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1 year ago

Given cosθ=√3/3 and sinθ<0. What is the value of sinθ?

1 answer:

5 0

$\sin^{2} \theta+\cos^{2} \theta=1 \\ \\ \sin^{2} \theta+\left(\frac{\sqrt{3}}{3} \right)^{2}=1 \\ \\ \sin^{2} \theta+\frac{1}{3}=1 \\ \\ \sin^{2} \theta=\frac{2}{3} \\ \\ \theta=-\frac{\sqrt{2}}{\sqrt{3}}=\boxed{-\frac{\sqrt{6}}{3}}$

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What is the base 2 representation of 129?

Diano4ka-milaya [45]

Answer:

either 81 or 81.8

Step-by-step explanation:

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3 years ago

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A pair of fair dice is cast. Let Edenote the event that the number landing uppermost on the first die is a 1 and let Fdenote the

iris [78.8K]

Answer:

They are not independent

Step-by-step explanation:

Given

E = Occurrence of 1 on first die

F = Sum of the uppermost occurrence in both die is 5

Required

Are E and F independent

First, we need to list the sample space of a roll of a die

$Event\ 1 = \{1,2,3,4,5,6\}$

Next, we list out the sample space of F

$Event\ 2 = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,\$

$6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}$

In (1): the sample space of E is:

$E = \{1\}$

So:

$P(E) = \frac{n(E)}{n(Event\ 1)}$

$P(E) = \frac{1}{6}$

In (2): the sample space of F is:

$F = \{5,5,5,5\}$

So:

$P(F) = \frac{n(F)}{n(Event\ 2)}$

$P(F) =\frac{4}{36}$

$P(F) =\frac{1}{9}$

For E and F to be independent:

$P(E\ and\ F) = P(E) * P(F)$

Substitute values for P(E) and P(F)

This gives:

$P(E\ and\ F) = \frac{1}{6} * \frac{1}{9}$

$P(E\ and\ F) = \frac{1}{54}$

However, the actual value of P(E and F) is 0.

This is so because $E = \{1\}$ and $F = \{5,5,5,5\}$ have 0 common elements:

So:

$P(E\ and\ F) = 0$

Compare $P(E\ and\ F) = \frac{1}{54}$ and $P(E\ and\ F) = 0$ .

These values are not equal.

Hence: the two events are not independent

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3 years ago

At the dog park on Monday, the ratio of small dogs to all dogs was three to seven. A total of 42 dogs were at the park. How many

faust18 [17]

Answer:

18 small dogs

Step-by-step explanation:

Given the ratio of small dogs to all dogs was 3:7

Total dogs that are there = 42 dogs

Number of small dogs there = ratio of small/ratio of all dogs * Total dogs

Number of small dogs there = 3/7 * 42

Number of small dogs there = 3 * 6

Number of small dogs there = 18

Hence there are 18 small dogs there

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3 years ago

24s2 - 30s + 12 ÷ 6s

Inessa [10]

Answer:

24x2

with MDAS :

=48/6

=30-7

=23+12

without MDAS:

=48-30

=18+12

=30/6

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3 years ago

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Eleni is n years old. In thirteen years she will be twenty four years old-

Alja [10]

Well do 24 - 13.

You should get 11.

N = 11.

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