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TiliK225
9 days ago
7

Make a box-and-whisker plot for the data. What is the lower quartile value? 42 48 43 65 58 47 60 56 52 64 51 66 56 62

Mathematics
2 answers:
Zina [11.9K]9 days ago
3 0

Initially, we organize our fourteen data points:


42 43 47 48 51 52 56 56 58 60 62 64 65 66


With fourteen points, the median will be the average of the 7th and 8th, while the lower quartile corresponds to the fourth and the upper quartile is the eleventh.



The median value is 56. The upper quartile is 62, while the lower quartile is, wait for it,


result: 48


The minimum observation is 42, and the maximum is 66. Therefore, our box-and-whisker plot will show a left whisker at 42, a left box edge at 48, median line at 56, right box edge at 62, and a right whisker at 66.



Zina [11.9K]9 days ago
3 0

Conclusion: 48

Detailed process:

The data provided: 42 48 43 65 58 47 60 56 52 64 51 66 56 62

Arrange in ascending order: 42, 43, 47, 48, 51, 52, 56, 56, 58, 60, 62, 64, 65, 66

As the lower quartile represents the median of the lower half.

the lower half of the dataset: 42, 43, 47, 48, 51, 52, 56

Median of the lower half = 48

Hence, the lower quartile = 48

The upper quartile denotes the median of the upper half.

Upper half of the dataset:  56, 58, 60, 62, 64, 65, 66

Median of the upper half = 62

Thus, the upper quartile = 62

Given that the number of data points is 14

The median constitutes the average of the two middlemost values.

Median of the dataset: \dfrac{56+56}{2}=56

Least value = 42

Highest value = 66

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The increase is linear since the data indicates that sunflowers grew by a consistent amount each month.

Step-by-step explanation:

Referring to the table

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Observe that the months progress incrementally (21-1, 3-2=1, 4-3=1).

Moreover

17.2-15=2.2\ [\text{from month 1 to month 2}]\\ \\19.4-17.2=2.2\ [\text{from month 2 to month 3}]\\ \\21.6-19.4=2.2\ [\text{from month 3 to month 4}]

This indicates a linear increase in sunflower count, as the data shows a consistent monthly rise.

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1 month ago
The law of cosines is a^2+b^2-2abcosC=c^2. Find the value of 2abcosC.
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2ab x cos(C) = 7 since

a^2 + b^2 - 2ab x cos(C) = c^2
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2ab x cos(C) = 7
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Response:

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Step-by-step breakdown:

The digits are related through a factor of 10 when they are identical. 4099 and 5011 have identical digits in the tens and units places. 4110 and 5909 do not share this property.

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The fox’s speed needs to exceed that of the rabbit to successfully catch up. Thus, the required speed for the fox is expressed as 35/t + 40.

The distance separating the rabbit from the fox is 35 feet.

The speed of the rabbit is 40 feet per second.

Fox's speed = F

To calculate a precise speed for the fox, a specific time for the pursuit must be provided.

Let’s denote the time as t.

Recall that:

Speed = distance / time

Distance = speed × time

The distance the rabbit moves away from the fox after time t will be:

35 + (40 × t) = 35 + 40t

The distance traveled by the fox after time t is: fox speed × t = F × t.

To catch the rabbit, both the fox and rabbit must cover the same distance:

Rabbit's distance at time t equals Fox's distance at that time.

35 + 40t = Ft

To determine F, the fox's speed:

Dividing both sides by t yields:

(35 + 40t) / t = Ft/t

35/t + 40 = F

<pThus, the speed of the fox should be: 35/t + 40

To find out the exact speed of the fox, a specific time value must be provided.

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