Dont doubt yourself you did good!
Answers:
In other words, only choice C is false while the others are true.
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Explanation:
The height of each bar represents the frequency for each group. It tells us how many students are in a certain interval. For example, the first bar has a height of 3 units to indicate there are 3 students between 140 and 155 cm.
Add up the heights of each bar to find the total number of students: 3+5+6+5+3+2 = 24
Statement A is correct because there are 24 students.
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Statement B is also correct. This is because the highest value on the x axis is 230 and the lowest is 140. The range is the distance or gap between them. Subtract the values: 230-140 = 90.
The distance from the shortest height (140 cm) and tallest height (230 cm) is 90 cm, which is the range.
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Unlike the previous two statements, choice C is not correct. Each bar represents a different interval. There are 6 bars, so there are 6 intervals (not 7).
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Choice D however, is correct. Focus on any single bar. Look at where its left and right endpoints are located. The first bar for instance starts at x = 140 and ends at x = 155. The gap is 155-140 = 15 units wide.
Answer:
(x, y, z) = (1, -1, -4)
Step-by-step explanation:
A suitable graphing or scientific calculator can find the reduced row-echelon form for you. There are on-line calculators that will do that, too.
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In general, if you want to do this by hand, you want to use row operations on the augmented matrix to make the diagonal elements 1 and the off-diagonal elements 0 as shown in the attached result.
If a[i,j] represents the element at row i, column j, you do that by dividing row i by a[i, i] (to make a[i, i] = 1), then subtracting the product of row i and a[k,i] from row k. (for all rows k ≠ i) For this 3-row matrix, repeat these steps for i = 1 to 3.
In the general case of an n by n+1 augmented matrix, you will be doing n^2 row operations, each one involving evaluation of n+1 expressions. The work rapidly grows with matrix size, so readily justifies use of a calculator.
As with many "elimination" problems, appropriate choice of sequence can reduce the work. The above algorithm always produces the reduced row-echelon form, but may result in messy arithmetic along the way.
Answer:
The first one, 10 15 20
45 -5 -35
55 25 -15
Step-by-step explanation:
Answer:
69
Step-by-step explanation:
it's the holy number jesus christ can confirm
