Mr. Itol's assistant takes twice as long to complete a computer task as Mr. Itol. If it takes both experts 6 hours to complete t
1 answer:
To tackle this problem, I will formulate an equation. Let's designate x as the number of hours Mr. Itol requires to finish a computer task, while since his assistant needs twice as long, we'll set 2x as the hours the assistant needs. We also know that together they complete the task in 6 hours, allowing us to establish the following equation:
Now, to solve this, we need to identify the least common denominator, allowing us to eliminate the denominators. The LCD is 6x, which modifies our equation to:
Next, we can eliminate the denominators, resulting in:
Thus, x = 9.
This tells us that Mr. Itol would take 9 hours to work on the task alone. To calculate the duration needed for his assistant to complete it independently, we substitute the x-value into 2x:
Consequently, the final determination is that Mr. Itol would need 9 hours to finish the task alone, while his assistant would require 18 hours (twice as long) to do so independently.
Hopefully, this is clear!:)
Now, to solve this, we need to identify the least common denominator, allowing us to eliminate the denominators. The LCD is 6x, which modifies our equation to:
Next, we can eliminate the denominators, resulting in:
Thus, x = 9.
This tells us that Mr. Itol would take 9 hours to work on the task alone. To calculate the duration needed for his assistant to complete it independently, we substitute the x-value into 2x:
Consequently, the final determination is that Mr. Itol would need 9 hours to finish the task alone, while his assistant would require 18 hours (twice as long) to do so independently.
Hopefully, this is clear!:)
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Answer:
0.75 = 75% chance that only one tag is lost, provided at least one tag is lost
Step-by-step explanation:
Independent events:
If A and B are independent events, then:
Conditional probability:
Here
P(B|A) refers to the probability of event B occurring, given that event A has occurred.
is the probability of both A and B occurring together.
P(A) is the probability of event A occurring.
In this scenario:
Event A: At least one tag is missing
Event B: Only one tag is missing.
Each tag has a 40% likelihood of being lost, which is equal to 0.4.
Probability of at least one tag missing:
The events can be considered as either no tags are missing or at least one is. Their probabilities sum to 1. Thus
p is the probability that none are lost. Each tag has a 60% = 0.6 chance of not being lost, and since they are independent,
p = 0.6*0.6 = 0.36
Then
Intersection:
The intersection of at least one lost (A) and exactly one lost (B) is precisely one lost.
Then
Probability of at least one lost:
The first being lost (0.4 chance) and the second not lost (0.6 chance)
Or
The first not being lost (0.6 chance) and the second lost (0.4 chance)
So
Calculate the probability that exactly one tag is lost, given that at least one tag is lost (round to two decimal places).
0.75 = 75% likelihood that precisely one tag is lost, assuming at least one tag is lost
Answer:
50 Educators
Step-by-step explanation:
To tackle this question, the initial step is to calculate the amount of teachers prior to the addition of new staff. For this, I devised Model 1. In this model, teachers are positioned at the top of the ratio and students at the bottom. The variable X represents the number of teachers we are determining. Utilizing this model, I computed 2,100 multiplied by 1 (2,100) and then divided by 14 to conclude there were 150 teachers. Next, I formed a similar model with the updated student-teacher ratio (Model 2). This time, I multiplied 2,100 by 2 (which is 4,200) and divided by 21 to ascertain there are 200 teachers. Having established both the initial and the increased counts of educators, subtracting the original from the new gives you the tally of new teachers, which results in an increase of 50 teachers.
