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e-lub [12.9K]
3 years ago
10

There were 23 students running in a race. How many different arrangements of first, second, and third place are possible?

Mathematics
1 answer:
Alex787 [66]3 years ago
7 0

Answer:

10626 different arrangements

Step-by-step explanation:

As we have a total of 23 students and we want to form groups of 3, where the order of the 3 students matters, we can solve this problem using a permutation of 23 choose 3.

The formula for a permutation of n choose p is:

P(n,p) = n! / (n-p)!

So, using n = 23 and p = 3, we have:

P(23,3) = 23! / (23-3)! = 23! / 20! = 23 * 22 * 21 = 10626

So we have a total of 10626 different arrangements of first, second and third place.

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Victoria had $200 in her account at the end of one year. At the first of each subsequent year she deposits $15 into the account
telo118 [61]

Answer:

A(t) = 200+15t(1+0.02)^{t}

Step-by-step explanation:

Since the interest is calculated on the new balance every year.

Hence the formula used for compound interest is:

A = P(1+\frac{r}{n}^{nt}

where, A =Amount after t years

P =Principal amount

200 is the initial balance and Since, here the $15 is added to the balance each year. Therefore, P = 200+15t

r = rate each year (0.02)

t = time (in years) (t)

n = no. of times the interest is compounded in a year (n=1)

Therefore, the recursive formula is:

A(t) = 200+15t(1+0.02)^{t}

6 0
3 years ago
Read 2 more answers
What is the value of x in 16 to the 2nd power = x
Zepler [3.9K]
16^2 is 16•16 so x would equal 256
4 0
3 years ago
Read 2 more answers
Express p in terms of q if
Irina-Kira [14]

p=x^2+\dfrac{1}{x^2}\\\\p=\dfrac{x^4}{x^2}+\dfrac{1}{x^2}\\\\p=\dfrac{x^4+1}{x^2}\qquad(*)

q=x+\dfrac{1}{x}\\\\q=\dfrac{x^2}{x}+\dfrac{1}{x}\\\\q=\dfrac{x^2+1}{x}\qquad\text{square both sides}\\\\q^2=\left(\dfrac{x^2+1}{x}\right)^2\\\\q^2=\dfrac{(x^2+1)^2}{x^2}\qquad\text{use}\ \ (a+b)^2=a^2+2ab+b^2\\\\q^2=\dfrac{(x^2)^2+2(x^2)(1)+1^2}{x^2}\\\\q^2=\dfrac{x^4+2x^2+1}{x^2}\\\\q^2=\dfrac{x^4+1}{x^2}+\dfrac{2x^2}{x^2}\\\\q^2=\dfrac{x^4+1}{x^2}+2\qquad\text{subtract 2 from both sides}\\\\q^2-2=\dfrac{x^4+1}{x^2}\\\\\text{From (*) we have}\\\\\boxed{p=q^2-2}

8 0
3 years ago
The length and width of a rectangle are in a 7:2 ratio. Find the width of the perimeter is 72.
scoray [572]
<span>length = 7x
</span><span>width = 2x

2(7x + 2x) = 72
7x + 2x = 72/2
9x = 36
x = 36/9
x = 4
</span>
width = 2x = 2 * 4 = 8 units<span>


</span>
7 0
3 years ago
Please help ASAP this Is due tomorrow
Grace [21]

Answer:

384 inches²

Step-by-step explanation:

The surface area of a cube is found by using 6a².

6 = the number of sides in a cube

a = the given dimension (in this case, 8 inches long)

SA = (6)8²

SA = 6(64)

SA = 384

Hope this helps, sorry if it’s not what you’re looking for :)

3 0
3 years ago
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