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goblinko [34]
3 years ago
13

The percentages of voters classed as Liberals in three different election districts are divided as follows: in the first distric

t, 21 percent; in the second district, 45 percent; and in the third district, 75 percent. If a district is selected at random and a voter is selected at random from that district, what is the probability that she will be a Liberal
Mathematics
1 answer:
ASHA 777 [7]3 years ago
8 0

Answer:

47%

Step-by-step explanation:

Chance of liberal in first district = 21%

Chance of liberal in second district = 45%

Chance of liberal in third district = 75%

Assuming that all districts are equally likely to be selected, the probability that a randomly selected voter is a liberal is given by the average of the probability of a voter being a liberal in each district:

P = \frac{0.21+0.45+0.75}{3}= 47\%

The probability that she will be a Liberal is 47%.

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Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo
mart [117]

Answer:

y  = -6(x - \frac{1}{2})^2 -\frac{7}{2}

Step-by-step explanation:

Given:

y = -6x^2 + 3x + 2

Required

Rewrite in vertex form

The vertex form of an equation is in form of: y = a(x - h)^2+ k

Solving: y = -6x^2 + 3x + 2

Subtract 2 from both sides

y - 2 = -6x^2 + 3x + 2 - 2

y - 2 = -6x^2 + 3x

Factorize expression on the right hand side by dividing through by the coefficient of x²

y - 2 = -6(x^2 + \frac{3x}{-6})

y - 2 = -6(x^2 - \frac{3x}{6})

y - 2 = -6(x^2 - \frac{x}{2})

Get a perfect square of coefficient of x; then add to both sides

------------------------------------------------------------------------------------

<em>Rough work</em>

The coefficient of x is \frac{-1}{2}

It's square is (\frac{-1}{2})^2 = \frac{1}{4}

Adding inside the bracket of -6(x^2 - \frac{x}{2}) to give: -6(x^2 - \frac{x}{2} + \frac{1}{4})

To balance the equation, the same expression must be added to the other side of the equation;

Equivalent expression is: -6(\frac{1}{4})

------------------------------------------------------------------------------------

The expression becomes

y - 2 -6(\frac{1}{4})= -6(x^2 - \frac{x}{2} + \frac{1}{4})

y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})

y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})

Factorize the expression on the right hand side

y - 2 -\frac{3}{2}= -6(x - \frac{1}{2})^2

y - (2 +\frac{3}{2})= -6(x - \frac{1}{2})^2

y - (\frac{4+3}{2})= -6(x - \frac{1}{2})^2

y - (\frac{7}{2})= -6(x - \frac{1}{2})^2

y  +\frac{7}{2} = -6(x - \frac{1}{2})^2

Make y the subject of formula

y  = -6(x - \frac{1}{2})^2 -\frac{7}{2}

<em>Solved</em>

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3 years ago
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$2,697 is correct :)


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Answer:

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Step-by-step explanation:

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