = x

The line y = x is a straight line with slope = 1  whereby since x >  log₂x, and y > log₂y  then the two lines are symmetric

4) The equation y=log₂x is the logarithmic form of y=2ˣ .

The above statement is not correct as log2ˣ = x log2 ≠  log₂x.

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation:

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40