C=√a²+b. square both sides
c²=a²+b². subtract a² from both sides
c²-a² = b². take the square root of both sides
b=±√c²-a²
but since length can never be negative we consider only the positive root
b=√c²- a²
There's really no way to solve this problem apriori (unless you can use tools like lagrange polynomials to interpolate points), so I'll just tell you how to approach problems like this.
First of all, we may try to see if the dependence is linear: the input is always increased by 4 (4, 8, 12, 16,...) and the output increases by 2: (5, 7, 9, 11). So, the answer is yes.
Now that we know that these points lay on a line, we can conclude the exercise in several ways:
- We already know that the slope is 1/2 (4 units up in the x direction correspond to 2 units up in the y direction). So, we only need the y-intercept. If we go back one step, we can see that the next point would be (0, 3) (I decreased the x coordinate by 4 and the y coordinate by 2). So, the y intercept is 3, and the equation of the line is
- We can use the equation of the line passing through two points:
Plug in two points of your choice and you'll get the same answer.
Of course, as a third alternative, you could just have eyeballed the answer: the fact that x grows twice as fast as y could have hinted the x/2 part, and then you could have seen that y is always 3 more than half of x, again leading to y=x/2+3.
Answer: if 1 represents the game at the top and 7 the game at the bottom, the order is 1, 6, 5, 2, 3, 7, 4
Step-by-step explanation:
in a game where the expected value is zero, if your probability to win is p and the entry cost is C, then you should win an amount W = C/p
then p = C/W
1) C = $5, W = $200
p = 5/200 = 0.025
2) C = $6, W = $300
p = 6/300 = 0.02
3) C = $9, W = $468
p = 9/468 = 0.019
4) C = $8, W = $440
´p = 8/440 = 0.0181
5) C = $7, W = $315
p = 7/315 = 0.0022
6) C = $4, W = $168
p= 4/168 = 0.024
7) C = $10, W = $540
p = 10/540 = 0.0185
Then the order, from least probability to greatest probability of winning is:
1, 6, 5, 2, 3, 7, 4
Answer:
+49 feet
Step-by-step explanation:
The inicial position that Suzie started her hike was 220 feet below sea level, so as this inicial position was negative, let's use the negative sign for it:
Inicial position = -220 feet
The final position of the hike was 171 feet below sea level, so:
Final position = -171 feet
So we calculate the change in elevation from the beginning to the end of the hike by making the difference between the final position and the inicial position:
Change in elevation = Final position - Inicial position = -171 - (-220) = -171 + 220 = +49 feet
The change in elevation was +49 feet (the positive sign indicates that the movement was upwards, in direction to "above sea level")
