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1 answer:
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Answer:
The number of edge stones needed has a constant rate of change, but the number of stones for the center does not.
Step-by-step explanation:
The complete question is shown in the picture attached below.
Two functions E(x) and C(x) are given in the table along with some of the function values. We have to identify if any of these functions show constant rate of change or not.
By constant rate of change we mean that the slope is constant or in other words, a linear relationship is shown by the function. For a Linear function, the first differences of the function values are same.
By first differences we mean the difference between two consecutive output values. We can see that difference between consecutive input values is constant i.e. 1. If the difference between consecutive output values of any of the functions is same, then that function will be a Linear Function and, therefore, the rate of change for that function will be constant.
Lets analyze E(x) first. The output values are:
34, 52, 70 and 88
The difference between consecutive output values is:
18, 18 and 18
Since, this difference is constant, we can conclude that E(x) is a Linear function with a constant rate of change.
Now lets analyze C(x). The output values are:
62, 133, 260 and 435
The difference between consecutive output values is:
71, 127 and 175
Since, the differences are not constant, C(x) is not a Linear Function and , therefore, the rate of change of C(x) is not constant.
Conclusion:
The number of edge stones which is represented by E(x) has a constant rate of change, but the number of stones for center which is represented by C(x) does not have constant rate of change. This makes the first option our correct answer.
Answer:
Test statistic is 0.67
Critical value is -2.33
Step-by-step explanation:
Consider the provided information.
The formula for testing a proportion is based on the z statistic.
Were is sample proportion.
hypothesized proportion and n is the smaple space,
Random sample of 100 adults, 12% say that they own a smart watch.
A company claims that less than 10% of adults own a smart watch.
Therefore, n = 100 = 0.12
,
= 0.10
Substitute the respective values in the above formula.
Hence, test statistic = 0.67
This is the left tailed test.
Now using the table the P value is:
P(z < 0.667) = 0.7476
P-value = 0.7476
Here, P-value > α therefore, we are fail to reject the null hypothesis.
Hence, Critical value is -2.33