The speed of the current is 7 miles per
hour.
Step-by-step explanation:
Let × represent speed of the current.
We have been given that a motorboat
maintained a constant speed of 11 miles per
hour relative to the water in going 18 miles
upstream and then returning.
The speed of motorboat while going
upstream would be 11
The speed of motorboat while going
downstream would be 11 + 2
Time
Distance
Speed
Answer:
x² + 2x - 48
Step-by-step explanation:
( x + 8 ) ( x - 6 )
= x ( x - 6 ) + 8 ( x - 6 )
= x*x - 6*x + 8*x + 8*( - 6 )
= x² - 6x + 8x - 48
= x² + 2x - 48
Reduce each ratio to its minimum expression to find if they are equal.
35:28
10:8
Since both ratios reduce to 5:4, they are equivalent.
Another way to check a:b is equivalent to c:d, is that a*d = b*c
In this case, this will be true if 35 times 8 is equal to 10 times 28:
Since both products are equal, then the ratios are equivalent.
Ranking is very critical in this problem. Therefore, the most applicable mathematical theory is permutations.
Ranking possible for the cellists:
Needed cellists = 5
Total available cellists = 10
Possible number of rankings = 10P5 = 10!/(10-5)! = 30240
Ranking possible for the violinists:
Needed violinists = 5
Total available = 16
Possible number of rankings = 16P5 = 16!/(16-5)! = 524160
Therefore,
Ratio of rankings (cellists to violinists) = 30240/524160 = 3/52
Answer:
C. 17, 12, 7
Step-by-step explanation:
In a triangle, the sum of the lengths of any two sides must be greater then the length of the third side. If you can show any two segments, the sum of whose lengths is less than the length of the third segment, that cannot form a triangle.
In choices A, B, and D, there is at least one sum of the lengths of two segments that is less then the length of the third segment. That shows that choices A, B, and D cannot form triangles.
A. 8 + 7 = 15 < 16 No
B. 9 + 7 = 16 = 16 No
D. 11 + 5 = 16 < 17 No
C.
17 + 12 = 29 > 7
12 + 7 = 19 > 17
17 + 7 = 24 > 12
Yes
