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3 years ago

A wood stove burns 4 same sized logs in 2 hours how many logs does the stove burn in 8 hours

2 answers:

8 0

By using the information you have, you can use make a proportion to solve this. You burn 4 logs in 2 hours or 4/2. You are comparing this to your unknown number, x, over 8 hours. So it looks like this 4/2 = x/8. You read it as four logs in two hours is x logs in eight hours. To solve you cross multiply. You do 2 times x and 4 times eight. That would be 2x= 32. Your goal is getting x alone, so divide each side by 2. Your answer is x= 16 logs in eight hours. You can solve this different and maybe easier ways but this is the best way if you want to get used to going this in algebra. Hope that helps! :)

rodikova [14]3 years ago

5 0

16 because 2 divided by 8 = 4 and 4×4 =16

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f) The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated indep

Step2247 [10]

Answer:

15.24% probability that at least 2 will still stand after 35 years

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution and the exponential distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Probability of a single tower being standing after 35 years:

Single tower, so exponential.

Mean of 25 years, so $m = 25, \mu = \frac{1}{25} = 0.04$

We have to find $P(X > 35)$

$P(X > 35) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-0.04*35} = 0.2466$

What is the probability that at least 2 will still stand after 35 years?

Now binomial.

Each tower has a 0.2466 probability of being standing after 35 years, so $p = 0.2466$

3 towers, so $n = 3$

We have to find:

$P(X \geq 2) = P(X = 2) + P(X = 3)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{3,2}.(0.2466)^{2}.(0.7534)^{1} = 0.1374$

$P(X = 3) = C_{3,3}.(0.2466)^{3}.(0.7534)^{0} = 0.0150$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.1374 + 0.0150 = 0.1524$

15.24% probability that at least 2 will still stand after 35 years

4 0

3 years ago

What number can replace the n in n/12 to make it equivalent to 1/2 ?<br> 6<br> 8<br> 9<br> 10

Ierofanga [76]

Answer:

i believe the answer is 6.

4 0

3 years ago

Read 2 more answers

A rectangular dartboard has an area of 648 square centimeters. The triangular part of the dartboard has an area of 162 square ce

never [62]

Answer:

The probability that the dart lands inside the triangle is 0.25

Step-by-step explanation:

* Lets explain how to find the probability of an event

- The probability of an Event = Number of favorable outcomes ÷ Total

number of possible outcomes

- P(A) = n(E) ÷ n(S) , where

# P(A) means finding the probability of an event A

# n(E) means the number of favorable outcomes of an event

# n(S) means set of all possible outcomes of an event

- P(A) < 1

* Lets solve the problem

- A rectangular dartboard has an area of 648 cm²

- The triangular part of the dartboard has an area of 162 cm²

- A dart is randomly thrown at the dartboard

- The dart lands in the rectangle

∴ The area of the rectangle is the set of all possible outcomes n(S)

- The probability P(A) that the dart lands inside the triangle

∴ The area of the triangle is set of favorable outcomes of an

event n(E)

∵ P(A) = n(E) ÷ n(S)

∴ P(T) = area of the triangle ÷ area of the rectangle

∵ Area of the rectangle is 648 cm²

∴ n(S) = 648

∵ The area of the triangle is 162 cm²

∴ n(E) = 162

∴ P(T) = 162 ÷ 648 = 1/4 = 0.25

* The probability that the dart lands inside the triangle is 0.25

5 0

3 years ago

Find the distance between the line 1.2x − 0.5y + 1.1=0 and the origin.

denpristay [2]

Answer:

The answer to your question is: d = 0.85 units

Step-by-step explanation:

Data

Line equation: 1.2 x − 0.5 y + 1.1 = 0 A = 1.2; B = -0.5; C = 1.1

Point (0, 0) x = 0; y = 0

Formula

d = | Ax + By + C | / √(A² + B²)

Process

d = |(1.2)(0) + (-0.5)(0) + 1.1 | / √ (1.2)² + (0.5)²

d = | 1.1 | / √ 1.44 + 0.25

d = 1.1 / √ 1.69

d = 1.1 / 1.3

d = 0.85 units

7 0

3 years ago

Express the area A of a circle as a function of its radius, r. Determine the area of a circle whose radius is 11 inches. That

nekit [7.7K]

<h2>Answer with explanation:</h2>

The function represents the area of a circle(A) is given by :-

$A(r)=2\pi r$

To determine the area of a circle whose radius is 11 inches. , we put the value of r=11 inches, we get

$A(11)=2\pi (11)$

Now, we put $\pi=\dfrac{22}{7}$ in the above function , we get

$A(11)=2(\dfrac{22}{7} )(11)\\\\\Rightarrow\ A=56.5714285714\approx56.57$

8 0

3 years ago