One Australian dollar is equivalent to 86 cents, or $0.86, in American money, so divide $600 dollars by this conversion factor. $600 is equivalent to

$\displaystyle 600 \div 0.86 \approx 698$ Australian dollars.

If there are 900 peanuts and 1 in 9 will be one-podded, that means that 100 will be one-podded. 

$\displaystyle 900\cdot \frac{1}{9}=100$

Three quarters of these 100 one-podded peanuts will be of smaller than average size. Three quarters of of 100 is 75. Therefore, 75 is the correct answer. 

The first step is to solve for x.  

$\displaystyle x=\frac{7}{2}\cdot \frac{4}{7}-1$

$\displaystyle x=2-1$

$\displaystyle x=1$

If there are 1x chocolate muffins and 2y banana muffins, for a total of 13 muffins then:

$\displaystyle 1x+2y=13$

$\displaystyle 1+2y=13$

$\displaystyle 2y=12$

Since the number of banana muffins remaining is 2y, there are 12 banana muffins left. 

First determine how many boys and girls are currently in the class.

$\displaystyle \frac{4}{9}\cdot 36=16$boys in the class, which means that there are 20 girls.

When the 6 students drop the new class size will be 30, which will be made up of $\displaystyle 20-2=18$ girls and $\displaystyle 16-4=12$ boys.

$\displaystyle \frac{18}{30}=60\%$

To find $\displaystyle \frac{1}{15}$ of one minute in terms of seconds, you need to first convert one minute to its value in seconds, which is 60 seconds.

Now, you just need to find the value for $\displaystyle \frac{1}{15}$ of 60, which you determine by multiplying the two values:

$\displaystyle \frac{1}{15} \times 60 = \frac{60}{15}$

You can simplify the above fraction by division, which will you give you your correct answer in seconds:

$\displaystyle \frac{60}{15} = 4$ 

Your answer is 4 seconds.

Since we are multiply fractions, multiply the numerator with numerator, and denominator with denominator.  Simplify if possible.

$\displaystyle \frac{6}{7}\times \frac{1}{7}= \frac{6}{49}$

Rewrite the expression using a division sign.

$\displaystyle \frac{2}{3}\div 6$

Convert the sign to a multiplication sign, and take the inverse of the second term.

$\displaystyle \frac{2}{3}\times \frac{1}{6} = \frac{1}{9}$

The ratio of the height of an object to the length of the shadow it casts at a point in time is the same for all objects, so, if we let the length of the shadow cast by the second tree be $\displaystyle N$:

$\displaystyle \frac{30}{N} = \frac{M}{20}$

Set the cross-products equal to each other and solve for $\displaystyle N$

$\displaystyle M \cdot N = 20 \cdot 30$

$\displaystyle M \cdot N = 600$

$\displaystyle M \cdot N\div M = 600 \div M$

$\displaystyle N = \frac{600}{M}$, the correct choice.

The ratio of the width of the scale model to its length is the same as the comparable ratio for the actual car, so we can set up this equation:

$\displaystyle \frac{W}{L} = \frac{1.8}{4.5} = \frac{1.8 \cdot 10 }{4.5\cdot 10 }= \frac{18 }{45}= \frac{18 \div 9}{45 \div 9}=\frac{2}{5}$

$\displaystyle \frac{W}{L} \cdot L =\frac{2}{5}\cdot L$

$\displaystyle W=\frac{2}{5} L$

An easier way to look at the number of cookies Edna can make with her sugar is as follows:

$\displaystyle 1\frac{1}{2}$ cups of sugar go into making 24 cookies, so

$\displaystyle 1\frac{1}{2} \times 2 = 3$ cups of sugar go into making $\displaystyle 24 \times 2 = 48$ cookies.

1 cup of sugar, therefore, goes into making $\displaystyle 48 \div 3 = 16$ cookies.

$\displaystyle N$ cups go into making $\displaystyle 16 \cdot N$, or $\displaystyle 16 N$, cookies. This is the correct response.