Three plants, C1, C2 and C3, produce respectively 10, 50 and 40 percent of a company’s output. Although plant C1 is a small plant, its manager believes in high quality and only 1 percent of its products are defective. The other two, C2 and C3, are worse and produce items that are 3 and 4 percent defective, respectively. All products are sent to a central warehouse. One item is selected at random and observed to be defective. Find the conditional probability that it comes from plant C1.

exactly you go it

step-by-step explanation:

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