Answer:
<em>A: For each increase in the number of procrastination days by 1, the predicted grade decreases by 3.64 points.</em>
Step-by-step explanation:
<u>The slope of a Regression Line</u>
A straight line can be represented in the slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
The slope describes how fast and in what direction the graph goes when x changes values.
If m is positive, increments in x imply increments in y.
If m is negative, increments in x imply decrements in y.
The regression line is:
ŷ = –3.64x + 96.5
Where:
x = the number of procrastination days
ŷ = the predicted grade
We can say the slope is m=-3.64. This means that:
A: For each increase in the number of procrastination days by 1, the predicted grade decreases by 3.64 points.
Answer: $1411.50
Step-by-step explanation:
Since the sale price is $35 each and there are 30 units, the cost will be:
= $35 × 30
= $1050
We then add the sales tax on the product which is 8%. This will be:
= $1050 + (8% × $1050)
= $1050 + (0.08 × $1050)
= $1050 + $84
= $1134
We then add Shipping price which is $15. This will be:
= $1134 + $15
= $1149
We then add the 25% rush charge on the sales price. This will be:
= $1050 × 25%
= $1050 × 0.25
= $262.50
To get total cost, this will be:
= $1149 + $262.50
= $1411.50
Answer:
x = 5
Step-by-step explanation:
Step 1: Write equation
-3/4 + 2/5x = 7/20x - 1/2
Step 2: Subtract 7/20x on both sides
-3/4 + 1/20x = -1/2
Step 3: Add 3/4 to both sides
1/20x = 1/4
Step 4: Divide 1/20 on both sides
x = 5
Answer:
<em>f(x) and g(x) and not inverse functions</em>
Step-by-step explanation:
Given
Required
Determine f(g(x))
Determine g(f(x))
Determine if both functions are inverse:
Calculating f(g(x))
Expand Brackets
Calculating g(f(x))
Expand Brackets
Checking for inverse functions
Represent f(x) with y
Swap positions of x and y
Subtract 9 from both sides
Divide through by 3
Take square root of both sides
Represent y with g(x)
Note that the resulting value of g(x) is not the same as
<em>Hence, f(x) and g(x) and not inverse functions</em>
For this case we have the following complex number:
1 + i
Its equivalent pair is given by:
root (2) * (cos (pi / 4) + i * sin (pi / 4))
Rewriting we have:
root (2) * (root (2) / 2 + i * (root (2) / 2))
(2/2 + i * (2/2))
(1 + i)
Answer:
option A represents a pair with the same complex number
