Solving this problem actually requires us the use of the
distance formula of point to a line.
The formula is:
distance = | a x + b y + c | / sqrt (a^2 + b^2)
So we are given the equation:
y = 2 x + 4
rewriting:
<span>y – 2 x – 4 = 0 -->
a = -2, b = 1, c = -4</span>
We are also given the points:
(-4, 11) = (x, y)
Using the distance formula at points (x, y):
distance = | -2 * -4 + 1 * 11 + -4 | / sqrt [(- 2)^2 +
(1)^2]
distance = 15 / sqrt (5)
distance = 6.7
<span>So the tree is about 6.7 ft away from the zip line.</span>
Answer:
<em>The probability is 42%</em>
Step-by-step explanation:
<u>Conditional Probability</u>
It's the probability of the occurrence of an event B knowing that an event A has already occurred and A and B are related (not independent).
If P(A) is the probability of occurrence of A, 
is the probability of both events to occur, and P(B|A) is the required probability occurrence of B:
We know a high school marching band has 125 members, from which 41 are seniors (event B), 24 play the trumpet (event A), and 10 are seniors who play the trumpet.
The probability that a randomly selected band member plays the trumpet is
The probability that he or she has both attributes is
Thus, the required conditional probability is
The probability is 42%
So in order to find the correct answer, we can just easily plug in the values to check which ordered pair matches the given inequality above. So based on my solutions, the correct answer would be the last pair.
<span> y − 2x ≤ 1
0 - 2(5)</span> ≤ 1
0-10 ≤ 1
-10 ≤ 1
Hope this answer helps.
Answer:
B. 1.2×10^-3 mm
Step-by-step explanation:
What constitutes an "appropriate" unit depends on the use of the number. Since we're not told of any particular use, we might choose the smallest of the available units: mm.
1.2×10^-3 mm
_____
<em>Additional comment</em>
The most appropriate unit would be the one that eliminates the power-of-ten multiplier:
= 1.2 µm
Answer:
x = 5m/s
Step-by-step explanation:
Distance flying out = 12 km (headwind)
Distance flying back = 12 km (tailwind)
total distance = 12 + 12 =24 km
wind speed = 1km/h
speed going out (with headwind) = (x - 1) km/h
speed coming back (with tailwind) = (x + 1) km/h
Time taken to go out = distance going out / speed going out
= 12 / (x-1)
Time taken to come back = distance coming back / speed coming back
= 12 / (x+1)
total time = time taken to go out + time taken to come back
5 =[ 12/(x-1) ] + [ 12/(x-1)]
expanding this, we will get
5x² - 24x - 5 = 0
solving quadratic equation, we will get
x = -1/5 (impossible because speed cannot be negative)
or
x = 5 (answer)
