A principal decides to survey the parents at her school to find out their opinion onstandardized testing. She calls randomly-chosen parents between 4:00 and 5:00 P.M.
every day for a week and collects data on their responses. Identify the population
and the sample. Give a reason why the sample could be biased.
Oa)
Population: All parents who respond to the survey
Sample: All parents with students at the school
Possible Bias: The parents who answered the phone may not be
representative of the whole population because younger parents are more
likely to answer the phone than older ones.
b)
Population: All parents with students at the school
Sample: All parents who respond to the survey
Possible Bias: Parents who are at home between 4:00 and 5:00 P.M. may not
be representative of the whole population.
Oc) Population: All parents with students at the school
Sample: All parents who respond to the survey
Possible Bias: Some parents do not like a particular teacher.
d)
Population: All parents who respond to the survey
Sample: All parents with students at the school
Possible Bias: Some of the people contacted did not answer every question

Final answer:

The expression that represents four more than the product of 23 and Greg's height is 23g + 4. Simplifying the expression gives us 5.385g.

Explanation:

The question is asking for an expression that represents four more than the product of 23 and Greg's height. We can represent Greg's height with the variable g. So the expression would be 23g + 4. If we simplify the expression, we get 5.385g.

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Answer:

is

Step-by-step explanation:

Property of inverse function:

The function should be bijective function ( one-to-one and onto)

Option A) f(x)=|x-4|+1

It is absolute function. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [1,∞)

False ( Inverse not possible )

Option B)

It is quadratic function. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [0,∞)

False ( Inverse not possible )

Option C)

It is polynomial function with even degree. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [0,∞)

False ( Inverse not possible )

Option D)

It is linear function. one-to-one and onto

Domain: All real (-∞,∞)

Range: All real (-∞,∞)

True ( Inverse possible )

Inverse of is

Hence, The function inverse function is

Answer: Hello there!

A function only can have an inverse if the function is injective and surjective (and continuous):

Then we need to see; if f(x1) = f(x2) = y, and x1 is different from x2, then f(x) has not an inverse:

a) f(x) = Ix - 4I + 1

for example, f(0) = I-4I + 1 = 5

and f(8) = I8 -4I + 1 = 4 + 1 = 5

then f(x) does not have an inverse

b) f(x) = 25x^2 + 70x + 49

This is a cuadratic function, wich is graphed as a arc going up or down, wich means that there are two values of x that give the same value for f(x), then this function has not inverse. (this will be the case for all even powers)

c) f(x) = x^4

Again, an even power. But let's probe it:

f(1) = 1^4 = 1

f(-1) = (-1)^4 = 1

f(x) does not have an inverse:

d) f(x) = x + 3/7

Ok, here we have a linear equation, wich means that is injective and surjective.

The inverse of this function can be g(x) = x - 3/7

proof:

f(g(x)) = f( x - 3/7) = (x - 3/7) + 3/7 = x

then f and g are inverses of each other.

(if in this case f(x) = (x + 3)/7 = x/7 + 3/7 is also a linear equation, so it is injective and surjective (and continuous), wich implies that has an inverse)