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Dimas [21]
4 years ago
11

find the five number summary and draw a box-and-whisker plot for the data set of scores on a history test. 52 99 85 78 52 89 95

100 55 93 84 89 66

Mathematics
1 answer:
Galina-37 [17]4 years ago
5 0
From the data set given, the number summary would be as follows:
<span>52 99 85 78 52 89 95 100 55 93 84 89 66
re-arranging the data in ascending order we obtain:
52,52,55, 66,78,84,85,89,89,93,95,99,100
Minimum=52
1st Quartile=66
Median=85
3rd Quartile=93
</span>Maximum=100
thus using the above, the box-whisker plot will be:

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Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0).
aliya0001 [1]

Answer:

The closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

Step-by-step explanation:

Let B(x, y, z) denote a point on the cone.

Therefore, the distance between the points (6, 2, 0) and B(x, y, z) is;

d = √[(x - 6)² + (y - 2)² + (z - 0)²]

d = √[(x - 6)² + (y - 2)² + z²]

Since we are given that z² = x² + y², we now have;

d = √[(x - 6)² + (y - 2)² + x² + y²]

Taking the square of both sides gives;

d² = [(x - 6)² + (y - 2)² + x² + y²]

x² is an increasing function. Thus, minimizing d is also the same as to minimize f (x, y) = d²

Thus, f' = 0. So;

df/dx = 2(x - 6) + 2x = 0

2x - 12 + 2x = 0

4x = 12

x = 12/4

x = 3

Similarly,

df/dy = 2(y - 2) + 2y = 0

2y - 4 + 2y = 0

4y - 4 = 0

4y = 4

y = 4/4

y = 1

Now,from earlier;

z² = x² + y²

Thus;

z = ±√(3² + 1²)

z = ±√10

Thus, the closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

7 0
4 years ago
There are 7 pens in a bag. Four of the pens are blue and the other 3 are red. What's the probability of pulling out a red
GarryVolchara [31]

Answer:

3/7

Step-by-step explanation:

P(red) = number of red pens / total number of pens

         = 3/7

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3 years ago
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Answer:

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Answer: 44.7

Step-by-step explanation:

Mean= total sum of data set/ number of data set

313÷7

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