Suppose a class of 50 students has 20 males and 30 females. The insturctor will pick 1 (different) student to compete in 3 different national competitions--in mathematics, chemistry, and English. a. What is the probability that there is exactly 1 female student selected?b. What is the probability that there are at least 2 male students selected?

(a)0.2908

(b)0.349

Step-by-step explanation:

Total Number of Students=50

Number of Male Students=20

Number of Female Students=30

Note that the selection is without replacement as each student selected is different. Also the student could be picked for any of Mathematics, Chemistry or English competitions in that order.

(a)Probability of Picking exactly one female student.

P(Exactly one Female)= P(FMM) OR P(MFM) OR P(MMF)

Where P(FMM) means a female is selected for Mathematics, Male for Chemistry and Male for English respectively.

P(FMM) OR P(MFM) OR P(MMF)

=0.2908

(b)Probability that at least 2 male students are selected.

P(at least 2 male students are selected) = P(FMM) OR P(MFM) OR P(MMF) OR P(MMM)

P(MMM) =0.0582

Recall from Part (a) that:

P(FMM) OR P(MFM) OR P(MMF) =0.2908

Therefore:

P(at least 2 male students are selected) =0.2908+0.0582 =0.349

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.

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