A bear loves visiting his friend, the piglet. The distance between their houses is 300m, and the bear always walks from his house to the piglet's house in exactly the same amount of time. But today, the bear stops at a beehive after walking 1/4 of the distance. He eats honey for 2.5 minutes and then continues to the piglet's house at a speed 15 m/min faster than usual. The total journey to the piglet's house takes the exact same amount of time as it usually does, when the bear does not stop for honey. How long does the journey take?

10 min.

Step-by-step explanation:

Remember d = rt

The distance from bear's house to beehive = 75m and 225m = distance from beehive to piglet's house

Let r = normal rate of speed

The normal time is 300/r without stopping

75/r = time from bear's house to beehive

225/(r + 15) = time from beehive to piglet's house

So, time from beehive to piglet's house + time at beehive + time from bear's house to beehive = normal time without stopping

225/(r + 15) + 2.5 + 75/r = 300/r

225r + 2.5r(r + 15) + 75(r + 15) = 300(r + 15)

225r + 2.5r^2 + 37.5r + 75r + 1125 = 300r + 4500 Let's remove the deceimal by multiplying thru by 10

2250r + 25r^2 + 375r + 750r + 11250 = 3000r + 45000

25r^2 + 3375r + 11250 =  3000r + 45000

25r^2 + 375r - 33750 = 0

25(r^2 + 15r - 1350) = 0

25(r - 30 )(r + 45) = 0

r = 30 or -45     But, the rate cannot be negative, therefore r = 30

The journey takes 300/30 = 10 min.

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: