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3 years ago

The results of an election are shown in the table below.

Mathematics

1 answer:

vazorg [7]3 years ago

4 0

We are given the results of an election:

Candidate Fraction of votes

Johnson = $\frac{1}{9}$

Smith = $\frac{7}{18}$

Dragovic = $\frac{1}{2}$

Now, we need to find the difference between the fractions of votes received by Dragovic and Johnson.

Therefore, difference is :

$\frac{1}{2} - \frac{1}{9}$

Taking common denominator of 2 and 9 is 18.

$=\frac{1\times9}{2\times 9} - \frac{1\times 2}{9\times 2}$

$=\frac{9}{18} - \frac{2}{18}$

$=\frac{9-2}{18}$

$=\frac{7}{18}$

Therefore, the difference between the fractions of votes received by Dragovic and Johnson is $\frac{7}{18}$ .

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2 years ago

What's the ratio equivalent to 15 to 60.

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levacccp [35]

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3 years ago

How do you solve x+4=10^x

raketka [301]

Two ways to solve the problem:

A. By graphing f(x)=10^x and g(x)=x+4.
The intersection(s) will be the solution.
See graph below, approximate solutions: (-4,0),(0.66, 4.67)

B. Refine approximate solutions using Newton's method
Let h(x)=f(x)-g(x) = 10^x-x-4 ...............(1)
we calculate the derivative, h'(x) = log(10)*10^x-1 [ note:log(x) means ln(x) ]
and use Newton's iterative formula to find successive approximations to the root, basically refining the approximate solutions.
The iterative formula for nth approximation $x_n$ is given by
$x_n$ = $x_{n-1}$ - h( $x_n$ ) / h'( $x_n$ )....(2)

Using initial approximation (-4,0), we have x0=-4
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=-4 - (10^(-4)-(-4)-4)/(log(10*10^(-4)-1)
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Repeating the same for second approximation, x2, we get
x2=-3.99989997696619 which is accurate to 14 places after decimal

Now we can refine the other approximate solution, x0=0.66 to find
x1=0.669356
x2=0.6692468481102326
x3=0.669246832877748
x4=0.6692468328777476
So we will accept x=0.669246832877748

So the solutions are S={-3.99989997696619,0.6692468328777476} both accurate to 14 places after the decimal

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3 years ago