Answer: they are similar because of the same side lengths
Step-by-step explanation:
You haven't told us whether ABC is a line or a triangle.
-- <u>IF</u> ABC is a line, and if 'B' is on the line between 'A' and 'C',
and if AB=3.7m and AC=8.5m, then . . .
BC = (8.5m - 3.7m) = <em>4.8meters</em>.
-- But <u>IF</u> ABC is a triangle, and if 'A', 'B', and 'C' are the vertices
of the triangle, and if AB=3.7m and AC=8.5m, then BC can be
<u>ANY</u> length that's more than 4.8 meters and less than 12.2 meters.
Answer:
See explanation
Step-by-step explanation:
Statement: P(n) = "a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps".
A. P(18) = a postage of 18 cents can be formed using two 7-cent stamps and one 4-cent stamp.
P(19) = a postage of 19 cents can be formed using one 7-cent stamp and three 4-cent stamps.
P(20) = a postage of 20 cents can be formed using five 4-cent stamps.
P(21) = a postage of 21 cents can be formed using three 7-cent stamps.
B. Inductive hypothesis is to assume that P(n) is true for all n < 18
C. In the inductive step we need to prove that P(n+1) is true.
D. Let k ≥ 21, then
- if k = 4l, we get the case of P(20);
- if k = 4l + 1, we get the case of P(21);
- if k = 4l + 2, we get the case of P(18);
- if k = 4l + 3, we get the case of P(19).
E. Since all natural numbers are of the form 4l, 4l + 1, 4l + 2, 4l + 3, we can state that P(n) is true for all n ≥ 18.
Answer:
0.4375
Step-by-step explanation:
Lets say that X is the random varaible that determine the arrival time of Bob and Y the random variable that determine the arrival time of Alice. Bot X and Y are Independent random variables with uniform [0,1] distribution. 15 minutes is the quarter of an hour, so we want to calculate P(|X-Y|) < 0.25.
Note that P(|X-Y| < 0.25) = P(|X-Y| < 0.25 | X ≥ Y) * P(X≥ Y) + P(|X-Y| < 0.25 | Y ≥ X) * P(Y ≥ X) = P(X-Y < 0.25 | X ≥Y) * P(X≥Y) + P(Y-X < 0.25 | Y≥X)*P(Y ≥ X).
For a simmetry argument, that expression is equivalent to 2*P(Y-X < 0.25 | Y≥X)*P(Y ≥ X) = 2*P(0 < Y-X < 0.25). The region 0 < Y-X < 0.25 is, for X between 0 and 0.75, a parallelogram, of base 0.75 and height 0.25, and for X between 0.75 and 1, it is a Triangle of base and height equal to 0.25. Therefore P(0 < Y-X < 0.25) = 0.25*0.75 + 0.25² * 0.5 = 7/32. Hence 2*P(0 < Y-X < 0.25) = 14/32 = 0.4375.
They will meet for lunch with probability 0.4375
-20 would be 20 (positive)
4 would be -4 (negative
95 would be -95 (negative)
-63 would be 63 (positive)