There are 20 families living in the Willbrook Farms Development. Of these families, 10 prepared their own federal income taxes for last year, 7 had their taxes prepared by a local professional, and the remaining 3 by H&R Block. a) What is the probability of selecting a family that prepared their own taxes? b) What is the probability of selecting two families, both of which prepared their own taxes?

a) 1/2

b) 9/40

Step-by-step explanation:

Given

Total number of families living in Willbrook Farms Development = 20

Number of families preparing their own federal income taxes for last year = 10

Number of families for which taxes were prepared by a local professional = 7

Number of families for which taxes were prepared by H&R Block = 3

a) Probability of selecting a family that prepared their own taxes = 10/20 = 1/2

b) The probability of selecting two families, both of which prepared their own taxes

10/20 * 9/20 = 9/40

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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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