Check all the statements that are true:

a. a probability of 1/10 indicates an unusual event.

b. when an event is almost certain to happen, its complement will be an unusual event.

c. you toss a coin and roll a die. the event "tossing tails and rolling a 1 or a 3" is a simple event

d. you toss a fair coin nine times and it lands tails up each time.

e. the probability it will land heads up on the tenth toss is greater than 0.5.

a , b,  d

Step-by-step explanation:

The probability of 1/10 is simply an unusual occurrence , while the complement or opposite of a certain event is an unusual event. Tossing a coin and rolling a die together is a compound event. A fair coin when tossed can land tails every other time but that does not change the probability for head or tail which is always 0.5.

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