There are six professors teaching the introductory discrete mathematics class at a university. The same final exam is given by all six professors. If the lowest possible score on the final is 0 and the highest possible score is 100, how many students must there be to guarantee that there are two students with the same professor who earned the same final examination score

Answers

Answer 1

Answer:

607 students

Step-by-step explanation:

To solve this question means we have to use Pigenhole principle which states that if y number of items are put into z number of containers, with y > z, then it means that that at least one container must definitely contain more than one item.

Now, let's find the number of boxes and objects:

If possible scores are from 0 to 100 with both inclusive it means number of possible scores = 101.

Now, If there was only one professor grading the students, in order to ensure that that there are two students with the same professor who earned the same final examination score,

The number of students would have to be = 101 + 1 = 102 students

Meanwhile, for each student, since there are 6 professors, the possible combination for a score will be = 6 possible combinations.

Therefore, number of students that will guarantee that there are two students with the same professor who earned the same final examination score must be a minimum of: (6 × 101) + 1 = 607


Related Questions

Find the surface area of the figure. Round to the nearest tenth.
WILL MARK BRAINLIEST!!! PLS HELP THIS IS DUE IN 10 MIN AND PLEASE NO DROP FILES!! :)

Answers

Answer:

14 x 6.9 x 8 = 56

Step-by-step explanation:

The graphs below have the same shape. Complete the equation of the red
graph.

Answers

Answer:

Step-by-step explanation:

F(x) = 2 - x²

Ruslan's figure has a length of 5cm, a width of 3cm, and a height of 4cm. What is the volume of Ruslan's figure?

Answers

Answer:

The colume of Ruslan's figure is 60 cubic centimeters.

Step-by-step explanation:

To find the volume of something, you have to multiply the length by the width, and then multiply that to the height. So you would multiply 5 and 3 to get 15, and then you would multiply 15 and 4 to which then you would get your answer of 60 cubic centimeters.

Answer:

60cm³ is your answer

Step-by-step explanation:

volume of cuboid =l×b×h=5×3×4=60cm³

Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 7 men employed by a medium sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 21.89 hours of personal time per year with a standard deviation of 3.29 hours. The correct 90% confidence interval for the difference between women and men in the average number of hours of personal time taken per year is ________.

Answers

Answer:

The correct 90% confidence interval for the difference between women and men in the average number of hours of personal time taken per year is

contained by the interval (0.54 , 5.18)

Step-by-step explanation:

Given that:

for women

sample size  = n₁ = 16

sample mean [tex](\bar X_1)[/tex] = 24.75

standard deviation s₁ = 2.84

for men

sample size for men = n₂ = 7

sample mean [tex](\bar X_2)[/tex] = 21.89

standard deviation s₂ = 3.29

degree of freedom = [tex](n_1 + n_2 )-2[/tex]

= 16 + 7 -2

= 21

The critical value for [tex]\alpha = 0.1 \ and \ df \ of \ 21 \ is :[/tex]

[tex]t_{0.005;21}= 1.721[/tex]

The pooled standard deviation can be calculated as follows since the population variances are assumed to be equivalent.

[tex]s_p = \sqrt{\dfrac{(n_1 -1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}[/tex]

[tex]s_p = \sqrt{\dfrac{(16 -1)2.84^2+(7-1)3.29^2}{16+7-2}}[/tex]

[tex]s_p = \sqrt{\dfrac{(15)8.0656+(6)10.8241}{21}}[/tex]

[tex]s_p = 2.976[/tex]

The standard error is estimated as follow:

[tex]se = s_p\sqrt{\dfrac{1}{n_1} + \dfrac{1}{n_2}}[/tex]

[tex]se = 2.976\sqrt{\dfrac{1}{16} + \dfrac{1}{7}}[/tex]

se = 1.348

Finally, the confidence interval [tex]C.I = ( x_1 -x_2 -t_c \times se \ \ ; \ \ x_1-x_2 +t_c \times se)[/tex]

[tex]=(24.75 - 21.89 -1.721 \times 1.348 \ \ , \ \ 2475 - 21.89 + 1.721 \times 1.348) \\ \\ \mathbf{ = (0.54 \ \ , \ \ 5.18)}[/tex]

A ship left at the port at 9:00 p.m. and arrived at the next port at 5:00 a.m.
the next day. The distance between the 2 ports was 200 km.
Find the average
speed of the ship.
show solution​

Answers

Answer:

25km/h

Step-by-step explanation:

It would be helpful to understand the 24 hour clock in this case so you don't get confused by the AM and PM. For reference, 5 AM is technically 17AM, since 5 + 12 = 17.

The ship departed at 9pm, subtract that from 17 and you'll get 8 hours.

17 - 9 = 8

We know that there are 8 hours total, and since the ship traveled 200km, we set up a fraction, which is 8hr/200km. Since we want the average speed, we'll go by km/hr. To do this, we need to set the hrs to 1.

8/x = 1

x = 8

200/8 = 25

Your answer is 25km/hr

What is the area of the triangle?

Answers

I think it is 30 !!!!!!!!!!!!!

Answer:

30 units²

Step-by-step explanation:

a=1/2 ×length × width

a=1/2 × 12 ×5

a=6×5

a=30units squared

10 POINTS FOR THE CORRECT ANSWER PLEASE HELP

Answers

Step-by-step explanation:

use pythagoras theorem

a squared +b squared =c squared

4.12 squared +8 squared =x squared

16.9744+64=x squared

take the square root of 80.9744

x=9

a^2 + b^2 = c^2
8^2 + radical 17^2 = c^2
64 + 17 = c^2
81 = c^2
9 = c
the answer is 9

What is the remainder when P(x)=2x3-3x2-5x-6 is divided by (x-3)

Answers

Answer:

remainder = 6

Step-by-step explanation:

Hope it helps.....

Tell whether the angles are complementary or supplementary. Then find the value of X​

Answers

the answer is x = 5!!!!

Hi his figure is made up of unit cubes, each with a volume of 1 cubic unit.
What is the volume of the figure?
( photo is attached)
(Will give brainliest if you help)

Answers

Answer:

D. 100 cubic units

Step-by-step explanation:

There are 10 cubes in each layer (count at the top) and 10 layers (from top to bottom) in total. Multiply these to get volume.

10 x 10 =100

Answer:

B. 60 cubic units

Step-by-step explanation:

Formulas for a cube:

The volume of a cube:

V = a3

The surface area of a cube:

the area of each face (a x a) times 6 faces

S = 6a2

Face diagonal of a cube:

By the Pythagorean theorem, we know that

f2 = a2 + a2

Then f2 = 2a2

solving for f we get

f = a√2

Diagonal of the solid cube:

Again, by the Pythagorean theorem, we know that

d2 = a2 + f2

substituting f into this equation we get

d2 = a2 + (a√2)2 = a2 + 2a2 = 3a2

solving for d we get

d = a√3

I need help please. I don’t know this

Answers

Answer:

y = 1x + 6

Step-by-step explanation:

y = mx + b is the formula we need to use. b is the y intercept which is clearly 6 on the graph. Then we need to use rise over run to find our m. We can see for every x value that increases by 1, y also increases at 1. This means our x is 1.

Answer:

(0,6) ,(4,10)

y=(10-6)/×=(4-0)

4/4= 1

Hannah decided to curl up and read a good book. She started reading at 10:00 a.m. and
finished reading at 11:43 a.m. How much time did she spend reading?

Answers

Answer:

she spend one hour and 43 minutes reading

Step-by-step explanation:

hope you have a great day kee learning

Find the missing side. Round
to the nearest tenth.
17
y
44°
Х
y=[?]

Answers

Answer:

The answer is 11.8

Step-by-step explanation:

The value of x and y is 12.2 and 11.8 respectively.

What is tangent of an angle?

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

What is sine of an angle?

The sine (sin) of an acute angle in a right angled triangle is the ratio between the side opposite the angle and the hypotenuse of the triangle.

According to the given question.

We have a right angled triangle.

In which one angle is 44 degrees and hypotenuse is 17 units.

Here,

With respect to angle 44 degrees the adjacent side is x and the opposite side is y.

Therefore,

Sine of 44 degrees is given by

[tex]sin44^{o} = \frac{opposite\ side }{Hypotenuse}[/tex]

[tex]\implies sin44^{o} = \frac{y }{17}[/tex]

[tex]\implies 0.6946 = \frac{y}{17}[/tex]

[tex]\implies 0.6946 \times 17 = y[/tex]

[tex]\implies y = 11.80[/tex]

[tex]\implies y = 11.8[/tex]

And, tangent of 44 degrees is give by

[tex]tan 44^{o} = \frac{opposite \ side }{adjacent \ side }[/tex]

[tex]\implies tan44^{o} = \frac{y}{x}[/tex]

[tex]\implies tan44^{o} = \frac{11.8}{x}[/tex]

[tex]\implies 0.9657 = \frac{11.8}{x}[/tex]

[tex]\implies x = \frac{11.8}{0.9657}[/tex]

[tex]\implies x = 12.22[/tex]

[tex]\implies x = 12.2[/tex]

Therefore, the value of x and y is 12.2 and 11.8 respectively.

Find out more information about tangent and sine of an angle here:

https://brainly.com/question/12465968

#SPJ3

please hurry will mark brainiest

Answers

Answer:

Step-by-step explanation:

x(x+8) = 450

x² + 8x - 450 = 0

Quadratic formula:

x = [-8±√(8²-4(1)(-450))]/[2(1)]

= [-8±2√466]/2

= -4±√466

≅ 17.59, -25.59

-25.59 is an extraneous solution, so x ≅ 17.6 inches.

The dimensions of the blackboard are 17.59 inches by 25.59 inches  

The hypotenuse in this 45-45-90 triangle is given. How would you find the length of a leg
of the triangle?
8 V2
45degrees

Answers

Answer:

The length of the legs of the triangle is 8 units.

Step-by-step explanation:

45-45-90 triangle

A 45-45-90 triangle is a special case of a right triangle in which both legs l have the same value and the hypothenuse is h. By the Pythagorean Theorem:

[tex]2l^2 = h^2[/tex]

Hypothenuse of 8 V2

This means that [tex]h = 8\sqrt{2}[/tex]

So

[tex]2l^2 = h^2[/tex]

[tex]2l^2 = (8\sqrt{2})^2[/tex]

[tex]2l^2 = 64*2[/tex]

[tex]l^2 = 64[/tex]

[tex]l = \sqrt{64}[/tex]

[tex]l = 8[/tex]

The length of the legs of the triangle is 8 units.

Write impossible, unlikely, as likely as not, likely, or certain. Then, tell whether the probability is 0,close to 0, 1/2, close to 1, or 1 Picking a red marble from 4 white marbles and 7 green marbles

Answers

Answer:

Step-by-step explanation:

What is the equation of the following line written in slope-intercept form?
y = -5x
y = 5x
y = 5/x

Answers

The equation is y=5x

Answer:

y=5x

Step-by-step explanation:

first, we know that a rising line's slope is always positive, so the first one is incorrect

let's figure out the slope: y-y'/x-x' is the formula.

now, -5-5/-1-1= -10/-2= 5. so the slope of this line is 5.

Sara reduced the time it takes her to run a mile from 12 minutes to 8 minutes. Which is closest to Sara's percent decrease in the time it takes her to run a mile?​

Answers

Answer:

33%

Step-by-step explanation:

Plz help me I am timed! Well mark brainliest if you are correct!

Answers

Answer:

A

Step-by-step explanation:

The point Y is the center of the circle

the correct answer for point y is c

Aubrey is going to invest $160 and leave it in an account for 7 years. Assuming the interest is compounded daily, what interest rate, to the nearest tenth of a percent, would be required in order for Aubrey to end up with $220?

Answers

Answer:

4.5%

Step-by-step explanation:

compound interest formula:

[tex]PV(1+\frac{i}{n})^{t*n}[/tex]

[tex]220=160(1+\frac{x}{365})^{365*7}\\\\1.375=(1+\frac{x}{365})^{2555}\\1.0001246=1+\frac{x}{365}\\x=.0454962254126[/tex]

this rounds to

x=4.5%

Aubrey would need an interest rate of 6.3%.

What is compound interest?

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

A = P [tex](1 + r/n)^{nt}[/tex]

A = the final amount (in this case, $220)

P = the initial investment (in this case, $160)

r = the interest rate (what we are trying to find)

n = the number of times the interest is compounded per year (since it's compounded daily, n = 365)

t = the time period (in years, in this case, 7)

Substituting in the given values and solving for r:

220 = 160(1 + r/365)^(3657)

220/160 = (1 + r/365)^(3657)

1.375 = (1 + r/365)^2555

ln(1.375) = 2555 ln(1 + r/365)

ln(1 + r/365) = ln(1.375)/2555

1 + r/365 = e^(ln(1.375)/2555)

r/365 = e^(ln(1.375)/2555) - 1

r = 365(e^(ln(1.375)/2555) - 1)

r ≈ 6.3%

Therefore,

Aubrey would need an interest rate of 6.3%.

Learn more about compound interest here:

https://brainly.com/question/13155407

#SPJ3

Please help! Answer and explanation please!

Answers

Answer:

B. 36π in²

Step-by-step explanation:

Given:

Volume = 54π in³

height (h) = 6 in.

Required:

Curved surface area of the can (area for the label needed to wrap around the can without overlapping)

Solution:

First, we need to find the radius (r) of the can.

Volume = πr²h

Plug in the given values and solve for r

54π = π*r²*6

54π = 6π*r²

54π/6π = r²

9 = r²

r = √9

r = 3 in

✔️Find the curved surface area:

Curved surface area = 2πrh

r = 3 in

h = 6 in

Plug in the values

C.S.A = 2*π*3*6

C.S.A = 36π in²

Pls help!!!! It is khan academy and I’m giving 15 points!

Answers

The inequality would be in the direction of the arrow
The arrow is <—— so the inequality is <
The circle is colored so -3 in including making it less than or equal
x<-3
_

Or B

Please help! Needed ASAP!

Answers

Answer:

1 bagel $3.5

1muffin $1.25

1ticket$9

1snack$2

Step-by-step explanation:

miffin(y)

bagel(x)

x+3y=7.25

x+2y=6

since x is similar in both equations you cancel it out

subtract this

3y=7.25

2y=6

y=$1.25(price for 1 muffin)since we had 3 muffins it will be 1.25×3=7.25,where you do 7.25 to get 3.5 (price for 1 bagel)

question 8:ticket(x)

snack(y)

2x+3y=24×3

3x+4y=35×2

×3 and ×2 so we can eliminate the x

6x+9y=72

6x+8y=70

eliminate x

y=2

so snack is $2

2x+(3×2)=24

24-6=18

18÷2x=9

so a ticket is $9

A circle passes through the points (3,2) and (7,2) and has radius 2√2. Find the two possible equations for this circle

Answers

Answer:

18 because of its addition

Step-by-step explanation:

πr²=3+2+7+2+2+2

=5+9+4

=18

James has a mass of 32.8 kg. Ricardo's mass is 8 3/4 kg more than James's. Winthorp's mass is 3.6 kg less than Ricardo's. What is the total mass of the three boys?

Answers

Answer:79.5

Step-by-step explanation:32.8+8.75=41.55 41.55-3.6=37.95 37.95+41.55+32.8=79.5

111.94 kg is the total mass of the three boys.

What is ratio?

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. An equation with two ratios set equal to one another is called a percentage.

given, James has a mass of 32.8 kg. Ricardo's mass is 8 3/4 kg more than James's. Winthrop's mass is 3.6 kg less than Ricardo's.

Since Mass of James = 32.8 kg

thus Mass of Ricardo = [tex]8\frac{3}{4}[/tex] + 32.8 = 41.55kg

And Mass of Winthrop = 41.55 - 3.6 = 37.59kg

Sum of mass of all three boys  = 32.8 + 41.55+ 37.59

Sum of the mass of all three boys = 111.94 kg

Therefore, the Total mass of the three boys is 111.94 kg.

Learn more about ratios here:

https://brainly.com/question/1504221

#SPJ2

Which graph represents the solution set of the following situation? Andrew is buying fruit for a fruit salad. Bananas cost $1 a pound and oranges cost $2 a pound. He plans to buy at least 10 pounds of fruit and spend no more than $20. Let x represent pounds of bananas and let y represent pounds of oranges..

Answers

Answer:

[tex]x + y \ge 10[/tex]

[tex]x + 2y \le 20[/tex]

Step-by-step explanation:

The question is incomplete as the graphs are not shown. So, I will derive the inequalities and plot the graph.

Given

[tex]Banana = \$1[/tex]

[tex]Orange = \$ 2[/tex]

[tex]Purchase = 10lb[/tex] --- At least

[tex]Spedings = \$20[/tex] --- Not more than

And we have:

[tex]x = Banana; y = Orange[/tex]

The number of purchase will be represented as:

[tex]x + y \ge Purchase[/tex] ---- (at least)

[tex]x + y \ge 10[/tex]

The amount spent will be represented as;

[tex]1 * x + 2 * y \le 20[/tex] --- (not more than)

[tex]x + 2y \le 20[/tex]

So, the inequalities are:

[tex]x + y \ge 10[/tex]

[tex]x + 2y \le 20[/tex]

See attachment for graph

A high school student working a part time as a cook

Answers

Answer:

Is there supposed to be a picture???

Step-by-step explanation:

Ummmm what’s the question???

answer and show proof for brainliest

Answers

i'm confused don't all of them explain pls

Answer:

The answer is A

Step-by-step explanation:

A closed circle means the number is included in the equation / solution. An open circle means it is not. The problem says greater than or equal to 36 inches tall which means that circle should be closed. And less than 48 inches. It does not say anything about being equal when it states the 48 inches so that one should be open.

Select all that apply.

Which two rays form ∠ACB?

1. CA
2. AC
3. CB
4. CE

Answers

Answer:

The 2 rays the form ACB ARE AC and CB

The fuel efficiency for a new helicopter engine is given by the continuous function r(c) where r is measured in gallons per mile ....

Answers

The question is incomplete. The complete question is :

The fuel efficiency for a new helicopter engine is given by the continuous function r(c) where r is measured in gallons per mile and c is measured in miles. What are the units of [tex]$\int_0^7 r(c) \ dc$[/tex]   ?

Solution :

The given continuous function is :

r(c), here c is measured in miles and the unit of r is measured in gallons per mile.

So the unit of  [tex]$\int_0^7 r(c) \ dc$[/tex] is given by :

= gallons per mile x mile

= gallons

So, the final unit is gallons.

Other Questions
"those who understand languages very well", what grammatical name is given to it and what's it's function. what types of government did Monroe not want in the western hemisphere A 12 oz. can of pinto beans is $2.15. What is the cost per ounce? * Prime Bank is offering your company the use of their lockbox services. They estimate that you can reduce your average mail time by 1.5 days and they can save you a combined clearing and processing time of 1 day by putting the checks into the clearing system sooner. Your firm receives 198 checks a day with an average value of $2,300 each. The current T-Bill rate is .011 percent per day. Assume a 365-day year. Prime Bank will charge your firm an annual fee of $27,500 plus $.20 per check. What is the annual net savings from installing this system How do glaciers shape the landscape? Market research does not provide enough information for businesses to use indecision making.True or False A student is observing an image of an object that could be a comet, meteoroid or asteroid. Which of the following questionswould BEST confirm that the object is a comet?A. Does the object contain ice?B. Does the object contain metals?C. Where is the object found? D. How big is the object? Alicia is solving a quadratic equation. She wants to find the value of x by taking the square root of both sides of the equation. Which equation allows her to do this? CLEAR CHECK x2+81x+18=54 x28x+24=17 x2+9x24=25 x2+16x+64=36 Why when I smell an onion and eat an apple, all I taste is the apple? I thought that you were supposed to taste the onion. Please help clarify. Explain how to find the slope of the line. We are the heirs of the ages, and yet we have had to pay few of the penaltiesThis line means that countries such as ours are few and far between other countries had a much easier time that we have had some countries will be forgotten soon by history we inherited much from our forefathers Chemical reactions and nuclear reactions cause matter to change in different ways. Which two statements describe how matter changes only in a nuclear reaction? PLZZZ HELP ME ASAP!!A.) Each atomic nucleus changesB.) The electrons of atoms are rearrangedC.) No new elements are formedD.) Atoms of new elements are formed differences between home trade and international trade PLZ HELP IM STUCK!!!!!!!!!! give atleast 10 or 5 that Words related to the word FOLLOW how is eubacteria organized? Help pleaseEvaluate the expression when a = -9 and b = - 4.a? - 2(b + 12) 36 POINTS!Please answer ALL questions! I really need to get this done. Thank you so much if you do. Please help me with this homework A 52-in TV measures 52 inches along its diagonal (corner to corner measure). If that TV is 33.6 inches high, how wide is it?