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3 years ago

11

If a pair of 6-sided dice is tossed, what is the probability that both dice will show a number that is a multiple of 3 (i.E. 3 o

r 6)

1 answer:

kondaur [170]3 years ago

5 0

There are 4 possibilities out of the 36 ways the dice can land:

... (3, 3), (3, 6), (6, 3), (6, 6)

Hence, the probability of an outcome in this set is 4/36 = 1/9.

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How to move from fractions as a part to whole to ratios?

elena55 [62]

What do you mean
<span>How to move from fractions as a part to whole to ratios?</span>

3 0

3 years ago

21. In 4 + In(4x - 15) = In(5x + 19)

Alexxx [7]

Answer:

$x=-30;\quad \:I\ne \:0$

Step-by-step explanation:

$In\cdot \:4+In\left(4x-15\right)=In\left(5x+19\right)$

$\:4+In\left(4x-15\right):\quad -11nI+4nxI\\In\cdot \:4+In\left(4x-15\right)\\=4nI+nI\left(4x-15\right)\\\\\:In\left(4x-15\right):\quad 4nxI-15nI\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=In,\:b=4x,\:c=15\\=In\cdot \:4x-In\cdot \:15\\=4nxI-15nI\\=In\cdot \:4+4nxI-15nI\\\mathrm{Simplify}\:In\cdot \:4+4nxI-15nI:\quad -11nI+4nxI\\In\cdot \:4+4nxI-15nI\\\mathrm{Group\:like\:terms}\\=4nI-15nI+4nxI\\\mathrm{Add\:similar\:elements:}\:4nI-15nI=-11nI\\=-11nI+4nxI\\$

$\mathrm{Expand\:}In\left(5x+19\right):\quad 5nxI+19nI\\In\left(5x+19\right)\\=nI\left(5x+19\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=In,\:b=5x,\:c=19\\=In\cdot \:5x+In\cdot \:19\\=5nxI+19nI\\\\-11nI+4nxI=5nxI+19nI\\\\\mathrm{Add\:}11nI\mathrm{\:to\:both\:sides}\\-11nI+4nxI+11nI=5nxI+19nI+11nI\\Simplify\\4nxI=5nxI+30nI\\\mathrm{Subtract\:}5nxI\mathrm{\:from\:both\:sides}\\4nxI-5nxI=5nxI+30nI-5nxI\\\mathrm{Simplify}\\-nxI=30nI\\$

$\mathrm{Divide\:both\:sides\:by\:}-nI;\quad \:I\ne \:0\\\frac{-nxI}{-nI}=\frac{30nI}{-nI};\quad \:I\ne \:0\\\mathrm{Simplify}\\\frac{-nxI}{-nI}=\frac{30nI}{-nI}\\\mathrm{Simplify\:}\frac{-nxI}{-nI}:\quad x\\\frac{-nxI}{-nI}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{nxI}{nI}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{xI}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=x\\\mathrm{Simplify\:}\frac{30nI}{-nI}:\quad -30\\\mathrm{Apply\:the\:fraction\:rule}:$

$\quad \frac{a}{-b}=-\frac{a}{b}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{30I}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=-30\\x=-30;\quad \:I\ne \:0$

3 0

3 years ago

If a 30-60-90 right triangle has a hypotenuse 6, what is the length of the short leg?

Anton [14]

Answer:

$\sqrt[3]{3}$

Step-by-step explanation:

use the Pythagoras Theorem

Since you have the hypotenuse (6"), just go backwards. 62 = 36 = a2 + b2.

6 0

3 years ago

Which of the following are techniques used in geometric constructions with

Alisiya [41]

Answer= A
Explication

6 0

3 years ago

Read 2 more answers

Write equation in standard form y-1= -1/4(x-6)

const2013 [10]

The standard form:

$Ax+By=C$

---------------------------------------

$y-1=-\dfrac{1}{4}(x-6)$ <em>use distributive property</em>

$y-1=-\dfrac{1}{4}x+\dfrac{3}{2}$ <em>multiply both sides by 8</em>

$8y-8=-2x+4\cdot3$

$8y-8=-2x+12$ <em>add 2x to both sides</em>

$2x+8y-8=12$ <em>add 8 to both sides</em>

$\boxed{2x+8y=20}$

6 0

3 years ago