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Sonja [21]
3 years ago
14

A teacher selects students from her class of 37 students to do 4 different jobs in the classroom: pick up homework, hand out per

mission slips, staple worksheets, and organize the classroom library. Each job is performed by exactly one student in the class and no student can get more than one job. How many ways are there for her to select students and assign them to the jobs?
Mathematics
1 answer:
dolphi86 [110]3 years ago
4 0

Answer:

66045 ways

Step-by-step explanation: There are actually total of 37 student, and total of 4 jobs. But if the jobs are to be done by only one person each, then we are selecting 4 students.

So the number of ways of selecting 4 out of 37 using combination is

=37C4

=37!/(37-4)!(4!)

=37!/33!4!

=66045

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4 years ago
The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial
maks197457 [2]

Answer:

The initial population P0 is 7500

Step-by-step explanation:

First of all, we are told that the population is proportional to time. This means that as time goes by, the population will increase. This type of relationship between two variables has the form of a linear equation expressed as:

y = mx + b,

where m is the slope of the curve and b is the intercept of it.

In this case we can state the following equation:

P = mt + P0

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Once we state the equation, let's see what we know:

If t = 0, then P = P0

If t = 3, then P = 12000 just as we are told

and if t = 5, then P = 2 P0 because after five years the population has doubled compared to the initial population (P0).

From the definition of the slope of the curve:

(Y2 - Y1)/(X2-X1) = m

and using the data described before we can formulate the slope value:

m = (2P0 - P0)/(5-0)

m = (2P0 - P0)/5

m = P0/5

Then, let's replace the value of m in the following equation:

P = mt + P0

12000 = (P0/5) × 3 + P0 → This is the equation presented when 3 years has gone by and we now have a population of 12000.

12000 = (3/5) P0 + P0

12000 = (8/5) P0

12000×5/8 = P0 = 7500

Then we can calculate the value of the slope m:

m = P0/5

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Now, knowing the value of m and the initial population P0 we are able to calculate the population at any value of "t".

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Answer:

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Step-by-step explanation:

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