The ratio of total members in the group stands at 5:7, meaning that among every 7 members, there are 5 men and 2 women. We can set it up as a proportion: 5:7 = x:735, leading to the equation 5/7 = x / 735. By cross-multiplying, we get 7*x = 5 * 735, simplifying to 7*x = 3675. Dividing this by 7 results in x = 525. Therefore, there will be 525 men in total.
The bathtub's depth measures 18 inches
It takes 2 minutes to fill 3 inches of the bathtub
Subsequently
The remaining depth needed for filling with water = (18-3) inches
= 15 inches
The time needed to fill the remaining 15 inches of the bathtub = (15*2)/3 minutes
= 30/3 minutes
= 10 minutes
Therefore, John is right in believing that it will require an additional 10 minutes to fill the tub to the brim at the same rate.
Hope this clarifies things!
Answer:
C. The hypotenuse measures twice the distance of the shorter leg.
B. The longer leg is √3 times the length of the shorter leg.
Step-by-step explanation:
A 30-60-90 triangle is considered a right triangle. Triangles containing a right angle are classified as right triangles. Only one right angle can exist in such a triangle. The representation of this case is illustrated below. Let’s clarify why the proposed statements are valid:
The hypotenuse of a right triangle is always opposite to the right angle. If we designate
as the shorter leg, the sine law affirms that the hypotenuse is:

This indicates that the hypotenuse is double the length of the shorter leg
The longer leg, which we can call
, can be determined with the Pythagorean Theorem:

Thus, it is accurate that the longer leg is √3 times longer than the shorter leg.