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kolezko [41]
3 years ago
11

In how many ways can 6 competitors finish a race assuming there are no ties?In how many ways can we sit n people on r < n cha

irs? In how many wayscan the gold, silver and bronze medals be awarded in a race of 8 people? Howmany 5-digit zip-codes are possible? How many different 3-person committeeswe can make with 10 people?
Mathematics
1 answer:
VLD [36.1K]3 years ago
6 0

Answer:  a) 720, b) ^nC_r=\dfrac{n!}{(n-r)!r!} c) 336, d) 30240 e) 120.

Step-by-step explanation:

Since we have given that

a) Number of competitors  = 6

We need to find the number of ways that 6 competitors can finish a race and there are no ties.

So, Number of ways would be

6!=720

b) number of people = n

Number of chairs = r (r<n)

so, the number of ways we can sit n people on r<n chairs is given by

^nC_r=\dfrac{n!}{(n-r)!r!}

c) If there are three awards :

Gold, silver, bronze.

We need to find the number of ways that these medals can be awarded.

Number of ways is given by

^8P_3\\\\=336

d) Number of 5-digit zip codes are possible is given by

^{10}P_5=30240

e) Number of poeple = 10

Number of people required in committee = 3

Number of different 3 person committee that are selected from 10 people is given by

^{10}C_3=120

Hence, a) 720, b) ^nC_r=\dfrac{n!}{(n-r)!r!} c) 336, d) 30240 e) 120.

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Cristal's gross semimonthly salary is $2968.50. What is the maximum amount she can afford to borrow for a home mortgage?
prohojiy [21]

Answer:

C) 142,488

Step-by-step explanation: by adding up here semimonthly, also took test.

8 0
3 years ago
Use absolute value notation to represent the distance between x and 8 is no more than 4
ivanzaharov [21]
The distance: use absolute value
Between x and 8: x-8

The distance between x and 8: | x-8 |

“is no more than” means it can be that or be less than that, so use ≤

The distance between x and 8 is no more than 4

| x-8 | ≤ 4
3 0
3 years ago
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year f
MA_775_DIABLO [31]

Answer:

Option D is the correct answer.

Step-by-step explanation:

Initial height = 4 feet

Given that the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5th taller than it was at the end of the 4th year.

Let the rate of growing each year be g.

After 6 years height of tree = 4 + 6g

After 4 years height of tree = 4 + 4g

At the end of the 6th year, the tree was 1/5th taller than it was at the end of the 4th year.

That is

                4+6g=4+4g+\frac{4+4g}{5}\\\\4+6g=\frac{20+20g+4+4g}{5}\\\\20+30g=24+24g\\\\6g=4\\\\g=\frac{2}{3}ft/year

Option D is the correct answer.    

8 0
3 years ago
SOS HURRY
Burka [1]

First, by using the distance formula for just one side, we can find the length of all sides (a square has 4 equal sides.) Then, we can apply the area of a square formula, which is a^2.

Distance formula:

\sqrt{(x.2 - x.1)^{2} + (y.2 - y.1)^{2}}

√((-2 + 5)^2 + (-8 + 4)^2)

√((3)^2 + (4)^2)

√9 + 16

√25

5

The side lengths of the square are each equal to 5, and by applying the formula for area, we can find the area of the square.

5^2 = 25

<h3>The area is 25.</h3>
3 0
3 years ago
What is the line of symmetry for the parabola whose equation is y = -x2 + x + 3?
iVinArrow [24]
Alright so if I do remember my math correctly, this is how it goes:

- y = -x^2 + x + 3

- x = -b/2a

- x = -1/2(-1)

- x = -1/-2, which = (1/2)

Not quite sure if this was correct, but if it was, hope this helps and you're welcome! :)
5 0
3 years ago
Read 2 more answers
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