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3 years ago

Find the probability for choosing a letter at random from the word: Probability P(not P) A.) 1/11 B.) 2/11 C.) 5/11 D.) 10/11

Mathematics

1 answer:

elixir [45]3 years ago

6 0

Answer:

D.) 10/11

Step-by-step explanation:

Here the given word Probability has 11 letters in it. And we have to calculate the Probability of not selecting a letter P from the above word.

So the formula for calculating any probability is Total Favorable outcomes / Total number of outcomes.

Here total number of outcomes are 11 as word Probability has 11 letters.

So the probability of selecting letter P from word Probability = $\frac{1}{11}$

Now the P(not P) = 1 - P(selecting letter P)

= 1 - $\frac{1}{11}$ = $\frac{10}{11}$

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Please someone help me to prove this..

Pachacha [2.7K]

Answer: see proof below

<u>Step-by-step explanation:</u>

Use the following Sum to Product Identities:

$\sin x+\sin y=2\sin \bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\sin x-\sin y=2\cos \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x+\cos y=2\cos \bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x+\cos y=-2\sin \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)$

<u>Proof LHS → RHS</u>

$\text{LHS:}\qquad \qquad \qquad \dfrac{\sin 5-\sin 15+\sin 25 - \sin 35}{\cos 5-\cos 15- \cos 25 + \cos 35}$

$\text{Reqroup:}\qquad \qquad \qquad \dfrac{(\sin 25+\sin 5)-(\sin 35 + \sin 15)}{(\cos 35+\cos 5)-(\cos 25 + \cos 15)}$

$\text{Sum to Product:}\quad \dfrac{2\sin \bigg(\dfrac{25+5}{2}\bigg)\cos \bigg(\dfrac{25-5}{2}\bigg)-2\sin \bigg(\dfrac{35+15}{2}\bigg)\cos \bigg(\dfrac{35-15}{2}\bigg)}{2\cos \bigg(\dfrac{25+15}{2}\bigg)\cos \bigg(\dfrac{25-15}{2}\bigg)-2\cos \bigg(\dfrac{35+5}{2}\bigg)\cos \bigg(\dfrac{35-5}{2}\bigg)}$ $\text{Simplify:}\qquad \qquad \dfrac{2\sin 15\cos 10-2\sin 25\cos 10}{2\cos 20\cos 15-2\cos 20\cos 5}$

$\text{Factor:}\qquad \qquad \dfrac{2\cos 10(\sin 15-\sin 25)}{2\cos 20(\cos 15-\cos 5)}$

$\text{Sum to Product:}\qquad \dfrac{\cos 10\bigg[2\cos \bigg(\dfrac{15+25}{2}\bigg)\sin \bigg(\dfrac{15-25}{2}\bigg)\bigg]}{\cos 20\bigg[-2\sin \bigg(\dfrac{15+5}{2}\bigg)\sin \bigg(\dfrac{15-5}{2}\bigg)\bigg]}$

$\text{Simplify:}\qquad \qquad \dfrac{\cos 10[2\cos 20\sin (-5)]}{\cos 20[-2\sin 10\sin 5]}\\\\\\.\qquad \qquad \qquad =\dfrac{-2\cos10 \cos 20 \sin 5}{-2\sin 10 \cos 20 \sin 5}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 10}{\sin 10}\\\\\\.\qquad \qquad \qquad =\cot 10$

LHS = RHS: cot 10 = cot 10 $\checkmark$

8 0

3 years ago

25 percent of what is 38?

AnnyKZ [126]

Answer: 152

Step-by-step explanation:

Let the number = x.

Therefore, x*25% = 38

25% as a decimal is 0.25.

So, 0.25x = 38

We can divide both sides by 0.25:

x = 152

8 0

2 years ago

How to prove it equal 8?

iogann1982 [59]

Answer:

The answer equals -8

Step-by-step explanation:

Order of Operations: BPEMDAS

FOIL - First, Outside, Inside, Last

Step 1: Write out expression

$(\sqrt{4-3i} -\sqrt{4+3i})^6$

Step 2: Expand

$(\sqrt{4-3i} -\sqrt{4+3i})(\sqrt{4-3i} -\sqrt{4+3i})(\sqrt{4-3i} -\sqrt{4+3i})(\sqrt{4-3i} -\sqrt{4+3i})(\sqrt{4-3i} -\sqrt{4+3i})(\sqrt{4-3i} -\sqrt{4+3i})$