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murzikaleks [220]
3 years ago
12

There are six professors teaching the introductory discrete mathematics class at someuniversity. The same final exam is given by

all five professors. The exam score is aninteger between 0 and 100 (inclusive, that is, both 0 and 100 are possible). How manystudents must there be to guarantee that there are two students with the same professorwho earned the same final examination score?
Mathematics
2 answers:
musickatia [10]3 years ago
5 0

Answer:

Step-by-step explanation:

zysi [14]3 years ago
5 0

Answer:

607 students to guarantee that there are two students with the same professorwho earned the same final examination score.

Step-by-step explanation:

This problem is an example of the Pigenhole principle.

The first step is finding the number of boxes and objects:

For each score, we have a box which contains the student who got that score.

If there were only one professor grading, there would need to be 101+1 = 102 students to ensure that that there are two students with the same professorwho earned the same final examination score.

However, for each student, there are a combination of six to five = 6 possible combinations for a score.

So there should be at least 6*101+1 = 607 students to guarantee that there are two students with the same professorwho earned the same final examination score.

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3 0
3 years ago
One less than half a number is 12. What is the number
olga_2 [115]
To find this, turn the word question into an equation.
"One less than" means - 1, which is 1 being subtracted from something.
"half a number" means 1/2x, since 1/2 is half and x is unknown.
"is 12" means = 12, which is something equals 12.
Putting this in order would be 1/2x, then - 1, then = 12.
As an equation, this is 1/2x - 1 = 12.
So the equation is 1/2x - 1 = 12

Now you must find the number by solving this equation.
1/2x - 1 = 12
First, add 1 to both sides.
12 + 1 = 13
1/2x = 13
Now multiply both sides by 2.
This way, x will be isolated since 1/2x • 2 = 1x, and 1x = x.
13 • 2 = 26
x = 26
The number is 26.
6 0
2 years ago
The volume of a sphere can be calculated by V = 4/3 * pi If the volume is 113.04 cm ^ 3 what is the radius?
lisov135 [29]

Answer:

2.99 cm

Step-by-step explanation:

V= \frac{4}{3}(pi)(r^3)=113.04cm^3

113.04/ \frac{4}{3}(pi) = r^3 = 26.99

r=\sqrt[3]{26.99} = 2.99cm

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3 years ago
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Aleks04 [339]

The triangle was only rotated. The size did not change, so the corresponding angles would remain identical.

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Step-by-step explanation:

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