how many lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed? choose all that apply.

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 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:

  (i)  No

  (ii)  The line and curve always intersect in two places

Step-by-step explanation:

You want to know if there are values of k such that the curve y = (k+3)x²-3x lies completely above the line y = x+k. And you want to know the relationship between the line and the curve.

The number of points of intersection between the line and the curve can be found by considering the discriminant of the quadratic equation for the difference of the y-values.

The line and curve will intersect when their y-values are equal:

  (k +3)x² -3x = x +k

  (k +3)x² -4x -k = 0 . . . . . compare to ax²+bx+c=0

The discriminant is the value of b²-4ac, so is ...

  d = (-4)² -4(k+3)(-k) = 16 +4k(k -3)

Writing this in vertex form, we have ...

  4(k² -3k) +16 = d

  4(k² -3k +2.25) +16 -4(2.25) = d . . . . . "complete the square"

  4(k -1.5)² +7 = d

The square is always positive, and it is added to a positive value (7), so the discriminant d is always positive. This means there are always two points of intersection between the curve and the line.

As we saw above, the line and curve will always intersect at two points. This means there are always parts of the curve both above and below the line.

__

Additional comment

For the value k=-3, the "curve" becomes a line with slope -3 through the origin. It will intersect the line y=x-3 at one point. It seems reasonable to exclude that case from consideration.

Answer: A = 19.6^2 ( 19.6 to the 2nd power )

Step-by-step explanation:

Area of a circle = 3.14 * r^2

A = 3.14 * 2.5^2

A = 19.625

19.625 rounded to the nearest tenth is 19.6

According to the information we can infer that the area of the circle with a radius of 2.5 is approximately 19.63 square units.

The area of a circle is given by the formula A = πr², where A represents the area and r represents the radius.

In this case, the radius is given as 2.5 units. Substituting this value into the formula, we have:

Using an approximate value of π as 3.14159, we can calculate the area:

So we can conclude that the area of the circle with a radius of 2.5 units is approximately 19.63 square units.

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Answer:

0.0000000105

Step-by-step explanation:

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

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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Answer:

175 calories

Step-by-step explanation:

75 / 6 = 12.5

12.5 x 14 = 175

x = 12.5 x 14

The difference of the maximum and minimum values is divided by the number of bins.

1. Identify the maximum and minimum values of the quantitative data

2. Subtract the minimum value from the maximum value to get the difference

3. Divide the difference by the number of bins to get the approximate width of each bin

The width of the bins in a frequency distribution of quantitative data can be estimated by dividing the difference between the maximum and minimum values of the data by the desired number of bins. This will provide an approximate size for each bin, which can then be used to construct the frequency distribution.

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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

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'.

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

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:

Step-by-step explanation:

4 cookies times 7 bags
4x7=28

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 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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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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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 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 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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Answer: 112i + 85.8j

Step-by-step explanation:

Answer:

[tex]\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}[/tex]

Step-by-step explanation:

To find the components of a vector given its magnitude and direction, use the following formula:

[tex]\large\boxed{\vec{u}=\left(||\vec{u}|| \cos(\theta),|| \vec{u}|| \sin(\theta)\right)}[/tex]

where:

Given:

Substitute the given values into the formula:

[tex]\vec{H}=\left(85.8 \cos(112^{\circ}),85.8 \sin(112^{\circ})\right)[/tex]

[tex]\vec{H}=\left(-32.1, 79.6\right)[/tex]

Therefore:

[tex]\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}[/tex]

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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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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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 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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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 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 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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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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