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3 years ago

The new 12 mile hiking trail is 150% of the length of the original trial. How long was the original trial?

Mathematics

1 answer:

Tamiku [17]3 years ago

4 0

Answer:

<h2>The answer is 8 miles</h2>

Step-by-step explanation:

Let the original trail be x

From the question 150% of the trail is

12 mile

That's

150% of x = 12

So we have

$\frac{150}{100} x = 12 \\ \\ \frac{3}{2} x = 12$

Multiply through by 2

That's

$2 \times \frac{3}{2} x = 12 \times 2$

We have

3x = 24

Divide both sides by 3

We have the final answer as

x = 8

Therefore the length of the original trail is

<h3>8 miles</h3>

Hope this helps you

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Find the cardinality of the set B = { 5, 6, 7, … , 100}

vaieri [72.5K]

The cardinality of the set B is given to be 96.

<h3>What is the cardinality of a set?</h3>

This is the term that is used to refer to the number of elements that a given set can be said to contain.

This is a set that has numbers that ranges from 5 to 100, this tells us that the numbers 1, 2, 3, 4 are excluded from the set.

Hence the total numbers excluded is 4. 100 - 4 = 96

Therefore from 5 to 100, the total 9 and the cardinality of the set B is 96.

Read more on the cardinality of a set here: brainly.com/question/23976339

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1 year ago

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponenti

melomori [17]

Answer:

a) 0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

b) Capacity of 252.6 cubic feet per second

Step-by-step explanation:

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:

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

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).

This means that $m = 100, \mu = \frac{1}{100} = 0.01$

(a) Find the probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.)

We have that:

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

This is P(X > 190). So

$P(X > 190) = e^{-0.01*190} = 0.1496$

0.1496 = 14.96% probability that the demand will exceed 190 cfs during the early afternoon on a randomly selected day.

(b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.08?

This is x for which:

$P(X > x) = 0.08$

$e^{-0.01x} = 0.08$

$\ln{e^{-0.01x}} = \ln{0.08}$

$-0.01x = \ln{0.08}$

$x = -\frac{\ln{0.08}}{0.01}$

$x = 252.6$

Capacity of 252.6 cubic feet per second

5 0

3 years ago

Is the difference between a positive mixed number and a negative mixed number always, sometimes, or never positive?

Annette [7]

Ok It depends upon what the order of the terms might be

If we consider that the positive mixed number is the first term and the negative mixed number is the second term and we consider "difference" to be subtraction.....then the result is positive

For example

(3 + 1/2) - [ -(1 + 1/2)] =

(3 +1/2) + (1 + 1/2) = 5 since subtracting a negative results in a positve

But....if we had the reverse order with the same operation, we would have

-(1 + 1/2) - (3 + 1/2) and the result is - 5

Hence.......I would go with "sometimes"

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3 years ago

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tamaranim1 [39]

C : B = D : E
6 : 5 = D : 3
D = 3.6

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3 years ago

Which of the following can be modeled with a linear function? Select all that apply.

kobusy [5.1K]

Answer:

Step-by-step explanation: ifk

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3 years ago