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Ugo [173]
1 year ago
12

Aadya is building towers by stacking identically shaped cubes of different colors on top of each other. She has $1$ red cube, $2

$ yellow cubes, $3$ green cubes, and $4$ blue cubes. How many different $10$-cube-high towers can Aadya build using these $10$ cubes so that neither of the bottom two cubes of the tower are green?
Mathematics
1 answer:
Vika [28.1K]1 year ago
8 0

Using the Fundamental Counting Theorem, it is found that Aadya can build 1,693,440 cube towers.

<h3>What is the Fundamental Counting Theorem?</h3>

It is a theorem that states that if there are n things, each with n_1, n_2, \cdots, n_n ways to be done, each thing independent of the other, the number of ways they can be done is:

N = n_1 \times n_2 \times \cdots \times n_n

Considering that she has 10 cubes, and the bottom and top cubes cannot be green, the parameters are given by:

n_1 = 7, n_10 = 6, n_2 = 8, n_3 = 7, \cdots n_9 = 1

Hence the number of cubes is given by:

N = 7 x 6 x 8! = 1,693,440.

Aadya can build 1,693,440 cube towers.

More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866

#SPJ1

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A 2-gallon bottle of fabric softener costs $16.64. What is the price per cup?
Burka [1]

Answer:

each cup would cost $0.52

Step-by-step explanation:

there are 16 cups in 1 gallon so you multiply that by two. Then you have 32 so you divide 16.64 by 32 and you end up with 0.52.   hope this helped :))

Tell me I got this wrong

3 0
2 years ago
Does 26/3 equal 182/21
brilliants [131]

Answer: Yes, they are equal

Step-by-step explanation:

Quick statement: To find equivalent fractions, multiply or divide them by the same number.

In this particular example, you can divide 182 by 7 and get 26 and 21 by 7 to get 3. This symbols that they are equal. If you try the inverse operation (multiplication), you could multiply 26 by 7 and get 182. Same goes for 21 and 3: you multiply 3 by 7 to get 21. Just remember to multiply or divide the two numbers (numerator and denominator) by the same number to get an equivalent fraction.

3 0
3 years ago
Read 2 more answers
Figure TUVS is a parallelogram.
poizon [28]

Angles T and V of the parallelogram are equal to 91°.

Calculating the Value of x

In the parallelogram TUVS, adjacent angles U and V are given as,

U = 4x+9

V = 6x-29

Since U and V are adjacent angles, and as per the properties of a parallelogram, sum of adjacent angles is equal to 180°.

4x+9 + 6x-29 = 180

10x - 20 =180

10x = 200

x = 20

Calculating the Angles of the Parallelogram

∠U = 4x + 9

∠U = 4(20) + 9

∠U = 80 + 9

∠U = 89°

∠V = 6x - 29

∠V = 6(20) - 29

∠V = 120 - 29

∠V = 91°

According to the properties of a parallelogram, opposite angles are of equal measure.

∴ ∠T = ∠V and ∠S = ∠U

⇒ ∠T = 91° and ∠S = 89°

Learn more about a parallelogram here:

brainly.com/question/1563728

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5 0
2 years ago
F = 2x + y<br> 3x + 5y = 45 x20 and y20<br> 2x + 4&lt;32
ipn [44]

Answer:

a

Step-by-step explanation:

6 0
3 years ago
<img src="https://tex.z-dn.net/?f=%5Chuge%5Cfbox%5Cpurple%7BQuestion%7D" id="TexFormula1" title="\huge\fbox\purple{Question}" al
ICE Princess25 [194]

The LCM of the given numbers have been determined.

<h3>What is LCM ?</h3>

LCM stands for Least Common Multiple .

For two numbers , LCM is the number that is the smallest number of which they both are a factor.

It is asked to determine

LCM of 6 and 9

6 = { 6 , 12 , 18 , 24 , 30 , 36 , 42 .....}

9 = { 9 , 18 ,27 .....}

The LCM of 6 , 9 is 18

LCM of 8 and 12

8 = { 8,16,24,32....}

12 = {12 , 24 ,36....}

The LCM of 8 and 12 is 24

LCM of 4 , 6 and 8

4 = {4 , 8 , 12 , 16 , 20,24,28 ....}

6 = { 6 ,12 ,18,24......}

8 = {8 , 16,24 .....}

The LCM of 4,6 and 8  is 24

The LCM of 6 and 15 is 30  

The LCM of 20 and 30 is  60

The LCM of 25,30 and 75 is 150

The image of the solution is attached .

To know more about LCM

brainly.com/question/20739723

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6 0
2 years ago
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