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3 years ago

Suppose a game of 3-D tic tac toe is played on a 6x6x6 cube. How many winning lines of 6-in-a-row are there through the cube?

1 answer:

7 0

On a cube of side k and n dimensions, there are
[(k+2)ⁿ - kⁿ] / 2
winning lines.

In your case,
k = 6
n = 3

Therefore:
[(6+2)³ - 6³] / 2
= (8³ - 6³) / 2
= (512 - 216) / 2
= 148

Hence, there are 148 6-in-a-row winning lines through the cube.

You might be interested in

F(x)=5^x+1 what’s the rate of change between x=0 and x=4

nalin [4]

Answer:

156

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Functions
Function Notation
Average Rate of Change: $\displaystyle \displaystyle \frac{f(b) - f(a)}{b - a}$

Step-by-step explanation:

Step 1; Define

Identify

f(x) = 5ˣ + 1

Interval x [0, 4] →b = 4, a = 0

Step 2: Find Rate of Change

Substitute in variables [Average Rate of Change]: $\displaystyle \displaystyle \frac{f(4) - f(0)}{4 - 0}$
[Average Rate of Change] Substitute in x [Function f(x)]: $\displaystyle \displaystyle \frac{(5^4 + 1) - (5^0 + 1)}{4 - 0}$
(Parenthesis) Evaluate exponents: $\displaystyle \displaystyle \frac{(625 + 1) - (1 + 1)}{4 - 0}$
(Parenthesis) Add: $\displaystyle \displaystyle \frac{626 - 2}{4 - 0}$
[Fraction] Subtract: $\displaystyle \displaystyle \frac{624}{4}$
Divide: $\displaystyle \displaystyle 156$

6 0

2 years ago

WHO WOULD WIN IN A FIGHT? A SHAOLIN MONK vs A NAGA SADHU

sertanlavr [38]

Answer:

Shaolin Monk

Step-by-step explanation:

They are epic gamers. no but fr

3 0

2 years ago

Katarina is a botanist studying the production of

CaHeK987 [17]

The Type B trees produces 120 pears.

<h3>What is meant by percentage?</h3>

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement.

<h3>How many pears did the Type B trees produce?</h3>

Type A trees produced 20 percent more pears than Type B trees did
Type A trees produced 144 pears.

Let us consider, Type B produced 100% pears.

So, Type A will produce 120%of B, that is 144

144 = 120/100 $*$ B

simplifying the above equation, we get

144 $*$ 100 = 120B

B = 14400/120

B = 120

The value of B = 120.

Hence, the Type B trees produces 120 pears

Therefore, the correct answer is option B) 120.

To learn more about percentage, refer to:

brainly.com/question/24304697

#SPJ4

5 0

1 year ago

If Joanne can paint a room in 3 hours and her sister Angela can paint the same room in 4 hours, how long (in h) would it take Jo

Gala2k [10]

Answer:

Step-by-step explanation:

If J can paint a room in 3 hours, in 1 hour she gets $\frac{1}{3}$ of the job done.

If A can paint a room in 4 hours, in 1 hour she gets $\frac{1}{4}$ of the job done. We need to find out how long it takes them if they paint together. The equation for this is:

$\frac{1}{3}+\frac{1}{4}=\frac{1}{x}$ where x is the number of hours it takes them to get the job done together. Multiply everything through by 12x to get

4x + 3x = 12 so

7x = 12 and

x = 1.7 hours to get the room painted together.

7 0

3 years ago

Graph the function

Oksana_A [137]

Answer:

To graph a rational function, you find the asymptotes and the intercepts, plot a few points, and then ... graphing showing vertical asymptote at x = 1 ... Next, I'll find any x- or y- intercepts.

6 0

2 years ago