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2 years ago

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Suppose that in a population of 1000 there are 300 defective items and 700 items that are not defective. if you are selecting tw

o items at random from this population, what is the probability they will both be defective?

1 answer:

natulia [17]2 years ago

4 0

This is a combinations problem.

The total number of possible 2-item combinations is (1000 choose 2)

The number of 2-defective combinations is (300 choose 2)

The probability = $\frac{300 C 2}{1000 C 2} = 0.09$

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Let Î be a Bernoulli random variable that indicates which one of two hypotheses is true, and let P(Î = 1) = p. Under the hypothe

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2 years ago

A student wants to know how far above the ground the top of a leaning flagpole is. At high noon, when the sun is almost directl

MariettaO [177]

Answer:

15.43 ft

Step-by-step explanation:

To solve this question, one should use the concept of similar triangles.

The pole's shadow and the distance to the ground (x) form a similar triangle to the distance of the plumb bob from the base and the length of the plumb bob, respectively. Note that we do not need to know the measurements of the third side of the triangles to solve the problem. Therefore, the distance of the top of the pole to the ground is:

$14 in = 1.1667 ft$

$1.1667x=6*3\\x = 15.43$

The distance of the top of the pole to the ground is 15.43 ft.

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2 years ago

The triangular prism shown has triangular _____face(s) and lateral face(s).

dmitriy555 [2]

Answer:

The triangular prism shown has 2 triangular face(s) and 3 lateral face(s).

The area of one triangular face is 7.5 mm²

The surface area of the triangular prism is 135 mm²

Step-by-step explanation:

A triangular face of the prism is the face that has a three sided figure while the lateral faces are faces with four-sided figure. As seen from the triangular prism, it has 2 triangular faces since it is made up of 2 right angled triangles and has 3 lateral faces since it is made up of 3 rectangles which are 4 sided each.

Area of one triangular face = $\frac{1}{2} * base * height$

Given base = 2.5 mm and height = 6 mm

Area of one triangular face = $\frac{1}{2} *2.5 * 6\\$

$= 3*2.5\\= 7.5mm^{2}$

Surface area of triangular prism = bh + pH

b= base of the triangle = 2.5 mm

h- height of the triangle = 6 mm

p= perimeter of the triangle = base + height + slant height = 2.5+6+6.5

p = 15 mm

H= height of the prism = 8mm

Surface area of triangular prism = 2.5(6)+15(8)

Surface area of triangular prism = 15 + 120

Surface area of triangular prism = 135mm²

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2 years ago

Ignatz repeatedly rolls a fair $6$-sided die. What is the probability that he rolls his first $5$ before he rolls his second (no

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Ignatz has a probability of rolling his first $5$ on a 6:1 probability.

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2 years ago

World poultry production was 77.2 million tons in the year 2004 and increasing at a continuous rate of 1.6% per year. Assume tha

dezoksy [38]

Answer:

A) $P(t)=77.2\cdot e^{0.016t}$

B) 89.157 million tons.

C) In year 2017.

Step-by-step explanation:

We have been given that world poultry production was 77.2 million tons in the year 2004 and increasing at a continuous rate of 1.6% per year.

A). We know that a continuous growth function is in form $y=a\cdot e^{kx}$ , where,

a = Initial value,

k = Growth rate in decimal form.

$1.6\%=\frac{1.6}{100}=0.016$

Upon substituting our given values, we will get:

$P(t)=77.2\cdot e^{0.016t}$

Therefore, our required function would be $P(t)=77.2\cdot e^{0.016t}$ , where, P represents world poultry production, in million tons, as a function of the number of years, t, since 2004.

B) To find the world poultry production in the year 2013, we will substitute $t=2013-2004=9$ in above formula as:

$P(9)=77.2\cdot e^{0.016(9)}$

$P(9)=77.2\cdot e^{0.144}$

$P(9)=77.2\cdot 1.1548841085249135$

$P(9)=89.1570531781\approx 89.157$

Therefore, the world poultry production in the year 2013 would be 89.157 million tons.

C) To find the number of years it will take for world poultry production to be over 95 million tons, we will equate our function with 95 as:

$95=77.2\cdot e^{0.016t}$

Divide both sides by 77.2:

$1.2305699481865285=e^{0.016t}$

Take natural log of both sides:

$\text{ln}(1.2305699481865285)=\text{ln}(e^{0.016t})$

$\text{ln}(1.2305699481865285)=0.016t\text{ln}(e)$

$0.20747743456981035=0.016t*1$

Divide both sides by 0.016:

$t=12.9673396606$

$t\approx 13$

Therefore, 13 years after in 2017 world poultry production goes over 95 million tons.

4 0

2 years ago