The probability that leah will make the aa barracudas is 0.5, and the probability that she will be selected to represent her school in a public-speaking contest is 0.6. the probability of leah achieving both of these goals is 0.4.
a) are these two goals mutually exclusive? explain.
b) are these two goals independent? explain.
c) what is the probability that leah is either makes the barracudas or is picked for the public-speaking contest?

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