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Anit [1.1K]
3 years ago
15

There are 10 computers and 5 students. How many ways are there for the students to sit at the computers if no computer has more

than one student and each student is seated at a computer?
Mathematics
1 answer:
mestny [16]3 years ago
6 0

Answer:

30,240 ways

Step-by-step explanation:

This question is bothered on permutation. Permutation has to do with arrangement.

If there are 10 computers and 5 students, the number of ways students will sit at the computers if no computer has more than one student can be expressed as;

10P5 = 10!/(10-5)!

10P5 = 10!/(5)!

10P5 = 10*9*8*7*6*5!/5!

10P5 = 10*9*8*7*6

10P5 = 30,240

Hence the number of ways is 30,240 ways

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Given: PS=RT, PQ=ST<br> Prove: QS=RS
ivanzaharov [21]

Answer:

I) Eq(1) reason: sum of segments of a straight line

II) Eq(2) reason: Given PQ = ST & PS = RT

III) Eq(3) reason: sum of segments of a straight line

IV) Eq(4) reason: Same value on right hand sides of eq(2) and eq(3) demands that we must equate their respective left hand sides

V) Eq(5) reason: Usage of collection of like terms and subtraction provided this equation.

Step-by-step explanation:

We are given that;

PS = RT and that PQ = ST

Now, we want to prove that QS = RS.

From the diagram, we can see that from concept of sum of segments of a straight line we can deduce that;

PQ + QS = PS - - - - (eq 1)

Now, from earlier we saw that PQ = ST & PS = RT

Thus putting ST for PQ & PS for RT in eq 1,we have;

ST + QS = RT - - - - (eq 2)

Again, from the line diagram, we can see that from concept of sum of segments of a straight line we can deduce that;

RS + ST = RT - - - - -(eq 3)

From eq(2) & eq(3) we can see that both left hand sides is equal to RT.

Thus, we can equate both left hand sides with each other to give;

ST + QS = RS + ST - - - (eq 4)

Subtracting ST from both sides gives;

ST - ST + QS = RS + ST - ST

This gives;

QS = RS - - - - (eq 5)

Thus;

QS = RS

Proved

5 0
3 years ago
A construction company is starting to build a new house. They need to put tape around the site to begin. The new home site is 20
jonny [76]

Answer:

20 meters

Step-by-step explanation:

A construction company is starting to build a new house. They need to put tape around the site to begin. The new home site is 20 meters wide by 40 meter long rectangle. The company already has 100 meters of tape. How much more tape does the company need to tape the site?

We would have to find the perimeter of this rectangle

Perimeter fo a rectangle = 2L + 2W

In the above question,

L = Length = 40 m

W = Width = 20 m

Hence:

Perimeter = 2(40m) + 2(20m)

= 80m + 40m

= 120m

Hence, he would need 120 meters of tape

From the above Question, the company already has 100m

Hence, the amount of tape that the company needs more =

120m - 100m = 20 m

5 0
3 years ago
A cash register contains $5 bills and $50 bills with a total value of $1060. If there are 32 bills total, then how many of each
kozerog [31]

Answer:

12 5 dollar bills

20 50 dollar bills

Step-by-step explanation:

Let x = number of five dollar bills

Let y = number of fifty dollar bills

We have a total of 32 bills

x+y = 32

The total amount is 1060

5x+50y = 1060

We have 2 equations and 2 unknowns

x+y = 32

5x+50y = 1060

Multiply the first equation by -5 so we can eliminate x

-5x -5y = -5*32

-5x -5y =-160

Add this to the second equation

5x+50y = 1060

-5x -5y =-160

------------------------

45 y    = 900

Divide each side by 45

45y/45 = 900/45

y = 20

There are 20 50 dollar bills

x+y = 32

x+20 = 32

Subtract 20 from each side

x+20-20 = 32-20

x = 12

There are 12 5 dollar bills

8 0
3 years ago
I got it incorrect so please help for where each one goes
OLEGan [10]

The first one is right and the third one is right, but you need to switch the 15% and the 95%.

In #2, it's asking for the kids that <em>are not</em> Michael, so it'd be 18/19. Which is then rounded to roughly 95%.

#4 asks for 6/40 = 15%

6 0
3 years ago
Read 2 more answers
Differentiate with respect to t
True [87]

Answer:

\displaystyle 2x\frac{dx}{dt}-3y^2\frac{dy}{dt}+4z^3\frac{dz}{dt}=0

Step-by-step explanation:

We want to differentiate the equation:

x^2-y^3+z^4=1

With respect to <em>t</em>, where <em>x, y, </em>and <em>z</em> are functions of <em>t. </em>

<em />

So:

\displaystyle \frac{d}{dt}\left[x^2-y^3+z^4\right]=\frac{d}{dt}\left[1\right]

Implicitly differentiate on the left. On the right, the derivative of a constant is simply zero. Hence:

\displaystyle 2x\frac{dx}{dt}-3y^2\frac{dy}{dt}+4z^3\frac{dz}{dt}=0

8 0
3 years ago
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