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Maksim231197 [3]
2 years ago
6

A public swimming pool that holds 45,000 gallons of water is going to be drained for maintenance at a rate of 100 gallons per mi

nute. The amount of water w (in gallons) in the pool after t minutes is given by the function w = 45,000 - 100t. Graph the function. Identify its domain and range. How much water is in the pool after 60 minutes? How many minutes will it take to empty the pool?
Mathematics
1 answer:
neonofarm [45]2 years ago
5 0

Answer: for the first question, after an hour there would be 39,000 gallons left and it would take 450 minutes to drain the pool

Step-by-step explanation:

You multiple the minutes with the rate or which the gallons are being drained and subtract it by the total amount,

Ps can I get the brainliest answer

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Let X be the temperature in at which a certain chemical reaction takes place, and let Y be the temperature in (so Y = 1.8X + 32)
Black_prince [1.1K]

Answer:

See explanation

Step-by-step explanation:

Solution:-

The random variable, Y be the temperature of chemical reaction in degree fahrenheit be a linear expression of a random variable X : The  temperature in at which a certain chemical reaction takes place.

                             Y = 1.8*X + 32

- The median of the random variate "X" is given to be equal to "η". We can mathematically express it as:

                             P ( X ≤ η ) = 0.5

- Then the median of "Y" distribution can be expressed with the help of the relation given:

                             P ( Y ≤ 1.8*η + 32 )

- The left hand side of the inequality can be replaced by the linear relation:

                             P ( 1.8*X + 32 ≤ 1.8*η + 32 )

                             P ( 1.8*X ≤ 1.8*η )   ..... Cancel "1.8" on both sides.

                            P ( X ≤ η ) = 0.5 ...... Proven

Hence,

- Through conjecture we proved that: (1.8*η + 32) has to be the median of distribution "Y".

b)

- Recall that the definition of proportion (p) of distribution that lie within the 90th percentile. It can be mathematically expressed as the probability of random variate "X" at 90th percentile :

                             P ( X ≤ p_.9 ) = 0.9 ..... 90th percentile

- Now use the conjecture given as a linear expression random variate "Y",

          P ( Y ≤ 1.8*p_0.9 + 32 ) = P ( 1.8*X + 32 ≤ 1.8*p_0.9 + 32 )

                                                 = P ( 1.8*X ≤ 1.8*p_0.9 )

                                                 = P ( X  ≤ p_0.9 )

                                                 = 0.9

- So from conjecture we saw that the 90th percentile of "X" distribution is also the 90th percentile of "Y" distribution.

c)

- The more general relation between two random variate "Y" and "X" is given:

                            Y = aX + b

Where, a : is either a positive or negative constant.

- Denote, (np) as the 100th percentile of the X distribution, so the corresponding 100th percentile of the Y distribution would be : (a*np + b).

- When a is positive,

                   P ( Y ≤ a*p_% + b ) = P ( a*X + b ≤ a*p_% + b )

                                                 = P ( a*X ≤ a*p_% )

                                                 = P ( X  ≤ p_% )

                                                 = np_%        

- When a is negative,

                   P ( Y ≤ a*p_% + b ) = P ( a*X + b ≤ a*p_% + b )

                                                 = P ( a*X ≤ a*p_% )

                                                 = P ( X  ≥ p_% )

                                                 = 1 - np_%        

                                                           

4 0
3 years ago
The graph of y=x^2 -7x+ 12 is a parabola with x-intercepts at
vesna_86 [32]

Answer:

<h2>x = 3 and x = 4 → (3, 0) and (4, 0)</h2>

Step-by-step explanation:

\text{x-intercept is for y = 0}.\\\\\text{We have the function:}\ y=x^2-7x+12.\\\\\text{Put y = 0 and calculate the value(s) of x.}\\\\x^2-7x+12=0\\\\x^2-3x-4x+12=0\\\\x(x-3)-4(x-3)=0\\\\(x-3)(x-4)=0\iff x-3=0\ \vee\ x-4=0\\\\x-3=0\qquad\text{add 3 to both sides}\\\boxed{x=3}\\\\x-4=0\qquad\text{add 4 to both sides}\\\boxed{x=4}

6 0
3 years ago
Kamden is a mind-reading alien. He had each friend draw and look at a card, then he guessed whether the card had a star on it.
klasskru [66]

Answer:

Step-by-step explanation:

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6 0
3 years ago
Solve x to the power of 2 = 4 where x is a real number. Please help fast
zimovet [89]

Answer:

It's 2

Step-by-step explanation:

X is 2 because if you multiply two by two you get 4

7 0
2 years ago
The population of Virginia is 24% less than the population of Georgia,. If the population of Georgia is 10.5 million what is the
zlopas [31]

The population of Virginia is 7,980,000 people.

  • Let the population of Virginia be V.
  • Let the population of Georgia be G.

<u>Given the following data:</u>

  • Population of Georgia = 10.5 million

To find the population of Virginia:

Translating the word problem into an algebraic expression, we have;

24% percent less:

\frac{24}{100} × 10500000

24 × 105000

24% of G = 2,520,000

Now, we can find the population of Virginia:

V = G - 2,520,000

V = 10,500,000 - 2,520,000

<em>V = 7,980,000 people.</em>

Therefore, the population of Virginia is 7,980,000 people.

Find more information: brainly.com/question/596290

5 0
2 years ago
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