Lexi is rehydrating after an intense workout. She drinks 1/4 of a gallon every 50 minutes, or 5/6 of an hour. How many gallons of water does she drink in one hour?

a. The transformed equation is given as follows: h(x) = |x - 2| - 3.

b. The graph of the two functions is shown by the image presented at the end of the answer.

The translations are movements to the triangle in each of these directions:

The parent function in this problem is given as follows:

f(x) = |x|.

The first translation was a vertical translation three units down, hence we have that:

g(x) = f(x) - 3 = |x| - 3.

The second translation was a horizontal translation two units right, hence the have that the definition of the transformed equation h(x) is given as follows:

h(x) = g(x - 2) = |x - 2| - 3.

The graph of the functions is given by the image shown at the end of the answer, and the translations are verified on every point of the function, but especially the vertices.

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Answer:

28

Step-by-step explanation:

substitute the given values into the expression

x(2 - 4y² )

= - 2(2 - 4(- 2)² )

= - 2(2 - 4(4))

= - 2(2 - 16)

= - 2(- 14)

= 28

The ratio of the area of a square inscribed in a semicircle to the area of a square inscribed in a circle is 2/5.

What is a semicircle?

A semicircle in mathematics is a one-dimensional locus of points that makes up one-half of a circle. A semicircle's entire arc always measures 180 degrees. There is only one symmetry line in it.

For instance, if the radius is known, we can use the formula, which states that the area of a semicircle is equal to half that of a circle. As a circle's area is r2, Therefore, a semicircle's area is equal to 1/2(r2), where r is its radius. 3.14, or 22/7, is the value of.

Solution Explained:

Let's assume and take

The dimensions of the little square ABCD = 2 x 2 =4

of the little triangle's hypotenuse Radius of the semi-circle for BCG

H=sqrt(5) = The semicircle's radius

IHJK = 2sqrt is the diagonal of the huge square (5)

One side of the large square is IHJK when sin(45) x 2sqrt(5) = sqrt(10).

Therefore, the area of ABCD/area of IHJK is equal to 4/sqrt(10)2 = 2/5.

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The measure of the angle RQP = 60 degrees and the value of x is 16 and the measure of the arc RMP is 240 degrees.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).

It is given that:

A circle:

The measure of the arc RMP = 360 - Arc RP

The measure of the arc RMP = 360 - 120 = 240 degrees

The measure of the angle RQP = 1/2[240 - 120]

The measure of the angle RQP = 60 degrees

In the second circle:

9(9 + x) = 15(15)

9 + x = 25

After solving we get:

x = 16

Thus, the measure of the angle RQP = 60 degrees and the value of x is 16 and the measure of the arc RMP is 240 degrees.

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Answer:

200

Step-by-step explanation:

To find that out, you divide 1,000 by 5.

1,000 ÷ 5 = 200

Could you please mark me as Brainliest? Thank you!

Answer: 200

Step-by-step explanation: 1000 divided by 5 = 200

Answer:

It should be 1/5

Since the fractional versions of the ratios are equal, the ratios are equivalent.

The equations out of the following that are true would be:

The remaining two I am not certain if they are true or not. The way they were laid out made little to no sense. If you could maybe evaluate further on the other options, perhaps I can double check them for you and see if there are any other remainder options that are true. However, I know for certain that A and B are true.

The number form that includes only rational numbers are

(-2/3, 0, 0.321, √49, 101/3}

A rational number is one that has the form p/q, where p and q are both integers and q is not zero

Rational function means that the equation will be a fraction

examining the numbers

(-2/3, 0, 0.321, √49, 101/3}

-2/3 is already a fraction

0 = 0/1 hence can be written as a fraction

√49 = 7 = 7/1

101/3 already a fraction

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The company is deploying chargeback type of IT funding model where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes.

Traditional IT and project finance methods offer a key business risk and, if not modified, jeopardize the future of technology-based enterprises.

This excerpt from the whitepaper Changing the Finance Method by Keanen Wold, Levi Geinert, Shaun Norris, Charles Betz, Beth Dumke, Sam Guckenheimer, and Troy Magennis discusses that contradiction over how traditional financing methods handle ethical concerns and also what Agile and DevOps teams require to execute successfully.

Balancing the high-risk investment in innovation (research and development department) with regular business-as-usual responsibilities has always been difficult for organizations. Too much risk might, in the case of an unexpected failure, result in a business's dissolution; too little innovation could ultimately cause the company to be overtaken and lose market share to rivals and new upstarts.

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If a certain unit of a commodity is produced with a marginal cost of [tex]\frac{dc}{da} =9x^{2}+4x+15x^{1/4} +10[/tex], the cost of producing the first 126 units is 289.4

How to differentiate a function?

Differentiation is a way of showing rate of change of a function at a given time.

The given function  [tex]\frac{dc}{da} =9x^{2}+4x+15x^{1/4} +10[/tex],

Differentiate with respect to x

[tex]\frac{dc}{da} =18x+4+\frac{15}{4} x-^{3/4}[/tex]

input the value 100 for the value of x,

This implies that [tex]\frac{dc}{da} =18x+4+\frac{15}{4} x-^{3/4}[/tex]

[tex]\frac{dc}{da}[/tex]=1800+4+[tex]\frac{15}{4}[/tex] x[tex]\frac{1}{\sqrt[4]{100^{3} } }[/tex]

[tex]\frac{dc}{da}=1800+4+\frac{15}{4}x\frac{1}{3.16}[/tex]

Simplifying further

[tex]\frac{da}{da} =1804+4.75[/tex]

[tex]\frac{dc}{da} =1808.75\\[/tex]

To produce the first 16 units,

[tex]\frac{1808.75}{100} }[/tex] x [tex]\frac{16}{1}[/tex]

The cost of producing the first 16 units is 289.4

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Assuming the person's weight and magnitude, we can estimate their weight to be 491N.

A mathematical object's magnitude or size defines whether it is greater or smaller than other items of its kind.

In formal terms, an object's size can be thought of as the outward manifestation of an ordering—of the class of objects to which it belongs.

So, the person's weight will be:

The scale calculates the floor's usual upward force on the passenger.

The most force is produced when going up (when starting an upward trip or ending a downward trip).

The normal force is lowest when there is a downward acceleration.

Regarding any such situation

∑F y​ =ma y changes to +391Nmg = ma for halting and +591Nmg=+ma for starting. (Where a represents the size of the acceleration.)

Add these two simultaneous equations to eliminate a and determine mg:

+591N−mg+391N−mg=0

OR

982N–2mg=0

Fg​ = mg = 982N/2​ = 491N

Therefore, assuming the person's weight and magnitude, we can estimate their weight to be 491N.

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Complete question:

A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591N. As the elevator later stops, the scale reading is 391N. Assuming the magnitude of the acceleration is the same during starting and stopping, determine the weight of the person.

Answer:i am pretty sure it is c

Step-by-step explanation:

this is because it says Which graph best shows how many days each project has lasted? and c is the only one that is talking about days

The dimensions of the rectangle that will maximize the area of the window are length, L = 3.41 feet and width, w = 3.41 feet

Given: Perimeter (P) = 19 feet

Perimeter of window = Perimeter of rectangle + Perimeter of semicircle

P = 2(2r + L) + πr

where r = radius of the semicircle and   L = length of the rectangle

width(w) of the rectangle = 2r

Note: the diameter of the semicircle is the width of the rectangle

19 =  2(2r + L) + πr

19 = 4r + 2L + πr

2L = 19-4r-πr

L = 19/2 -2r- πr/2

Find the area (A) of the window:

A = Area of Rectangle + Area of Semicircle

A = 2rL + 1/2πr²

Put L into A = 2rL + 1/2πr²:

A = 2r(19/2 -2r- πr/2) + 1/2πr²

A = 19r - 4r² - πr² + 1/2πr²

A = 19r - 4r² - 1/2πr²

To maximize the area, differentiate both sides and set A' = 0

A = 19r - 4r² - 1/2πr²

A'  = 19 - 8r - πr

0  = 19 - 8r - πr

8r + πr = 19

r(8 + π) = 19

r = 25/(8 + π)

width(w) = 2r

w = 2[19/(8 + π)]

w = 38/(8 + π)

w = 3.41 feet

put r = 19/(8 + π) into L = 25/2 -2r- πr/2:

L = 19/2 -2(19/(8 + π))- π(19/(8 + π))/2

L = 19/2 - 38/(8 + π) - 19π/2(8 + π)

L = [19(8 + π) - 19(2)- 19π] / [2(8 + π)]

L = 38/(8 + π)

L =  3.41 feet

Therefore, the dimensions of the rectangle are length of 3.41 feet and width of 3.41 feet

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Answer:

32−4x=12,

25 over x end fraction plus 4 equals 9 ((25)/(x)+ 4 equals 9), and

x over 5 end fraction plus 5 equals 6 ((x)/(5) plus 5 equals 6)

Step-by-step explanation:

hope this help

Each of the three angles of the triangles whose sum of angles is 180 degree measures 75°, 65°, and 40°

An easy geometric instrument like a protractor is used to measure angles. A protractor is employed more frequently than a compass. Angle measurement is important for determining the precise angle. In geometry, there are several sorts of angles that we face in our daily lives, and we may measure angles using these tools.

Basic geometric instruments like a protractor and a compass are used to measure angles. These instruments aid in determining an angle's precise measurement. A protractor aids in producing an accurate angle measurement, while a compass aids in creating the angle. Angles can be measured in three different ways: in degrees, radians, and revolutions.

Here, we have

Let the largest angle be x degrees, the median y, and the smallest z.

x = 2y - 55

z = y - 25

x + y + z = 180

Substituting for x in the last equation:

2y - 55 + y + z = 180

3y + z = 235  

From the second equation:

- y + z = -25     Subtract this from the last equation:

4y = 260

y = 65 degrees

z = 65 - 25 = 40 degrees.

and x = 180 - 65 - 40 = 75 degrees.

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Answer: 4 hours

Step-by-step explanation:

322.58 - 200.14 = 122.44

122.44 divided by 30.61 = 4

Based on the slopes of both lines, the relationship between both lines is: D. a and b are perpendicular.

The relationship between two lines that are parallel is that they have the same slope, while the relationship between perpendicular lines is that their slopes are negative reciprocals of each other.

Find the slope of the line that passes through (-5, -2) and (-5, -5):

Slope (m) = change in y / change in x = (-5 -(-2)) / (-5 -(-5))

m = (-5 + 2) / (-5 + 5)

m = -3/0 [cannot divide, therefore, the slope is undefined).

The line is therefore a vertical line.

Find the slope of the line that passes through (0, 4) and (5, 4):

Slope (m) = change in y / change in x = (4 - 4) / (5 - 0)

m = 0/5

m = 0

This line is an horizontal line.

In conclusion, the relationship between a vertical and a horizontal line is that they are perpendicular to each other, therefore, the answer is: D. a and b are perpendicular.

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Answer:

The answer is third one, 6 and 7/20.

Step-by-step explanation:

First, rewrite the decimal number as a fraction with 1 as the denominator.

[tex]\frac{6.35}{1}[/tex]

Then, multiply to remove 2 decimal places.

[tex]\frac{6.35}{1} *\frac{100}{100} = \frac{635}{100}[/tex]

Next, find the GCF(Greatest common factor) of 635 and 100, which is 5.

Divide both the numerator (top) and denominator (bottom) by the GCF (5)

Simply the improper fraction.

There you go!

The value of the side c which is the hypotenuse of the given right angle triangle using Pythagoras theorem is; c = √148

Pythagoras Theorem is simply the way that we can find the missing length of a right angled triangle. The right angle triangle has three sides, namely the hypotenuse (which is the longest side), Opposite (which does not touch the hypotenuse) and then the adjacent side (which is between the opposite side and the hypotenuse).

The formula is literally;

c² = a² + b²

where;

c is hypotenuse and a and b are opposite and adjacent sides. Thus;

c² = 2² + 12²

c² = 4 + 144

c² = 148

c = √148

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Answer:

144 if u multiply u will get ur answer because it is asking for the least number if 144 is to high that its got to be 1 which it can't that's if u divide it answer - 144

The given series [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] is convergence and the sum of the series is 33/28.

In the given question we have to check whether the series converge or not. If the series does converge, then we have to find the sum.

The given series is [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex].

Firstly we check the convergence of the given series.

When a series approaches a limit, it is considered to be convergent if both convergent and divergent behaviour occur. The deletion of a finite number of terms from the beginning of a series has no impact on convergence or divergence.

We can write the series as:

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex]

As |0.3|<1 and |0.2|<1

Then [tex]\sum_{n=1}^{\infty}(0.3)^{n-1}\text{ and }\sum_{n=1}^{\infty}(0.2)^n[/tex] is convergent.

So [tex]\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex] is also convergent.

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-(0.2)\sum_{n=1}^{\infty}(0.2)^{n-1} \right[/tex]

Series [tex]\sum_{n=1}^{\infty}(x)^{n-1}[/tex] converges to 1/x-1 for |x|<1.

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{1-0.3}-(0.2)\frac{1}{1-0.2}[/tex]

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{0.7}-\frac{0.2}{0.8}[/tex]

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 10/7 - 1/4

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 33/28

Hence, the sum of the given series is 33/28.

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The right question is:

Determine whether the series is convergent or divergent.

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex]

If is is convergent, find the sum. (If the quantity diverges, enter diverges.)

Answer:

45, odd

Step-by-step explanation:

54-9=45

The gain Renata Corporation got from the sale of equipment is $16420

The tax depreciation method used in the United States is called MACRS, or Modified Accelerated Cost Recovery System. In other words, the method used to determine your business's tax deductions based on the depreciation of your tangible (depreciable) assets is known as MACRS depreciation.

Equipment Book value =

Purchase price - MACRS depreciation

= $328, 400 - $147,780

=$1,80,620

Gain = sale price - Book value

= $197, 040 - $180620

=$ 16420

Gain up to total depreciation is to be treated as ordinary income, that is up to $147, 780. since the gain is $16,420 within depreciation, it is treated as ordinary income.

Renata Corporation has a gain of $16,420 of which $16, 420 is treated as ordinary income due to the section 1245 recapture

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Given that the pay was $44,000 last year and $53,000 this year, the compensation will have increased by 20.45%.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal parts are considered to make up the whole.

Here,

Salary of staff last year=$44,000

Salary of staff this year=$53,000

The percent increase,

=(53000-44000)/44000*100

=20.45%

The percent increase in the salary will be 20.45% as the salary last year was $44,000 and the salary this year is $53,000.

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The probability that you win the game is 50%.

The game is symmetrical for you and your opponent. Thus, your probability of winning is as good as your opponent's, so, you have a 50% of winning.

Symmetry goes into play in probability theory in this way: if different outcomes are equivalent, they would have the same probability.

A symmetrical distribution happens when the values of variables come at regular frequencies and usually the mean, median, and mode all happen at the same point.

In general, if there are N symmetrical outcomes, the probability of any given one of them happening is taken to be 1/N.

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It will take Lian's dog 12.5 weeks to finish the remaining food

Fractions are numbers written as a quotient, in which a numerator is divided by a denominator

Given that:

Lian's dog eats 1/20 of a bag of dog food each week

Lian currently has of a bag 5/8 remaining

Since Lian's dog eats 1/20 in one week and 5/8 is remaining.

In order to find the number of weeks it will take the dog to finish the remaining food. We can say:

Number of weeks = remaining food / food for one week

Number of weeks = (5/8) / (1/20) = 12.5 weeks

Therefore,  it will take Lian's dog 12.5 weeks to finish the remaining food

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Complete Question

Lian's dog eats 1/20 of a bag of dog food each week. Lian currently has 5/8 of a bag remaining.

How many weeks will it take Lian's dog to finish this remaining food?

The number of files sorted in the first one and a half hours of sorting is 945.

Here, we are given that a group of clerks must sort 1775 files.

Each clerk sorts at a constant rate of 30 files per hour.

Let the number of clerks who start working initially be x.

Thus, they will sort 30x files in the first hour.

After the first hour, let the number of clerks who stop working be a

Thus, the number of files sorted in the second hour will be 30(x - a)

Similarly, the number of files sorted in the third hour will be 30(x - 2a)x

In the last 10 minutes, the number of files sorted will be 5(x - 3a)

Thus, we can form the following equation-

30x + 30(x - a) + 30(x - 2a) + 5(x - 3a) = 1775

30x + 30x - 30a + 30x - 60a + 5x - 15a = 1775

95x - 105a = 1775

19x - 21a = 355

x = (355 + 21a)/ 19

since x and a both have to be integers, (355 + 21a) must be divisible by 19.

This is the case when a = 3

⇒ x = (355 + 21*3)/ 19

x = 418/ 9

x = 22

Now, the number of files sorted in first one and a half hours will be-

30x + 15(x - a)

= 30*22 + 15(22 - 3)

= 660 + 15*19

= 660 + 285

= 945

Thus, the number of files sorted in the first one and a half hours of sorting is 945.

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The students weren't assigned the treatments (new menu item) at random.

In an experiment, randomization refers to assigning volunteers randomly to the treatment. For example, we may define randomization as setting people to therapy at random.  

The results are fair because randomization eliminates bias. To make the results of the experiment precise, it ensures that the groups created for experimenting are as similar to one another as possible.

In the given example, the menu items are not randomly assigned. Because the students were given a choice to choose a menu item instead of selecting the new menu item randomly.  If randomly assigned all the new menu items will have an equal probability of being chosen.

Therefore, option b is the correct option.

The complete question is -

Thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for a cafeteria. Each student was given a choice between the macaroni and cheese and the Cajun potato barrels. From the sample, 20 students selected macaroni and cheese and 16 students chose the Cajun potato barrels. Each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). Which of the following prevents this study from being a well-designed experiment?

a) There was no replication because students did not eat both menu items.

b) The treatments (new menu item) were not randomly assigned to the students.

c) An item that is currently on the menu should have been used as a control.

d) Students should not have been randomly selected.

e) There were no problems, and the study was a well-designed experiment.

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Emma would need to invest about $320 to increase her value by $480 over the course of 8 years.

We may use the compound interest formula to determine how much Emma would need to invest:

[tex]\mathrm{A = P(1 + r/n)^{(nt)}}[/tex]

Where:

A is equal to the final sum, in this case $480.

P is the principal sum, which represents the initial investment that we're looking for.

r = the yearly interest rate (0.055 in decimal form, or 5.5%)

n = the number of times the interest is compounded annually (in this case, n = 1 because it is compounded annually).

t = the number of years, in this instance 8 years.

Let's substitute the known values into the formula and solve for P:

[tex]\mathrm{480 = P(1 + 0.055/1)^{(1\times8)}}[/tex]

Simplifying:

[tex]480 = \mathrm P(1.055)^8[/tex]

Dividing both sides by (1.055)⁸:

[tex]\mathrm {P = \frac{480 }{ (1.055)^8}}[/tex]

P ≈ $480 / 1.50

P ≈ $320

Hence the amount to be invested is $320.

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