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galben [10]
3 years ago
6

Find the number of distinguishable permutations of the letters m, i, s, s, i, s, s, i, p, p, i.

Mathematics
1 answer:
Tatiana [17]3 years ago
4 0

Solution:

we have been asked to find the number of distinguishable permutations of the letters m, i, s, s, i, s, s, i, p, p, i.

Here we can see

m appears 1 time.

i appears 4 times.

S appears 4 times.

p appears 2 times.

Total number of letters are 11.

we will divide the permutation of total number of letters by the permutation of the number of each kind of letters.

The number of distinguishable permutations=\frac{11!}{1!2!4!4!} \\

Hence the number of distinguishable permutations=\frac{11!}{1!2!4!4!}=34650 \\

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Tcecarenko [31]
Let s equal the number of shirts she can buy

140 > $28.50 + $20.75s
111.50 > 20.75s
5.37 > s

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4 0
2 years ago
Complete the general form equation of the parabola that passes through (4, -11) with vertex at : (2, -3).
fomenos

Answer:

Step-by-step explanation:

You're given a coordinate in the form of (x, y) and you're also given the vertex in the form of (h, k). We will use those in the vertex form of the equation

y=a(x-h)^2+k and solve for a. Filling in:

-11=a(4-2)^2-3 which simplifies a bit to

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-8 = 4a so

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The equation, then, is

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3 years ago
What is the total surface area of a square pyramid with a base length of 10 meters and a slant height of 13 meters?
Harlamova29_29 [7]
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Orbet used 24 square tiles to make a rectangle. The perimeter of the rectangle is 20 units. What would be the perimeters of the
Dmitriy789 [7]

Answer:

The perimeter of other rectangles are 50, 28, 22 units

The area of all possible rectangles are same and equals to 24 unit²

Step-by-step explanation:

Given - Orbet used 24 square tiles to make a rectangle. The perimeter of the rectangle is 20 units.

To find -  What would be the perimeters of the other rectangles Orbet could make using only these 24 tiles? How do the areas of the rectangles compare?

Proof -

We know that

Are of Rectangle = Length × Breadth

And Perimeter of Rectangle = 2 (Length + Breadth )

Now,

Given that,

Orbet used 24 square tiles

And perimeter of the rectangle made = 20

So,

Possible Length of rectangle = 6

Possible breadth of Rectangle = 4

Or Vice-versa.

Total number of Rectangles possible = 4

Possibilities are -  1 × 24, 2 × 12, 3 × 8, 4 × 6

Case I :

Length of rectangle = 1

Breadth of rectangle = 24

∴ Perimeter of rectangle = 2(1 + 24) = 2(25) = 50 units

Area of rectangle = 1 × 24 = 24 unit²

Case II :

Length of rectangle = 2

Breadth of rectangle = 12

∴ Perimeter of rectangle = 2(2 + 12) = 2(14) = 28 units

Area of rectangle = 2 × 12 = 24 unit²

Case III :

Length of rectangle = 3

Breadth of rectangle = 8

∴ Perimeter of rectangle = 2(3 + 8) = 2(11) = 22 units

Area of rectangle = 3 × 8 = 24 unit²

Case IV :

Length of rectangle = 4

Breadth of rectangle = 6

∴ Perimeter of rectangle = 2(4 + 6) = 2(10) = 20 units

Area of rectangle = 4 × 6 = 24 unit²

∴ we get

The perimeter of other rectangles are 50, 28, 22 units

The area of all possible rectangles are same and equals to 24 unit²

5 0
3 years ago
Suppose that the concentration of a bacteria sample is 60 comma 000 bacteria per milliliter. If the concentration triples in 4 ​
Elodia [21]

Answer:

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Step-by-step explanation:

The inicial concentration is 60,000, and this concentration triples every 4 days, so we can write the equation:

P = Po * r^t

where P is the final concentration after t periods of 4 days, Po is the inicial concentration and r is the ratio that the concentration increases (r = 3)

Then, we have that:

102000 = 60000 * 3^t

3^t = 102/60 = 1.7

log(3^t) = log(1.7)

t*log(3) = log(1.7)

t = log(1.7)/log(3) = 0.483

so the number of days that will take is 4*0.483 = 1.932 days (or approximatelly 1 day, 22 hours and 22 minutes)

3 0
3 years ago
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