There were 680 gallons of water ALREADY in a 1600-gallon pool. Water is being pumped into the pool at the rate of 320 gallons per hour. Let x represents the number of hours. Find how many hours it will take to fill the pool.

Table a and table c defines a relationship between an input x and an output y of function.

A function is a set of ordered pairs (x, y) in which each value of x corresponds to exactly one value of y. In other words, for a given value of x, there should be only one corresponding value of y.

Looking at the tables, we can see that Table a and Table d both satisfy this condition. In both tables, for each value of x, there is only one corresponding value of y. Therefore, Tables a and d represent functions.

Table b and Table c do not satisfy this condition, because there are multiple values of y for some of the values of x.

For example, in Table b, the value of x is 24 for both (24, 53) and (24, 29). Similarly, in Table c, the value of x is 24 for both (24, 53) and (24, 29). Therefore, Tables b and c do not represent functions.

Therefore table a and table c represents function of input x and output y.

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A function is a collection of ordered pairs (x, y) where each x-value is matched up with exactly one y-value. In other words, there should only be one value of y that corresponds to a certain value of x.

We can see from the tables that Tables a and Table d both meet this requirement. In both tables, there is only one value of y that corresponds to each value of x. Tables a and d so depict functions.

Because there are many possibilities of y for some of the values of x, Tables b and c do not meet this requirement.

For instance, the value of x in Table b is 24 for both (24, 53) and (24, 29). The value of x is 24 in Table c for both (24, 53) and (24, 29). Tables b and c do not, therefore, represent functions.

Tables a and c therefore show the function of input x and output y.

A function f of three real variables assigns a real number f(x, y, z) to each set of real numbers (x, y, z) in the domain of the function.

Now, According to the question:

Three-Variable Calculus considers functions of three real variables. A function f of three real variables assigns a real number f(x, y, z) to each set of real numbers (x, y, z) in the domain of the function. The domain of a function of three variables is a subset of coordinate 3-space { (x,y,z) | x, y, z ∈ {R} }.

A real-valued function f defined on a subset  D  of  [tex]R^2[/tex]  is a rule that assigns to each point  f(x ,y)  in  D  a real number  f(x ,y) . The largest possible set  D  in  [tex]R^2[/tex]  on which  f  is defined is called the domain of  f , and the range of  f  is the set of all real numbers  f(x ,y)  as  (x ,y)  varies over the domain  D . A similar definition holds for functions  f(x ,y ,z)  defined on points  (x ,y ,z)  in  [tex]R^3[/tex] .

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The value of x is x=34.

What is angles?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The angles are corresponding angles so they are equal if m is parallel to n

x+27 = 2x -7

Subtract x from each side

x+27 -x =2x-x-7

27 = x-7

Add 7 to each side

27+7 = x-7+7

34 =x

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If the two sides on one triangle are congruent to the corresponding two sides of the other triangle and the included angles are congruent in both triangles, then the triangles are congruent by SAS (side-angle-side).

SAS theorem of congruence: The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle, then the two triangles are congruent.

Use the SAS theorem of congruence to determine if the triangles in the figure below are congruent.

From fig(1) is congruent to fig(2).

For each triangle, find two labeled sides with labeled included angle (side-angle-side in order).

For ΔABC, we have:

|AC|=10,m∠A=46∘, |AB|=7

For ΔXYZ, we have:

|XZ|=10,m∠Z=46∘, |YZ|=7

Compare the results from step. If the two sides on one triangle are congruent to the corresponding two sides of the other triangle and the included angles are congruent in both triangles, then the triangles are congruent by SAS.

So, |AC|=|XZ|, m∠A=m∠Z, |AB|=|YZ| the triangles are congruent by SAS.

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The required real proportion's 95% confidence interval is (0.301; 0.359).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

So, the sample size is 1000.

Phat = 0.33

(1 - phat) = 1 - 0.33 = 0.67

Zcritical = 1.96 at 95%

The confidence range is as follows:

Phat ± margin of error

Margin of Error = Zcritical * sqrt[(phat(1 - phat)) /n]

Margin of Error = 1.96 * sqrt[(0.33 * 0.67) / 1000]

Margin of Error = 1.96 * 0.0148694

Margin of Error = 0.0291440

Lower boundary = (0.33 - 0.0291440) = 0.300856

Upper boundary = (0.33 + 0.0291440) = 0.359144

Therefore, the required real proportion's 95% confidence interval is (0.301; 0.359).

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Correct question:
Cyber Monday Shopping A survey of 1000 U.S. adults found that 33% of people said that they would get no work done on Cyber Monday since they would spend all day shopping online. Find the 95% confidence interval of the true proportion.

There are three types of roots in mathematics which are real , repeated and non real roots.

When the value of the roots obtained are less than 0 then the roots obtained are known as not real or imaginary roots.

When the roots are greater than zero then they are known as real roots.

When the value of roots obtained is equal to 0 then we conclude that the roots are repeated.

We can get the roots of a function by factorizing the given expression or we can also find them using the determinant method. Or we can also use the graphical method to find the roots.

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Answer:

4xyxy

Step-by-step explanation:

there is a baby 2 so add 2 more x and y. ;)

Answer:

Step-by-step explanation:

Answer:

11.1

Step-by-step explanation:

sin 46 · x = 8

0.71934 x = 8

x  = 8/0.71934

x = 11.121306

In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

Integral is a term derived form the word integration. Integration in calculus is the opposite of differentiation

Integration is used to get the whole by combining combine slices or smaller portions.

Finding areas, volumes, central points, and many other important things may be done with integration. However, it is simplest to begin by calculating the distance between a function and the x-axis.

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The solution of the given system of equations 3x + y = 10 ,  x - y = 2 is equal to x = 3 and y = 1.

As given in the question,

Given system of equations are :

3x + y = 10      ____(1)

x - y = 2    _____(2)

Add equation (1) and  (2) to eliminate y and get the value of x we have,

3x + y = 10

x - y = 2

4x      = 12

⇒x = 12 / 4

⇒ x = 3

Substitute value of x = 3 in equation (1) to get the value of y for the given equation,

3(3) + y = 10

⇒ 9 + y = 10

⇒ y = 10 - 9

⇒ y = 1

Therefore, the solution of the given system of equations is equal to x = 3 and y =1.

The above question is incomplete, the complete question is:

What is the solution of the system of equations 3x + y = 10 ,  x - y = 2?

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Answer:

Below

Step-by-step explanation:

1/a + 1/r = 1/3        a = aaron rate   r = rosa rate    3 = rate of both

1/5 + 1/r = 1/3

1/r = 2/15

r = 15/2 = 7.5 hr for rosa alone

you can rent the boat 55.92 hour if It costs $$3535 per hour to rent a boat at the lake. You also need to pay a $$2525 fee for safety equipment.

What is an example of an equation?

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

It costs $$3535 per hour to rent a boat at the lake.

You also need to pay a $$2525 fee for safety equipment.

You have $$200200.

safety fee only once

so 200200-2525 = 197675

if one hour fees is 3535

then 197675/3535

= 55.92

hence he rent boat at the lake 55.92 hour

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The given values are 2,6,5,3,0,3,4,3,2,4,5,2,4

There are the following values as shown in the given data.

To find the mode first we have to assign each value that how many times it appears.

1. 2-3 the number 2 appears only Three times.

2. 6-1 the number 6 appears one time.

3. 5-2 the number 5 appears only two times.

4. 3-3 the number 3 appears only three times.

5. 0-1 the number 1 appears only one time.

6. 4-3 the number 4 appears only Three times.

So, the mode of the given data is 4,3,2 as it appears the most number of times.

If a given set of values with two modes is bimodal, a given set of numbers with three modes is trimodal, and any set of numbers with more than one mode is multimodal.

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The graph of linear inequalities is straight line bounded by solid or dashed region.

The graphing system of linear inequalities is different from linear eqaution because of  using equal to inequal sign such as ≥ and ≤ or inequal sign < and >.

when we plot the poins on XY axis we get a straight line. The region that satisfy the inequalities of variables are bounded by either solid line or dashed line.

hence, the graphing system of linear variables has shaded portion where straights line is the boundary.

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Both median and mean originate from the Latin medianus, meaning in the middle, the former by way of the Anglo-French meiene. Median is the middle number in a sorted list of numbers. To determine the median value in a sequence of numbers, the numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest.  

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed.

The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result.

This is why it is called a median.

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Answer:

sh. 32

Step-by-step explanation:

Before the reduction, the cost was [tex]35(8/7)=[/tex]sh. 40.

Therefore, the price before the increase was [tex]40(4/5)=[/tex]sh. 32.

Answer:

x = -2.75 and y = 1.5.

Step-by-step explanation:

To solve the system of equations 4x - 2y = -2 and -3x + 5y = -9, we can use the elimination method. This method involves adding or subtracting the equations in a way that eliminates one of the variables, leaving us with an equation in terms of the remaining variable.

First, we can add the equations together to eliminate the y variable:

(4x - 2y) + (-3x + 5y) = (-2) + (-9)

Combining like terms on the left side of the equation gives us:

x + 3y = -11

Next, we can solve for x by dividing both sides of the equation by 4 to get:

x = (-11) / 4 = -2.75

Once we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the second equation, -3x + 5y = -9, and substitute -2.75 for x:

-3(-2.75) + 5y = -9

Solving for y, we get:

y = (-9 - (-8.25)) / 5 = 1.5

Therefore, the solution to the system of equations 4x - 2y = -2 and -3x + 5y = -9 is x = -2.75 and y = 1.5.

The law of cosines generalizes the Pythagorean formula to all triangles. It says that c^2, the square of one side of the triangle, is equal to a^2 + b^2, the sum of the squares of the the other two sides, minus 2ab cos C, twice their product times the cosine of the opposite angle. When the angle C is right, it becomes the Pythagorean formula.

c^2=a^2 + b^2 - 2abcosC

Pythagorean formula

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

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The graph f(x) = (x – 5) The x-axis is touched at -2 by 3(x + 2).

By examining the power of the factor, you may determine whether the graph will cross the x-axis or only touch it.

(x - 5)

3 is an odd number because it has a power of 3. A power of ODD indicates that the graph will pass through the x-axis.

(x + 2)

A power of 2, or even number, exists in the number 2. In the case of an EVEN power, the graph will contact the x-axis.

Set the factor equal to zero and solve to determine the location where it will touch the axis.

Subtract 2 from both sides so that (x + 2) = 0.

x = -2

The complete question is:-

At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x-axis?

A. -5

B. -2

C. 2

D. 5

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x=1/2 and x=-4 are zeros of the polynomial 2x²+7x-4=0.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is 2x²+7x-4=0

To find the zero of 2x²+7x-4=0 we need to find the roots of polynomial.

2x²+7x-4=0

2x²+8x-x-4=0

Take 2x as common from first two terms

2x(x+4)-(x+4)=0

(2x-1)(x+4)=0

2x-1=0

2x=1

x=1/2 and x=-4 are zeros.

Hence, x=1/2 and x=-4 are zeros of the polynomial 2x²+7x-4=0.

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The yield of stock at yesterday's closing price is 3.43%.

Annual dividend is the profit of the stock which is divided among the shareholders, both common and preferred shareholders annually.

Given,

Annual dividend = $1.20

Today's closing price = $34.50

Net change = -$0.50

Let x be yesterday's closing price.

Net change = Today's closing price - yesterday's closing price

⇒ -0.50 = 34.50 - x

⇒ x = 34.50 + 0.50

⇒ x = 35

Yield = [tex]\frac{Annual dividend}{Price}[/tex] × 100

         = [tex]\frac{1.2}{35}[/tex] × 100

         = 3.4286 % ≈ 3.43 %

Hence the stock's yield at yesterday's closing price of preferred stock is 3.43 %.

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b. if two parallel lines are cut by a transversal, then corresponding angles are congruent.

c. if two parallel lines are cut by a transversal, then alternate interior angles are congruent.

d. points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.

The required factor of the given equation 6x²+17x+5 is (3x+1)(2x+5).

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

For instance, the polynomial x² - 4 and the integer 15 can both be factored by the number 3 * 5.

So, we have the equation:

6x²+17x+5

Now, factorize as follows:

6x2+17x+5

6x2+15x+2x+5

3x(2x+5)+1(2x+5)

(3x+1)(2x+5)

Therefore, the required factor of the given equation 6x²+17x+5 is (3x+1)(2x+5).

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Correct question:

Factorise: 6x²+17x+5.

Answer:

Hence, x=28.

Step-by-step explanation:

you will find that the slope, or m, is equal to 4/5 and that b is the coordinates 0 and -4

What is the slope of the relation y 4 5x 4?

The first step that needs to be done is to convert the equation into the y=mx+b format where m is the slope and b is the intersection of the y-intercept. Simply solve the equation for Y and you get Y=4/5X-4. From this, you will find that the slope, or m, is equal to 4/5 and that b is the coordinates 0 and -4

if the slopes are:

L1: slope 3

L2: slope -3

L3: slope -1/3

So now multiply the slopes of each pair of lines:

L1 and L2: 3 * (-3) = - 9 => No, they are not perpendicular

L2 and L3: (-3) * (-1/3) = 1 => No, they are not perpendicular

L1 and L3: (3) *  (-1/3) = -1 => Yes, they are penpendicular.

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The expected number that will arrive on time is; 151.23

The standard deviation of this distribution is; 6.62

We are given;

Percentage of the flights involved in the study arrived on time; p = 71% = 0.71

Sample size; n = 213

Now, the formula for the mean which is the expected number that will arrive on time is;

μ = np

μ = 213 * 0.71

μ = 151.23

The formula for the standard deviation of the distribution is;

σ = √(np(1 - p))

σ = √(213*0.71(1 - 0.71))

σ = 6.62

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Answer:

  d.  f(x) → +∞, x → +∞; f(x) → -∞, x → -∞

Step-by-step explanation:

You want the end behavior of the cube root function f(x) = 2∛x +3.

The vertical translation upward 3 units can be ignored when considering the end behavior. The sign of a cube root matches the sign of the argument, so the signs of x and f(x) will match when both get large.

  f(x) → +∞, x → +∞; f(x) → -∞, x → -∞