Find the slope of the line through the given points. (10, 11) and (15, 16)
1 answer:
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Não, não podemos fazer um triângulo com os comprimentos dos lados de 2 cm, 3 cm e 10 cm. Isso ocorre porque a soma de 2+3 < 10. (in english: No, we cannot make a triangle with the side lengths of measurement 2 cm, 3 cm, and 10 cm. This is because sum of 2+3 < 10).
<h3>What is triangle inequality theorem?</h3>Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
Now, for this case, the sides given are:
- a =2 cm,
- b = 3 cm,
- and c = 10 cm
But we see that:
a+ b = 5 cm which is < c which is of 10 cm.
Thus, these lengths don't satisfy the triangle inequality theorem, and therefore, cannot be sides of any triangle.
Learn more about triangle inequality theorem here:
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Answer:
(a) 0.152
(b) 0.789
(c) 0.906
Step-by-step explanation:
Let's denote the events as follows:
<em>F</em> = The word free occurs in an email
<em>S</em> = The email is spam
<em>V</em> = The email is valid.
The information provided to us are:
- The probability of the word free occurring in a spam message is,
- The probability of the word free occurring in a valid message is,
- The probability of spam messages is,
First let's compute the probability of valid messages:
(a)
To compute the probability of messages that contains the word free use the rule of total probability.
The rule of total probability is:
The probability that a message contains the word free is:
The probability of a message containing the word free is 0.152
(b)
To compute the probability of messages that are spam given that they contain the word free use the Bayes' Theorem.
The Bayes' theorem is used to determine the probability of an event based on the fact that another event has already occurred. That is,
The probability that a message is spam provided that it contains free is:
The probability that a message is spam provided that it contains free is approximately 0.789.
(c)
To compute the probability of messages that are valid given that they do not contain the word free use the Bayes' Theorem. That is,
The probability that a message is valid provided that it does not contain free is:
The probability that a message is valid provided that it does not contain free is approximately 0.906.