Answer:
c = -24
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
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Step-by-step explanation:
<u>Step 1: Define</u>
6c - 1 - 4c = -49
<u>Step 2: Solve for </u><em><u>c</u></em>
- Combine like terms: 2c - 1 = -49
- Isolate <em>c</em> term: 2c = -48
- Isolate <em>c</em>: c = -24
Answer:
Horizontal shift of 4 units to the left.
Vertical translation of 8 units downward.
Step-by-step explanation:
Given the quadratic function, y = (x + 4)² - 8, which represents the horizontal and vertical translations of the parent graph, y = x²:
The vertex form of the quadratic function is y = a(x - h)² + k
Where:
The vertex is (h , k), which is either the <u>minimum</u> (upward facing graph) or <u>maximum</u> (downward-facing graph).
The axis of symmetry occurs at <em>x = h</em>.
<em>a</em> = determines whether the graph opens up or down, and makes the graph wider or narrower.
<em>h</em> = determines how far left or right the parent function is translated.
<em>k</em> = determines how far up or down the parent function is translated.
Going back to your quadratic function,
y = (x + 4)² - 8
- The vertex occrs at (-4, -8)
- a is assumed to have a value of 1.
- Given the value of <em>h</em> = -4, then it means that the graph shifted horizontally by <u>4 units to the left</u>.
- Since k = -8, then it implies that the graph translated vertically at <u>8 units downward</u>.
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Answer:
C. The difference of the medians is 4 times the interquartile range.
Step-by-step explanation:
The diagram show two box plots.
<u>Mahoney's box plot:</u>
Median 
Interquartile range 
<u>Martin's box plot:</u>
Median 
Interquartile range 
The interquartile ranges are the same.
The difference of the medians 
Hence, the difference of the medians is 4 times the interquartile range.
Answer:
0.024
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean
and standard deviation 
Suppose the true proportion of high school juniors who skateboard is 0.18.
This means that 
Samples of 250 high school juniors are taken
This means that 
By how much would their sample proportions typically vary from the true proportion?
This is the standard error, so:



So 0.024 is the answer.