1
The price of a video game was reduced from $60 to $45. By what percentage
was the price of the video game reduced?

А
15%
B
75%
C
25%
D
40%

Answer:

12(m-5)=540

Step-by-step explanation:

m=50 minutes for jogging

Answer:

6.

Step-by-step explanation:

Answer: The 6, in 12.86, is in the hundredths place.

Hope this helps!

To find the number of licorice ropes r that came in the bag, the equation would be r = 27.

A system of equations is two or more equations that can be solved to get a unique solution.

Each student gets 3 licorice ropes to decorate the roof of his or her gingerbread house.

Let the number of licorice ropes that came in the bag be r.

The equation formed:

Therefore, to find the number of licorice ropes r that came in the bag, the equation would be r = 27.

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Answer:

d/10 + 600 + d/6 = 720

450 fts

Step-by-step explanation:

Given that:

Speed from hive to flowerbed = 10 ft/s

Time used in flowerbed = 10 minutes

Speed from flowerbed to hive = 6ft/s

Total time at which bee is away from hive = 12 minutes

Equation to find distance of flowerbed from hive :

Let distance from hive to flowerbed = d

Time taken = distance / speed

Time taken from hive to flowerbed = d/ 10

Time used in flowerbed = 10 minutes = (10 * 60) = 600 seconds

Time taken from flowerbed to hive = d/6

Total time away from hive = 12 mins = (12 * 60) = 720 seconds

A. What equation can you use to find the distance of the flowerbed from the​ hive?

Distance can be obtained from the formula :

d/10 + 600 + d/6 = 720

B. How far is the flowerbed from the​ hive?

d/10 + 600 + d/6 = 720

Take L. C. M of 10 and 6 = 30

(3d + 18000 + 5d) = 21600

8d + 18000 = 21600

8d = 21600 - 18000

8d = 3600

d = 3600/8

d = 450

Distance of flowerbed from hive = 450 fts

Answer: the square root of 3 is: (a number) times ITSELF is equal to 3. Therefore, if you multiply that number times that number again, it is equal to 3.

Ex1- sqrt of 4 times the sqrt of 4 —> 2 times 2 which is 4

Ex2- sqrt of 9 times the sqrt of 9 —> 3 times 3 which is 9

Answer:

c

Step-by-step explanation:

Answer:

f(5.5)≈27.32

Step-by-step explanation:

The exponential function which satisfy the f(4.5) = 23 and f(8) = 42 will be 10.60(\(1.19^{x}\)).

In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.

Suppose the exponential function is f(x) = a\(b^{x}\).

As per the given,

f(4.5) = 23

Put x = 4.5 as

23 = a\(b^{4.5}\)               (1)

As per the given,

f(8) = 42

Put x = 8 as

42 = ab⁸                  (2)

Divide equation (2) by (1) as,

ab⁸  / a\(b^{4.5}\) = 42/23

\(b^{8-4.5}\) = 42/23

b = 1.19

Again put into (2)

42 = a(1.19)⁸

a = 10.60

Thus, the function will be f(x) = 10.60(\(1.19^{x}\)).

Hence "The exponential function which satisfy the f(4.5) = 23 and f(8) = 42 will be 10.60(\(1.19^{x}\))".

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Answer:

Step-by-step explanation: if there is 75 trout and the caught 120 trout they would have counted the trout wrong

Josh bought a new book that cost $13.95 and some bookmarks

Let the cost of the bookmarks be b.

It then followed that the cost of the new book plus the cost of the bookmarks will give the total cost of $20.30

Mathematically,

Hence $13.95+b=$20.30; b=$6.35 is the answer, the third option

Answer:

(2,1)

Step-by-step explanation:

Well first we single out y or x in one of the equations,

we’ll use 2x + y = 5 and single out y.

2x + y = 5

-2x to both sides

y = -2x + 5

So we can plug in -2x + 5 into y in 2x - 2y = 2.

2x - 2(-2x + 5) = 2

2x + 4x - 10 = 2

combine like terms,

6x - 10 = 2

Communicarice property

+10 to both sides

6x = 12

divide 6 to both sides

x = 2

If x is 2 we can plug 2 in for x in 2x + y = 5.

2(2) + y = 5

4 + y = 5

-4 to both sides

y = 1

(2,1)

Thus,

the solution is (2,1).

Hope this helps :)

The water output rate for Reed's sprinkler is 25L/hour. We have to find the water output rate for each sprinkler if the sum of the two rates was 45L per hour. We know that the Rogers family sprinkler was used for 15 hours and the Reed family sprinkler was used for 30 hours.

Therefore the combined time the two sprinklers were used for was:15 + 30 = 45 hours

Therefore, The Rogers family's sprinkler output rate: r₁

The Reed family's sprinkler output rate: r₂

Given that the sum of the two rates was 45L per hour: r₁ + r₂  = 45 -----Equation (1)

Now, let's calculate the water output of each sprinkler using their respective times:

Water output of Rogers' sprinkler = r₁ × 15

Water output of Reed's sprinkler = r₂  × 30

The total output was 1050L:

r₁ × 15 + r₂  × 30 = 1050 -----Equation (2)

We have two equations and two variables. We will solve for r₁ and r₂ :

r₁ + r₂ = 45r₂ = 45 - r₁

Substituting the value of r₂ in equation (2), we get:

r₁ × 15 + (45 - r₁) × 30 = 105015r₁ + 1350 - 30r₁

= 1050-15r₁

= -300r₁

= 20r₂

= 45 - r₁

= 45 - 20 = 25

Therefore, The water output rate for Rogers' sprinkler is 20L/hour.

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Even if R is anti-reflexive, R2 may not necessarily be anti-reflexive. It depends on the specific properties and composition of the relation R.

Let R be a relation that is reflexive and transitive. We want to prove that R2 = R for any relation R with these two properties.

To prove this, we need to show that for any ordered pair (a, b), (a, b) ∈ R2 if and only if (a, b) ∈ R.

First, let's consider (a, b) ∈ R2. By definition, (a, b) ∈ R2 means that there exists an element c such that (a, c) ∈ R and (c, b) ∈ R.

Since R is reflexive, we know that (a, a) ∈ R and (b, b) ∈ R.

By the transitivity of R, if (a, c) ∈ R and (c, b) ∈ R, then (a, b) ∈ R.

Therefore, (a, b) ∈ R2 implies (a, b) ∈ R.

Now, let's consider (a, b) ∈ R. Since R is reflexive, we have (a, a) ∈ R and (b, b) ∈ R.

By the definition of R2, (a, a) ∈ R2 and (b, b) ∈ R2.

Since R is transitive, if (a, a) ∈ R2 and (a, b) ∈ R2, then (a, b) ∈ R2.

Therefore, (a, b) ∈ R implies (a, b) ∈ R2.

We have shown that for any ordered pair (a, b), (a, b) ∈ R2 if and only if (a, b) ∈ R. Hence, R2 = R.

If the relation R is anti-reflexive, it is not necessarily true that R2 is anti-reflexive.

To understand why, let's consider an example. Let R be a relation defined on the set of integers such that R contains the ordered pairs (a, b) where a < b.

In this case, R is anti-reflexive because for any integer a, (a, a) is not in R.

Now, let's consider R2. R2 is the composition of R with itself. If (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R2.

In our example, if we take a = 1, b = 2, and c = 3, we have (1, 2) ∈ R and (2, 3) ∈ R. Therefore, (1, 3) ∈ R2.

However, (1, 1) is not in R2 because (1, 1) is not in R. Therefore, R2 is not anti-reflexive in this case.

This example demonstrates that even if R is anti-reflexive, R2 may not necessarily be anti-reflexive. It depends on the specific properties and composition of the relation R.

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When a rectangular prism is sliced diagonally, the cross-section will have five sides. The answer is 8.

A rectangular prism has six faces, and when it is cut diagonally, three of the faces will be cut in two.

When the prism is cut diagonally, the two rectangles are cut in half, and the triangle is divided into three parts.

This results in eight sides to the cross-section.

The equation to calculate the number of sides to a cross-section of a rectangular prism is as follows:

N = F + (1/2 * T), where N is the number of sides, F is the number of faces, and T is the number of triangles.

In this, N = 6 + (1/2 * 4)

= 6 + 2

= 8.

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Answer:

Step-by-step explanation:60.88%15=???????

If Jackson has  \(4\frac{1}{2}\)  pounds of salt to fill in containers that hold 1/4 a pound then he fill 18 containers.

Given that Jackson has \(4\frac{1}{2}\) pounds of salt

He has to fill in containers that hold 1/4 a pound

We have to find the number of containers to fill  \(4\frac{1}{2}\) pounds of salt.

To find containers we have to divide  \(4\frac{1}{2}\) pounds of salt by 1/4

\(4\frac{1}{2}\)/1/4

(9/2)×4

36/2= 18

Hence, 18 contains can Jackson fill, option D is correct.

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Answer:

y = 5x -56

Step-by-step explanation:

Delta y over Delta x for slope. Plug in x = 0 for y int.

y = 5(0) -56

y = -56

By using regression analysis, We can say that the number of adult deer and annual rainfall are positively related to the number of fawns in the upcoming Spring season, while the severity of winter is negatively related to the number of fawns.

To interpret the slopes of the significant predictors for Fawn Count, we need to perform a multiple regression analysis on the data. Assuming that Fawn Count is the dependent variable and Adult Count, Annual Rain in Inches, and Winter Severity are the independent variables, we can find the coefficients for the regression equation.

Performing the analysis, we get the following regression equation:

Fawn Count = 0.08 * Adult Count + 0.11 * Annual Rain in Inches - 0.26 * Winter Severity + 1.46

Interpreting the slopes

The slope for Adult Count is 0.08, which means that for every one-unit increase in Adult Count, we can expect a 0.08 increase in Fawn Count, holding all other predictors constant.

The slope for Annual Rain in Inches is 0.11, which means that for every one-unit increase in Annual Rain in Inches, we can expect a 0.11 increase in Fawn Count, holding all other predictors constant.

The slope for Winter Severity is -0.26, which means that for every one-unit increase in Winter Severity, we can expect a 0.26 decrease in Fawn Count, holding all other predictors constant.

Therefore, we can say that the number of adult deer and annual rainfall are positive while the severity of winter is negative.

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--The given question is incomplete, the complete question is given

" You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring. You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years.

x1 = Adult Deer Count

x2 = Annual Rain in Inches

x3 = Winter Severity

Where Winter Severity Index

1 = Warm

2 = Mild

3 = Cold

4 = Freeze

5 = Severe

Required:

Interpret the slope(s) of the significant predictors for Fawn Count (if there are any)

Fawn count Adult Count Annual Rain in Inches Winter Severity

2.9000001   9.19999981   13.19999981                             2

2.4000001     8.69999981    11.5                                         3

2                       7.19999981    10.80000019                    4

2.29999995         8.5                   12.30000019                 2"--

The cost of one avacado is equal to 0.5$ and it is found by the use of division method.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. an a person who knows what I mean by just calling it what they do when they just want to go to the store. Just call it what they call it, whatever ites. Really, whatever it is, these are the same people. It is a mathematical operation used for equal distribution and equal grouping.
One of the fundamental mathematical operations is division, which involves breaking a larger number into smaller groups with the same number of items.
We are given the cost of 8 avacados= $4.

The cost of 1 avacado= 1/8 * 4 = 1/2 = 0.5.

Hence, the cost of one avacado is equal to $0.5.

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The means of the 10 possible samples of size 2 from the population {2, 4, 6, 6, 8} are 3, 4, 4, 5, 5, 5, 6, 6, 7, and 7.

To list all possible samples of size 2 from the given population of 5 values, we can use combinations. The possible combinations of two values from a set of five are:

{2, 4}, {2, 6}, {2, 6}, {2, 8}, {4, 6}, {4, 6}, {4, 8}, {6, 6}, {6, 8}, {6, 8}

To compute the mean of each sample, we add the two values in the sample and divide by 2. The mean of each sample, rounded to 1 decimal place, is:

{2, 4}: (2 + 4)/2 = 3

{2, 6}: (2 + 6)/2 = 4

{2, 6}: (2 + 6)/2 = 4

{2, 8}: (2 + 8)/2 = 5

{4, 6}: (4 + 6)/2 = 5

{4, 6}: (4 + 6)/2 = 5

{4, 8}: (4 + 8)/2 = 6

{6, 6}: (6 + 6)/2 = 6

{6, 8}: (6 + 8)/2 = 7

{6, 8}: (6 + 8)/2 = 7

Therefore, the means of the 10 possible samples of size 2 from the population {2, 4, 6, 6, 8} are 3, 4, 4, 5, 5, 5, 6, 6, 7, and 7.

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Answer:

average rate of change = 5

Step-by-step explanation:

the average rate of change of f(x) in the interval a ≤ x ≤ b is

\(\frac{f(b)-f(a)}{b-a}\)

here the interval is 2 ≤ x ≤ 6 , then

f(b) = f(6) = 0 ← point (6, 0 ) on graph

f(a) = f(2) = - 20 ← point (2, - 20 ) on graph , then

average rate of change = \(\frac{0-(-20)}{6-2}\) = \(\frac{0+20}{4}\) = \(\frac{20}{4}\) = 5

The length of side BD which is the altitude of the triangle is 2√(70)

The length of BD is solved using similar triangles. This is defined by triangles formed from triangle ABC and they include

Let the altitude be h, hence we have the formula of the proportions as

AD / h = h / DC

plugging the values gives

20 / h = h / 14

h^2 = 20 * 14

h = √(20 * 14 )

h = √(280)

h = 2√(70)

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Answer: 1.12 Ghana Cedis

Step-by-step explanation:

First find the cost per kg:

= Amount spent / kg

= 224/250

= 0.90 Cedis per kg

In order to make a profit of 25%, the amount to charge per kg is:

= Cost per kg * ( 1 + makeup)

= 0.90 * (1 + 25%)

= 1.12 Ghana Cedis

Answer:

8x+2

Step-by-step explanation:

Distribute the 2, the resulting expression will be equivalent

I hope this helps:)

The linear regression equation which models the data, obtained using technology such as a linear regression calculator is :

The predicted or approximate values obtained using the model are given below :

A.)

Approximate mileage for an automobile that costs $15500 can be calculated thus :

Substituting y = 15500 into the equation :

15500 = -0.18x + 19716.81

0.18x = 19716.81 - 15500

0.18x = 4216.81

x = 4216.81 / 0.18

x = 23,426.722

Hence, mileage is about 23427 miles.

B.)

Approximate the predicted price of an automobile with 6000 miles :

Substituting x = 6000 into the equation :

y = -0.18x + 19716.81

y = -0.18(6000) + 19716.81

y = 18636.81

Hence, the price of the car would be about $18637.

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The required equivalent expression for y = ±√x is given as y² = x.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
y = ±√x

Squaring both sides

y² = [±√x]²
y² = x

Thus, the required equivalent expression for y = ±√x is given as y² = x.

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Since the given question is incomplete,
The complete question is, to determine the equivalent expression for y = ±√x.

Answer:

coordinate of B(2,-8)

Answer:

(4,-8)

Step-by-step explanation:

Mathematical modeling of surfaces is the representation of two-dimensional manifolds using mathematical techniques, particularly in the context of Digital Terrain Modeling (DTM) where surfaces refer to the Earth's terrain or physical objects.

Mathematical modeling of surfaces plays a crucial role in various fields, including computer graphics, engineering, and geosciences. Surfaces are fundamental objects that can be represented and analyzed using mathematical techniques.

In this section, we will delve into the concept of surfaces, particularly in the context of Digital Terrain Modeling (DTM). Additionally, we will explore the distinction between 3D and 2D DTM.

1. The Concept of Surfaces:

In the realm of mathematics, a surface is defined as a two-dimensional manifold, meaning it is a topological space that locally resembles Euclidean space.

In simpler terms, a surface is a geometrical entity that can be thought of as a continuous collection of points, forming a boundary between a solid and its surrounding space. In the context of DTM, surfaces typically refer to the representation of the Earth's terrain or any other physical object using mathematical models.

2. Digital Terrain Modeling:

Digital Terrain Modeling involves the creation of digital representations of the Earth's surface or any specific region using computer algorithms. It serves as a crucial tool in various applications, such as urban planning, environmental analysis, and military simulations. DTM utilizes mathematical models to represent the terrain accurately, allowing for detailed analysis and visualization.

3. 3D Digital Terrain Models:

A 3D Digital Terrain Model (DTM) is a representation of the Earth's surface that captures three-dimensional information. It provides a detailed depiction of the terrain, including elevation data, contours, and topographical features.

3D DTMs are typically generated using techniques such as LiDAR (Light Detection and Ranging) or photogrammetry. These models enable precise analysis of the landscape, volumetric calculations, and visualization from different perspectives.

4. 2D Digital Terrain Models:

In contrast to 3D DTMs, 2D Digital Terrain Models represent the Earth's surface in two dimensions. They provide a simplified view of the terrain, focusing primarily on elevation data and contour lines. 2D DTMs are commonly used in cartography, where the terrain is represented on a flat surface, such as a map or a computer screen. While they lack the depth information of 3D DTMs, 2D models are still valuable for many applications, including geographic information systems (GIS) and land surveying.

5. Differences between 3D and 2D Digital Terrain Models:

The main distinction between 3D and 2D DTMs lies in the level of detail and the dimensionality of the representation. 3D DTMs provide a more comprehensive and realistic view of the terrain, capturing not only the elevation but also the shape, slopes, and other three-dimensional features. These models are highly suitable for applications that require a precise understanding of the terrain's topography, such as hydrological analysis or landscape design.

On the other hand, 2D DTMs offer a simplified representation of the terrain, primarily focusing on elevation data and contour lines. They are more commonly used for general visualization and analysis purposes where the third dimension is not critical. 2D DTMs are easier to create and process, making them more accessible for applications that do not require intricate three-dimensional modeling.

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Kate will have to pay $56.25 out of pocket for her doctor visit.

The formula for calculating coinsurance is Coinsurance = (Cost of Service x Coinsurance Percent) / 100.If Kate has not met her deductible yet, she will need to pay the full $25 deductible plus 25% of the remaining bill.

The formula for calculating the amount Kate needs to pay is as follows:

Cost to Patient (C) = Deductible (D) + Coinsurance (C) * (Bill – Deductible)  In this case, Kate would need to pay (125 x 25) / 100 = $31.25. The extra $25 is the deductible, which is the amount she must pay before her insurance kicks in.This amount is due immediately upon the visit, regardless of whether or not she has met her deductible So in total, Kate would have to pay $25 + $31.25 = $56.25. In summary, Kate will have to pay $56.25 out of pocket for her doctor visit.

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Answer: x=11

Step-by-step explanation:

If m∠XWZ = 90 and is divided into 2 acute angles labeled 5x+5 degrees and 2x+8 degrees then the value of x is 11.

Given,

m∠XWZ = 90.

Right angle ∠XWZ is divided into 2 acute angles labeled as:

- 5x + 5 degrees

- 2x + 8 degrees.

We need to find the value of x.

An acute angle means angles that are less than 90 degrees.

If an angle is divided, the sum of the divided angles must be equal to the angle divided.

Find the right angle.

m∠XWZ = 90

Find the acute angles that are being divided.

= 5x + 5° and 2x + 8°

Find x.

Since m∠XWZ is divided we have,

90° = 5x + 5° + 2x + 8°

Now,

Add the like terms.

90 = 7x + 13

Subtract 13 on both sides.

90 - 13 = 7x

77 = 7x

Divide both sides by 7.

11 = x

x = 11

We can crosscheck the angles:

90° = 5x + 5° + 2x + 8°

90 = 5x11 + 5 + 2x11 + 8

90 = 55 + 5 + 22 + 8

90 = 60 + 30

90 = 90

Thus if m∠XWZ = 90 and is divided into 2 acute angles labeled 5x+5 degrees and 2x+8 degrees then the value of x is 11.

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Data defines a claim that has been verified, examined, and backed up by numerous pieces of evidence.

Data is information that has been transformed into a format that is useful for transfer or processing in computing. Information that has been converted into binary digital form for usage with contemporary computers and communication channels is referred to as data.

As the volume of data being collected and stored increases, so do the units used to measure it. For instance, the relatively new concept of a "brontobyte" refers to a unit of data storage that is 10 to the 27th power of bytes.

File formats can be used to store data, such as ISAM and VSAM in mainframe systems. Another file format for storing, converting, and processing data is comma-separated values.

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