Which of the following is the quotient of the rational expressions shown below? 5x/2x+3 / x+1/3x

Final answer:

Miguel paid 70% of the original price for the bicycle. The original price was calculated as approximately $175 by dividing the price Miguel paid ($122.50) by 70% (the remaining percentage after the 30% discount).

Explanation:

Miguel paid $122.50 for a bicycle which was discounted by 30%. So, the $122.50 represents the 70% of the original price (because 100% - 30% = 70%). To find out what 100% (the original price) is, we need to perform a calculation where we divide the price paid by Miguel ($122.50) by 70% (in decimal format, that's 0.70).

The formula would structure as below:

Original Price = Price Paid / Percentage of Original Price Paid

Substituting in the values provided, the equation would be:

Original Price = $122.50 / 0.70

Following through with this calculation, we find that the original price of the bicycle was approximately $175. Therefore, Miguel paid 70% of the original price, as that's the remaining percentage after the 30% discount.

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Answer:

i-2.4j

Step-by-step explanation:

Given that,

The surface of a mountain is modeled by the equation as follows :

A mountain climber is at the point (500, 300, 4390).

We need to find the direction in which he should move in order to ascend at the greatest rate.

To find direction, first finding the gradient of h as follows :

Now put x = 500 and y = 300

So,

The direction of the climber is i-2.4j

Answer:

about 83%

Step-by-step explanation:

Put the given value in the formula and do the arithmetic.

... P(66) = 90/(1 +271·e^(-0.122·66))

... = 90/(1 +271·e^-8.052)

... = 90/(1 +271·0.00031846)

... = 90/(1 +0.0863)

... = 90/1.0863

... = 82.8 . . . . percentage with some coronary heart disease

Answer:

I think the answer is D but I'm not 100 percent sure. I hope this helps

Step-by-step explanation:

I think I took this test before

Answer:

a. The probability that the next auto will arrive within 6 seconds (0.1 minute) is 99.33%.

b. The probability that the next auto will arrive within 3 seconds (0.05 minute) is 91.79%.

c. What are the answers to (a) and (b) if the rate of arrival of autos is 60 per minute?

For c(a.), the probability that the next auto will arrive within 6 seconds (0.1 minute) is now 99.75%.

For c(b.), the probability that the next auto will arrive within 3 seconds (0.05 minute) is now 99.75%.

d. What are the answers to (a) and (b) if the rate of arrival of autos is 30 per minute?

For d(a.), the probability that the next auto will arrive within 6 seconds (0.1 minute) is now 95.02%.

For d(b.), the probability that the next auto will arrive within 3 seconds (0.05 minute) is now 77.67%.

Step-by-step explanation:

a. What is the probability that the next auto will arrive within 6 seconds (0.1 minute)?

Assume that x represents the exponential distribution with parameter v = 50,

Given this, we can therefore estimate the probability that the next auto will arrive within 6 seconds (0.1 minute) as follows:

P(x < x) = 1 – e^-(vx)

Where;

v = parameter = rate of autos that arrive per minute = 50

x = Number of minutes of arrival = 0.1 minutes

Therefore, we specifically define the probability and solve as follows:

P(x ≤ 0.1) = 1 – e^-(50 * 0.10)

P(x ≤ 0.1) = 1 – e^-5

P(x ≤ 0.1) = 1 – 0.00673794699908547

P(x ≤ 0.1) = 0.9933, or 99.33%

Therefore, the probability that the next auto will arrive within 6 seconds (0.1 minute) is 99.33%.

b. What is the probability that the next auto will arrive within 3 seconds (0.05 minute)?

Following the same process in part a, x is now equal to 0.05 and the specific probability to solve is as follows:

P(x ≤ 0.05) = 1 – e^-(50 * 0.05)

P(x ≤ 0.05) = 1 – e^-2.50

P(x ≤ 0.05) = 1 – 0.0820849986238988

P(x ≤ 0.05) = 0.9179, or 91.79%

Therefore, the probability that the next auto will arrive within 3 seconds (0.05 minute) is 91.79%.

c. What are the answers to (a) and (b) if the rate of arrival of autos is 60 per minute?

For c(a.) Now we have:

v = parameter = rate of autos that arrive per minute = 60

x = Number of minutes of arrival = 0.1 minutes

Therefore, we specifically define the probability and solve as follows:

P(x ≤ 0.1) = 1 – e^-(60 * 0.10)

P(x ≤ 0.1) = 1 – e^-6

P(x ≤ 0.1) = 1 – 0.00247875217666636

P(x ≤ 0.1) = 0.9975, or 99.75%

Therefore, the probability that the next auto will arrive within 6 seconds (0.1 minute) is now 99.75%.

For c(b.) Now we have:

v = parameter = rate of autos that arrive per minute = 60

x = Number of minutes of arrival = 0.05 minutes

Therefore, we specifically define the probability and solve as follows:

P(x ≤ 0.05) = 1 – e^-(60 * 0.05)

P(x ≤ 0.05) = 1 – e^-3

P(x ≤ 0.05) = 1 – 0.0497870683678639

P(x ≤ 0.05) = 0.950212931632136, or 95.02%

Therefore, the probability that the next auto will arrive within 3 seconds (0.05 minute) is now 99.75%.

d. What are the answers to (a) and (b) if the rate of arrival of autos is 30 per minute?

For d(a.) Now we have:

v = parameter = rate of autos that arrive per minute = 30

x = Number of minutes of arrival = 0.1 minutes

Therefore, we specifically define the probability and solve as follows:

P(x ≤ 0.1) = 1 – e^-(30 * 0.10)

P(x ≤ 0.1) = 1 – e^-3

P(x ≤ 0.1) = 1 – 0.0497870683678639

P(x ≤ 0.1) = 0.950212931632136, or 95.02%

Therefore, the probability that the next auto will arrive within 6 seconds (0.1 minute) is now 95.02%.

For d(b.) Now we have:

v = parameter = rate of autos that arrive per minute = 30

x = Number of minutes of arrival = 0.05 minutes

Therefore, we specifically define the probability and solve as follows:

P(x ≤ 0.05) = 1 – e^-(30 * 0.05)

P(x ≤ 0.05) = 1 – e^-1.50

P(x ≤ 0.05) = 1 – 0.22313016014843

P(x ≤ 0.05) = 0.7767, or 77.67%

Therefore, the probability that the next auto will arrive within 3 seconds (0.05 minute) is now 77.67%.

Final answer:

The probabilities of an auto arriving within a given time frame can be determined using the exponential distribution formula. When the rate of arrival is 50 per minute, the probability of an auto arriving within 6 seconds is approximately 0.9933 and within 3 seconds is approximately 0.9820. These probabilities increase with a higher rate of arrival and decrease with a lower rate of arrival.

Explanation:

To determine the probabilities of an auto arriving within a given time frame, we can use the exponential distribution formula. The exponential distribution is used to model the time until the next event occurs in a Poisson process, which is applicable in this scenario. The formula for the exponential distribution is: P(X <= t) = 1 - e-λt, where λ is the rate of arrival.

1. For a rate of arrival of 50 per minute, we can calculate the probability that the next auto will arrive within 6 seconds (0.1 minute) as: P(X <= 0.1) = 1 - e-50*0.1 = 1 - e-5 ≈ 0.9933.
2. Similarly, for the next auto to arrive within 3 seconds (0.05 minute), we can use the formula: P(X <= 0.05) = 1 - e-50*0.05 = 1 - e-2.5 ≈ 0.9820.
3. When the rate of arrival is 60 per minute, the probabilities will be slightly higher. The probability of the next auto arriving within 6 seconds would be approximately 0.9955, and within 3 seconds would be approximately 0.9838.
4. When the rate of arrival is 30 per minute, the probabilities will be slightly lower. The probability of the next auto arriving within 6 seconds would be approximately 0.9866, and within 3 seconds would be approximately 0.9641.

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