Archimedes drained the water in his tub. The amount of water left in the tub (in liters) as a function of time (in minutes) is graphed. How long did it take each time 18 liters of water were drained?

So, 32% of the field is red, which is equivalent to 192 square feet.

To find out how many square feet of the field is red, we need to use the percentage of the field that is red in the calculation. We know that 32% of the field is red, and the total size of the field is 600 square feet.

To calculate the number of square feet of the field that is red, we can use the following formula:

(32/100) * 600 square feet = 192 square feet

This calculation shows us that 32/100 of the field is red. To express this fraction in decimal we divide 32 by 100, which equals 0.32. To find the area of the field that is red, we then multiply 0.32 by 600 square feet.

So, the field has 192 square feet of the field is red.

Another way to think about it is: 32% is equal to 0.32, so we can multiply 600 square feet by 0.32, which also gives us 192 square feet.

Therefore, 32% of the field is red, which is equivalent to 192 square feet.

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We have that the Density of metal X  is mathematically given as

∅ = 5048.33 Kg/[tex]m^{3}[/tex]

Density is a word we use to describe how much space an object or substance takes up (its volume) in relation to the amount of matter in that object or substance (its mass). Another way to put it is that density is the amount of mass per unit of volume. If an object is heavy and compact, it has a high density.

Density of metal,

Generally the equation for the side of fcc  is mathematically given as

fcc = 2 × [tex]\sqrt{2}[/tex] × radius of metal

fcc = 2 × 1.414 × 135

fcc = 381.78 ×  [tex]10^{-12}[/tex] m.

where, volume of 1 unit cell of fcc

fccV = ( 381.78 ×  [tex]10^{-12}[/tex] ) ^3

fccV = 55,646,713.615752 ×  [tex]10^{-36}[/tex] [tex]m^{3}[/tex]

And

weight of 1 atom

Wa = molecular weight / avagadro number

Wa = 42.3/(6.023 × [tex]10^{23}[/tex])

Wa = 7.023 × [tex]10^{-23}[/tex] gm/atom

Therefore, density is

∅ = (28.0923 ×  [tex]10^{-26}[/tex]) / (55,646,713.615752 ×  [tex]10^{-36}[/tex] )

∅ = 5048.33 Kg/[tex]m^{3}[/tex]

Therefore, we have that the Density of metal X  is mathematically given as  ∅ = 5048.33 Kg/[tex]m^{3}[/tex]

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Answer:

bsbsnhs

Step-by-step explanation:

gsgdhbdjdnndnsnnsbsbdnhidfgdhhdjjdndjsjkekkekekekkekkekejekkdir

The vertices of the feasible region are  (0,100) (0,700) (400,500)

The minimum profit is (0,100)  and the maximum profit is (400,500)

Given that, P=14x+22y-900  where p is the profit

y > x +100    y must exceed the production of x by at least 100 units

x+2y<1400

x>0

y>0

We cannot produce negative quantities

Substitute y = x+100 into x+2y <1400

x+2(x+100) < 1400

x+2x+200 <1400

3x+200<1400

Subtract 200 from each side

3x<1200

Divide by 3

x<400

y = x+100

y = 400+100

y = 500

(400,500)

y > x +100

when x=0  y > 100  

x+2y <1400

0+2y <1400

2y <1400

y <700

When x=0  y = 700

a)  The vertices of the feasible region are  (0,100) (0,700) (400,500)

b)  Maximum and minimum profit occur at the vertices.

P=14x+22y-900

P(0,100) = 14(0) +22(100)-900 =2200-900=1300

P(0,700) = 14(0) +22(700)-900 =15400-900=14500

P(400,500) = 14(400) +22(500)-900 =5600+11000-900=15700

Thus, The vertices of the feasible region are  (0,100) (0,700) (400,500)

The minimum profit is (0,100)  and the maximum profit is (400,500)

Complete question: A factory can produce two products, x and y, with a profit approximated by P=14x+22y-900. The production of y must exceed the production of x by at least 100 units. Moreover, production levels are limited by the formula x+2y<1400.

a) Identify the vertices of the feasible region.

b) What production levels yield the maximum profit, and what is the maximum profit?

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When two expressions can be written similarly or when they can be combined into a single, simpler expression, they are said to be equivalent.

Let's evaluate each expression pair separately.

8. (n2+4)-n2 and 4n. (n2+4)-n2 = n2+ 4 - n2 = 4, which is not the same as 4n.

NOT THE SAME

9. The product of 3x + 5 and 2(x + 3) 2(x + 3) equals 2x + 6, not 3x + 5.

NOT THE SAME

10. 15 - 6x and 15(1 - 6x) (1 - 6x)

In other words, 15(1 - 6x) = 15 - 90x, which is not equal to 15 - 6x, is NOT EQUAL.

11. (y + y + 2 + y) + 3y and 6y + 2 (y + y + 2 + y) + 3y equals y+y+y+y +2 + 3y, which equals 3y + 2 + 3y and 6y + 2.

It is equivalent to the other phrase.

EQUIVALENT

12. 8y - 3 + 10y and 3 (6 - 1)

8y - 3 + 10y = 8y + 10y - 3 = 18y - 3 3(6 - 1) = 3(5) = 15

Both of the expressions are incompatible.

NOT THE SAME.

Only the expressions shown in position 11 are equivalent.

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Sine of a right-angled triangle is 1 i.e., sin 90°=1

One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function. The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.

Let the base of the triangle be ‘x’ and the perpendicular be ‘y’ and θ  be the angle

Sine acts as the ratio of the lengths of the opposing side and the hypotenuse side for any right-angled triangle measured from any angle.

sin θ =y/1

When the angle measurement hits the positive y-axis, it will have reached 90°, starting with the first quadrant. Since it now contacts the circle's rim, the value of y changes to 1. Consequently, y's value is changed to 1.

sin θ =y/1=1/1

Therefore, sin 90°=1/1

or, sin 90°=1

Hence, proved.

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Answer:(x+y)/2

Step-by-step explanation:

Only a and c represent function

How is a sequence defined?

In mathematics, a sequence is a list of items that is in order (or events). It has members and is similar to a set (also called elements, or terms). The number of ordered elements determines the length of the sequence (potentially infinite).

a. The sequence 2, 4, 6, 8, 10, ... represents a function. The domain of the function is the set of natural numbers, and the range is the set of even natural numbers. We can create a mapping by using the rule "multiply by 2" to match each input value of the domain with its corresponding output value in the range. For example, 2 maps to 4, 4 maps to 8, 6 maps to 12, and so on.

b. The sequence 1, 0, 1, 0, 1, ... does not represent a function. The reason is that for any given input value, the output value is not unique. For example, the input value of 1 maps to both 1 and 0, which means that the function is not well-defined.

c. The sequence 0, 5, 10, 15, 20, ... represents a function. The domain of the function is the set of natural numbers, and the range is the set of multiples of 5. We can create a mapping by using the rule "multiply by 5" to match each input value of the domain with its corresponding output value in the range. For example, 0 maps to 0, 1 maps to 5, 2 maps to 10, and so on.

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Answer:

$9.60

Step-by-step explanation:

This is a tricky question because it uses different units.

Let's first convert everything to one unit to make things simpler

1 cup = 16 tablespoons

1/2 cup = 8 tablespoons

Each lemon yields 2 tablespoons of juice

Each lemon pie requires 1/2 cup of juice = 8 tablespoons of juice

4 lemon pies will require 4 x  8 = 32 tablespoons of juice

To get 32 tablespoons at 2 tablespoons per lemon we will require 32/2 = 16 lemons

16 lemons at $0.60 per lemon will cost 16 x 0.60 = $9.60 ANS

Answer:

4:5

Step-by-step explanation:

We know that 1 minute is equals to 60 seconds.

So the ratio is now:

48 seconds : 60 seconds

We need to simplify the ratio in its simplest form. 12 goes into both 48 and 60 so:

48/12 = 4 seconds

60/12 = 5 seconds

So the ratio 48 seconds: 1 minute in its simplest form is:

4 seconds : 5 seconds

Answer : -4

explained:

you would have to sub 2 from -2x and -30(-30 - 2 = -32) to get x by it self then divide 8 by 8(equals) x then divide -32 with 8 = -4

your welcome!

Answer:

Julia parcourt 1200 km par mois en voiture, donc elle parcourt 1200 x 12 = 14400 km par an.

Sa voiture actuelle consomme 6 L d'essence par 100 km, donc elle consomme 6/100 x 14400 = 864 L d'essence par an.

Si elle remplaçait sa voiture actuelle par une voiture hybride qui consomme moins d'essence, elle économiserait 864 L d'essence par an.

Si le prix d'un litre d'essence est de 1,30 $, alors Julia économiserait 864 x 1,30 = 1129,20 $ par an si elle remplaçait sa voiture actuelle par une voiture hybride.

Answer:

1- Reflection about the x-axis: The equation for this transformation would be: f(x) = -(-5^x + 10) = 5^x - 10. This flips the graph of the original function over the x-axis.

2- Reflection about the y axis: The equation for this transformation would be: f(x) = -(5^x + 10) = -5^x -10. This flips the graph of the original function over the y-axis.

3- Vertical shift upwards by 10: The equation for this transformation would be: f(x) = 5^x +10 + 10 = 5^x + 20. This shifts the graph of the original function upward by 10 units on the y-axis.

4- Vertical shift downward by 10: The equation for this transformation would be: f(x) = 5^x + 10 - 10 = 5^x. This shifts the graph of the original function downward by 10 units on the y-axis.

5- Horizontal shift to the right by 10: The equation for this transformation would be: f(x) = 5^(x-10) + 10. This shifts the graph of the original function to the right by 10 units on the x-axis.

Answer:1- Reflection about the x-axis: The equation for this transformation would be: f(x) = -(-5^x + 10) = 5^x - 10. This flips the graph of the original function over the x-axis.

2- Reflection about the y axis: The equation for this transformation would be: f(x) = -(5^x + 10) = -5^x -10. This flips the graph of the original function over the y-axis.

3- Vertical shift upwards by 10: The equation for this transformation would be: f(x) = 5^x +10 + 10 = 5^x + 20. This shifts the graph of the original function upward by 10 units on the y-axis.

4- Vertical shift downward by 10: The equation for this transformation would be: f(x) = 5^x + 10 - 10 = 5^x. This shifts the graph of the original function downward by 10 units on the y-axis.

5- Horizontal shift to the right by 10: The equation for this transformation would be: f(x) = 5^(x-10) + 10. This shifts the graph of the original function to the right by 10 units on the x-axis.

Step-by-step explanation:

The answer  for algebraic expression is Option B 3(-3)

A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression. In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. However, both forms provide the same outcome when the values are entered into the formula.

Given

9-12+(-2)+3(-3)

Subtract: 9 - 12 = -3

Add: the result of step No. 1 + (-2) = -3 + (-2) = -5

Multiple: 3 * (-3) = -9

Add: the result of step No. 2 + the result of step No. 3 = -5 + (-9) = -14

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The population in 48 year becomes 580,000.

what is Doubling ?

Doubling or Double numbers or doubles simply represent twice the given amount or number.

To double means to add an amount equal to what you already have. An example: If you have one bottle of coke, and you get one more bottle, you have two bottles of coke. Two is the double of one, because, which means you have doubled the amount of coke you had.

As given, if the current population is = 145,000

and after 24 year, it will double its size = 145,000×2 = 290,000

and then in the next 24 years i.e. (48 years later) = 290,000×2 = 580,000

Therefore, the population in 48 year becomes 580,000.

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The general form of linear equation is expressed in the form of ax+b=0 where a and b are the integers and X is the variable and has the only one solution and the general form of a linear equation in two variables is ax + by + c = 0, where a and b cannot be zero simultaneously.

An equation is a statement that two mathematical expressions having one or more variables are equal And the equations in which the powers of all the variables involved are one are called linear equations. The degree of a linear equation is always one.

Define Linear Equation in One Variable

A linear equation with one variable is one with a single variable of order 1 or less. Where x is the variable, it has the form a x +b = 0.

There is just one solution to this equation. Examples include:

3x = 1

22x-1=0

4x+9=-11

A simple equation is deemed to be a linear equation of two variables when it is given the form ax+by+c=0, according to the Linear Equations in Two Variables CLass 10 textbook. A, B, and C in this scenario should all be constants or real integers, such 2, 3, 4, etc. The a and b coefficients of x and y in this situation shouldn't be equal to zero. Given that a, b, and c are real values, the two unknown variables in this case would be x and y. An illustration of a two-variable linear equation is 4x+5y+3=12.

therefore , the general form of linear equation in one variable and intwo variable are ax+b=0 and ax+by+c=0

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The given expression is expressed in an algebraic expression as:  3x^2 - 7 and the value of the number is √7/3

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

In mathematics, when we express "square" we mean an exponent equal to two. So the expression “the square of a number ” is represented by:

x^2

When we express “three times” we mean a multiplication by three. So the expression "three time the square of a number"  is represented by:

3x^2

When we express “sum” we mean an addition. So the expression "the um of three time the square of a number and -7"  is represented by:

3x^2 + ( - 7)

The complete expression "the um of three time the square of a number and -7" in an algebraic expression represented by: 3x^2 - 7 = 0

Finding the value of the constant we get:

3x^2 - 7 = 0

3x^2 = 7

x^2 = 7/3

x = √(7/3)

x = 1.53

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Correctly written question:

Write an expression to represent the sum of three time the square of a number and -7. In your expression, what is the value of the constant?

The parabola has an axis of symmetry at x= -1.

Step-by-step explanation:

The value of n is 1/8. A ratio in math displays how many times one number is contained in another.

A ratio in math displays how many times one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit. In a similar way, the ratio of oranges to all other fruits is 8:14, while the ratio of lemons to oranges is 6:8.

The ratio shows how many times one value is contained in another value.

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

800g : 1kg = 1 : n

This can be written as,

800g/1kg = 1/n

Cross multiply.

n = 1kg/800g

[ 1 kg = 1000g ]

n = 1000g/8000g

n = 1/8

Thus,

The value of n is 1/8.

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Answer:

F

Step-by-step explanation:

(x + 2)² + (y - 3)² = 37

intersection points with the x-axis means that their y-values are 0 !

that is the whole trick, as I am sure you experienced already with lines and y-intersects (x = 0) and x-intersects (y =0).

so, we need to solve for x, when y = 0 :

(x + 2)² + (-3)² = 37

x² + 4x + 4 + 9 = 37

x² + 4x - 24 = 0

the solution to a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (-4 ± sqrt(4² - 4×1×-24))/(2×1) =

= (-4 ± sqrt(16 + 96))/2 = (-4 ± sqrt(112))/2 =

= (-4 ± sqrt(16×7))/2 = (-4 ± 4×sqrt(7))/2 =

= -2 ± 2×sqrt(7)

x1 = -2 + 2×sqrt(7)

x2 = -2 - 2×sqrt(7)

so, F is the right answer.

The value of the upper quartile is 65.

The lower quartile, which is represented by the left border of the box, is the value that the first 25% of the data falls within. 25% of the data are to the right of the upper quartile value, which is indicated by the upper quartile at the right border of the box.

The left whisker represents the bottom 25% of the data, the left half of the box represents the second 25%, the right half of the box represents the third 25%, and the right whisker represents the top 25%.

The value of the upper quartile is 65.          

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If everyone paid equal share of amount of rent, then Terry paid $365 per month.

A property is considered to be rented out if it is occupied by someone other than the owner and the tenant consistently pays the owner a set rent. A person is renting when they desire to pay a landlord to live on that landlord's property. The term "letting" refers to the process of someone transferring ownership of their property in return for cash.

The total amount per month for the rent is given as $1095.

Since there are three persons including Terry, The rent is divided equally among all three people.

So, the toal amount should be divided by three to get individual amount

= 1095 / 3

= $365

Hence Terry paid $365 per month as the apartment rent.

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When given a quadratic function and a line, the points of intersection can be found by solving for x using the Quadratic Formula.

The Quadratic Formula states that:

x² + ax+ b = 0

where the constants are a, b, and c. We utilise this equation to solve for x in order to determine the places of intersection. In order to accomplish this, we must be aware of both the line's slope and the quadratic function's y-intercept.

The slope of the line can be found by dividing the y-intercept by the distance between the points of intersection (x1 and x2), and then multiplying that number by the slope of the line (y/x).

The y-intercept can be found by simply plugging in x1 into the equation above. Once we have these two pieces of information, we can solve for x using algebraic equations.

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In point-slope form, the equation of the line through the indicated points is y - 2 = -4/3. ( x - 4 ).

Y - Y1 = m is the line's equation in point slope form (x – x1).As a result, the equation for a line passing through the origin and having a slope of m is given by y - 0 = m(x = 0), which equals y = mx. Given the information in the query;

A Point (4, 2)

x₁ = 4

y₁ = 2

B Point (1, 6)

x₂ = 1

y₂ = 6

We start by figuring out the line's slope.

Slope m is equal to (y2 - y1)/(x2 - x1)

Slope: m = (6 - 2) ( 1 - 4 )

(4)/ Slope m ( -3)

Slope m=-4/3

Then, simplify the point slope formula y - y1 = m(x - x1) using the slope -4/3 and point (4,2).

y - y₁ = m(x - x₁)

y - 2 = -4/3( x - 4 ) ( x - 4 )

As a result, y - 2 is the equation of the line in point-slope form that passes through the indicated places.

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Answer: 8/17

Step-by-step explanation:

sinA = opp.side/hypotenuse

 = BC/AB

 = 8/1

Answer:

5, -1

Step-by-step explanation:

Hope it helps! =D

The length of the base of the rectangle is B = 11 yards  

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the value of A is

Let the base of the rectangle be represented as B

Area of rectangle A = 209 yards²

The length of the rectangle L = 19 yards

And , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of Rectangle = 19 x B

209 = 19 B

Divide by 19 on both sides of the equation , we get

B = 209 / 19

B = 11 yards

Hence , the length of the base of rectangle is 11 yards

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A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

The side opposite the right angle is always the hypotenuse of a right triangle. In a right triangle, it is the longest side. The opposing and neighboring sides are the other two sides. The labels on these sides relate to an angle.

One side is opposite the other at a specific angle. The non-hypotenuse side that lies next to a particular angle is known as the neighboring side. The terms hypotenuse, opposite, and adjacent are used to define the trigonometric functions sine, cosine, and tangent.

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The coordinates of the vertex C​' will be (-5, -4). And the graph is given below.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The reflection does not change the shape and size of the geometry. But flipped the image.

The vertices of ΔABC are A(−5,4)​, B(−2,3)​, and C(−3,2). If ΔABC is reflected across the line y = −1 to produce the image Δ​A'B'C'.

Then the coordinate of the triangle Δ​A'B'C' will be given as,

(x', y') = (x, -y - 2)

A' = (-5, -4 - 2) = (-5, -6)

B' = (-2, -3 - 2) = (-5, -5)

C' = (-3, -2 - 2) = (-5, -4)

The coordinates of the vertex C​' will be (-5, -4). And the graph is given below.

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