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3 years ago

When a number is decreased by 45%, the result is 9. What is the original number to the nearest tenth?

Mathematics

1 answer:

Paul [167]3 years ago

3 0

Answer:

16.4

Step-by-step explanation:

To decrease a number by 45% of its value, you subtract the 45%. To get 45%, you multiply the number by 0.45.

So, if x is the original number, then the equation for this word problem would be x - 0.45x = 9.

To solve, we first subtract 0.45x from x, which is 0.55x. This means that 0.55x is equal to 9. To simplify, we can divide both sides by 0.55. 9/0.55 is 16.36363636..., etc. The nearest tenth would be 0.4, so your answer is 16.4

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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

Heidi and Andrew designed two raised flowerbeds for their garden. Heidi’s flower bed was 5 feet long by 3 feet wide, and Andrew’

Alona [7]

Answer:

90 ft³

Step-by-step explanation:

Volume is calculated as length × width × height.

Heidi: 5×3×2 = 30 ft³

Andres: 5×6×2 = 60 ft³

Total: 30 + 60 = 90 ft³

3 0

3 years ago

What is the approximate surface area of the sphere 15yd?

tekilochka [14]

<span>The surface area of a sphere is equal to [4 x Pi x R^2]. In other words, four multiplied by 3.14 multiplied by the radius squared. If the radius of a sphere is 15 yards, the approximate surface area is [4 x 3.14 x (15x15)] = [12.5 x 225] = [2,812 yd^2]. The surface area of a sphere with radius 15 yd is approximately 2,800 yards.</span>

7 0

4 years ago

Simplify.

natima [27]

Its 2y+7z hope dis helps

5 0

3 years ago

Read 2 more answers

2. A dance floor is a square with an area of 1,444 FT(2). What are the dimensions of the dance floor?

svet-max [94.6K]

Answer:

The answer is C use a calculator

Step-by-step explanation:

not that hard lol

8 0

3 years ago