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Genrish500 [490]

3 years ago

14

Find the probability of rolling the product 6 with a pair of two 6 sided dice

1 answer:

aliina [53]3 years ago

8 0

Answer:

1/9, or 0.111...

Step-by-step explanation:

There are 4 possible ways to roll 2 dice to get them to make a product of 6. (1 * 6), (2 * 3), (3 * 2), and (6 * 1). There are 36 possible rolls you can make.

Therefor, the probability of rolling the product 6 is 4/36.

4/36 = 1/9

1/9 = 0.111...

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Find all solutions of each equation on the interval 0 ≤ x < 2π.

Korvikt [17]

Answer:

$x = 0$ or $x = \pi$ .

Step-by-step explanation:

How are tangents and secants related to sines and cosines?

$\displaystyle \tan{x} = \frac{\sin{x}}{\cos{x}}$ .

$\displaystyle \sec{x} = \frac{1}{\cos{x}}$ .

Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, $\sin^{2}{x} = 1 - \cos^{2}{x}$ . Therefore, for the square of tangents,

$\displaystyle \tan^{2}{x} = \frac{\sin^{2}{x}}{\cos^{2}{x}} = \frac{1 - \cos^{2}{x}}{\cos^{2}{x}}$ .

This equation will thus become:

$\displaystyle \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} \cdot \frac{1}{\cos^{2}{x}} + \frac{2}{\cos^{2}{x}} - \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} = 2$ .

To simplify the calculations, replace all $\cos^{2}{x}$ with another variable. For example, let $u = \cos^{2}{x}$ . Keep in mind that $0 \le \cos^{2}{x} \le 1 \implies 0 \le u \le 1$ .

$\displaystyle \frac{1 - u}{u^{2}} + \frac{2}{u} - \frac{1 - u}{u} = 2$ .

$\displaystyle \frac{(1 - u) + u - u \cdot (1- u)}{u^{2}} = 2$ .

Solve this equation for $u$ :

$\displaystyle \frac{u^{2} + 1}{u^{2}} = 2$ .

$u^{2} + 1 = 2 u^{2}$ .

$u^{2} = 1$ .

Given that $0 \le u \le 1$ , $u = 1$ is the only possible solution.

$\cos^{2}{x} = 1$ ,

$x = k \pi$ , where $k\in \mathbb{Z}$ (i.e., $k$ is an integer.)

Given that $0 \le x < 2\pi$ ,

$0 \le k$ .

$k = 0$ or $k = 1$ . Accordingly,

$x = 0$ or $x = \pi$ .

8 0

2 years ago

Read 2 more answers

What is the distance between (3, -8) and (0, -2)

faltersainse [42]

The answer is 3√5. You use the distance formula: √((x2-x1)^2+(y2-y1)^2)

3 0

3 years ago

Read 2 more answers

Gelneren [198K]

<h3>Answer: Choice (a) $1,653.66</h3>

=====================================================

Work Shown:

Use the compound interest formula

A = P*(1+r/n)^(n*t)

A = 10000(1+0.039/1)^(1*4)

A = 11,653.65589441

A = 11,653.66

That's the amount of money Tammy will have at the end of 4 years.

Subtract off the principal from this value to get the interest.

interest = A - P

interest = 11,653.66 - 10,000

interest = 1,653.66

7 0

3 years ago

Find the missing dimension use the scale factor 1:12 model 32 cm find the actual in m

gizmo_the_mogwai [7]

Given:

The scale factor is 1:12.

Dimension of model = 32 cm

To find:

The actual dimension in m.

Solution:

Let x be the actual dimension.

The scale factor is 1:12 and the dimension of model is 32 cm.

$\dfrac{1}{12}=\dfrac{32}{x}$

On cross multiplication, we get

$x=32\times 12$

$x=384\ cm$

$x=3.84\ m$ $[\because 1\ m=100\ cm]$

Therefore, the actual dimension is 3.84 m.

6 0

2 years ago

-3(p-7) > 21 solve for p

Goryan [66]

Answer:

p < 0

Step-by-step explanation:

Given

- 3(p - 7) > 21

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.

p - 7 < - 7 ( add 7 to both sides )

p < 0

5 0

3 years ago