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1 month ago

(Please Hurry!) Which expression is equivalent to the following complex fraction?

Mathematics

1 answer:

lawyer [12.5K]1 month ago

6 0

Answer:

The equivalent expression for the provided complex fraction is

$\frac{-2x+5y}{3x-2y}$

Step-by-step explanation:

To simplify the complex fraction, calculating the numerator and denominator individually is effective.

Numerator:

$\frac{-2}{x} + \frac{5}{y}\\ = \frac{-2y + 5x}{xy}$

Denominator:

$\frac{3}{y} + \frac{-2}{x}\\ = \frac{3x - 2y}{xy}$

Resolving the complex fraction:

$[\frac{-2}{x} + \frac{5}{y}] / [\frac{3}{y} + \frac{-2}{x}]\\= [\frac{-2y + 5x}{xy}] / [\frac{3x - 2y}{xy}]$

$=\frac{-2y + 5x}{xy} * \frac{xy}{3x - 2y}$

Common terms in the numerator and denominator will cancel out (Cross multiplication):

$= \frac{-2y + 5x}{3x - 2y}$

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1 European euro = 1.3687 US dollars. While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on

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Answer:

$145.64

Because 250 USD = (1.03069 Euro /1 USD) = 257.6725

So, 257.6725-150=107.6725

Thus, 107.6725 Euro = (1.35261 USD/ 1 Euro) = 145.64

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1 month ago

The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.3 and the probability that a r

Svet_ta [12734]

Answer:

The likelihood of selecting an individual with high blood pressure who is also a runner is 2/3.

Step-by-step explanation:

Based on the data provided:

P( Choosing someone with high blood pressure ) = 0.3

or stated as P(H) = 0.3

P( Choosing a runner ) = 0.4

or stated as P(R) = 0.4

Now, P( Selecting a person with high blood pressure as well as being a runner) = 0.2

⇒ P(H∩ R) = 0.2

Next, we want to calculate the P(the selected individual is a runner, given they have high blood pressure)

which means we need to determine: P(R/H)

Using BAYES THEOREM:

$P(R/H) = \frac{P(R\cap H)}{P(H)}$

$\implies P(R/H) = \frac{0.2}{0.3 } = \frac{2}{3}$

So, the chance of choosing a person with high blood pressure who is a runner stands at 2/3.

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1 month ago

Kevin is buying water for his camping trip. He knows he needs at least 20 gallons of water for the trip. He already has five and

PIT_PIT [12445]

Response:

$5.5+0.25x\geq 20$

Step-by-step breakdown:

Kevin has already gathered five and a half gallons of water for his trip

He understands that he requires a minimum of 20 gallons of water for the journey.

The water is packaged in 32-fluid ounce (quarter-gallon) containers.

1 fluid ounce equals 0.0078125 gallons

32-fluid ounce $=32 \times 0.0078125 =0.25$

Let x represent the number of 32-fluid ounce (quarter-gallon) containers needed to collect at least 20 gallons of water for the trip.

One container holds 0.25 gallons of water

Therefore, x containers hold 0.25x gallons of water

Thus, Kevin's total gallons of water = $5.5+0.25x$

Since it is given that he needs at least 20 gallons of water for the trip.

Hence, $5.5+0.25x\geq 20$

Thus, the algebraic inequality representing this scenario is $5.5+0.25x\geq 20$

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29 days ago

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Vicky did a survey to answer the following question: What is the average fitness score of grade 8 students? The mean fitness sco

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The mean is found by summing all data values and dividing that total by the number of values.

The mean fitness score equals 3.2 points. If every student had the identical score, each student's fitness score would be 3.2 points.

Therefore, the correct choice is D. 3.2 points.

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22 days ago

The table shows the estimated number of lines of code written by computer programmers per hour when x people are working.

Zina [12379]

Answer:

Therefore, the data is best represented by:

$y=26.9x-1.3$

Step-by-step explanation:

We have a table indicating the estimated lines of code produced by computer programmers per hour when x individuals are engaged.

The question asks which model accurately reflects this data.

To determine this, we will substitute the values of x into each function to see which one accurately produces the corresponding y (f(x)) values provided in the table:

We are presented with four functions, which are:

$y = 47(1.191)^x$

$y=34\times (1.204)^x$

$y=26.9x-1.3$

$y=27x-4$

We'll create a table displaying these values at various x levels.

x A B C D

2 66.66 49.3 52.5 50

4 94.57 71.44 106.3 104

6 134.14 103.57 160.1 158

8 190.27 150.14 213.9 212

10 269.91 217.64 267.7 266

12 382.85 315.5 321.5 320.

Thus, the function that suitably represents the data is:

Option C.

y=26.9x-1.3

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