y=4x^2-16x+2 in vertex form

Answer:

(x-5)^2

Step-by-step explanation:

No; the coefficient shows that as a percentage of the mean, the quarter-milers' times show more variability.

To summarize the variability in the data, we can calculate the standard deviation and the coefficient of variation for both the quarter-mile and mile runners.

Standard deviation:

Quarter-mile times:

mean = (0.92 + 0.96 + 1.04 + 0.93 + 1.00) / 5 = 0.97

differences from mean = [0.92 - 0.97, 0.96 - 0.97, 1.04 - 0.97, 0.93 - 0.97, 1.00 - 0.97] = [-0.05, -0.01, 0.07, -0.04, 0.03]

squared differences = [0.0025, 0.0001, 0.0049, 0.0016, 0.0009]

sum of squared differences = 0.01

standard deviation = √(sum of squared differences / (number of data points - 1)) = sqrt(0.01 / 4) = 0.049

Mile times:

mean = (4.52 + 4.35 + 4.60 + 4.71 + 4.51) / 5 = 4.56

differences from mean = [4.52 - 4.56, 4.35 - 4.56, 4.60 - 4.56, 4.71 - 4.56, 4.51 - 4.56] = [-0.04, -0.21, 0.04, 0.15, -0.05]

squared differences = [0.0016, 0.0441, 0.0016, 0.0225, 0.0025]

sum of squared differences = 0.0727

standard deviation = √(sum of squared differences / (number of data points - 1)) = sqrt(0.0727 / 4) = 0.139

Coefficient of variation:

Quarter-mile times: coefficient of variation = standard deviation / mean = 0.049 / 0.97 = 0.051 (to 2 decimal places)

Mile times: coefficient of variation = standard deviation / mean = 0.139 / 4.56 = 0.0305 (to 4 decimal places)

The use of the coefficient of variation indicates that the coach's statement should be qualified. The coefficient shows that as a percentage of the mean, the mile runners' times have less variability (3.05%) compared to the quarter-mile runners' times (5.1%). So, the answer is (ii) no; the coefficient shows that as a percentage of the mean, the quarter-milers' times show more variability.

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The amount the women would pay for 2.4 kg of chicken and 2 kg of meat in total is $15.2

The meaning of unit price is a price quoted in terms of so much per agreed or standard unit of product or service

Given that, a woman bought 1.8 kg of chicken and 1.6 kg of meat. The chicken cost $5.40 and the meat cost $6.40,

We need to find, if she had bought 2.4 kg of chicken and 2 kg of meat, how much would she have had to pay,

To find the same, we will first find the unit price of each,

Unit price = total price / total quantity

Since, 1.8 kg of chicken costs $5.40,

Therefore, 1 kg will cost = 5.40 / 1.8 = $3

Similarly,

If 1.6 kg of meat costs $6.40,

Therefore, 1 kg will cost = 6.40 / 1.6 = $4

Now, to find the cost of 2.4 kg of chicken and 2 kg of meat, we will multiply the unit prices to the required quantities,

Therefore,

2.4 kg of chicken will cost = 2.4 x 3 = $7.2

2 kg of meat will cost = 2 x 4 = $8

In total, she had to pay = 8+7.2 = $15.2

Hence, the amount the women would pay for 2.4 kg of chicken and 2 kg of meat in total is $15.2

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The solution of the initial value problem is y = -3x/(3㏑x - 1)

An initial value problem is a differential equation in which the initial value of the function is given.

Now we have the initial value problem

y' = (xy + y²)/x² , y(1) = 3.

We notice that it is a homogeneous differential equation.

A homogeneous differential equation is a differential equation in which the powers of x and y are the same.

So, we proceed to solve the equation as folows.

Let y = vx.

So,

y/x = v and

dy/dx = xdv/dx + v

We now substitute these into the differential equation, we have that

y' = (xy + y²)/x²

dy/dx = (xy/x² + y²/x²

xdv/dx + v = y/x + (y/x)²

xdv/dx + v = v + v²

xdv/dx = v²

So using the method of separation of variables, we have

dv/v² = dx/x

Thus Integrating both sides, we have

∫dv/v² = ∫dx/x

-v⁻¹ = ㏑x + C

-1/v = ㏑x + C

We now substitute v = y/x into the equation, we have

- 1/y/x = ㏑x + C

-x/y = ㏑x + C

So, making y subject of the formula, we have

y = -x/(㏑x + C)

Since y(1) = 3, we have

3 = -1/(㏑1 + C)

3 = -1/(0 + C)

3 = -1/C

C = -1/3

So, y = -x/(㏑x + (-1/3))

y = -x/(㏑x - 1/3)

y = -x/(3㏑x - 1)/3

y = -3x/(3㏑x - 1)

So, the solution is y = -3x/(3㏑x - 1)

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The numerical value of cosh(7) is 25.78543.

The  hyperbolic cosine function, cosh(x), is the inverse of the hyperbolic sine function, sinh(x). It is defined as the sum of the series cosh(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + …, where x is any real number and n! is the factorial of n.

To find the numerical value of cosh(7), we need to evaluate the series at x = 7. To do this, we start by calculating the first two terms of the series, 1 and 7²/2!. The first term is 1, and the second term is 7²/2! = 49/2 = 24.5. Then we add them together to get the result cosh(7) = 25.5.

To get a more accurate result, we can add more terms to the series. For instance, by adding the third term, 7⁴/4!, we get cosh(7) = 25.5 + 585/24 = 25.70833. We can continue this process to get an even more accurate result.

After adding the sixth term, 7⁶/6!, we get cosh(7) = 25.70833 + 90090/720 = 25.78542.

Finally, we round the result to five decimal places to get cosh(7) = 25.78542 ≈ 25.78543.

The numerical value of cosh(7) is 25.78543.

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The solutions are 1+i and 1-i of the quadratic equation x²-2x+2=0

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The quadratic formula to find solution of an equation is

x=-b±√b²-4ac/2a

The given equation is x²-2x+2=0

a=1, b=-2, c=2

x=2±√4-4(1)(2)/2(1)

x=2±√-4/2

x=2±2i/2

x=1+i, 1-i

Hence, the solutions are 1+i and 1-i of the quadratic equation x²-2x+2=0

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Answer:

I'm sorry, but without additional information such as the magnitude, direction, and orientation of the two forces, it is impossible to determine the magnitude of the resultant.

The ratio of bp to cp in equilateral triangle abc, with a on circle omega(Ω), bc tangent to circle omega(Ω), and p being the intersection of ao and bc, is [tex]\frac{2}{\sqrt{3} }[/tex].

Let's label the center of the larger circle omega(Ω) as O, and the center of the smaller circle gamma(Γ)as G. Draw a perpendicular from O to the line containing side overline{BC}, and label the intersection point as X. By tangency, GX is a radius of gamma(Γ), so GX = 17.

Also, $\overline{OX} = 20. By the Pythagorean Theorem, OP = [tex]\sqrt{OX^{2} -PX^{2} }[/tex] = [tex]\sqrt{20^{2}-17^{2} }[/tex] = [tex]\sqrt{289}[/tex]. Let BP = x. Then CP = [tex]\frac{BC}{2} -x[/tex] = [tex]\frac{BC}{2} -x[/tex] = [tex]\frac{BC-2x}{2}[/tex]. Therefore, [tex]\frac{BP}{CP}[/tex] = [tex]\frac{x}{\frac{BC-2x}{2} }[/tex]= [tex]\frac{2x}{BC-2x}[/tex] = [tex]\frac{2x}{BC}[/tex].

To find BC, we use the fact that ΔABC$ is equilateral. Therefore, AO = BO = CO = 20. Let's apply the Law of Cosines to triangle ABO:

[tex]AB^{2} =AO^{2} +BO^{2} -2.AO.BO.cosA[/tex]

[tex]AB^{2} =20^{2} +20^{2} -2.20.20.cos(60)[/tex]

[tex]AB^{2} =800[/tex]

[tex]AB=\sqrt{800} =20\sqrt{2}[/tex].

Therefore, [tex]BC=AB=20\sqrt{2}[/tex], and [tex]\frac{BP}{CP} =\frac{2x}{BC}=\frac{2x}{20\sqrt{2} }[/tex].

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The distance between two points in three-dimensional space is a measure of the separation between the two points. In this case, the two points are the center of a sphere and a point that the sphere passes through.

To find the distance, we can use the distance formula in three dimensions, which is an extension of the distance formula in two dimensions. The distance formula is:

d = √((x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2)

where (x1, y1, z1) is the center of the sphere and (x2, y2, z2) is the point that the sphere passes through. The square root of the sum of the squares of the differences between the corresponding coordinates gives the distance between the two points.

In this problem, the center of the sphere is not given, so it is not possible to calculate the distance between the sphere and the point. The center of the sphere is a crucial piece of information needed to solve this problem.

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There could be 150 sequences of rolls

Let's find the sets of 5 integers less than or equal to 6 that could multiply to 300 (where order doesn't matter for right now):

1, 2, 5, 5, 6

1, 3, 4, 5, 5

2, 2, 3, 5, 5

Now let's find the number of unique ways we could reorder these sets

There are

5!/2!=60 ways to order {1, 2, 5, 5, 6}

There are

5!/2! =60 ways to order {1, 3, 4, 5, 5}

There are

5!/2!2! =30 ways to order {2, 2, 3, 5, 5}

There could have, therefore, been 60 + 60 + 30 = 150 different sequences of rolls

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Answer:

2

Step-by-step explanation:

well I so yeah and this plus that

The greatest common factor of 50,12,and 8 is,

⇒ 2

We have to given that,

All the numbers are,

⇒ 50, 12 and 8

Now, We know that,

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Here, Numbers are,

50 = 2 x 5 x 5

12 = 2 x 2 x 3

8 = 2 x 2 x 2

Hence, The greatest common factor of 50,12,and 8 is,

⇒ 2

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a) The proportion of observations, P(z < -0.67) = 0.2514.

b) The proportion of observations, P(z > -0.67) = 0.7486.

c) The proportion of observations, P(z < 1.46) = 0.9279.

d) The proportion of observations, P(-0.67< z < 1.46) = 0.6765.

A z-table, or standard normal table, helps to reveals what percentage of values fall below a certain z-score in a normal distribution. We have a standard normal table present above .

a) P( z < -0.67 )

Split -0.67 such as (-0.6 + 0.07 ) and look -0.6 in first column and 0.07 in first row then look cross value. So, P( z < -0.67 )

= 0.2514

b) P( z > - 0.67 ) = 1 - P( z < -0.67 )

From part (a ) , P( z < -0.67 ) = 0.2514

So, P( z > - 0.67 ) = 1 - 0.2514 = 0.7486

=> P( z > - 0.67 ) = 0.7486

c ) P( z < 1.46 ) = 1 - P( z < -1.46 )

Using Table, P( z < -1.46 ) is,

=> P( z < -1.46 ) = 0.0721

So, P( z < 1.46 ) = 1 - 0.0721 = 0.9279

=> P( z < 1.46 ) = 0.9279

d) P(-0.67 < z < 1.46 ) = P( z < 1.46) - P( z < -0.67 ) from part( a) , P( z < -0.67 ) = 0.2514

and from par (c) , P( z < 1.46 ) = 0.9279

So, P(-0.67 < z < 1.46 ) = 0.9279 - 0.2514

= 0.6765

=> P(-0.67 < z < 1.46 ) = 0.6765

Hence, all the required proportion are determined.

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Complete question:

Use The above table A to find the proportion of observations from a standard Normal distribution that satisfies each of the following statements. Give your answers to four decimal places.

a) z < -0.67=

b) z > -0.67=

c) z < 1.46=

d) -0.67 < z < 1.46=

In linear function, 2027 is  the year in which the population will reach 15,000.

What is another name for a linear function?

A linear function, also known as a polynomial function of degree zero or one, is a function in calculus and related fields that has a graph that is a straight line.

                        The phrase "affine function" is frequently used to distinguish such a linear function from the other idea.

Let linear function

Since 2004

In 2004, t=0  ,P=6200

6200=a(0)+b

b=6200

In 2009, t=5 ,P =8100

8100=5a+6200

5a=8100-6200

5a=1900

a=1900/5

a=380

a)Substitute value of a and b in linear function equation .

    P = 380t + 6,200

B)In 2013 ,t =2013-2004=9

P=380(9)+6200

P=9620

C) P=15000

15000=380t+6200

380t=15000-6200

t=8800/380

t=23.16

t=23(nearest year)

Year=2004+23=2027

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Answer: The domain of the function f refers to the set of all input values (x) for which the function is defined. Based on the information provided, it is not possible to determine the full domain of the function f. The only information provided are the outputs (f(1)=10, f(2)=-7, f(3)=4) for specific input values (1, 2, 3).

Step-by-step explanation:

Answer:

Is 3/5 greater than 1/4? Is 3/5 bigger than 1/4? Is 3/5 larger than 1/4? These are all the same questions with one answer.

To get the answer, we first convert each fraction into decimal numbers. We do this by dividing the numerator by the denominator for each fraction as illustrated below:

3/5 = 0.6

1/4 = 0.25

Then, we compare the two decimal numbers to get the answer.

0.6 is greater than 0.25.

Therefore, 3/5 is greater than 1/4 and the answer to the question "Is 3/5 greater than 1/4?" is yes.

Which means that this equation is also true: 3/5 > 1/4

Step-by-step explanation:

Note: When comparing fractions such as 3/5 and 1/4, you could also convert the fractions (if necessary) so they have the same denominator and then compare which numerator is larger.

The joint density function of xy and [tex]z^{2}[/tex] [tex]& f_T(t)=\frac{1}{2 \sqrt{t}} \quad \leqslant t \leq 1 \\&[/tex].

From the given data

x, y, z are independent and uniformly distributed on [0,1] and also Independent.

⇒[tex]& f(x, y)=f_x(x) \quad f y(y) \\[/tex]

⇒[tex]& \omega=x y \\[/tex]

⇒[tex]& f_\omega(\omega)=P(\omega \leq \omega) \\[/tex]

[tex]& =\int_A \int_1 1 d x d y \\[/tex]

⇒[tex]& A \rightarrow\left\{(x, y): \quad \begin{array}{ll} & 0 \leq x \leq 1 \\0 \leq y \leq 1\end{array} \quad x y \leq \omega\right\} \\[/tex]

⇒[tex]& f_\omega(w)=\omega+\int_z^1 \int_0^x(y) d y d x \\[/tex]

[tex]& =\omega+\int_z^1[y]_0^{w / x} d x \\[/tex]

[tex]& =\omega+y / w(\omega / x) d x \\[/tex]

[tex]& =\omega+\omega[\ln x]_\omega^{\prime} \omega \\[/tex]

[tex]& =\omega+\omega(0-\ln \omega) \\[/tex]

⇒[tex]& f_\omega(\omega)=\omega-\omega \ln . \\[/tex]

⇒[tex]& f_\omega(\omega)=\frac{\partial}{\partial \omega}(f \omega(\omega)) \\[/tex]

[tex]& =1-[\omega / \omega+\ln \omega] \\[/tex]

⇒[tex]& f_\omega(\omega)=-\ln \omega \quad \quad 0 \leq \omega \leq 1 \\[/tex]

⇒[tex]& \text { Pdf of } z^2 \\[/tex]

⇒[tex]& T=z^2 \\[/tex]

⇒[tex]& f_T(t)=P(T \leq t) \\[/tex]

[tex]& =p\left(z^2 \leq t\right) \\[/tex]

[tex]& =p(r \leqslant \sqrt{t}) \\[/tex]

[tex]& =\int_0^{\sqrt{t}} 1 d z \\[/tex]

[tex]& =[z]_0^{\sqrt{t}} \\[/tex]

[tex]& =\sqrt{t} \\[/tex]

⇒[tex]& 0 \leq t \leq 1 \\[/tex]

⇒[tex]& F_T(t)=\sqrt{t} \\[/tex]

⇒[tex]& F_T(t)=F_T^{\prime}(t) \\[/tex]

⇒[tex]& f_T(t)=\frac{1}{2 \sqrt{t}} \quad \leqslant t \leq 1 \\&[/tex]

Therefore, the joint density function of xy and [tex]z^{2}[/tex] [tex]& f_T(t)=\frac{1}{2 \sqrt{t}} \quad \leqslant t \leq 1 \\&[/tex]

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Number of  gallon containers of paint required are 2.

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.

Given;

A gallon of paint can cover 250 square feet

The paint should be bought to paint 3 coats on each wall of a rectangular room with dimensions 16 feet by 8 feet and walls that are 10-feet tall.

Now,

The surface area for 3 coats on the wall;

=2(16*10)+2(8*10)

=320+160

=480

1gallon covers 250sq ft

For 480sq ft

=480/250

=1.92

Therefore, to paint he room of given area approximately 2 cans will be required.

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If intersection of A & B null set and P(A) = 0.4, P(A ∪ B) = 0.9 then P(B) = 0.5

In mathematics, a set is a collection of distinct objects, called elements, which can be anything from numbers, to letters, to functions, or even other sets. The objects in a set are unordered, meaning their position or arrangement doesn't matter. Sets are often denoted using curly braces {} and the elements within the set are separated by commas.

For example, the set of positive even numbers less than 10 can be written as {2, 4, 6, 8}.

Given that,

A ∩ B = ∅,

P(A) = 0.4,

P(A ∪ B) = 0.9,

P(B) = ?

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

0.9 = 0.4 + P(B) - 0

P(B) = 0.9 - 0.4

       = 0.5

Hence, the probability of event B is 0.5

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Answer:

It depends on the question as x and y are variables. so they can be any number

Step-by-step explanation:

Andre walks more steps than Priya

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

To solve this problem, we have to state the equation using the information of the problem:

Calculating Andre's steps we have:

y(Andre) = 6000 steps/50 minutes

y(Andre) = 120 steps/ minute

If the total of hours is 5 hours we convert hours to minutes and we have:

5 hours * (60 minutes/ 1 hours) = 300 minutes

Andre's steps in 300 minutes are:

y(Andre) = 120 steps/ minute * 300 minutes

y(Andre) = 36000 steps

Now we calculate the steps of Pria with the equation given:

y=118x

y(Pria) = 118*300

y(Pria) = 35400 steps

36000 steps > 35400 steps

y(Andre) > y(Pria)

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Correctly written question:

Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walk for a total of 5 hours. Who walks more steps?

The expected average of all your quizzes is 92%.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

Expected score when you study = 100%

Expected score when you don't study = 60%

Probability that you study = 0.8

Probability that you don't study = 1 - 0.8 = 0.2

Expected Value or mean of the random variable X is,

E(X) = Σ(x P(x))

Expected average = (100 × 0.8) + (60 × 0.2)

                               = 92

Hence the expected value of all your quizzes is 92%.

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The expression tan(arcsec(x/3)) can be written   [tex]1/3 \sqrt{x^2-9}[/tex]  in algebraic form.

The inverse secant function, or arcsecant, is defined as the inverse of the secant function, which is the ratio of the length of the hypotenuse of a right triangle to the length of the adjacent side. Given x/3 as the length of the adjacent side, arcsec(x/3) is the measure of the angle that has a secant equal to x/3.

The tangent function is the ratio of the length of the opposite side of a right triangle to the length of the adjacent side. By substituting arcsec(x/3) as the measure of the angle in a right triangle, we can use the tangent function to find the ratio of the lengths of the opposite and adjacent sides, which is equal to [tex]1/3 \sqrt{x^2-9}[/tex].

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A logical inference on the composition of the marbles in the bag is that there are approximately 3 green, 2 blue, 4 red, and 3 yellow marbles.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, A bag containing 12 colored marbles. Dan drew a single marble from the bag 25 times, replacing the marble each time.

He recorded drawing a red marble 9 times.

Thus, the number of red marvels = 12 * 9 /25

the number of red marvels = 4.32 or 4

He recorded drawing a yellow marble 6 times,

Thus, the number of yellow marbles = 12 *6/25

the number of yellow marbles = 2.88 or 3 approx

He recorded drawing a blue marble 4 times,

Thus, the number of blue marbles = 12 *4/25

the number of blue marbles =  1.92 or 2 approx

He recorded drawing and a green marble 6 times.

Thus, the number of green marbles = 12 *6/25

the number of green marbles = 2.88 or 3 approx,

Therefore, A reasonable conclusion about the makeup of the marbles in the bag is that there are approx 3 green marbles, 2 blue marbles, 4 red marbles, and 3 yellow marbles.

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Items in A and C, but not B is the required region.

Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

Given:

A ∩ B' ∩ C

That means,

A intersection not B intersection C.

B' is the complement of set B.

So, the region is,

Items in A and C, but not B.

Therefore, the items in A and C but not in B.

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The percent of infections for Hospital 6 is given as follows:

44.81%.

The percentage is obtained applying the proportions in the context of this problem.

A proportion is applied because a percentage is calculated with the division of the number of desired outcomes by the number of total outcomes, a result which is then multiplied by 100%.

Out of 540 patients in Hospital 6, 67 were infected in hospital and 175 after release, hence the percentage is obtained as follows:

P = (67 + 175)/540 = 44.81%.

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The figure on the left illustrates a society that produces more capital goods than consumer goods, as indicated by a Total Value of Goods difference of $200.

The figure on the left illustrates a society that produces more capital goods than consumer goods. This is because the total value of the capital goods is greater than the total value of the consumer goods. This can be calculated using the formula Total Value of Goods (TVG) = Price of Goods x Quantity of Goods. By using this formula we can calculate that the TVG of the capital goods is $400 (20 x 20) and the TVG of the consumer goods is $200 (10 x 20). The difference between the two is $200, indicating that the society is producing more capital goods than consumer goods.

The figure on the left illustrates a society that produces more capital goods than consumer goods, as indicated by a Total Value of Goods difference of $200.

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An equation represent the given scenario is 725=y-12.5x.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the Buckingham fountain holds 725 gallons of water.

Due to the harsh winter, it was discovered that it was cracked and leaking rate of 12.5 gallons per hour.

Let y represent the amount of water in gallons after x hours of leaking.

Now, equation is 725=y-12.5x

Therefore, an equation is 725=y-12.5x.

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Answer:

Step-by-step explanation:

it would take 30minutes

Answer:

The number can be expressed in multiple forms

Fraction form [tex]x=\frac{2962}{67}[/tex]  or decimal form  [tex]x=44.21[/tex]

Step-by-step explanation:

Lets break the problem down

"times" is multiplication *

The difference between 2 numbers is subtraction  [tex](x-y)[/tex]

A number plus a number is addition [tex]x+y[/tex]

[tex]68(x-45)=x+-98[/tex]

Lets solve for [tex]x[/tex].

Lets start on the left side.

Distribute 68 to the terms inside the parenthesis.

[tex]68x-3060=x+-98[/tex]

A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign.

[tex]68x-3060=x-98[/tex]

Subtract [tex]x[/tex] from both sides of the equation.

[tex]68x-3060-x=-98[/tex]

Subtract [tex]x[/tex] from [tex]68x[/tex].

[tex]67x-3060=-98[/tex]

Add 3060 to both sides of the equation.

[tex]67x=2962[/tex]

Divide both sides of the equation by 67.

[tex]x=\frac{2962}{67}[/tex] or as a decimal [tex]x=44.21[/tex]