When Jane starts she has a total of 30 pens, 9 black, 10 blue and 11 red. Two of the blue pens were lost. This dropped the number of blue pens to 8 and the total count of pens to 28.

To find the probability of something happening, take the total amount of things in question, the blue pens or 8, and compare them to total amount of pens which is now 28 pens.

 chance to draw a blue pen from the bag.

*The pitfall for these types of questions is to realize that not only does the count of blue pens decrease but also the total count of pens. Make sure to adjust both values. 

To find the probability of an event, find the number of ways that even could happen divided by the total number of outcomes of the event.

Number of ways we could spin a number divisible by 3: 
3,6,9 for 3 total
Number of different outcomes: 10.

Thus the probability is:

Probability of getting a head: 0.5
Probability of getting a tail: 0.5


The probability of not getting ANY tails = 0.5 * 0.5 * 0.5 * 0.5 * 0.5= 0.03125

The probability of getting AT LEAST 1 tail = 1 - 0.03125 = 0.969

Total Chocolates = 1/3 * 42 = 14

Total Coconuts = 1/6 * 42 = 7

There are 14 chocolates and 7 coconuts to choose from 42 total candies, and note that each time you select one candy, the total number of candies decreases by one. 

So assume that to arrive at the desired outcome of two chocolate and one coconut, you chose two chocolates and then a coconut. After picking out the first chocolate, there are now 13 chocolates to choose from 41 total candies. And after picking out the second chocolate, that leaves 7 coconuts to choose from 40 total candies.

The probability of that outcome = (14/42)(13/41)(7/40) = 0.01849, or just under 1.85%

However, there are two other sequences that could arrive at that desired outcome: chocolate, coconut, chocolate (which would be 14/42 * 7/41 * 13/40 = 1.85%) and coconut, chocolate, chocolate (which would be 7/42 * 14/41 * 13/40 = 1.85%). So summing all three probabilities of favorable outcomes gives you approximately 5.5% 

Tangent = Opposite / Adjacent

The tangent of an angle x is defined as

Use the definition of the tangent and plug in the values given:

tangent C = Opposite / Adjacent = AB / BC = 3 / 7

Therefore, BC = 7.

The cosine of the angle is  and since that is a reduced fraction, we know the hypotenuse is  and the adjacent side equals .  

The sine of the angle equals , and since the hyptenuse is already  we know that we must multiply the numerator and denominator by  to get the common denominator of .  Therefore, the opposite side equals .  

Since , the answer is . 

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.