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wariber [46]
3 years ago
13

Which angles are vertical angles?

Mathematics
1 answer:
Nadya [2.5K]3 years ago
3 0

Answer:

∠8 and ∠5

Step-by-step explanation:

Vertical angles are angles that are across from each other.

∠8 and ∠5 are across from each other.

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An amount of $350,000 is borrowed for a period of 30 years at an interest rate of 5.5%. The amortization schedule for this
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350,000 . 250,00 . 1,987.26
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the planet jupiter has an average distance of about 0.00008 LIght years from the sun. What is this distance in scientific notati
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Answer :The planet Jupiter

Step-by-step explanation:  It has an average distance from the sun of about  

4.837

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10

8

. The planet Venus average distance from the sun of about  

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On average, how much farther from the sun is Jupiter than Venus?

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3 years ago
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A disk with radius 3 units is inscribed in a regular hexagon. Find the approximate area of the inscribed disk using the regular
Oksi-84 [34.3K]

Answer:

The approximate are of the inscribed disk using the regular hexagon is A=18\sqrt{3}\ units^2

Step-by-step explanation:

we know that

we can divide the regular hexagon into 6 identical equilateral triangles

see the attached figure to better understand the problem

The approximate area of the circle is approximately the area of the six equilateral triangles

Remember that

In an equilateral triangle the interior measurement of each angle is 60 degrees

We take one triangle OAB, with O as the centre of the hexagon or circle, and AB as one side of the regular hexagon

Let

M  ----> the mid-point of AB

OM ----> the perpendicular bisector of AB

x ----> the measure of angle AOM

m\angle AOM =30^o

In the right triangle OAM

tan(30^o)=\frac{(a/2)}{r}=\frac{a}{2r}\\\\tan(30^o)=\frac{\sqrt{3}}{3}

so

\frac{a}{2r}=\frac{\sqrt{3}}{3}

we have

r=3\ units

substitute

\frac{a}{2(3)}=\frac{\sqrt{3}}{3}\\\\a=2\sqrt{3}\ units

Find the area of six equilateral triangles

A=6[\frac{1}{2}(r)(a)]

simplify

A=3(r)(a)

we have

r=3\ units\\a=2\sqrt{3}\ units

substitute

A=3(3)(2\sqrt{3})\\A=18\sqrt{3}\ units^2

Therefore

The approximate are of the inscribed disk using the regular hexagon is A=18\sqrt{3}\ units^2

6 0
3 years ago
Find the value -2/3÷ 4/6. <br> A -1<br> B 4/9<br> C -9/4<br> D 1
Allushta [10]



Answer should be -1
4 0
2 years ago
Read 2 more answers
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let
vladimir1956 [14]

Answer:

a) P(X ≤ 2) = 0.87

b)  P(X ≥ 5) = 0.01

c) P(1 ≤ X ≤ 4) = 0.71

d) P ( X = 0 ) = 0.28

e) σ(X) = 1.09 , E(X) = 1.25

Step-by-step explanation:

Given:

- Let X = the number of defective boards in a random sample of size n = 25, so X ~ Bin(25, 0.05)

Where, n = 25 and p = 0.05

Find:

(a) Determine P(X ≤ 2).(b) Determine P(X ≥ 5).(c) Determine P(1 ≤ X ≤ 4).(d) What is the probability that none of the 25 boards is defective?(e) Calculate the expected value and standard deviation of X.

Solution:

- The probability mass function for a binomial distribution is given by:

                         P ( X = x ) = nCr * (p)^r * ( 1 - p )^(n-r)

a) P(X ≤ 2):

                         P(X ≤ 2) = P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 )

                         = (0.95)^25 + 25*0.05*0.95^24 + 25C2*0.05^2*0.95^23

                         = 0.87

b) P(X ≥ 5):

            P(X ≥ 5) = 1 - [P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P(X=4)

            = 1 - [ 0.87 + 25C3*0.05^3*0.95^22 + 25C4*0.05^4*0.95^21]

            = 1 - 0.98994

            = 0.01

c) P(1 ≤ X ≤ 4):

            P(1 ≤ X ≤ 4) = P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P(X=4)

            = ( 0.87 - 0.95^25) + 0.11994

           = 0.71

d) P( X = 0 )

            P ( X = 0 ) = 0.95^25 = 0.28

e) E(X) & σ(X):

            E(X) = n*p

            E(X) = 25*0.05 = 1.25

            σ(X) = sqrt ( Var (X) )

            σ(X) = sqrt ( n*p*(1-p) ) = sqrt ( 25*0.05*0.95 )

            σ(X) = 1.09

4 0
2 years ago
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