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Ann [662]
3 years ago
12

A data set of 27 different numbers has a mean of 33 and a median of 33. A new data set is

Mathematics
1 answer:
Svetllana [295]3 years ago
6 0

Answer:

Option D.

Step-by-step explanation:

Suppose that we have a set of N values:

{x₁, x₂, ..., xₙ}

The median is the value in the middle, and the mean is calculated as:

M = \frac{(x_1 + x_2 + x_3 ... + x_n)}{N}

Because here we have "the median" then we will assume that N is odd, and there is only one median, the value "k"  (if N was even, the median would be the mean of the two middle values, that case is really similar to the case where N is odd, so solving only one of the cases is enough)

Now we add 7 to all the values greater than the median

We subtract 7 to all values smaller than the median.

Then the median remains unchanged (because we did not add nor subtract anything to the median).

The new mean will be:

M' = \frac{(x_1 - 7) + (x_2 - 7) + ... + (x_{k}) + ... + (x_n + 7)}{N} = \frac{(x_1 + x_2 + ... + x_n) + (-7)*(n/2 - 0.5) + 7*(n/2 - 0.5)}{N}  = \frac{(x_1 + x_2 + ... + x_n)}{N} = M

So the mean does not change.

Because the mean is computed as the sum of the numbers divided by N, and the mean does not change, and N does not change, then the sum of the numbers does not change.

Finally, the standard deviation is computed as:

SD = \sqrt{\frac{(x_1 - M)^2 + ... + (xn - M)^2}{N} }

Because M does not change, if we add or subtract numbers to some of the values, the standard deviation will change (Because all the terms are squared, so the added and subtracted sevens don't cancel like in the previous cases)

Then the only value that does not have the same value in both the original and new data sets is the standard deviation.

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The mathematical expression that is equivalent to negative two raised to the fourth power divided by negative two raised to the second power is negative two raised to the sixth power divided by negative two raised to the fourth power; option D.

<h3>What is a mathematical expression?</h3>

A mathematical expression is an expression which uses mathematical symbols and mathematical operations to represent an idea.

Two mathematical expressions are equivalent if they have the same value

The expression that is equivalent to negative two raised to the fourth power divided by negative two raised to the second power can be written as (-2)⁴/(-2)² = 2²

An equivalent expression is negative two raised to the sixth power divided by negative two raised to the fourth power written as : (-2)⁶/(-2)⁴ = 2²

In conclusion, two mathematical expressions are equivalent if they have the same value when fully expressed.

Learn more about mathematical expression at: brainly.com/question/4344214

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5 0
1 year ago
Tim buys a torch and battery the torch costs 11 times as much as the battery Tim pays with a ?10 note and he gets ?4.84 change h
KengaRu [80]

The cost of 1 battery is 0.43

Step-by-step explanation:

Let the cost of 1 battery be x

We are given that the torch costs 11 times as much as the battery

Cost of torch = 11x

Total cost of 1 battery and torch = 11x+x=12x

Tim pays $10

He receives change of $4.84

Total cost of 1 torch and battery = 10 - 4.84 =$5.16

So,12x= 5.16

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Wich situation can NOT represent a proportional relationship
aliya0001 [1]

Answer:

We need an image or more info

Step-by-step explanation:

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An archaeologist at a dig sets up a coordinate system using string. Two similar artifacts are found one at position (1, 4) and t
myrzilka [38]

Given:

Positions of two artifacts are at points (1, 4) and (5, 2).

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The distance between these two artifacts.

Solution:

Distance formula: The distance between two points is

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Using distance formula, the distance between two points (1, 4) and (5, 2) is

d=\sqrt{(5-1)^2+(2-4)^2}

d=\sqrt{(4)^2+(-2)^2}

d=\sqrt{16+4}

d=\sqrt{20}

d=4.4721359

Round to the nearest tenth of a unit.

d\approx 4.5

Therefore, the distance between two artifacts is 4.5 units.

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3 years ago
SECOND TIME ASKING PLS HELP: A multiple choice question has 3 options. What is the percentage that you will chose the WRONG opti
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Answer:

2/3 or 66.67%

Step-by-step explanation:

2 wrong options, 3 total options. 2 over 3.

<em>Big Brain</em>

Hope this helps!! :)

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