ANSWER
Find out the how long will the Yellow balloon be higher than the orange balloon.
To proof
Now the diagram is given below
As given
A yellow hot-air balloon is 100 feet off the ground and rising at rate of 8 feet per second.
i.e height of the yellow baloon off the ground = 100 feet
rising at rate = 8 feet per second.
.An orange hot-air balloon is 160 feet off the ground and rising at a rate of 5 feet per second.
i.e height of the orange baloon off the ground = 160 feet
rising at rate = 5feet per second.
Formula
Relative velocity = rising rate of yellow balloon - rising rate of orange balloon
= 8 -5
= 3 feet per second
Relative distance = height of the yellow baloon off the ground - height of the orange baloon off the ground
= 160 -100
= 60 feet
put in the formula
= 20 second
after 20 second Yellow balloon will be higher than the orange balloon.
Hence proved
Answer:
The probability is 1/8 or 0.125
Step-by-step explanation:
In this question, we are concerned with calculating the probability that when a coin is flipped there would be a show of heads three times.
In flipping of a coin, there are only two possible results with equal probability. The probability of both events i.e P(H) and P(T) is equal and that is 1/2
Thus the probability of getting heads three times in a row will be P(HHH) meaning P(H) and another P(H) and another P(H)
When we have and in a probability question, that means we are to multiply the probabilities together.
Hence, P(HHH) = 1/2 * 1/2 * 1/2 = 1/8
To have roots as described, that means we have the following factors: From multiplicity 2 at x=1 has (x-1)^2 as its factor From multiplicity 1 at x=0 has x as a factor From multiplicity 1 at x = -4 has a factor of x+4 Putting these together we get that P(x) = A (x) (x+4) (x-1)^2 Multiply these out and find P(x) = A (x^2 + 4x) (x^2 - 2x + 1) A ( x^4 - 2x^3 + x^2 + 4x^3 - 8x^2 + 4x ) Combine like terms and find P(x) = A (x^4 + 2x^3 - 7x^2 + 4x) To find A, we use the point they gave us (5, 72) P(5) = A [ (5)^4 + 2(5)^3 - 7(5)^2 + 4(5) ] = 72 A [ 625 + 250 - 175 + 20 ] = 72 A [ 720 ] = 72 Divide both sides by 720 and find that A = 0.1 Final answer: P(x) = 0.1 ( x^4 + 2x^3 - 7x^2 + 4x) or P(x) = 0.1 x^4 + 0.2 x^3 - 0.7x^2 + 0.4x
11 • 55 = 55
The starfish had 55 arms all together.
Hope this helps!
Answer:
Trevon received
$
12
for cleaning the attic.
Explanation:
Since Trevon had
29
on Friday and
41
now after cleaning the attic over the weekend, the amount he received,
x
, can be determined by the equation:
x
=
41
−
29
x
=
12
