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4 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:
[<span>(6+2)³ - 6³] / 2
= (8</span>³ - 6³) / 2
= (512 - 216) / 2
= 148

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

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Does the table represent a function? Why or why not? X 2 3 3 4 5 y 4 5 6 7 7

QveST [7]

Answer:

Step-by-step explanation:

8 0

3 years ago

The distribution of income tax refunds follow an approximate normal distribution with a mean of $7010 and a standard deviation o

Andrej [43]

Answer:

A refund must be above $7,139 before it is audited.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 7010, standard deviation = 43.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

The empirical rule is symmetric, which means that the lowest (100-99.7)/2 = 0.15% is at least 3 standard deviations below the mean, and the upper 0.15% is at least 3 standard deviations above the mean.

Use the Empirical Rule to determine approximately above what dollar value must a refund be before it is audited.

3 standard deviations above the mean, so:

7010 + 3*43 = 7139.

A refund must be above $7,139 before it is audited.

5 0

3 years ago

Help I'm not sure if this is the answer?<br><br> (This question is about trigonometric ratios)

dem82 [27]

9514 1404 393

Answer:

(b) 15.32

Step-by-step explanation:

You can use your triangle sense to answer this.

The side x will always be shorter than the hypotenuse, 20. This eliminates the last two choices.

If the angle is 45°, then the sides are equal at about 0.707 times the length of the hypotenuse. That would make them 0.707×20 = 14.14. Since the angle is greater than 45°, the opposite side will be greater than 14.14. Only one answer choice fits between 14 and 20: the second choice -- 15.32.

The mnemonic SOH CAH TOA reminds you of the relation ...

Sin = Opposite/Hypotenuse

sin(50°) = x/20

x = 20×sin(50°) . . . . multiply by 20 to find x

x ≈ 15.32 . . . . . . . . . use your calculator to evaluate

The attachment is intended to show how the triangle side lengths change with angle.

3 0

3 years ago

3(2x-1)=5x+3+7x I do t get this cause I’m stupid

DiKsa [7]

Answer:

x = -1

Step-by-step explanation:

Solve for x:

3 (2 x - 1) = 7 x + 5 x + 3

Grouping like terms, 7 x + 5 x + 3 = (5 x + 7 x) + 3:

3 (2 x - 1) = (5 x + 7 x) + 3

5 x + 7 x = 12 x:

3 (2 x - 1) = 12 x + 3

Expand out terms of the left hand side:

6 x - 3 = 12 x + 3

Subtract 12 x from both sides:

(6 x - 12 x) - 3 = (12 x - 12 x) + 3

6 x - 12 x = -6 x:

-6 x - 3 = (12 x - 12 x) + 3

12 x - 12 x = 0:

-6 x - 3 = 3

Add 3 to both sides:

(3 - 3) - 6 x = 3 + 3

3 - 3 = 0:

-6 x = 3 + 3

3 + 3 = 6:

-6 x = 6

Divide both sides of -6 x = 6 by -6:

(-6 x)/(-6) = 6/(-6)

(-6)/(-6) = 1:

x = 6/(-6)

The gcd of 6 and -6 is 6, so 6/(-6) = (6×1)/(6 (-1)) = 6/6×1/(-1) = 1/(-1):

x = 1/(-1)

1/(-1) = -1:

Answer: x = -1

7 0

4 years ago

A hotel has a large rectangular swimming pool. The hotel wants to build a children's pool that is half the length and half the w

wel

Answer:

The answer is 1898.625

Step-by-step explanation:

Multiply the swimming pool’s length by the width to find the area.

If you want to find the area of the children’s swimming pool, divide the answer by 2.

6 0

3 years ago