Hello!
We can find the area of the trapezoid using the formula for area of a trapezoid:
FORMULA:
A = [(b + b) * h / 2]
SUBSTITUTE:
A = [(13.5 + 27.5) * 14 / 2]
SOLVE:
A = 41 * 14 / 2
A = 574 / 2
A = 287 cm²
So, the area of the trapezoid is 287 cm².
Answer:
These two triangles are <em>similar triangles. </em>This means that their side lengths are proportional to each other.
Thus, making line segment EC equal to "x", and BC equal to "y" we can write:
8/y = 28/(10+y)
The next step is to get rid of the fractions, which can be done by cross multiplying.
So we have:
8(10+y) = 28(y)
After distribution and some simplification, you should get the value of y.
80+8y = 28y
80 = 20y
80/20 = 20y/20
4 = y
y = 4
Knowing that y = BC, and y = 4, it is clear that BC = 4.
Since BC = 4, one can use the Pythagorean Theorem to solve for segment EC.
Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the side lengths of a right triangle, and c is the hypotenuse (in other words the longest side)
In our case, a and b are 8 and 4 (the order doesn't really matter here).
So we have: 8^2 + 4^2 = c^2
64 + 16 = c^2
80 = c^2
c = sqrt 80
c = 4 sqrt 5
And we arrive at the answer- EC = 4 sqrt 5, making B the correct choice.
Hope this helps!
Answer:
0.5234 = 52.34% probability that at least three of these students are in favor of the proposal to change the dress code.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they are in favor, or they are not. Students are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
18% of the students are in favor of changing the dress code.
This means that 
You randomly select 15 students
This means that 
What is the probability that at least three of these students are in favor of the proposal to change the dress code?
This is
In which
In which
0.5234 = 52.34% probability that at least three of these students are in favor of the proposal to change the dress code.
slightly over 88, so you will need 89 drums.
