At the beginning of the school year dance, the ratio of the number of boys to the number of girls was 3: 7 , if there were 100 more girls than boys, how many boys were at the dance? …. how many girls were at the dance?

boys (b): b

girls (g): b + 100

total (T) = b + g

I am going to set up the proportion as "boys" to "total"

⇒

⇒ 3(2b + 100) = 10(b)

⇒ 6b + 300 = 10b

⇒          300 = 4b

⇒            75 = b

girls (g): b + 100   = (75) + 100   = 175

boys = 75, girls = 175

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq