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3 years ago

If f(x) = 5x, what is f^-1(x)? F(x) = -5x of(x)- F(x) = 5* O F(x) = 5x

Mathematics

1 answer:

Oksana_A [137]3 years ago

3 0

Answer:

f^-1 (x) = x/5

Step-by-step explanation:

f(x) = 5x

Replace f(x) with y

y= 5x

Exchange x and y

x = 5y

Solve for y

Divide each side by 5

x/5 = 5y/5

x/5 = y

The inverse is x/5

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Indicate the general rule for the arithmetic sequence with a3 = -12 and a8 = -37

Mandarinka [93]

Answer:

The general rule is $a_n = -2 - 5(n-1)$

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.

The general rule of an arithmetic sequence is given by:

$a_{n} = a_1 + (n-1)d$

In which $a_1$ is the first term and d is the common difference.

We can also find the nth term as a function of a term m, using:

$a_n = a_m + (n-m)d$

a3 = -12 and a8 = -37

First we find the common difference. So

$a_n = a_m + (n-m)d$

$a_8 = a_3 + (8-3)d$

$-37 = -12 + 5d$

$5d = -25$

$d = -\frac{25}{5}$

$d = -5$

$a_n = a_1 - 5(n-1)$

Finding the first term:

$a_n = a_1 - 5(n-1)$

Since $a_3 = -12$

$a_n = a_1 - 5(n-1)$

$a_3 = a_1 - 5(3-1)$

$a_1 = a_3 + 10 = -12 + 10 = -2$

So the general rule is:

$a_n = a_1 - 5(n-1)$

$a_n = -2 - 5(n-1)$

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3 years ago

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Answer:

Step-by-step explanation:

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There is a 70% chance that your car will get stuck in the snow during the next big snow fall. Given that you are already stuck i

nikdorinn [45]

Answer:

63%

Step-by-step explanation:

This is a problem of conditional probability.

The two events that are given are:

Car stuck in the snow - Let it be event S. P(S) = 70% = 0.70
Require a tow truck - Let it be event T.

We have to find the probability of being stuck in the snow AND requiring a tow truck which can be given as P(S and T)

We are also given the conditional probability, which is P(T | S) = 90% = 0.90

Using the given formula for our case we can modify the formula as:

$P(T|S)=\frac{P(S \cap T)}{P(S)}$

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Therefore, there is 63% (0.63) chance that you will get stuck in the snow with your car AND require a tow truck to pull you out

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MaRussiya [10]

Answer:

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