Find 3 points
(0,-9), (3,-4), (-3,-14)
Plot these points and draw a line through them
Answers:
- Discrete
- Continuous
- Discrete
- Continuous
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Explanations:
- This is discrete because we can't have half a basketball, or any non-whole decimal value to represent the number of basketballs. We can only consider positive whole numbers {1,2,3,4,...}. A discrete set like this has gaps between items. In other words, the midpoint of 2 and 3 (the value 2.5) isn't a valid number of basketballs.
- This is continuous because time values are continuous. We can take any two different markers in time, and find a midpoint between them. For example, the midpoint of 5 minutes and 17 minutes is 11 minutes since (5+17)/2 = 22/2 = 11. Continuous sets like this do not have any gaps between items. We can consider this to be densely packed.
- This is the same as problem 1, so we have another discrete function. You either score a bullseye or you don't. We can't score half a bullseye. The only possible values are {1,2,3,4,...}
- This is similar to problem 2. This function is continuous. Pick any two different positive real numbers to represent the amount of gallons of water. You will always be able to find a midpoint between those values (eg: we can have half a gallon) and such a measurement makes sense.
So in short, always try to ask the question: Can I pick two different values, compute the midpoint, and have that midpoint make sense? If so, then you're dealing with a continuous variable. Otherwise, the data is discrete.
Step-by-step explanation:
add all marbles together:
4 (green) + 3 (red) + 3 (yellow) = 10 marbles total
if we pick a yellow marble out of the bag and do not replace it, then we have 2 yellow marbles left.
we need to add marbles again with one yellow marble subtracted.
4 (green) + 3 (red) + 2 (yellow) =
new Total is 9 marbles.
so then we have 2 yellow marbles out of 9 total marbles.
2:9
or 2/9
or .22 (22%)
is the probability
This figure is a triangle. Using the definition of triangles, it is determined that angles 1, 2, and 3 add up to 180 degrees. In this instance, we know the values of 2 combined angles. With this information it is only necessary to subtract the values of angles 1 and 2 (134) from 180 degrees to find the value of angle 3. This leads us to the solution that angle 3 has a value of 46 degrees.
y = x + 2
Step-by-step explanation:
General formula for any straight line:
y = mx + c
Where
m = gradient
c = constant
m = y2 - y1/x2 - x1
m = (4 - ( -2))/(2 - ( -4))
m = 6/6
m = 1
y = (1)x + c
y = x + c
Substitute any coordinate from the line of the equation.
4 = 2 + c
c = 2
substitute m and c into general formula
y = mx + c
y = x + 2
