The ages of people on the camp bus are listed. 10, 15, 14, 8, 18, 11, 12, 12, 10, 10, 17, 16 What is the mode of the ages?
2 answers:
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Problem 5
The function is continuous for the given domain
This is because y = (-5/6)x+5 is itself continuous, and any interval subset of this function is also continuous. We can plug in any real number that is equal to 6 or larger, and get some y output. If we plugged in x = 6, then we'd get
y = (-5/6)x+5
y = (-5/6)*6 + 5
y = -5+5
y = 0
This is the largest y value possible. Why? Because y = (-5/6)x+5 has a negative slope, so the graph is going downhill as you read it from left to right. As x gets bigger, y gets smaller. The smallest x value allowed in the domain produces the largest y value in the range. There is no smallest y value as the y values keep going down forever.
The range is therefore
In interval notation, you can write the range as . The square bracket indicates "include this endpoint as part of the range".
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Problem 6
The function is discrete for this given domain. The domain itself is a discrete list of values. We cannot plug in values between say 0 and 2. We can only substitute one of those values from the list given. Consequently, the y values will also be a list, and not an interval like problem 5 had.
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If you plugged in x = -4, then you should get...
y = (-1/2)*(-4)+2
y = 2+2
y = 4
So the input x = -4 lead the output y = 4
Repeat for x = -2
y = (-1/2)x+2
y = (-1/2)*(-2)+2
y = 1+2
y = 3
and the same for x = 0 as well
y = (-1/2)x+2
y = (-1/2)*0 + 2
y = 0 + 2
y = 2
and x = 2 also
y = (-1/2)x+2
y = (-1/2)*2 + 2
y = -1+2
y = 1
Finally, plug in x = 4
y = (-1/2)x+2
y = (-1/2)*4+2
y = -2+2
y = 0
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If we plugged each of these x values {-4, -2, 0, 2, 4} one at a time into the equation y = (-1/2)x+2, then we get this list of values {4, 3, 2, 1, 0}
Sorting the values from smallest to largest, we have this range {0, 1, 2, 3, 4}
Using simple mathematical operations, the missing values are as follows:
(B) Dijon Mustard: 18g
- Increased by 20 = 360g
(C) Barbeque sauce: 70g
- Increased by 5 = 350g
- Increased by 20 = 1,400g
(D) Worcestershire sauce: 10.35g
- Increased by 5 = 51.75g
- Increased by 20 = 207g
(E) Kosher salt: 1.5g
- Increased by 5 = 7.5g
- Increased by 20 = 30g
(F) Ground black pepper: 2.3g
- Increased by 5 = 11.5g
- Increased by 20 = 46g
(G) Crushed red pepper: 1.15g
- Increased by 5 = 5.75g
- Increased by 20 = 23g
- A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
- There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.
- The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation.
- We can recall the PEMDAS steps in the following order: Parentheses, Exponents, Multiplication, Division (from Left to Right), Addition, and Subtraction (from left to right).
So, we can calculate missing values as follows:
(B) Dijon Mustard: 18g
- Increased by 20 = 18×20 = 360g
(C) Barbeque sauce: 70g
- Increased by 5 = 70×5 = 350g
- Increased by 20 = 70×20 = 1,400g
(D) Worcestershire sauce: 10.35g
- Increased by 5 = 10.35×5 = 51.75g
- Increased by 20 = 10.35×20 = 207g
(E) Kosher salt: 1.5g
- Increased by 5 = 1.5×5 = 7.5g
- Increased by 20 = 1.5×20 = 30g
(F) Ground black pepper: 2.3g
- Increased by 5 = 2.3×5 = 11.5g
- Increased by 20 = 2.3×20 = 46g
(G) Crushed red pepper: 1.15g
- Increased by 5 = 1.15×5 = 5.75g
- Increased by 20 = 1.15×20 = 23g
Therefore, using simple mathematical operations, the missing values are as follows:
(B) Dijon Mustard: 18g
- Increased by 20 = 360g
(C) Barbeque sauce: 70g
- Increased by 5 = 350g
- Increased by 20 = 1,400g
(D) Worcestershire sauce: 10.35g
- Increased by 5 = 51.75g
- Increased by 20 = 207g
(E) Kosher salt: 1.5g
- Increased by 5 = 7.5g
- Increased by 20 = 30g
(F) Ground black pepper: 2.3g
- Increased by 5 = 11.5g
- Increased by 20 = 46g
(G) Crushed red pepper: 1.15g
- Increased by 5 = 5.75g
- Increased by 20 = 23g
Know more about mathematical operations here:
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