Step 1) Graph the line y = (-1/2)x + 3. This line goes through (0,3) as its y intercept and it also goes through (2,2). You can start at (0,3) and move down one unit and to the right two units to arrive at (2,2). The slope of the boundary line is -1/2, meaning that the rise is -1 and the run is 2. A negative rise indicates we go down instead of up.
Step 2) Make the line in step 1 to be a dashed line. This is because there is no "or equal to" as part of the inequality sign. The dashed line says that points on this line are not part of the solution set.
Step 3) Shade above the dashed line. We shade above due to the "greater than" sign. Points above the dashed line are in the shaded solution set. An alternative is to test a point like (x,y) = (0,0) and you'll find y > (-1/2)x+3 turn into 0 > 3 which is a false statement; therefore, (0,0) is not in the solution set. This is expected as (0,0) is below the dashed line.
The final result is what you see in the attached image below. Points A and B help set up the dashed boundary line. Point C is the test point mentioned above which is not in the blue shaded solution region.
Note: the points shown in the diagram are optional when it comes to showing the final answer to your teacher. All you need really is the boundary line and its proper shaded region.
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:
1 1/3 I think
Step-by-step explanation:
Hope I helped :D
Answer:
6.5 cm
Step-by-step explanation:
Here, <em>the tangent line squared is equal to the secant line times the secant line outside the circle</em>.
That is <em>20.2² = 14.7 * (14.7 + 2x)</em> --> it is 2x because the secant goes through <em>the whole circle</em>.
Simplify: <em>408.04 = 216.09 + 29.4x</em>
Subtract: <em>191.95 = 29.4x</em>
Divide: <em>x = 6.528911565</em> ≈ 6.5 cm
Answer:
Step-by-step explanation:
Let's look at the prime factors of 210.
210 = 2 * 3 * 5 * 7
Since no factor appears more than once, this radical cannot be simplified.
