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Gnom [1K]
3 years ago
5

What is the inverse of the function? f(x)=3^x−1

Mathematics
1 answer:
geniusboy [140]3 years ago
7 0

y = f(x) = 3^{x} - 1

let x be y and y be the x, so we have

x = 3^{y} - 1

3^{y} = x + 1

log_{3}(3)^{y} = log_3(x + 1)

y = log_{3}(x+1)



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There are 6 red marbles 4 blue marbles to yellow marbles. Sabrina picks 2 marbles without putting the first one back what is the
Yanka [14]

Answer:

P = 3/11

Step-by-step explanation:

There are:

6 red marbles

4 blue marbles

2 yellow marbles.

So there are a total of 12 marbles in the bag, such that each one has the same probability of being randomly picked.

We want to find the probability that the first pick is not yellow (so it can be either blue or red), and the second pick is a blue marble.

Now there are two cases.

The first marble is red and the second blue

the first marble is blue and the second blue

We need to find the probability in each case.

The probability that the first marble is red is equal to the quotient between the number of red marbles (6) and the total number of marbles (12)

p = 6/12

Now, for the second draw, we need a blue marble, the probability in this case is the quotient between the number of blue marbles (4) and the total number of marbles in the bag (now there are 11, because one is already taken)

q = 4/11

The joint probability is equal to the product of the individual probabilities, then:

P₁ = p*q = (6/12)*(4/11) = 2/11

And for the other case, we draw two blue marbles:

For the first draw, the probability is:

p = 4/12

And for the second draw, now there are 3 blue marbles and 11 total marbles, then the probability is:

q = 3/11

The joint probability is:

P₂ = (4/12)*(3/11) = 1/11

The total probability is then:

P = P₁ + P₂ = 2/11 + 1/11 = 3/11

4 0
3 years ago
A countertop is in the shape of a trapezoid.
RideAnS [48]
Uhhhhh yes.?

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4 0
2 years ago
How much difference do a couple of weeks make for birth weight? Late-preterm babies are born with 34 to 36 completed weeks of ge
stiks02 [169]

Answer:

a) 0.3277

b) 0.0128

Step-by-step explanation:

We are given the following information in the question:

N(2750, 560).

Mean, μ = 2750

Standard Deviation, σ = 560

We are given that the distribution of distribution of birth weights is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P (less than 2500 grams)

P(x < 2500)

P( x < 2500) = P( z < \displaystyle\frac{2500 - 2750}{560}) = P(z < -0.4464)

Calculation the value from standard normal z table, we have,  

P(x < 2500) = P(z < -0.4464) = 0.3277 = 32.77\%

b) P ((less than 1500 grams)

P(x < 1500)

P( x < 1500) = P( z < \displaystyle\frac{1500 - 2750}{560}) = P(z < -2.2321)

Calculation the value from standard normal z table, we have,  

P(x < 1500) = P(z < -2.2321) = 0.0128 = 1.28\%

3 0
3 years ago
Olivia’s age plus twice John’s age is 30. Three times Olivia’s age plus 8 times John’s age is 108. How old are Olivia and John?
andrezito [222]

Answer:

John is 9 and Olivia is 12

Step-by-step explanation:

12+18= 20

36+ (9x8)= 108

4 0
2 years ago
Helene wrote a report. It took her 4 hours to write 24 pages.
sammy [17]

Answer:

C

Step-by-step explanation:

24÷6= 6 Hope this helps.

4 0
3 years ago
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