Answer:
here's a link to help as well
Step-by-step explanation:
https://www.prodigygame.com/blog/distributive-property/#exponents
Expand the equation.
Multiply (distribute) the first numbers of each set, outer numbers of each set, inner numbers of each set, and the last numbers of each set.
Combine like terms.
Solve the equation and simplify, if needed.
If you put this info into a distance/rate/time table, you would have "against the wind" and "with the wind" as your 2 situations. If the distance from PA to AZ is 1800 miles, then the distance backwards, from AZ to PA is 1800 miles also. That number would go into the distance category for both situations. The rate is what we are looking for. The rate for "against the wind" is the speed of the plane minus the speed of the wind since the wind is blowing into the plane, slowing it down a bit. That looks like this: p - w where p is the speed of the plane and w is the speed of the wind. The rate for "with the wind" is p + w since the wind is pushing the plane along with it, making it fly faster. It took 3.6 hours to get from PA to AZ (you have to convert the 36 minutes into hours) and it took 3 hours to go from AZ to PA. In table form that looks like this:
distance = rate x time
against wind 1800 = p - w x 3.6
with wind 1800 = p + w x 3
Since distance = rate times time, then the first equation going along in the first row is 1800 = 3.6(p - w) and
1800 = 3.6p - 3.6w
Going along in the second row we have 1800 = 3p + 3w. Let's solve this equation for p: 1800 - 3w = 3p and dividing everything by 3 we have
600 - w = p. Now we have a viable substitution to make into the first equation we wrote. If p = 600 - w, then 1800 = 3.6(600 - w) - 3.6w
and 1800 = 2160 - 3.6w - 3.6w. Combining like terms we have
-360 = -7.2w and solving for w we have that w = 50. That means that the speed of the wind is 50 mph. Now we can sub that value in for w to solve for p. 600 - w = p so 600 - 50 = p. That means that p = 550mph. The wind blows at a rate of 50 mph while the plane travels at a rate of 550 mph. There you go!
Answer:
Step-by-step explanation:
Part A: 5/26
Part B: 5/26+ 1/2 which is 18/26 or 9/13
Part C: 5/26 +21/25. 'without replacing' means there is one less option in the bag. So denominator becomes 26-1=25. Numerator is 21 because there are a total of 21 consonants in the alphabet. Since we removed a vowel and not a consonant, it will remain 21.
Answer:
4.2
Step-by-step explanation:
The given data contains points which are 1/5, 1/25, 1/125, and 1/625. From these we are able to conclude that the given is a geometric sequence with r equal to 1/5 and the first term is equal to 1/5. The sum of these term can be computed as,
S = a1/(1 - r)
Solving,
S = ((1/5)/(1 - 1/5) = 1/4
Thus, the sequence is convergent because the sum is a finite number.
