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Alex787 [66]
3 years ago
7

Suppose that 10% of all homeowners in an earthquake-prone area of California are insured against earthquake damage. Four homeown

ers are selected at random. Define the random variable x as the number among the four who have earthquake insurance.
Mathematics
1 answer:
guapka [62]3 years ago
5 0

Remainder of question:

Find the probability distribution of x

Answer:

The random variable x is defined as: X = {0, 1, 2, 3, 4}

The probability distribution of X:

P(X = 0) = 0.656

P(X = 1) = 0.2916

P(X= 2) = 0.0486

P(X=3) = 0.0036

P(X = 4) = 0.0001

Step-by-step explanation:

Sample size, n = 4

Random variable, X = {0, 1, 2, 3, 4}

10% (0.1) of the homeowners are insured against earthquake, p = 0.1

Proportion of homeowners who are not insured against earthquake, q = 1 - 0.1

q = 0.9

Probability distribution of x,

P(X = r) = ^nC_r *p^r q^{n-r} \\\\P(X= 0) =(^4C_0 *p^1 q^4 )\\P(X=0) = (^4C_0 *0.1^0 0.9^4 ) = 0.656\\P(X= 1)= (^4C_1 *p^1 q^3 )\\P(X=1) = (^4C_1 *0.1^1 0.9^3 ) = 0.2916\\P(X= 2)=( ^4C_2 *p^2 q^2) \\P(X=2) = (^4C_2 *0.1^2 0.9^2 ) = 0.0486\\P(X= 3) = (^4C_3 *p^3 q^3) \\ P(X=3) = (^4C_3 *0.1^3 0.9^1 ) = 0.0036\\P(X= 4) =  (^4C_4 *p^4 q^0 )\\ P(X=4) =(^4C_4 *0.1^4 0.9^0 ) = 0.0001

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Answer:

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Step-by-step explanation:

The measure of an inscribed angle is 1/2 the measure of the intercepted arc

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Now m of arc SPQ = 360 - 114 = 246

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3 years ago
The diameter of a soda can is 2.6 inches. What is the total length of the diameters of 5
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3 years ago
If c(x) = 4x-2 and d(x) = x^2 + 5x is is (c•d) (x)
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<h3>Answer: (c * d)(x) = 4x^3 + 18x^2 - 10x</h3>

Work Shown:

I'm assuming the dot means multiplication. If so, then,

(c * d)(x) = c(x)*d(x)

(c * d)(x) = [ c(x) ] * [ d(x) ]

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(c * d)(x) = 4x(x^2+5x) - 2(x^2+5x) ... distribute

(c * d)(x) = 4x(x^2)+4x(5x) - 2(x^2)-2(5x) ... distribute again

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2 years ago
What is the most precise name for a quadrilateral with the following vertices:
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Answer:

The most precise name for a quadrilateral ABCD is a parallelogram

Step-by-step explanation:

we have

A(2,3) B(7,2) C(6,-1) D(1,0)

Plot the quadrilateral'

using a graphing tool

The quadrilateral ABCD in the attached figure

Verify the length of the sides

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

step 1

Find distance AB

A(2,3) B(7,2)

substitute

d=\sqrt{(2-3)^{2}+(7-2)^{2}}

d=\sqrt{(-1)^{2}+(5)^{2}}

d_A_B=\sqrt{26}\ units

step 2

Find distance BC

B(7,2) C(6,-1)

substitute

d=\sqrt{(-1-2)^{2}+(6-7)^{2}}

d=\sqrt{(-3)^{2}+(-1)^{2}}

d_B_C=\sqrt{10}\ units

step 3

Find distance CD

C(6,-1) D(1,0)

substitute

d=\sqrt{(0+1)^{2}+(1-6)^{2}}

d=\sqrt{(1)^{2}+(-5)^{2}}

d_C_D=\sqrt{26}\ units

step 4

Find distance AD

A(2,3) D(1,0)

substitute

d=\sqrt{(0-3)^{2}+(1-2)^{2}}

d=\sqrt{(-3)^{2}+(-1)^{2}}

d_A_D=\sqrt{10}\ units

step 5

Compare the length sides

AB=CD

BC=AD

Opposite sides are congruent

<em>Verify the slope of the sides</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

step 1

Find slope AB

A(2,3) B(7,2)

substitute

m=\frac{2-3}{7-2}

m=\frac{-1}{5}

m_A_B=-\frac{1}{5}

step 2

Find slope BC

B(7,2) C(6,-1)

substitute

m=\frac{-1-2}{6-7}

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step 3

Find slope CD

C(6,-1) D(1,0)

substitute

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step 4

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A(2,3) D(1,0)

substitute

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step 5

Compare the slopes

m_A_B=m_C_D

m_B_C=m_A_D

The slope of the opposite sides are equal, that means, opposite sides are parallel

The slopes of consecutive sides are not opposite reciprocal, that means, consecutive sides are not perpendicular

therefore

The most precise name for a quadrilateral ABCD is a parallelogram

8 0
3 years ago
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4x - 4x - 5 = -5
4x - 4x = -5 + 5
0 = 0

this equation has infinite solutions
3 0
3 years ago
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