You are camping with Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 21.0 m from yours, in the direction 23.0° south of east. Karl’s tent is 32.0 m from yours, in the direction 37.0° north of east. What is the distance between Karl’s tent and Joe’s tent?

Step-by-step explanation:

According to the flaring, the triangle expressed in the figure is formed.

Now we have a vector A and vector B, whose components are Ax, Ay and Bx and By respectively.

To calculate these components you must use the following formulas:

Ax = A * cos [angle a] = 32 * cos 37 ° = 25.6

Ay = A * sin [angle a] = 32 * sin 37 ° = 19.3

Bx = B * cos [angle a] = 21 * cos 23 ° = 19.3

By = B * sin [angle b] = 21 * sin 23 ° = - 8.2

In the figure it can be seen that vector B is the result of vector A and vector C

Thus:

B = A + C

reorganizing is:

C = B - A

Now to calculate Cx and Cy, we will do it with the previously calculated components:

Cx = Bx - Ax = 19.3 - 25.6 = -6.3

Cy = By - Ay = -8.2 - 19.3 = -27.5

Now to calculate the value of vector C, we apply the following formula:

C ^ 2 = Cx ^ 2 + Cy ^ 2

Rearranging:

C = (Cx ^ 2 + Cy ^ 2) ^ (1/2)

C = [(-6.3 ^ 2) + (27.5 ^ 2)] ^ (1/2) = 28.2

Then the distance would be 28.2 meters.

d

step-by-step explanation:

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.