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3 years ago

ABCDEFGH is a regular octagon, of side length 1cm. Calculate the exact length of AD. (Please ignore writing in pen)

Mathematics

1 answer:

Fynjy0 [20]3 years ago

5 0

Let P be the last point in the triangle you have drawn from AB.. It is isosceles and rectangle hence AB^2=2BP^2 hence AP=BP=sqrt(2).

Let Q be the last point in the triangle you have drawn from CD. By the same reasoning, CQ=DQ=sqrt(2)

What is more, AD=AP+PQ+QD=2sqrt(2)+1

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How do u simplify these radicals???

AlladinOne [14]

1. √48 → √16 * √3  =  4√3

3. √12 → √4 * √3 = 2√3

7. √125  → √25 * √5 = 5√5

8. √20  →  √4 *  √5 = 2√5

9.  √18  →  √9 *  √2 = 3√2

10. √32  →  √16 *  √2 = 4√2

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12.  √27  →  √9 * √3 = 3√3

4 0

3 years ago

Based on FAA estimates the average age of the fleets of the 10 largest U.S. commercial passenger carriers is 13.4 years with a s

Aliun [14]

Answer : 0.0129

Step-by-step explanation:

Given : Based on FAA estimates the average age of the fleets of the 10 largest U.S. commercial passenger carriers is $\mu=13.4$ years and standard deviation is $\sigma=1.7$ years.

Sample size : $n=40$

Let X be the random variable that represents the age of fleets.

We assume that the ages of the fleets of the 10 largest U.S. commercial passenger carriers are normally distributed.

For z-score,

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x=14

$z=\dfrac{14-13.4}{\dfrac{1.7}{\sqrt{40}}}\approx2.23$

By using the standard normal distribution table , the probability that the average age of these 40 airplanes is at least 14 years old will be :-

$P(x\geq 14)=P(z\geq2.23)\\\\=1-P(z$

Hence, the required probability = 0.0129

6 0

3 years ago

Determine which side is the smallest in the diagram

AnnyKZ [126]

the shortest side is always opposite the smallest angle.

In triangle ABC the shortest side is AC

In triangle ADC the shortest side is DC

DC<AC since they are in the same triangle.

5 0

3 years ago

The bases of a trapezoid are 16.8 yards and 6.9 yards. If the height is 2 yards, what is the area of the trapezoid?

Svet_ta [14]

Hello,
Here is the formula to find the area of the trapezoid:
A=1/2(b1+b2)×h
Where b1 represent big base
b2 represent small base
and h represent height
Now, we just need to replace the number to get the final answer:
A=1/2(16.8+6.9)×2
A=1/2(23.7)×2
A=23.7 square yards. As a result, the area of the trapezoid is 23.7 square yards. Hope it help!

8 0

3 years ago

Four different paints are advertised as having the same drying time. To check the manufacturer's claims, five samples were teste

iogann1982 [59]

Answer:

Explained below.

Step-by-step explanation:

The data provided is for the dying time of four different types of paint.

One-way ANOVA can be used to determine whether all the four paints have the same drying time.

Use Excel to perform the one-way ANOVA.

Go to Data → Data Analysis → Anova: Single Factor

A dialog box will open.

Select the data.

Select "Grouping" as Columns.

Press OK.

The output is attached below.

The required values are as follows:

(1)

Sum of Squares of Treatment (Between Subjects):

SST = 330

(2)

Sum of Squares of Error (Within Subjects):

SSE = 692

(3)

Mean Squares Treatment (Between Subjects):

MST = 110

(4)

Mean Squares Error (Within Subjects):

MSE = 43.25

6 0

3 years ago