Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switches, each one set on or off. The receiver (wired to the door) must be set with the same pattern as the transmitter. If six neighbors with the same type of opener set their switches independently.<u>The probability of at least one pair of neighbors using the same settings is 0.65633</u>
Step-by-step explanation:
<u>Step 1</u>
In the question it is given that
Automatic garage door opener utilizes a transmitter control with four independent switches
<u>So .the number of Combinations possible with the Transmitters </u>=
2*2*2*2= 16
<u>
Step 2</u>
Probability of at least one pair of neighbors using the same settings = 1- Probability of All Neighbors using different settings.
= 1- 16*15*14*13*12*11/(16^6)
<u>
Step 3</u>
Probability of at least one pair of neighbors using the same settings=
= 1- 0.343666
<u>
Step 4</u>
<u>So the probability of at least </u>one pair of neighbors using the same settings
is 0.65633
Answer:
Step-by-step explanation:
The Side-Angle-Side method cana only be used when information given shows that an included angle which is between two sides of a ∆, as well as the two sides of the ∆ are congruent to the included side and two sides of the other ∆.
Thus, since John already knows that 
and 
, therefore, an additional information showing that the angle between 
and 
in ∆ABC is congruent to the angle between 
and 
in ∆DEF.
For John to prove that ∆ABC is congruent to ∆DEF using the Side-Angle-Side method, the additional information needed would be .
See attachment for the diagram that has been drawn with the necessary information needed for John to prove that ∆ABC is congruent to ∆DEF.
Answer: Choice A, x=-4
Step-by-step explanation:
1. 9x−(3x+9)=2x−25
2. 9x-3x-9=2x-25
3. 6x-9=2x-25
4. 6x-9=2x-25
-2x -2x
5. 4x-9=-25
+9 +9
6. 4x=-16 (divide both sides by 4)
7. x=-4
Answer:
(-12, -1)
Step-by-step explanation:
(8, -1) => (-2/3x, f(-2/3x))
therefore
-2/3x = 8
x = 8 *-3/2
x = -12
f(-2/3x) = -1
therefore, the corresponding point is:
(-12,-1)
Answer:
length of BC = 5 1/4 feet
Step-by-step explanation:
Area of a triangle = 1/2×base×height
Area = 4 3/8 square feet
Base = AC= 1 2/3 feet
Height = BC = ?
Area of a triangle = 1/2×base×height
4 3/8 = 1/2 × 1 2/3 × height
35/8 = 1/2 × 5/3 × height
35/8 = 5/6 × height
Height = 35/8 ÷ 5/6
= 35/8 × 6/5
= (35 × 6) / (8 × 5)
= 210 / 40
= 5 1/4 feet
Height = BC = 5 1/4 feet
length of BC = 5 1/4 feet
