All Answers 358087 Answers

planters      plntrs   6 consonants out of 8 letters

P that the first one is  a consonant is 6/8

P that the second one is a consonant is 5/7

P that the 3rd one is a consonant is 4/6

p(all 3 are consonants) =    $${\frac{{\mathtt{6}}}{{\mathtt{8}}}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{5}}}{{\mathtt{7}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{4}}}{{\mathtt{6}}}}\right) = {\frac{{\mathtt{5}}}{{\mathtt{14}}}} = {\mathtt{0.357\: \!142\: \!857\: \!142\: \!857\: \!1}}$$

$$\\\boxed{a^3+b^3=(a+b)(a^2-ab+b^2)}\\\\
x^3+\left(\frac{1}{8}\right)^3
=\left(x+\frac{1}{8}\right)\left(x^2-\frac{x}{8}+\frac{1}{64}\right)$$

I'll give you more points too saseflower because you always give such good answers:D

Anon's answer is correct. :)

Here is another answer :)   they will give the same answer.

$$\\1.06^x=2\\\\
log(1.06^x)=log2\\\\
xlog1.06=log2\\\\
x=\frac{log2}{log1.06}\\\\$$

1+1=2

if u didnt kno...

the web2 calc is really good  for many things but its graphing features are not great.

I suggest that you use

$$\\12<3y<6 \\
4

this has no solutions.

if 4<y    then     y>4  

Y cannot be  greater than 4 and less than 2 at the same time.  :)

Use Desmos

Maybe this will help.  There are a lot of good resources on the net. 

Given that C must be between 0 and pi/3, the graph below shows that there is only one solution:

I don't know why WolframAlpha doesn't find this.

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Hi SoulReaper.  It is easier to multiply both sides by 10 first to get rid of all the fractions.

But the answer will be the same.  :))

I'm all dolled up, packed my essential.

I feel soooo good

Who's on the menu tonight.

Where's that Zee-man

I am so excited (and hungry).

Thanks Alan,

Usin Alan's pic

(II) if SinB+SinC=1, then what is the shape of this triangle?

sinB = 1/2

SinC=1/2

so statement is true

So B=C=pi/6    is one answer.

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May I ask 2 questions please Alan

1) How do you know that is the only answer?    and

2) Why didn't Wolfram|alpha give me that answer?

Thankyou.:)

$$3x+2[4-10x+5]$$

$$3x+8-20x+10$$

$$-17x+18?$$

$$\\f(x)= 3x^3-x^2-\frac{2x}{x}(x+1)^2\\
x\ne0\\
f(x)= 3x^3-x^2-2(x+1)^2\\$$

$${\mathtt{9}}{\mathtt{\,\times\,}}{\mathtt{45}} = {\mathtt{405}}$$

1+1 can be: 
- 10 in base 2 
- 2 in base n, for n>2 
- 1.99999967 If you have a crappy computer. >_>

Yes.

The formula for time is: T (period) = 1 / f (frequency)

The frequency (f) is the reciprocal of the period (T) : f = 1/T

A team consists of 6 boys and 4 girls and the other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?

Consider team A

girl 1 three to choose from

girl 2 three to choose from

etc

3*4=12

boys

6*5=30

Total=  12+30=42

Maybe, if you are very lucky that might be right.  

35.

100% of 100 is 100, or in fraction form, 100/100.

Similarly, 10% of 100 is 10, 20% of 100 is 20, and 30% of 100 is 30.

Therefore 35% * 100 = 35.

15log(2x) = 60

Divide both sides by 15

log(2x) = 4

10^log(2x) is the same as just 2x, so

10^log(2x)= 10⁴  gives 2x = 10⁴

so x = 10⁴/2 or x = 5000

Check:

$${\mathtt{15}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{5\,000}}\right) = {\mathtt{60}}$$ 

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I get the same as Melody, though my derivation is much longer!

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$${{log}}_{{\mathtt{1.06}}}{\left({\mathtt{2}}\right)}$$

Have a look at the following for part (ii):

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