Question

please answer all questions for full credit. no electronic devices are allowed when taking the quiz

1. define in your own words the following concepts

a) statistics
b) data

1. establish differences between population and sample
2. establish differences between qualitative data and quantitative data
3. true and false: age and temperature are qualitative data
4. establish differences between observational study and experiment
5. solve this equation: -2(4x + 5)=-\frac{1}{4}(x + 3)

Explanation:

Step1: Expand both sides

Expand -2(4x + 5) to -8x - 10 and -\frac{1}{4}(x + 3) to -\frac{1}{4}x-\frac{3}{4}. So the equation becomes -8x - 10=-\frac{1}{4}x-\frac{3}{4}.

Step2: Move x - terms to one - side

Add \(\frac{1}{4}x\) to both sides: -8x+\frac{1}{4}x - 10=-\frac{3}{4}. Combine like - terms: \((-8+\frac{1}{4})x-10 = -\frac{3}{4}\), \((-\frac{32}{4}+\frac{1}{4})x-10=-\frac{3}{4}\), \(-\frac{31}{4}x-10 = -\frac{3}{4}\).

Step3: Move constant terms to one - side

Add 10 to both sides: -\frac{31}{4}x=-\frac{3}{4}+10. Calculate -\frac{3}{4}+10=\frac{-3 + 40}{4}=\frac{37}{4}. So -\frac{31}{4}x=\frac{37}{4}.

Step4: Solve for x

Multiply both sides by -\frac{4}{31}: x=\frac{37}{4}\times(-\frac{4}{31})=-\frac{37}{31}.

Answer:

\(x = -\frac{37}{31}\)