In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achi
2 answers:
Response:
Move 2 units to the left
Reflect the graph across the y-axis
Expand horizontally by a factor of 2
Lift vertically by 2 units
Detailed explanation:
Provided:
Basic function:
Transformed function:
Extract -2 from the transformation function f(x)
Now, we can observe the step-by-step transformations
Move 2 units to the left ( x → x+2 )
Reflect the graph across the y-axis ( (x+2) → - (x+2) )
Expand horizontally by a factor of 2 [ -x(x+2) → -2(x+2) ]
Lift vertically by 2 units [ f(x) → f(x) + 2 ]
Simplifying the function:
Thus, applying four transformation steps results in the new function
In order to determine the transformations applied to the parent function, 
, to derive the graph of 
, the following steps outline the process: First, we will express the transformed function by factoring out -2. Step 1 involves shifting the graph 2 units to the left, which is represented mathematically as f(x)→f(x+b) for a b unit left shift in the parent function. Step 2 consists of reflecting the graph over the y-axis, so f(x) transforms to -f(x). Step 3 entails horizontally stretching the graph by a factor of 2, where f(x) morphs into f(bx) for a horizontal stretch of b units. Finally, Step 4 requires shifting the graph upwards by 2 units, or f(x) becoming f(x)+b for a vertical shift of b units. After completing these four steps, the transformation is accomplished.
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Answer:
The anticipated number of tests required to identify 680 acceptable circuits is 907.
Step-by-step explanation:
For any circuit, there are two potential results: it either passes the test or it fails. The likelihood of passing is independent between circuits. Therefore, we apply the binomial probability distribution to address this scenario.
Binomial probability distribution
This distribution calculates the chance of obtaining exactly x successes across n trials, where x has only two possible outcomes.
To find the expected number of trials to achieve r successes with a probability p, the formula is given by:
Circuits from a specific factory pass a certain quality evaluation with a probability of 0.75.
Thus, to determine the expected number of tests needed for 680 acceptable circuits, let’s denote this as E where r = 680.
The expected number of tests necessary to find 680 acceptable circuits is 907.
The average speed for his entire journey from York to Blackpool is about 61.41 km/h.
Here’s a breakdown of how we arrive at this:
The distance he travelled from York to Leeds is 45 km,
and the speed during that section was 54 km/h.
Therefore, the time taken to travel from York to Leeds is 45/54 hours (since Time = Distance/Speed).
Next, the distance from Leeds to Blackpool is 42 km,
and the time for that leg of the journey is 35 minutes, which is 35/60 hours.
This leads to the total duration for his trip as
hours.
The cumulative distance covered equals 45 + 42 = 87 km.
Thus, his average speed is calculated as: