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finlep [7]
3 years ago
8

data set A is {30, 45, 32, 50, 33, 40, 44, 32}. Data set B is {28, 43, 30, 48, 35, 42, 46, 34}. which statement best compares th

e two data sets
Mathematics
1 answer:
3241004551 [841]3 years ago
8 0

Answer:

the mean in set B is equal to the mean in set A (option C)

Question:

The question is incomplete as the answer choices were not given.Let's consider the following question:

Data set A is {30, 45, 32, 50, 33, 40, 44, 32}. Data set B is {28, 43, 30, 48, 35, 42, 46, 34}. which statement best compares the two data sets?

a) median for set A is equal to the median for set B

b) Range for set A is greater than range for set B 

c) The mean in set B is equal to the mean in set A

Step by step explanation:

We can describe a data set using four ways:

Center, spread, shape and unusual features.

Let's consider the center and spread.

Center: This is the median of the distribution.

Spread: This is the variation of the data set. If the range is wide, the spread is larger and If the range is small, the spread is smaller.

Rearranging the data set:

A = {30, 32, 32, 33, 40, 44, 45, 50}

B = {28, 30, 34, 35, 42, 43, 46, 48}

From the data:

The median for set A = (33+40)/2 = 73/2= 36.5

The median for set B = (35+42)/2 = 77/2= 38.5

Range = highest value - lowest value

The data ranges from 30 to 50 (range = 20) for A 

The data ranges from  28 to 48 (range = 20) for B

Mean for set A = (30+32+32+33+40+4445+50)/8 = 306/8 = 38.25

Mean for set B = (28+30+34+35+42+43+46+48)/8= 306/8 = 38.25

In both data set the mean is equal to 38.25.

Therefore the statement that best compares the two data sets is the mean in set B is equal to the mean in set A (C)

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A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi
mestny [16]

Answer:

  • Base Length of 84cm
  • Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, V=x^2h=296352

h=\dfrac{296352}{x^2}

Surface Area of the box = Base Area + Area of 4 sides

A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}

Step 2: Find the derivative of A(x)

If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}

Step 3: Set A'(x)=0 and solve for x

A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42

Therefore, the dimensions that minimizes the box surface area are:

  • Base Length of 84cm
  • Height of 42 cm.
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Alenkinab [10]

Answer:

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Step-by-step explanation:

The closer the correlation coefficient is to the number 1 the stronger the correlation is.

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