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Gwar [14]
3 years ago
12

In how many different, distinguishable orders can the letters of the word mathematics be arranged?

Mathematics
1 answer:
Natalka [10]3 years ago
7 0

Answer:

B)4,989,600

Step-by-step explanation:

The letters of 'MATHEMATICS'  contains 11 letters.

The following letters repeats twice, TT,MM,AA.

When we talk of distinguishable wasy, we are referring to arrangement without repetition.

Therefore the letters of "MATHEMATICS" can be arranged in \frac{11!}{2!2!2!}=4,989,600 distinguishable ways.

The correct answer is B.

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What is the area of the regular hexagon ABCEF? Explain your reasoning.
Reil [10]

Answer:

1350\sqrt{3} units²

Step-by-step explanation:

The regular hexagon consists of 6 equiangular triangles

The area (A) of a equilateral triangle is calculated as

A = \frac{s^2\sqrt{3} }{4} ( s is the side length )

Here s = 30 , then

A = \frac{30^2\sqrt{3} }{4} = \frac{900\sqrt{3} }{4} = 225\sqrt{3} units²

Thus the area of the regular hexagon is

area = 6 × 225\sqrt{3}

        = 1350\sqrt{3} units² ← exact value

         ≈ 2338.3 units² ( to 1 dec. place )

4 0
3 years ago
To find the product of 42.12 and 10³, move the decimal point in 42.12 __ places to the right because 10³ has __ zeros.
Yakvenalex [24]
<h3>To find the product of 42.12 and 10^3,  move the decimal point in 42.12 3 places to the right because 10^3 has 3 zeros</h3>

<em><u>Solution:</u></em>

Given that,

\text{ product of } 42.12 \text{ and } 10^3

Which means,

42.12 \times 10^3

Here, the exponent of 10 is positive ( which is 3)

When the exponent is positive, we have to move the decimal point to right

When you multiply a number by a power of 10, ( 10!, 10^2, and so on ) move the decimal point of the number to the right the same number of places as the number of zeros in the power of 10

Here, exponent is 3 , therefore move the decimal point right 3 places in 42.12

Therefore,

42.12 \times 10^3 = 42120

7 0
4 years ago
How many solutions does this linear system have? one solution: (0, 0) one solution: (1, –4) no solution infinite number of solut
Anna35 [415]

The system of equations has infinite solutions.

<h2>Given to us,</h2>
  • y=-6x+2
  • -12x-2y=-4

<h3>Equation 2,</h3>

The value of y is already given in equation 1,

-12x-2y=-4

substituting the value of y in equation 2,

-12x-2(-6x+2)=-4\\-12x +12x-4=-4\\-12x+12x=-4+4\\0=0

The solution of the two equations is 0. Also, we can see that both the equations are in ratio.

Further, the image also shows that the line of the two equations are coinciding.

Hence, the system of equations has infinite solutions.

Learn more about System of solutions:

brainly.com/question/14264175

3 0
2 years ago
10 kilograms =?grams
max2010maxim [7]

10 kilograms is equal to 10,000 grams

Step-by-step explanation:

1 kilogram = 1000 grams

To know how many grams does 10 kilograms consists is we need to multiply with 1000 to 10 then we can obtain 10 kilograms in grams.

10 kilograms = 10 × 1000

10 kilograms = 10,000 grams.

"Kilogram" is the unit of "mass". The standard unit of "mass" in the "International system" of units the "mass" is represented by "Kilogram".

The symbol for "Kilogram" is "Kg".

8 0
3 years ago
Factor completely -2x^3 + 6x^2
Bumek [7]

We can factor a -2 and an x^2 out of this using GCF.

<h3><u>-2x^2(x - 3) is what we're left with, and is the fully factored form.</u></h3>
3 0
3 years ago
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