Answer:
First, we need to know when the function is increasing, and when is decreasing.
When a function is increasing, it's because to higher <em>x-values </em>belong higher <em>y-values. </em>On the other hand, a function is decreasing when to higher <em>x-values </em>belong lower <em>y-values. </em>The effect in the graph will be a upwards direction of the function when is increasing, and a downwards direction when is decreasing.
So, according to the given graph, we see that between 0 and 4 is increasing, the higher x-values are, higher y-values are. Between 4 and 6 is decreasing, is downwards. Between 6 and 8 is increasing. Between 8 and 10 is decreasing. In finally, between 10 and 14 is neither decreasing or increasing, it remains horizontal.
All these interpretations we can expressed using math language, specifically inequalities:
- 0 < x < 4: increasing.
- 4 < x < 6: decreasing.
- 6 < x < 8: increasing.
- 8 < x < 10: decreasing.
- 10 < x < 14: neither increasing or decreasing.
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Answer:
y= 3x +11
Step-by-step explanation:
<u>slope-intercept form:</u>
y= mx+c, where m is the gradient and c is the y-intercept.
Given that the slope is 3, m=3
substitute m=3 into the equation:
y= 3x +c
To find the value of c, substitute a coordinate.
When x= -3, y=2,
2= 3(-3) +c
c -9= 2
c= 9 +2 <em>(</em><em>+</em><em>9</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em><em>)</em>
c= 11 <em>(</em><em>s</em><em>implify</em><em>)</em>
Thus, the equation of the line is y= 3x +11.
We have to define an interval about the mean that contains 75% of the values. This means half of the values will lie above the mean and half of the values lie below the mean.
So, 37.5% of the values will lie above the mean and 37.5% of the values lie below the mean.
In a Z-table, mean is located at the center of the data. So the position of the mean is at 50% of the data. So the position of point 37.5% above the mean will be located at 50 + 37.5 = 87.5% of the overall data
Similarly position of the point 37.5% below the mean will be located at
50 - 37.5% = 12.5% of the overall data
From the z table, we can find the z value for both these points. 12.5% converted to z score is -1.15 and 87.5% converted to z score is 1.15.
Using these z scores, we can find the values which contain 75% of the values about the mean.
z score of -1.15 means 1.15 standard deviations below the mean. So this value comes out to be:
150 - 1.15(25) = 121.25
z score of 1.15 means 1.15 standard deviations above the mean. So this value comes out to be:
150 + 1.15(25) = 178.75
So, the interval from 121.25 to 178.75 contains the 75% of the data values.
To determine the expected number of sales after 3 years of a product, we need an equation that would relate time with the number of sales. In this case, we use the equation above which expresses the number of sales as a function of time. We simply substitute the time which would be 3 years to the equation and evaluate the value of N. We do as follows:
<span> N = 9200 ln (5t + 3)
</span><span> N = 9200 ln (5 ( 3 ) + 3)
</span><span> N = 9200 ln 18
N = 26591.42
Therefore, the correct answer would be option B. The number of sales after 3 years would be about 26591.</span>
