X^2+8x+x+8 simplifies to x^2+9x+8
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Answer is -15</h3>
We read this out as "negative 15" or you could write "negative fifteen".
The negative indicates the temperature went down. It doesn't necessarily mean that the final temperature is -15 degrees.
For example, if it starts being 50 degrees F, and drops by 15 degrees, then 50+(-15) = 50-15 = 35 degrees is the temperature after that drop. It might help to use a vertical number line.
Patricia drove for 3 hours. Carlos drove for twice that, 6 hours. 6+3=9
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.
Answers:
- prime number = {2,3,5}
- composite number = {4,6}
- number less than four = {1,2,3}
- number more than or equal to three = {3,4,5,6}
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Explanation:
The list of all possible outcomes on a single standard die is {1,2,3,4,5,6}. The curly braces indicate set notation.
A prime number is a number where its only factors are 1 and itself. The value 1 is not prime, and it's not composite either.
Something like 3 is prime because its only factors are 1 and 3. Something like 4 is composite because 4 = 2*2. A composite value has factors other than 1 and itself.
Parts (iii) and (iv) are fairly straight forward. You simply list items less than four for part (iii) and you list items that are three or greater for part (iv).
