Primary school students are playing hide and seek at recess as the counting begins Jon runs 100 feet east , turns 45 degrees north of east and runs another 120 feet to find a hiding spot . Lisa finds her hiding spot by running 120 feet west , turning 32 degrees south of west , and continuing another 100 feet which students hiding spot is closer to starting point ?

Jon's hiding spot is closer to the starting point.

Step-by-step explanation:

Jon's final position forms a triangle with sides 100 ft and 120 ft respectively with an angle of 180 - 45 = 135 between them. Since the angle between the 100 ft direct east and 120 ft direction is 45, since Jon turns 45 after moving for 100 ft and then moves another 120 ft to his final destination.

Also, Lisa's final position forms a triangle with sides 120 ft and 100 ft respectively with an angle of 180 - 32 = 148 between them. Since the angle between the 120 ft direction west and 100 ft direction south of west is 45, since Lisa turns 32 after moving for 120 ft and then moves another 100 ft to her final destination.

Using the cosine rule,

a² = b² + c² - 2abcosФ,  we find the length of the third side of each triangle which is their distance from the starting point.

So, for Jon

a² = b² + c² - 2abcosФ where b = 100 ft, c = 120 ft and Ф = 135°

Thus,

a² = (100 ft)² + (120 ft)² - 2(100 ft)(120 ft)cos135°

a² = 10000 ft² + 14400 ft² - 24000 ft²cos135°

a² = 10000 ft² + 14400 ft² - 24000 ft²(-0.7071)

a² = 24400 ft² + 16970.56 ft²

a² = 41370.56 ft²

a = √(41370.56 ft²)

a = 203.4 ft

for Lisa

a'² = b'² + c'² - 2a'b'cosФ' where b = 120 ft, c = 100 ft and Ф = 148°

Thus,

a'² = (120 ft)² + (100 ft)² - 2(120 ft)(100 ft)cos148°

a'² = 14400 ft² + 10000 ft² - 24000 ft²cos148°

a'² = 14400 ft² + 10000 ft² - 24000 ft²(-0.8481)

a'² = 24400 ft² + 20353.15 ft²

a'² = 44753.15 ft²

a' = √(44753.15 ft²)

a' = 211.56 ft

a' ≅ 211.6 ft

Since a = 203.4 ft < a' = 211.6 ft,

Jon's hiding spot is closer to the starting point.

its kind of blurry. can you put a clearer pic?

step-by-step explanation:

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: