Raymond can type 40 words each minute. How many words can he type in 8 minutes?
2 answers:
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Answer:
1.15%
Step-by-step explanation:
To get the probability of m independent events you multiply the individual probability of each event. In this case we have m independent events, each one with the same probability, therefore:
This is a particlar scenario of binomial distribution problem. So the binomial distribution questions are about the number of success of m independent events, where every individual event has the same p probability. In the question we have 20 events and each event has a probability of 80%. The binomial distribution formula is:
n is the number of events
k is the number of success
p is the probability of each individual event
is the binomial coefficient
the binomial coefficient allows to find the subsets of k elements in a set of n elements. In this case there is only one subset possible since the only way to get 20 of 20 correct questions is to getting right all questions (for getting 19 of 20 questions there are many ways, for example getting the first question wrong and all the other questions right, or getting second questions wrong and all the other questions right, etc).
therefore, for this questions we have:
Answer:
114.02 meters
Step-by-step explanation:
The information you're given about the tree will form a triangle, with the three corners being the top of the tree, the point where the tree meets the ground, and the specified point 41.5 meters from the tree. The angle of elevation (70°) is the angle made where the line representing the ground and the line connecting the top of the tree to the ground at the specified point connect.
The angle where the tree meets the ground is 90°, so the triangle a right triangle.
So this all means you know one angle of a right triangle (70°) and the side adjacent to this angle (41.5 meters). You're solving for the height of the tree, which is the side opposite of the angle you know. You can solve using either <em>Sine, Cosine, </em>or <em>Tangent.</em>
Use the acronym SOHCAHTOA to figure out which of those three functions to use. Feel free to look this up for more information if you haven't heard of it before. In this case, we're using Tangent (TOA = Tangent, Opposite side, Adjacent side)
To solve using any of those three functions, you'll need a scientific calculator. On your calculator, you'll see the buttons <em>SIN, COS, </em>and<em>TAN.</em> For this problem, press <em>TAN</em> and you'll see something appear that says <em>tan (___)</em>. You'll need to input a number to get your answer, and here's how to find that number:
Again referencing SOHCAHTOA, the "TOA" part lists Opposite first and then Adjacent. This is because you're going to write a fraction with those two numbers, and since Opposite is first, it's the numerator. That means that Adjacent is the denominator. We don't know the value of the opposite side, so it'll be represented by <em>x</em>, and we do know the value of the adjacent side, 41.5. This means the fraction is .
This isn't the number to input into the calculator -- you need to isolate the variable:
The original equation is:
tan 70 = x/41.5
Multiply both sides by 41.5 (To cancel out the denominator and isolate <em>x</em>)
tan 70 (41.5) = x
Now you've got the equation for <em>x, </em>you're ready to put this in your calculator.
What appeared on your calculator was:
tan(__)
Input like follows:
(tan(70))41.5
The brackets are needed like that so the calculator knows to multiply the entire thing by 41.5. You might get a wrong answer otherwise.
Hit enter, and you'l get the height of the tree:
114.02 meters