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.
Answer: the solutions to the system of equations are x = 2 and x = 1
Step-by-step explanation:
The system of equations given equation is
y = 3x - 2 - - - - - - - - - - 1
y = x^2 - - - - - - - - - - - - 2
Substituting 1 into equation 2, it becomes
x^2 = 3x - 2
x^2 - 3x + 2 = 0
We would apply the method of factorization in solving the equation. We will get two numbers such that when added, the result would be - 3x and when multiplied, the result would be 2x^2. The numbers are - 2x and - x. It becomes
x^2 - 2x - x + 2 = 0
x(x - 2) - 1(x - 2) = 0
(x - 2)(x - 1) = 0
x - 2 = 0 or x - 1 = 0
x = 2 or x = 1
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Answer:
9
Step-by-step explanation:
listing the factors
27 : 1, 3, 9, 27
36 : 1, 2, 3, 4, 9, 12, 18, 36
the common factors are 1, 3, 9
the highest common factor is 9
let x represent granddaughter and x +2 for grandson and together they = 12
so then we have the equation of x+2+x = 12
combine like terms 2x +2 =12
-2 from both sides to isolate x
2x=10 divide both sides by 2 to get x by itself
so we get x = 5 then add 2 +5=7
so grandson is 7 and granddaughter is 5
22828.l of a period of 3 years.
