There were 3 bananas, 4 apples, and 3 oranges in a basket. What is the probability that Ace will pick a banana from the basket?

Mathematics

1 answer:

Jlenok [28]4 years ago

5 0

0.3 or 30%. The probability that Ace pick a banana from a basket that content others fruits is 0.3.

The key to solve this problem is using the equation of probability $P(A)=\frac{n(A)}{n}$ where n(A) the numbers of favorables outcomes and n the numbers of possible outcomes.

There are in the basket 10 fruits in total (3 bananas + 4 apples + 3 oranges = 10fruits). Then, extract a fruit can occur in 10 ways, this is n. There is only 3 bananas in the basket, so the fruit that ACE will pick be a banana can occur in 3 ways out of 10, so 3 is n(A).

Solving the equation:

$P(A)=\frac{3}{10}=0.3$

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Given sin(−θ)=−1/6 and tanθ=−√35/35 What is the value of cosθ?

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Answer:

$cos(\theta)=-\frac{\sqrt{35} }{6}$

Step-by-step explanation:

Recall the negative angle identity for the sine function:

$sin(- \theta)=-sin(\theta)$

Then, we can find the value of $sin(\theta)$ :

$sin(\theta)=-sin(-\theta)\\sin(\theta) =-(-\frac{1}{6} )\\sin(\theta)= \frac{1}{6}$

Now recall the definition of the tangent function:

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

Therefore, now that we know the value of $sin(\theta)$ , we can solve in this equation for $cos(\theta)$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\\-\frac{\sqrt{35} }{35} =\frac{1/6}{cos(\theta)} \\cos(\theta)=-\frac{\frac{1}{6} }{\frac{\sqrt{35} }{35} } \\cos(\theta)=-\frac{35}{6\,\sqrt{35} } \\cos(\theta)=-\frac{\sqrt{35} }{6}$