Directions: Type your solutions into this document and be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit. PROBLEM 1
A website reports that 70% of its users are from outside a certain country, and 60% of its users log on the website every day. Suppose that for its users from inside the country, that 80% of them log on every day. What is the probability that a person is from the country given that he logs on the website every day? Has the probability that he is from the country increased or decreased with the additional information?

The  probability is  

Yes with the additional information that the person logs on everyday the probability increased from    to

Step-by-step explanation:

From the question we are told that

   The probability that the user is from outside the country is  

    The probability that the user log on everyday is  

    The  probability that the user log on everyday and he/she is from inside the country  is  

Generally using Bayes theorem the the probability that a person is from the country given that he logs on the website every day is mathematically represented as

Here is the probability that the person log on every day and it is mathematically evaluated as

So

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places