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Mathematics

1 answer:

Drupady [299]3 years ago

3 0

Answer: The answer is Yes. A square is a rectangle because it possesses all the properties of a rectangle. These properties are: Interior angles measure 90∘ each.

Explanation:

Definition of a Rectangle:

A 4-sided flat shape with straight sides where all interior angles are right angles (90°).

Also, opposite sides are parallel and of equal length.

Definition of a Square:

A 4-sided flat shape with straight sides where all interior angles are right angles (90°).

Also, all sides have equal length

As you can see the first part of the definition of a square and rectangle are the same.

However, a square is a special case of a rectangle.

When all 4 sides of a rectangle are equal then the rectangle is a square.

So, a rectangle can also sometimes be a square.

Step-by-step explanation:

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The mean number of hours per day spent on the phone, according to a national survey, is four hours, with a standard deviation of

Reika [66]

Answer:

The new mean is 5.

The new standard deviation is also 2.

Step-by-step explanation:

Let the sample space of hours be as follows, S = {x₁, x₂, x₃...xₙ}

The mean of this sample is 4. That is, $\bar x=\frac{x_{1}+x_{2}+x_{3}+...+x_{n}}{n}=4$

The standard deviation of this sample is 2. That is, $s=\frac{1}{n-1}\sum (x_{i}-\bar x)^{2}=2$ .

Now it is stated that each of the sample values was increased by 1 hour.

The new sample is: S = {x₁ + 1, x₂ + 1, x₃ + 1...xₙ + 1}

Compute the mean of this sample as follows:

$\bar x_{N}=\frac{x_{1}+1+x_{2}+1+x_{3}+1+...+x_{n}+1}{n}\\=\frac{(x_{1}+x_{2}+x_{3}+...+x_{n})}{n}+\frac{(1+1+1+...n\ times)}{n}\\=\bar x+1\\=4+1\\=5$

The new mean is 5.

Compute the standard deviation of this sample as follows:

$s_{N}=\frac{1}{n-1}\sum (x_{i}-\bar x)^{2}\\=\frac{1}{n-1}\sum ((x_{i}+1)-(\bar x+1))^{2}\\=\frac{1}{n-1}\sum (x_{i}+1-\bar x-1)^{2}\\=\frac{1}{n-1}\sum (x_{i}-\bar x)^{2}\\=s$