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kykrilka [37]
3 years ago
8

The lengths, in order, of four consecutive sides of an equiangular hexagon are 1, 7, 2 and 4 units, respectively. what is the su

m of the lengths of the two remaining sides?

Mathematics
1 answer:
Scilla [17]3 years ago
8 0
Let ABCDEF be an equilanqular hexagon with consecutive sides 1,7,4,2, respectively. All angles of this hexagon are equal to 120° (because total anglea sum is 720°).

Draw lines: CG parallel to ED, PG and AH parallel to BC and EG parallel to CD. You obtain three parallelograms CGED, PGEF, ABCH and one trapezoid APGH.

Since CGED is parallelogram, CG=ED=2, GE=CD=4.

Since ABCH is parallelogram, AH=BC=7, AB+CH=1. Then GH=CG-CH=2-1=1.
Since PFEG is parallelogram, PF=EG=4, EF=PG. Let's find GP. APGH is equilateral trapezoid, then AP=GH=1 ahd thus FA=1+4=5 and GP=AH-0.5-0.5=7-0.5-0.5=6.

Answer: All sides have lengths 1,7,4,2,6,5, respectively.










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Answer:

MZA = 140

Step-by-step explanation:

5x+25°+ x + 17°=180°(Supplimentary Angles)

6x + 42° =180°

6x =180 - 42

6x=138

(divide by 6 both sides)

X= 23

substitution X into the given angle

5x +25

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140

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3 years ago
) All human blood can be typed as one of O, A, B, or AB. The distribution of the type varies a bit with race. For African-Americ
ivann1987 [24]

Answer:

The correct option is 1 - [(0.8)¹⁰+10*0.2*(0.8)⁹]= 0.6242

Step-by-step explanation:

Hello!

Given the distribution of probabilities for blood types for African-Americans:

O: 0.4

A: 0.2

B: 0.32

AB: 0.08

A random sample of 10 African-American is chosen, what is the probability that 2 or more of them have Type A blood?

Let X represent "Number of African-Americans with Type A blood in a sample of 10.

Then you have two possible outcomes,

"Success" the person selected has Type A blood, with an associated probability p= 0.2

"Failure" the selected person doesn't have Type A blood, with an associated probability q= 0.8

(You can calculate it as "1-p" or adding all associated probabilities of the remaining blood types: 0.4+0.32+0.08)

Considering, that there is a fixed number of trials n=10, with only two possible outcomes: success and failure. Each experimental unit is independent of the rest and the probability of success remains constant p=0.2, you can say that this variable has a Binomial distribution:

X~Bi(n;p)

You can symbolize the asked probability as:

P(X≥2)

This expression includes the probabilities: X=2, X=3, X=4, X=5, X=6, X=7, X=8, X=9, X=10

And it's equal to

1 - P(X<2)

Where only the probabilities of X=0 and X=1 are included.

There are two ways of calculating this probability:

1) Using the formula:

P(X)= \frac{n!}{(n-X)!X!} *p^{x} * q^{n-x}

With this formula, you can calculate the point probability for each value of X=x₀ ∀ x₀=1, 2, 3, 4, 5, 6, 7, 8, 9, 10

So to reach the asked probability you can:

a) Calculate all probabilities included in the expression and add them:

P(X≥2)= P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + X=10

b) Use the complement rule and calculate only two probabilities:

1 - P(X<2)= 1 - [P(X=0)+P(X=1)]

2) Using the tables of the binomial distribution.

These tables have the cumulative probabilities listed for n: P(X≤x₀)

Using the number of trials, the probability of success, and the expected value of X you can directly attain the corresponding cumulative probability without making any calculations.

>Since you are allowed to use the complement rule I'll show you how to calculate the probability using the formula:

P(X≥2) = 1 - P(X<2)= 1 - [P(X=0)+P(X=1)] ⇒

P(X=0)= \frac{10!}{(10-)0!0!} *0.2^{0} * 0.8^{10-0}= 0.1074

P(X=1)= \frac{10!}{(10-1)!1!} *0.2^{1} * 0.8^{10-1}= 0.2684

⇒ 1 - (0.1074+0.2684)= 0.6242

*-*

Using the table:

P(X≥2) = 1 - P(X<2)= 1 - P(X≤1)

You look in the corresponding table of n=10 p=0.2 for P(X≤1)= 0.3758

1 - P(X≤1)= 1 - 0.3758= 0.6242

*-*

Full text in attachment.

I hope it helps!

8 0
3 years ago
The diagonal of a rectangle is of length a. It splits each corner forming two angles with a ratio of 1:2. The area of the rectan
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Answer:

Step-by-step explanation:

Given

Length of diagonal is a

Diagonal divides the angle in 1:2

such that \theta +2\theta =90 (because angle between two sides is 90)

3\theta =90

\theta =30^{\circ}

width of rectangle is b=a\sin \theta =\frac{a}{2}

Length of rectangle is L=a\cos 30=\frac{\sqrt{3}}{2}a

Area of rectangle A=L\cdot b

A=\frac{\sqrt{3}}{2}a\times \frac{a}{2}

A=\frac{\sqrt{3}}{4}a^2

5 0
3 years ago
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