The measure of ∠BAF is 54°.
Solution:
DF and CE are intersecting lines.
m∠EAF = 72° and AB bisects ∠CAF.
∠EAF and ∠DAC are vertically opposite angles.
Vertical angle theorem:
<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>
∠DAC ≅ ∠EAF
m∠DAC = 72°
<em>Sum of the adjacent angles in a straight line = 180°</em>
m∠DAE + m∠EAF = 180°
m∠DAE + 72° = 180°
Subtract 72° from both sides.
m∠DAE = 108°
∠CAF and ∠DAE are vertically opposite angles.
⇒ m∠CAF = m∠DAE
⇒ m∠CAF = 108°
AB bisects ∠CAF means ∠CAB = ∠BAF
m∠CAB + m∠BAF = 108°
m∠BAF + m∠BAF = 108°
2 m∠BAF = 108°
Divide by 2 on both sides, we get
m∠BAF = 54°
Hence the measure of ∠BAF is 54°.
Answer:
E. Each trial is independent
Step-by-step explanation:
I'm not completely sure why all binomial distribution trials are independent, but there are requirements for binomial distributions.
These requirements are:
- Each outcome is either a success (p) or a failure (Q)
- All trials are independent
- There are a fixed number of "n" trials
- The probability of success (p) is the same for each trial
I also just took the test and got this right.
<h2>135 cubic feet of concrete are required to create the platform.</h2>
Step-by-step explanation:
The dimension of lower step is 6 ft× 3 ft× 1.5 ft
and the dimension of upper step is 6 ft ×(9-3)ft × (1.5+1.5)ft = 6 ft × 6 ft ×3 ft
Therefore concrete are required to make lower step = (6×3×1.5) cubic feet
= 27 cubic feet
and concrete are required to make upper step = (6×6×3) cubic feet
=108 cubic feet
<h3>∴(108+27) cubic feet =
135 cubic feet of concrete are required.</h3>
