Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup.


How many grams of 25% sugar syrup did Samantha use?

Pls help :D Thxs

Answer:

Step-by-step explanation:

Inverse variation functions have the form y = k / x, where k is a constant.

When k > 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k > 0, the hyperbola opens upwards and the two branches of the hyperbola move away from the x-axis as x increases. This means that as x increases, the value of y decreases. When x approaches 0 from the right, y approaches positive infinity, and when x approaches 0 from the left, y approaches negative infinity.

On the other hand, when k < 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k < 0, the hyperbola opens downwards and the two branches of the hyperbola move toward the x-axis as x increases. This means that as x increases, the value of y increases. When x approaches 0 from the right or left, y approaches negative infinity.

In both cases, the inverse variation function is undefined for x = 0, as division by zero is undefined.

Answer:

14√2

Step-by-step explanation:

28/√2

Since you can't have a square root as the denominator of a fraction, we must multiply the denominator and the numerator to get rid of the square root.

Hence,

28 x √2 , √2 x √2

Your problem would now be:

28√2 / 2

Reduce the fraction by canceling out the common factor of 2

ANS = 14√2

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12m² is the area of the table top in rectangle .

What is a rectangle, exactly?

The parallel sides of a rectangle are equal to one another, and each of its four vertices is 90 degrees, making it a form of quadrilateral. As a result, it is sometimes referred to as an equiangular quadrilateral.

                               The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

area = length x width

We know that the width is 2 meters, and since the length is three times the width, the length would be 6 meters.

Therefore, the area of the table = 2 x 6 = 12 m2.

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The old tree in 54 feet height.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that Two apple trees are going next to each other

the oldest tree has a 36 ft Shadow

the smaller Creek has a 12-in shadow and the tree  is 8 ft tall.

We need to find the height of the older tree.

Let x be the height of older tree.

36/x=8/12

36×12=8x

432=8x

Divide both sides by 8

54=x

Hence, the old tree in 54 feet height.

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Answer:

175 calories

Step-by-step explanation:

75 / 6 = 12.5

12.5 x 14 = 175

x = 12.5 x 14

Answer:

0.0000000105

Step-by-step explanation:

Simply move the decimal 8 places to the left, since it is a negative exponent.

Figure RSTU is transformed into Figure R1 S T 1 U1 by moving down two units and reflecting on the y axis.

Deformations are four alternative approaches that can be utilized to change a point, line, or mathematical figure's orientation and/or shape. Both the Pre-Image, who describes the shape of the object there at initial state, and the Photograph, which describes the final state and location of the object following change, are words. Translations, reflection, and dilations are the three types of transformations that can be differentiated. A function can undergo two different types mathematical transformations: vertical (it affects the y-values) and sideways (affects the x-values). Its function's equation is provided below, and it comprises the share the information variables (a, b, h, and k). modifying the log.  observation. even by square root, invert.

given

From the figure RSTU to R'S'T'U' R moved from P(5,2) to P(-3,0), translating 8 units to the left.

Hence, 5-(-3)= 8 = 2-0 = 0.

Down two units.

as well as reflection on the y axis.

Figure RSTU is transformed into Figure R1 S T 1 U1 by moving down two units and reflecting on the y axis.

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The graph for the functions is attached.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

Given

A: graph of y = f(x)

since the graph is in form of a parabola so the function is a quadratic function,

f(x) = ax² + bx + c

the vertex of the graph is at (2, 0)

here in the given curve, the value of the y-axis is 0,

and y = f(x) - 3

in the equation y = f(x) - 3

the shape of the curve will be the same but only change in the vertex of the curve, the new vertex for the curve is (2, -3)

for x = 0 y = -3.

B: given y =g(x)

the graph shows the negative cubic function,

g(x) = -x³

and y = g(x + 4)

= -(x + 4)²

the graph will shift towards 4 units left.

Hence the graph is attached for both equations.

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The ratio of baking powder to flour is 1/192 teaspoon of baking powder for every teaspoon of flour.

The amount of baking powder per unit of flour is the unit rate for baking powder and flour. The amount of flour in this situation equals 1 2/3 cups. We must change the baking powder measurement to the same unit as the flour measurement in order to calculate the unit rate.

For every 1 2/3 cups of flour, 1/4 teaspoon of baking powder should be used as follows:

1/4 teaspoon / (1 2/3 cups)

By changing the numerator and denominator of the fraction on the right side to a standard unit, such as teaspoons, we may make it simpler. 1 2/3 cups equal 48 teaspoons, so:

1/4 teaspoon / (1 2/3 cups) = 1/4 teaspoon / (48 teaspoons)

The ratio of baking powder to teaspoons is as follows:

1/4 teaspoon / (48 teaspoons) = 1/192 teaspoon per teaspoon

So The ratio of baking powder to flour is 1/192 teaspoon of baking powder for every teaspoon of flour.

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[tex]-4z+31\geqslant 17z+23\implies 31\geqslant 13z+23\implies 8\geqslant 13z\implies \cfrac{8}{13}\geqslant z[/tex]

The longest line segment that can be drawn in a right rectangular prism is 21.1 cm.

Let us assume the right rectangular prism be labelled as shown in figure. Now the longest possible line here is the diagonal between two most far points like A and G. So, finding the length of AG from triangle AGC.

But, prior to this calculation, we need to find AC. It will be calculated from the traingle ABC.

So, AC² = AB² + BC²

AC² = 14² + 13²

AC² = 196 + 169

AC² = 365

AC = 19.1 cm

Now, finding length of AG.

AG² = AC² + GC²

AG² = 365 + 9²

AG² = 365 + 81

AG² = 446 cm

AG = ✓446

AG = 21.1 cm

Thus, the diagonal AG is 21.1 cm.

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(-6,-5), (-2,3), (2,-5), (6,3) are the ordered pairs given on the graph.

In mathematics, a transformation is a process that changes the position, size, or orientation of a geometric shape or figure. The term is used in various branches of mathematics, including geometry, algebra, and calculus.

In geometry, transformations include translations, rotations, reflections, and dilations. A translation involves moving a shape a certain distance in a certain direction, while a rotation involves rotating a shape around a fixed point. A reflection involves flipping a shape over a line, and a dilation involves stretching or shrinking a shape by a given scale factor.

In algebra, transformations can involve changing the form of an equation, such as solving for a variable, transforming an equation into a different coordinate system, or solving a system of equations.

In calculus, transformations can involve changing the form of a function, such as finding its derivative or integral, or transforming a function from one coordinate system to another.

To find the ordered pairs that are on the transformations of the function, we can apply the transformations to the original point (-2, -1) to obtain the points on each transformation.

y = f(x-4) - 4: If we apply the x-4 transformation to the x-coordinate of the original point, we get -2-4 = -6. So, the point is (-6, f(-6) - 4).

y = f(x-4) + 4: The x-coordinate of the point is -6, so the point is (-6, f(-6) + 4).

y = f(x+4) - 4: If we apply the x+4 transformation to the x-coordinate of the original point, we get -2+4 = 2. So, the point is (2, f(2) - 4).

y = f(x+4) + 4: The x-coordinate of the point is 2, so the point is (2, f(2) + 4).

So, the ordered pairs that must be on each of the transformations of f(x) are:

y = f(x-4) - 4: (-6, f(-6) - 4)

y = f(x-4) + 4: (-6, f(-6) + 4)

y = f(x+4) - 4: (2, f(2) - 4)

y = f(x+4) + 4: (2, f(2) + 4)

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Answer:

(i) The complement of the intersection of Sets A and B, denoted by (A∩B)', is the set of all elements that are not in the intersection of Sets A and B. It can be found by taking the union of the complements of Sets A and B, denoted by A' and B'. Hence, (AnB)' = A' U B'.

(ii) The complement of the union of Sets A and C, denoted by (A U C)', is the set of all elements that are not in the union of Sets A and C. It can be found by taking the intersection of the complements of Sets A and C. Hence, (A U C)' = A' ∩ C'.

(iii) The complement of the union of Sets A, B, and C, denoted by (A U B U C)', is the set of all elements that are not in the union of Sets A, B, and C. It can be found by taking the intersection of the complements of Sets A, B, and C. Hence, (A U B U C)' = A' ∩ B' ∩ C'.

If the volume of cube is 9261 cubic centimeters, then the surface area of the cube is 2646 square centimeters.

It is given that a cube has volume 9261 cubic centimeters. Let the length of the side of cube is 'a' centimeters.

The formula of volume of a cube is  [tex]a^{3}[/tex]

9261 cubic centimeters = [tex]a^{3}[/tex]

     a = [tex]\sqrt{9261}[/tex]

      a = [tex]\sqrt{21\times21\times21}[/tex]

      a = 21 cm

The surface area of cube = [tex]6a^{2}[/tex]

The surface area of cube = [tex]6\times21^{2}[/tex]

The surface area of cube = 2646 square centimeters.

Also the area of one face of the cube = [tex]a^{2}[/tex]

The area of one face of the cube is 441 square centimeters.

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The product which cost less is Tide which has a cost value of $15.99 with 20% off.

This is referred to as the expenditure required to create and sell products and services, or to acquire assets.

Tide was $15.99 with 20% off which when calculated = 20/100 × $15.99 = $3.198.

Gain was $17.55 with 25% off which when calculated = 25/100 × $17.55 =  $4.388.

Therefore the cheaper alternative will be Tide detergent.

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The full question:

Mrs. Klein went to Target in search of a good deal on laundry detergent (Owen is one messy boy!). She found Tide was $15.99 with 20% off. Gain was $17.55 with 25% off. She has a target red card and gets 5% off her total purchase. which one of the products costs less?

The measure of the angles of the triangles are 90° , 67.380° and 22.620°

The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

Given data ,

Let the triangle be represented as ΔPQR

Now , the measure of ∠PQR = 90°

The measure of side PR = 13 cm

The measure of side PQ = 5 cm

The measure of side QR = 12 cm

From the law of sines , we get

a / sin A = b / sin B = c / sin C

Substituting the value sin the equation , we get

12 / sin P = 13 / sin 90°

From the trigonometric relations , sin 90° = 1

So , Multiply by sin P on both sides of the equation , we get

sin P = 12/13

Taking inverse on both sides of the equation , we get

sin⁻¹ ( 12/13 ) = 67.380°

Therefore , the measure of ∠QPR = 67.380°

And , the measure of ∠PRQ = 180 - ( 90° + 67.380° )

The measure of ∠PRQ = 22.620°

Hence , the angles of triangles is solved

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Step-by-step explanation:

The frequency of the first harmonic of a string fixed at both ends can be determined using the formula:

f = (1 / 2L) * √(T / μ)

where f is the frequency, L is the length of the string, T is the tension, and μ is the linear mass density. Plugging in the given values:

f = (1 / 2 * L) * √(100 N / 2 kg/m)

= (1 / 2 * L) * √(50 N/m)

So, the frequency of the first harmonic depends on the length of the string, which is not specified in the problem.

Answer:

Step-by-step explanation:

The frequency of the first harmonic of a string fixed at both ends can be calculated using the formula:

f = (1 / 2L) * (T / μ)^(1/2)

where:
f = frequency
L = length of the string
T = tension
μ = linear density of the string

Plugging in the values:
f = (1 / 2 * L) * (100 N / 2 kg/m)^(1/2)
f = (1 / 2L) * (10 N/kg)^(1/2)

We don't have the length of the string, L, so we can't calculate the frequency.

The area of the figure as a monomial with the sides [tex]p^{2} q^{4}[/tex] and [tex]p^{2} q^{4}[/tex] is [tex]p^{4} q^{8}[/tex].

As per the given data we to express the area of the figure as a monomial.

Figure attached at the end of solution.

A polynomial with only one term is called a monomial. An algebraic expression known as a monomial has only one term but might have more than one variable and a higher degree.

As the sides are equal we use the area of the square formula.

Area of the square formula:

The formula for the area of a square is side × side

Simple multiplication is the answer to the equation.

Area of the given figure:

= [tex]p^{2} q^{4} \times p^{2} q^{4}[/tex]

= [tex]p^{4} q^{8}[/tex]

[tex]p^{4} q^{8}[/tex] is a monomial as it is expressed as a single term.

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Step 1: Calculate the number of laps the cars have completed. To calculate the number of laps the cars have completed, divide the total time (150 seconds) by the time it takes car A to complete one lap (30 seconds), which gives us a total of 5 laps.

Step 2: Calculate the possible times for car B. To calculate the possible times for car B, we need to find out how many times car B must complete a lap in order to keep up with car A. Since car A takes 30 seconds to complete one lap and the cars have completed 5 laps in 150 seconds, car B must take the same amount of time as car A, i.e. 30 seconds, in order to keep up with car A. Therefore, the possible times for car B are 30, 60, 90, and 120 seconds.

Therefore, the four possible times that car B could take to complete one lap are 30, 60, 90, and 120 seconds.

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The expression that represents the amount in dollars the salesperson makes, before taxes, would be equal to 7x + 100 = 40.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol that can also be used to indicate the logical syntax's order of operations and other features.

Given that car sales person makes $7.00 per hour plus $100.00 for every car sold.

Therefore, we have,

7x + 100 = 40

The expression that represents the amount in dollars the salesperson makes, 7x + 100 = 40.

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the expression 24x - 48 is equivalent to 36x + 12

The label 24x - 48 applies to the expression because it is the same as itself. The value obtained by multiplying 24 by x and then taking 48 out is represented by this expression.

The label "36x + 12" applies to the expression because it is the same as itself. The value generated by multiplying 36 by x and then adding 12 is represented by this expression.

Since the formulations in both situations have distinct coefficients for x and various constant terms, they are not comparable to one another. Since both expressions are equal to one another, the term "neither" does not apply to them.

Therefore, the expression 24x - 48 is equivalent to 36x + 12

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Answer:

1,325,000,000 people

Step-by-step explanation:

Million = 1,000,000

Number = 1,324,671,354

The 1st 4 is in the millionth place. 6 > 4 so round 4 up to 5.

Rounded = 1,325,000,000 people

The distance the plane traveled from point A to point B is 10,802.1 feet.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given the height of the plane = 5925 feet

let the distance between A to B be x and distance from B to the position of the plane is y as shown in the image,

angle of elevation from point A = 16°

the angle of elevation from point B = 31°

using trigonometric functions,

tanα = perpendicular/base

base =  x + y

perpendicular = 5925 feet

tan(16) = 5925/(x + y)

x + y = 5925/tan(16)

y  = 5925/tan(16) - x.........(1)

and tan(32) = 5925/y

y = 5925/tan(32)

substitute the value of y from equation 1

5925/tan(16) - x = 5925/tan(32)

5925/tan(16) - 5925/tan(32) = x

x = 10,802.1 feet

Hence the distance covered by points A to B is 10,802.1 feet.

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After dilation with the scale factor 1/4 is A'(0, 1), B'(1, 1) and C'(-1, -1).

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, the scale factor is k= 1/4.

From the given figure, vertices of triangle ABC are

A(0, 4), B(4, 4) and C(-4, -4)

After dilation with the scale factor 1/4, we get

A(0, 4)→1/4 (0, 4) =A'(0, 1)

B(4, 4)→1/4 (4, 4) =B'(1, 1)

C(-4, -4)→1/4 (-4, -4) =C'(-1, -1)

Therefore, after dilation with the scale factor 1/4 is A'(0, 1), B'(1, 1) and C'(-1, -1).

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The man can wear 27 different shirt and tie combinations.

Therefore the answer is 27.

The number of different shirt and tie combinations that a man can wear can be calculated by multiplying the number of choices for each item.

Number of choices for shirts = 3

Number of choices for ties = 9

Since the man has three different shirts and nine different ties, and each shirt can be paired with any one of the nine ties, the number of combinations is:

Combinations = 3 * 9 = 27

So the man can wear 27 different shirt and tie combinations.

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The inequality best describes the number of paperback books 'p' and the number of hardback books 'h' that can be purchased for $45.00 or less

is 5p + 9h ≤ 45.  

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Two types of books paperbacks are represented by 'p', and hardbacks are represented by 'h'.

Also, we can only buy two types of books for $45 or less.

Therefore, The inequality representing the context is,

5p + 9h ≤ 45.  (As the cost van be $45 or less not only less)

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On solving the provided question, we can say that Point (1,1) must be on the graph of f if point (x,1) is on the graph of f. (x).

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

Given that y=f(x) and g(x)=f (x)

Flipping the graph of y=f(x) across the y axis, as shown in the image, will give you the graph of g(x)=f(x).

For instance, the point (2,2) must be on the graph of f if point (2,2) is on the graph of f(x) (x).

Point (3,1) must be on the graph of f if point (3,1) is on the graph of f(x) (x).

Point (1,1) must be on the graph of f if point (1,1) is on the graph of f(x) (x).

Point (1,1) must be on the graph of f if point (x,1) is on the graph of f. (x).

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Answer: 40 degrees

Step-by-step explanation:

m/CBA = m/CED

16 + 6x = 48 - 2x; add 2x on both sides and subtract 16 on both

8x = 32; divide 8 on both sides to isolate the x

x = 4

m/CBA = 16+6(4) = 40

The values that are solutions to inequality are -6 and 5.

Options A and D are the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

x² + 3x - 4 > 0

Now,

Substituting x = -6, -2, 0, 5

(-6)² + 3(-6) - 4 > 0

36 - 18 - 4 > 0

36 - 22 > 0

14 > 0

True.

x² + 3x - 4 > 0

(-2)² + 3 x (-2) - 4 > 0

4 - 6 - 4 > 0

-6 > 0

This is not true.

x² + 3x - 4 > 0

0 + 3 x 0 - 4 > 0

0 + 0 - 4 > 0

-4 > 0

This is not true.

x² + 3x - 4 > 0

5² + 3 x 5 - 4 > 0

25 + 15 - 4 > 0

40 - 4 > 0

36 > 0

This is true.

Thus,

-6 and 5 are the solutions to inequality.

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