For the first option, the range is a measure of variability which measures the spread of the data set from the least value to the greatest value, but it does not take into account the variability of the other data values of the data set. The range is easily affected by the presence of outliers (data points that are away from other data points). Thus the range is regarded as a weak measure of variability and is not used when other measures of variability are available. Thus, that the range of the two data sets are equal does not mean that the data sets have the same variability. Therefore, the first option is not the correct answer.
For the second option, the median is not a measure of variability. Thus, that a data set has a greater median than another data set does not mean that the data set would have a greater variability. Therefore, the second option is not the correct answer.
For the third option, the inter-quartile range (IQR) is a better measure of variability than the range because it takes into account more data points than the range. Now, because, the the IQR of Team 2 is less than the IQR of Team 1, this shows that Team 1 have greater variability than Team 2 and thus the conclusion of the coaches are inaccurate. Therefore, the third option is the correct answer.
For the fourth option, the mean absolute deviation, MAD, is a better measure of variability than the IQR because it takes into account all the points of the data set. While IQR measures variability with respect to the median, MAD measures variability with respect to the mean. Because we are told that the data sets are not symmetrical, the median will be a better measure of the center than the mean, thus the IQR will present a better measure of the variability of the data sets. Thus, though the MAD for Team 2 was calculated to be a larger number than the MAD for Team 1, the information can be misleading in arriving at a conclusion on which data set has more variability because the data sets are not symmetrical. Therefore, the fourth option is not the correct answer.
Answer:
Step-by-step explanation:
B. A coordinate plane has an x axis from 0 to 5 in increments of 1 and a y axis from 0 to 5 in increments of 1. Point A (3,1) is plotted 3 units to the right and 1 unit above the origin. Point B (0,3) is plotted 3 units above the origin. Point C (1,3) is plotted 1 unit to the right and 3 units above the origin.
Answer:
For f(x) to be differentiable at 2, k = 5.
Step-by-step explanation:
For f(x) to be differentiable at x = 2, f(x) has to be continuous at 2.
For f(x) to be continuous at 2, the limit of f(2 – h) = f(2) = f(2 + h) as h tends to 0.
Now,
f(2 – h) = 2(2 – h) + 1 = 4 – 2h + 1 = 5 – 2h.
As h tends to 0, lim (5 – 2h) = 5
Also
f(2 + h) = 3(2 + h) – 1 = 6 + 3h – 1 = 5 + 3h
As h tends to 0, lim (5 + 3h) = 5.
So, for f(2) to be continuous k = 5
Answer:
The answer in the procedure
Step-by-step explanation:
The question does not present the graph, however it can be answered to help the student solve similar problems.
we know that
The equation of a vertical parabola into vertex form is equal to
where
a is a coefficient
(h,k) is the vertex
If the coefficient a is positive then the parabola open up and the vertex is a minimum
If the coefficient a is negative then the parabola open down and the vertex is a maximum
case A) we have
The vertex is the point (-4,-6)
a=3
therefore
The parabola open up, the vertex is a minimum
case B) we have
The vertex is the point (-4,-38)
a=3
therefore
The parabola open up, the vertex is a minimum
case C) we have
The vertex is the point (4,-6)
a=3
therefore
The parabola open up, the vertex is a minimum
case D) we have
The vertex is the point (4,-38)
a=3
therefore
The parabola open up, the vertex is a minimum
Answer:
The correct answer is that there will be 45 remaining apples.
Step-by-step explanation:
So, you start off with 89 and then you take 72 away, that leaves you with 17 apples. Then, you buy 14 more which brings it up to 31. After that, you give 12 more away which brings your total down to 19. Next, you go out and buy 42 more, which adds up to 61 remaining apples. Finally, you give away 16 more, which brings you to a grand total of, 45 apples left.
Hope this helps!
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