Break it down into two parts. First, what is the probability of drawing a blue marble on the first draw?Since there are 5 blue marbles and 10 total, the probability is 5⁄10, or 1/2. Now since we no longer have that blue marble, there are 4 blue marbles and 9 total. The chances of drawing a blue marble are 4/9. Therefore, the chance that both marbles drawn are blue is the chance that the first one is blue times the chance that the second one is blue. 1/2 * 4/9 = 4/18 = 2/9 Remember, math is always trying to trick you. It wants you to try and do the whole big problem at once, which can be difficult. Break it down into smaller problems, then use your answers to small parts to find the answer to the big question. Hope that helps,

7 0

3 years ago

Convert 62% into a fraction

NISA [10]

Answer:

62% = 31 / 50

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

2ᵃ = 5ᵇ = 10ⁿ. Show that n = <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bab%7D%7Ba%20%2B%20b%7D%20" id="TexFormula1" titl

11Alexandr11 [23.1K]

There are two ways you can go about this: I'll explain both ways.

Solution 1: Using logarithmic properties
The first way is to use logarithmic properties.

We can take the natural logarithm to all three terms to utilise our exponents.

Hence, ln2ᵃ = ln5ᵇ = ln10ⁿ becomes:
aln2 = bln5 = nln10.

What's so neat about ln10 is that it's ln(5·2).
Using our logarithmic rule (log(ab) = log(a) + log(b),
we can rewrite it as aln2 = bln5 = n(ln2 + ln5)

Since it's equal (given to us), we can let it all equal to another variable "c".

So, c = aln2 = bln5 = n(ln2 + ln5) and the reason why we do this, is so that we may find ln2 and ln5 respectively.

c = aln2; ln2 = $\frac{c}{a}$
c = bln5; ln5 = $\frac{c}{b}$

Hence, c = n(ln2 + ln5) = n( $\frac{c}{a}$ + $\frac{c}{b}$ )
Factorise c outside on the right hand side.

c = cn( $\frac{1}{a}$ + $\frac{1}{b}$ )
1 = n( $\frac{1}{a}$ + $\frac{1}{b}$ )
$\frac{1}{n}$ = $\frac{1}{a}$ + $\frac{1}{b}$

$\frac{1}{n}$ = $\frac{a + b}{ab}$
and thus, n = $\frac{ab}{a + b}$

Solution 2: Using exponent rules
In this solution, we'll be taking advantage of exponents.

So, let c = 2ᵃ = 5ᵇ = 10ⁿ
Since c = 2ᵃ, 2 = $\sqrt[a]{c}$ = $c^{\frac{1}{a}}$

Then, 5 = $c^{\frac{1}{b}}$
and 10 = $c^{\frac{1}{n}}$

But, 10 = 5·2, so 10 = $c^{\frac{1}{b}}$ · $c^{\frac{1}{a}}$
∴ $c^{\frac{1}{n}}$ = $c^{\frac{1}{b}}$ · $c^{\frac{1}{a}}$

$\frac{1}{n}$ = $\frac{1}{a}$ + $\frac{1}{b}$
and n = $\frac{ab}{a + b}$

4 0

3 years ago