The correct equation for this transformation is given as (x, y) ⇒ (x - 9, -(y + 2))
<h3>What is a
transformation?</h3>
Transformation is the movement of a point from its initial location to a new location. Types of transformation are <em>reflection, translation, rotation and dilation.</em>
Translation is the movement of a point either<em> up, down, left or right</em> on the coordinate plane.
The graph of √(5x - x²) was translated 9 units left and 2 units up, then reflected over the x axis to get the new graph.
The correct equation for this transformation is given as (x, y) ⇒ (x - 9, -(y + 2))
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Answer:
Forced need to stretch 1414 inches = 129830.91 pounds
Step-by-step explanation:
Force ∝ Distance
F = KD where K is constant of proportionality
K = F/D = 6060/66 = 91.818182
Hence Force needed to stretch 1414 inches =
F = 6060/66 x 1414 = 129830.91 pounds
Answer:
Angle 3 is 75 degrees
Angles 8 is 105 degrees
Step-by-step explanation:
Angle 3: One line t, angle 3 and the one measure 105 are supplementary and equal to 180 degrees. Subtract 105 from 180.
Angles 8: The angle that measures 105 and angle 8 are alternate exterior angles. This means both angles are equal.
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Complete Question
The complete question is shown on the first uploaded image
Answer:
The 95% confidence interval is 
This means that there is 95% chance that the true population mean is within this interval
Step-by-step explanation:
From the question we are told that
The sample size is n = 30
The sample mean is 
The population standard deviation is 
Given that the confidence level is 95% then the level of confidence is evaluate as
Next we obtain the critical value of 
from the normal distribution table , the values is
Generally the margin of error is mathematically represented as
substituting values
The 95% confidence interval is mathematically represented as
substituting values
The amount she should invest today in the annuity is $455,450.40.
<h3>How much should be invested today?</h3>
The first step is to determine the future value of the monthly annuity.
Future value = monthly payment x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
- r = interest rate = 3.6/12 = 0.3%
- n = number of periods : 15 x 12 = 180
Future value : 3250 x [(1.003^180) - 1] / 0.003 = 774,171.92
The second step is to determine the present value of this future annuity:
774, 171.92 / (1.036^15) = $455,450.40
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