For this case we have the following table:
x f(x)
<span><span><span>0 2
</span><span>1 5
</span><span>2 10
</span><span>3 17
</span></span></span> The equation that best fits the data in the table, for this case, is given by a quadratic function.
<span><span><span> </span></span></span>The quadratic function in its standard form is:
f (x) = x2 + 2x + 2
Answer:
f (x) = x2 + 2x + 2
Let x be the mystery number
25% = 0.25
So, 24/x = 0.25
Now, we have to rearrange the equation to get:
x = 24/0.25 = 96
Don't hesitate to ask any further questions!
Hope I helped! xx
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.
When finding the percent difference between two numbers, there are two ways you can do this.
1. The first way is how to calculate the percentage INCREASE of two numbers:
-The formula is Increase / Original Number × 100 = % increase
Step 1: Find out the difference between the two numbers you're comparing. New number - Original number = Increase.
Step 2: Divide the increase by the original number and then multiply your answer by 100. (If your answer is a negative number, then it is a percent decrease, not a percent increase.)
2. The second way is how to calculate the percentage DECREASE of two numbers:
Step 1: Find out the difference between the two numbers you're comparing. Original number - New number = Decrease.
Step 2: Divide the decrease by the original number and then multiply your answer by 100. Decrease ÷ Original Number × 100
= % Decrease. (If your answer is a negative number, then is is a percent increase, not a percent decrease.)
