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A flow diagram shows a rule that transforms input values into output values. Some input and output values are missing. Determine the input values, the output values, and the rule.
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4 partsStep-by-step solution
6 stepsHere are the solutions based on the flow diagram:
Part i· 2 steps
What are the input values?
Identify the given input values from the diagram.
The given input values are $5, 2, 7, 11$.
Use the rule to find the missing input values.
The rule is "multiply by 5, then subtract 4". So, if is the input and is the output, the rule is .
We have output values 26 and 41 with missing inputs.
For output 26:For output 41:
The complete list of input values is .
The input values are:
Part ii
What are the output values?
Identify the given output values from the diagram.
The given output values are $26, 41$.
Use the rule to find the missing output values.
The rule is .
For input 5:For input 2:
For input 7:
For input 11:
The complete list of output values is .
The output values are:
Part iv
What is the rule?
The rule shown in the flow diagram is to multiply the input by 5, then subtract 4.
The rule is:
Part v
Number sentences
Based on the input and output values and the rule :
Part vi
What will the output values be if the rule is ?
Interpret the new rule.
The rule is given as . This simplifies to . So, the new rule is to multiply the input by .
Let be the input, the new rule is .Use the input values from the original diagram ($5, 2, 6, 9, 7, 11$) with the new rule.
For input 5:
For input 2:
For input 6:
For input 9:
For input 7:
For input 11:
The output values will be:
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