Answer:
Part 1) 
The value of x is 
Part 2) 
Step-by-step explanation:
Part 1) Simplify the given equation
we have

In the left side, remove the parenthesis and apply the distributive property
Remember that

so


Combine like terms left side

Adds 7x both sides

subtract 15 both sides

Divide by 7 both sides

Part 2) Solve for x.

Apply distributive property both sides

Group terms that contain the same variable

Combine like terms

Consider such events:
A - selected student is freshmen
B - selected student is girl
- selected student is freshman is girl
- choosen girl is freshmen.
Use formula
.
From the table you can see that girls that are freshmen are 4 from all 30 people, then
. There are 18 girls, then
. Substitute into the formula:
.
Answer:
.
Answer:
Step 3.
m∠ AEB = m∠ CED .........By Vertical Angles Theorem.
Step-by-step explanation:
Vertical Angles Theorem:
Vertical angle theorem states that vertical angles, angles that are opposite each other and formed by two intersecting lines,are congruent.
If two lines intersect each other we have two pair of vertical opposite angles. As shown in the figure.
Here,
∠ 1 and ∠ 2 are vertical opposite angles and also they are equal.
∠ 3 and ∠ 4 are also vertical opposite angles and also they are equal.
For,
step 3. m∠ AEB = m∠ CED
Therefore, the reason for step 3 of this proof is Vertical Angles Theorem.
Answer:
2403.2
Step-by-step explanation:
We get the length of the hypotenuse, and the base angle. To find the length of the base, we use the cosine of 16° since it is equal to the adjacent side length/ hypotenuse side length or cos 16°= x/2500. The isolate x by multiplying both sides by 2500. The cos 16° is around 0.96126, multiplied by 2500 (cos 16°(2500)) = 2403.1
Answer: 9 students
Step-by-step explanation:
10 X 3 = 30
3 X 3 = 9 students