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3 years ago

Suppose that $g(x)=f^{-1}(x)$. If $g(-15)=0$, $g(0)=3$, $g(3)=9$ and $g(9)=20$, what is $f(f(9))$?

Mathematics

1 answer:

never [62]3 years ago

8 0

Answer:

Step-by-step explanation:

$\text{If } g(x)=f^{-1}(x);$ and:$\\g(-15)=0,$ g(0)=3, g(3)=9, g(9)=20$

We are to determine the value of $f(f(9)).$

Now:

$g(0)=f^{-1}(0)=3\\g(3)=f^{-1}(3)=9$

From:

$g(3)=f^{-1}(3)=9\\f(9)=3$

From:

$g(0)=f^{-1}(0)=3\\f(3)=0$

Therefore:

$f(f(9))=f(3)=0$

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Naily [24]

Answer: 136 square feet

=======================================================

Explanation:

The front face is a triangle with base 6 and height 4.

The area is 0.5*base*height = 0.5*6*4 = 12 square feet

The back face is also 12 square feet since the front and back faces are identical triangles.

So far we have 12+12 = 24 square feet of surface area.

--------------------

The bottom face, that runs along the floor or ground, is a rectangle that is 6 ft by 7 ft. So we have 6*7 = 42 square feet of surface area here. This adds onto the 24 we found earlier to get 24+42 = 66 square feet so far.

To find the left and right upper faces, we'll need to find the length of the hypotenuse first. The 6 ft cuts in half to 3 ft. The right triangle on the left has side lengths of 4 ft and 3 ft as the two legs. Use the pythagorean theorem to find the hypotenuse is 5 ft. We have a 3-4-5 right triangle.

This means the upper left face is 5 ft by 7 ft leading to an area of 5*7 = 35 square feet. The same can be said about the upper right face.

So we add on 35+35 = 70 more square feet to the 66 we found earlier to get a grand total of 70+66 = 136 square feet of surface area.

4 0

3 years ago

An arcade booth at a county fair has a person pick a coin from two possible coins available and then toss it. If the coin chosen

nydimaria [60]

Answer:

Step-by-step explanation:

<u>Conditional Probability</u>

Suppose two events A and B are not independent, i.e. they can occur simultaneously. It means there is a space where the intersection of A and B is not empty:

$P(A\cap B) \neq 0$

If we already know event B has occurred, we can compute the probability that event A has also occurred with the conditional probability formula

$\displaystyle P(A|B)=\frac{P(A\cap B)}{P(B)}$

Now analyze the situation presented in the question. Let's call F to the fair coin with 50%-50% probability to get heads-tails, and U to the unfair coin with 32%-68% to get heads-tails respectively.

Since the probability to pick either coin is one half each, we have

$P(U)=P(F)=50\%=0.5$

If we had picked the fair coin, the probability of getting heads is 0.5 also, so

$P(F\cap H)=0.5\cdot 0.5=0.25$

If we had picked the unfair coin, the probability of getting heads is 0.32, so

$P(U\cap H)=0.32\cdot 0.5=0.16$

Being A the event of choosing the fair coin, and B the event of getting heads, then

$P(B)=P(F\cap H)+P(U\cap H)=0.25+0.16=0.41$

$P(A\cap B)=P(F\cap H)=0.25$

$\displaystyle P(A|B)=\frac{0.25}{0.41}=0.61$

The closest answer is

b. 0.6024

7 0

3 years ago

Karina is driving from her house to her cottage. If she drives at 10 kilometers per hour, she will arrive at 6 PM. If she drives

aev [14]

Answer:

12.5 kilometers per hour

Step-by-step explanation:

$(10+15)/2=25/2=12.5$

5 0

3 years ago

(HELP FINAL EXAM) If two states are selected at random from a group of 40 states, determine the number of possible outcomes if

Hitman42 [59]

Answer:

With replacement, there are 1600 possible outcomes.

Without replacement, there are 1560 possible outcomes.

Step-by-step explanation:

Chosen with replacement:

State is chosen, then put back in the group, then another state can be chosen. In both cases, there will be 40 possible outcomes, as the first taken state is placed back. So

40*40 = 1600

With replacement, there are 1600 possible outcomes.

Chosen without replacement:

State and chosen and is not replaced.

So, for the second state, there will be only 39 possible outcomes.

40*39 = 1560

Without replacement, there are 1560 possible outcomes.

7 0

3 years ago

What is the greatest common factor (GCF) of 48 and 32?

Nat2105 [25]

Answer:

The greatest common factor of 48 and 32 is 16

6 0

3 years ago

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