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2 years ago

HELLPP

1 answer:

3 0

Detailed Answer:

Let ‘n’ be the middle term of three consecutive even integers. Therefore, (n) is also an even number. Hence, the even number preceding it will be (n - 2) and the even number after it will be (n + 2), since we need consecutive even integers.

Hence, we have (n - 2), (n), (n + 2).

Sum of the Integers :-
= (n - 2) + (n) + (n + 2)
= n - 2 + n + n + 2
= n + n + n + 2 - 2
= n + n + n
=> 3n

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I NEED HELP QUICK!

ivanzaharov [21]

<h2>Answers:</h2>

a. What properties do these shapes have in common?

The square, the rectangle and the rhombus are in the quadrilaterals group (shapes or figures with four sides) and in the parallelogram sub-group (shapes or figures with four sides in which opposite sides are parallel).

In other words,

<h2>what these three shapes have in common is that they are Parallelograms.</h2>

Hence, they have the same properties of a parallelogram, such as:

1. Opposite sides parallel and with the same length

2. Opposite angles are congruent (equal angles, or angles with the same value)

3. Consecutive angles are supplementary (angles that add up to 180°)

Also the general properties of a quadrilateral:

1. It has four sides

2. It is a 2-dimensions shape

3. It is a closed figure

4. It has four corners (called vertices), and four interior angles, as well.

5. The sum of their four interior angles is 360º

b. How are these two shapes different?

In this case we are going to talk about the differences between the Rectangle and the Rhombus, because the square is a special case of both.

Now, the differences between the Rectangle and the Rhombus are:

1. In the Rectangle only the opposite sides are of the same length, while in the rhombus all of its sides are of the same length.

2. If you trace two diagonal lines inside the Rectangle, they will have the same length. But if you trace two diagonal lines inside the Rhombus they will have different lengths.

3. When the two diagonals in the Rectangle are intersected, they are not perpendicular, but in the case of the Rhombus they are perpendicular (both lines form an angle of 90º)

4. All the angles of the rectangle have the same value: 90º. But in the case of the rhombus only the opposite angles have the same value.

c. What conclusion can you make about the square, rhombus and rectangle?

These three shapes belong to the parallelogram group (which is also part of the quadrilaterals group). They have a lot of things in common for being quadrilaterals, with some differences related to their own shape.

The square is a special case of these three figures, is a rhombus (four equal sides) and a rectangle (four equal 90º angles), as well.

5 0

4 years ago

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airp

ale4655 [162]

Answer:

$6.26-2.01\frac{2.47}{\sqrt{50}}=5.56$

$6.26+2.01\frac{2.47}{\sqrt{50}}=6.96$

So on this case the 95% confidence interval would be given by (5.56;6.96)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=6.26$

The sample deviation calculated $s=2.47$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=50-1=49$

Assuming a Confidence of 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that $t_{\alpha/2}=2.01$