Step-by-step explanation:
(-5)² + (-2)² + 3²
= 25 + 4 + 9
= 38
Answer:
4
Step-by-step explanation:
First we need to find the total area of the garden so we can see how many bags she will need. The area of a rectangle is its length multiplied by its width, so the area of her garden is 12 (the length) x 10 (the width). 12 x 10 = 120 square feet. If each bag covers 30 square feet, then she will need 120/30 = 4.
4 bags of fertilizer to cover the 120 square feet of the garden area.
Hope this helped!
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%.
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.
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.
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Answer:
the slope is 4 and the y intercept is (0,-3)
Step-by-step explanation:
When working with this its best to remember y=mx+b, the slope will always be in front of the X. so for example 7x+y=5 ( not a real problem ) but the slope would be 7 because its in front of the X.
Answer: 0.25
Step-by-step explanation:
The relative frequency of the customers that buy computers is equal to the number of customers that bought a computer divided the total number of customers that entered the shop.
p = 25/100 = 0.25
If we take this as the probability, then the probability that the next customer that enters the shop buys a computer is 0.25 or 25%
The probability that the next customer will purchase a computer, computed using the relative frequency method, is 0.25 or 25%.
The subject at hand relates to the basic concept of probability, specifically the method of computing probability using the relative frequency approach. This is a common topic within high school Mathematics, specifically within statistical studies.
To calculate the relative frequency probability of an event, one divides the number of times the event occurred by the total number of trials. In this case, the event is a customer purchasing a computer from the shop. Given that the event has occurred 25 times out of the last 100 trials (customers entering the shop), the relative frequency probability can be computed as follows:
Probability = (Number of times event occurred) / (Total number of trials) = 25 / 100 = 0.25 (or 25% when expressed as a percentage).
Therefore, using the relative frequency method of computing probability, the probability that the next customer will purchase a computer is 0.25 or 25%.
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Answer:
The imaginary part is: z = 19
Step-by-step explanation:
For real numbers a and b, a number written in form a+bi is called a acomplex number. The value a is called the real part and b is called the imaginary part of complex number.
Answer: Segment FE
Step-by-step explanation:
never intesects with segment BC