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2 years ago

En Vision Algebra 2

Mathematics

1 answer:

jeyben [28]2 years ago

5 0

Step-by-step explanation:

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Question 9 20% of a particular brand of light bulbs fail in one year. What is the probability that three bulbs out of a random c

Delvig [45]

Answer:

The correct answer is 0.15

Step-by-step explanation:

According to the given scenario, the probability is as follows:

X $\sim$ Bin (n,p)

Here

n = 8

p = 0.20 or 20%

Now this is a binomial probability distribution

$P(X) = ^nC_x \times p^x \tmes (1 - p)^{n-x}\\\\P(3) = ^8C_3 \tims 0.20^3 \times (1 - 0.20)^5$

= 0.15

Hence, the correct answer is 0.15

5 0

2 years ago

Suppose that the length of a side of a cube X is uniformly distributed in the interval 9

Nastasia [14]

Answer:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

Step-by-step explanation:

Given

$9 < x < 10$ --- interval

Required

The probability density of the volume of the cube

The volume of a cube is:

$v = x^3$

For a uniform distribution, we have:

$x \to U(a,b)$

and

$f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.$

$9 < x < 10$ implies that:

$(a,b) = (9,10)$

So, we have:

$f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Solve

$f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Recall that:

$v = x^3$

Make x the subject

$x = v^\frac{1}{3}$

So, the cumulative density is:

$F(x) = P(x < v^\frac{1}{3})$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$ becomes

$f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.$

The CDF is:

$F(x) = \int\limits^{v^\frac{1}{3}}_9 1\ dx$

Integrate

$F(x) = [v]\limits^{v^\frac{1}{3}}_9$

Expand

$F(x) = v^\frac{1}{3} - 9$

The density function of the volume F(v) is:

$F(v) = F'(x)$

Differentiate F(x) to give:

$F(x) = v^\frac{1}{3} - 9$

$F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}$

$F'(x) = \frac{1}{3}v^{-\frac{2}{3}}$

$F(v) = \frac{1}{3}v^{-\frac{2}{3}}$

So:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

8 0

2 years ago

PLEASE HELP

Crank

Answer:

Listeriosis is an infection caused by the bacteria Listeria monocytogenes. People become infected by eating foods contaminated with the bacteria. Listeria may infect many different sites in the body, such as the brain, spinal cord membranes, or the bloodstream

Step-by-step explanation:

People with invasive listeriosis usually report symptoms starting 1 to 4 weeks after eating food contaminated with Listeria

5 0

2 years ago

Read 2 more answers

Helpppppppppppppppppppppppppppppppp

Dafna1 [17]

Answer:
1/625

Explanation:
In case of multiplication of numbers with same base, we add the powers.
This means that:
a^x * a^y = a^(x+y)

Applying this to the given, we will find that:
(5^-1) * (5^-3) = 5^(-1-3)
= 5^-4
= 1/625

Hope this helps :)

4 0

3 years ago

Read 2 more answers

The number of bacteria (b) in a batch of refrigerated food is given by the function b(t) = 20t2 − 70t + 300, where t is the temp

Setler79 [48]

If the number of bacteria $b(t)$ is a function only of temperature $t$ , and the temperature $t(h)$ is a function only of time in hours $h$ , then

$b(t(h))=b(2h+3)=20(2h+3)^4-70(2h+3)+300$
$b(t(h))=320h^4+1920h^3+4320h^2+4180h+1710$

4 0

2 years ago