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4 years ago

Use the equation e^x+e^-x/e^x-e^-x=t tosolve for x

Mathematics

2 answers:

EleoNora [17]4 years ago

7 0

Answer:

Step-by-step explanation:

I assume that the equation is

$e^x+\frac{e^{-x}}{e^x} -e^{-x}=t \\$

$e^x+\frac{1}{e^{2x}}-\frac{1}{e^x} = t$

$e^{3x}+1-e^x=e^{2x}t$

$e^{3x}-te^{2x}-e^x=-1$

Let u = e^x

$u^3-tu^2-u=-1$

$u(u^2-tu-1) = -1$

if u=1, then $u^2-tu-1 =-1 \longleftrightarrow u^2-tu=0$

then u = 0 (reject) or u = t

So far, we have u = 1 and u = t

if u =1, e^x =1 , then x = 0

if u = t, then e^x = t or x = lnt

lana66690 [7]4 years ago

4 0

Answer:

Solve the rational equation by combining expressions and isolating the variable

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The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

Two cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a heart and a club in tha

Katyanochek1 [597]

Answer:

4/663

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

Since we are to draw from a pack of card, the total outcome will be 52

Since there are 4 hearts;

Pr(selecting heart) = 4/52 = 1/13

If a club is then selected without replacement, the total number of card remaining will be 51;

Pr(selecting a heart) = 4/51

probability of drawing a heart and a club in that order = 4/52 * 4/51

probability of drawing a heart and a club in that order = 16/2652

probability of drawing a heart and a club in that order = 4/663

8 0

3 years ago

IM GIVING BRAINLIEST

nignag [31]

Answer:

Step-by-step explanation:

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3 years ago

. At a clothing store, 12 people purchased blue sweaters, 8 purchased green sweaters, 4 purchased gray sweaters, and 7 purchased

DedPeter [7]

Answer:

The probability that they purchased a green or a gray sweater is $\frac{12}{31}$

Step-by-step explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

$P(A)=\frac{number of favorable cases}{number of possible cases}$

The addition rule is used when you want to know the probability that 2 or more events will occur. The addition rule or addition rule states that if we have an event A and an event B, the probability of event A or event B occurring is calculated as follows:

P(A∪B)= P(A) + P(B) - P(A∩B)

Where:

P (A): probability of event A occurring.

P (B): probability that event B occurs.

P (A⋃B): probability that event A or event B occurs.

P (A⋂B): probability of event A and event B occurring at the same time.

Mutually exclusive events are things that cannot happen at the same time. Then P (A⋂B) = 0. So, P(A∪B)= P(A) + P(B)

In this case, being:

P(A)= the probability that they purchased a green sweater
P(B)= the probability that they purchased a gray sweater
Mutually exclusive events

You know:

8 purchased green sweaters
4 purchased gray sweaters
number of possible cases= 12 + 8 + 4+ 7= 21

So:

$P(A)=\frac{8}{31}$

$P(B)=\frac{4}{31}$

P(A⋂B) = 0

Then:

P(A∪B)= P(A) + P(B)

P(A∪B)= $\frac{8}{31}+ \frac{4}{31}$

P(A∪B)= $\frac{12}{31}$

<u><em>The probability that they purchased a green or a gray sweater is </em></u> $\frac{12}{31}$ <u><em></em></u>

5 0

3 years ago

Kelly is three years younger than her sister. The sum of their ages is 34 years. How old is Kelly and how old is her sister?

Kazeer [188]

Answer:

Kelly is 20

Her sister is 14

Step-by-step explanation:

34 ÷ 2 = 17 (average)

17 + 3 = <u>20</u>

17 - 3 = <u>14</u>

4 0

4 years ago