There are 7 unsatisfied numbers : 1 ; 7 ; 11 ; 13 ; 17 ; 19 ; 23one of The number of satisfied numbers is : 25 - 7 = 18

The answer is : \(\dfrac{18}{25}\)

The similarity coefficient of 2 triangles is : \(\dfrac{10}{18}=\dfrac{5}{9}\)

The answer is : \(\left(\dfrac{5}{9}\right)^2=\dfrac{25}{81}\)

Let q and d be the number of quarter and dimes in the box respectively, then the total value of the money in the box is 25q + 10d cents. We have :

\(\left(1+10\%\right)\times25q+10d=\left(1+7.5\%\right)\left(25q+10d\right)\)

\(\Leftrightarrow110\%\times25q+10d=107.5\%\left(25q+10d\right)\)

\(\Leftrightarrow110\%\times25q-107.5\%\times25q=107.5\%\times10d-10d\)

\(\Leftrightarrow2.5\%\times25q=7.5\%\times10d\)

\(\Leftrightarrow\dfrac{q}{d}=\dfrac{7.5\%\times10}{2.5\%\times25}=\dfrac{3\times2}{5}=\dfrac{6}{5}\)

So, the answer is \(\dfrac{6}{5}\)

Applying the Thales theorem (intercept theorem), we deduce that the coordinates of P are :

\(\left(5\times\dfrac{2}{3};2\times\dfrac{1}{3}\right)=\left(\dfrac{10}{3};\dfrac{2}{3}\right)\)

We have : \(\dfrac{2}{3}=k.\dfrac{10}{3}\Leftrightarrow k=\dfrac{1}{5}\)

The answer is : \(30:10=3\) (cm)

The answer is : \(\dfrac{1}{3}=0.\left(3\right)\approx0.33\)

The answer is :

\(20\times10\%-20\times1\%=20\times9\%=1.8\) (km/h)

The answer is : \(\dfrac{12}{5}=2.4\) (mi)

The answer is : \(\dfrac{5}{3}=1.\left(6\right)\approx1.7\) (km)

Rolling the die twice can lead to : 8 x 8 = 64 (results)

There are : \(8+7+6+...+1=\dfrac{8.9}{2}=36\) (results) that the second number rolled is not smaller than the first number 

The answer is : \(\dfrac{36}{64}=\dfrac{9}{16}\)

AD = (AB + AD) - AB = 34 : 2 - 5 = 12 (cm)

Applying the Pythagorean theorem, we have :

\(BD=\sqrt{AB^2+AD^2}=\sqrt{5^2+12^2}=13\) (cm)

The answer is : \(12+5+13=30\) (cm)

7 feet = 84 inches

Since 84 = 16 x 5 + 4, Sue can cut 16 5-inch-pieces

Applying the Pythagorean theorem, we deduce that the answer is :

\(\sqrt{3^2+4^2}=5\) (units)

We notice that each of the first and the last table has 1 more person than the remaining tables (5 - 4 = 1). Let n be the number of the tables in the row, then :

\(4n+1+1=50\Leftrightarrow4n=48\Leftrightarrow n=12\)

So, the answer is 12

The change is : \(5.00-1.57\times3=0.29\)

So, Gloria could get 5 coins at least, including 1 quarter and 4 pennies

The answer is :

\(3.16\times10^{-23}\times10^9=3.16\times10^{-14}\) (g)

There are 3 choices to choose the appetizer, 4 choices to choose the entrée, \(\dfrac{5.4}{2}=10\) choices to choose 2 side dishes and 6 choices to choose the dessert

So, the answer is : \(3.4.10.6=720\) (meals)

It takes 15 machines : \(15\times\dfrac{6000}{500}=180\) (minutes) to make 6000 raviolis

It takes 75 machines : \(180:\dfrac{75}{15}=36\) (minutes) to make 6000 raviolis

M is the 13^th letter in the alphabet, so M is at 12

The answer is :

\(\dfrac{\left(M-4\right)+\left(M+4\right)}{2}=M=12\)

Applying the Pythagorean theorem, the length of AB is :

\(\sqrt{8^2+2^2}=2\sqrt{17}\) (units)