there are 1700 bottles of water arranged into 4 groups. the second group has 20 more bottles than the first group. the third group has twice as many bottles as the second group. the fourth group has 10 more bottles than the third group. how many bottles are in each group? solve this problem in two ways: with the aid of a diagram and with algebraic equations. explain both solu-tion methods, and discuss how they are related.

A graph of the solution (4, 4) for the system of linear equations is shown in the image attached below.

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In this context, we would replace the y-value of the first equation 4x - 2y = 8 with zero (0) as follows;

4x - 2(0) = 8

4x = 8

x = 2 ⇒ (2, 0).

For the y-intercept of the first equation 4x - 2y = 8, we would substitute the x-value with zero (0) as follows;

4(0) - 2y = 8

2y = -8

y = -4 ⇒ (0, -4).

For the y-intercept of the first equation y = 3x/2 - 2, we would substitute the x-value with zero (0) as follows;

y = 3(0)/2 - 2

y = -2 ⇒ (0, -2).

By critically observing the graph of the given system of linear equations (see attachment), we can logically deduce that their solution lie at the point of intersection of the lines on the graph representing each of them, which is in Quadrant I and it is given by the ordered pair (4, 4).

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Answer:

see attached

Step-by-step explanation:

3 triangles

3 variables

so you'll get 3 equations

memorize right triangle's property

short side 1 ²  + short side 2 ² = long side ²

see attached

Candle A is taller than candle B at the beginning of the burning. The correct option is D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Candle, A is taken from the mould at 223mm of height initially. Candle B is represented by the function h = 200 - 5t.

The initial height of candle A:-  223 mm

The initial height of candle B is:-

h = 200 - 5 t

h = 200 - 5 x 0

h = 200 mm

Candle A > Candle B

Hence, the height of candle A is greater than the height of candle B.

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To determine if a system of equations has infinitely many solutions, we can use the method of elimination or substitution to solve for one variable in one equation and substitute it into the other equation.

If the resulting equation is an identity, then the system has infinitely many solutions.

In this case, we can solve for one variable in each equation and substitute the solution into the other equation to check for Consistency. If the resulting equation is an identity, then the system has infinitely many solutions.

After solving each system individually, it appears that the system of equations 4x - 3y = 6 and 3x - y = 14 produces infinitely many solutions. This is because when we substitute the solution for x from the first equation into the second equation, we get:

3(4) - y = 14

12 - y = 14

y = 2

This means that for any value of x that's Satisfies the first equation, y will always equal 2. Therefore, the two equations represent the same line in the xy-plane, and the system has infinitely many solutions.

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Answer:

104

Step-by-step explanation:

it says it in the question

Step-by-step explanation:

Slope-Intercept form is Y = mx + b

So we have to turn 9x + 3y = -9 into that.

A ideal first step would be subtracting 9x on both sides, that would make it

3y = -9x-9

Next step would be dividing by 3 on both sides. This can get the y all alone

[tex]y = \frac{ - 9x - 9}{3} [/tex]

Since the denominator is below multiple numbers, we can separate it as so

[tex]y = \frac{ - 9x}{3} - \frac{9}{3} [/tex]

Simplifying 9/3 goes to 3/1. 3/1 is the same as 3, because any number over 1 is that number. Doing that to both will get our answer.

[tex]y = - 3x - 3[/tex]

The equation of the graph is y = 1 / 2 x - 3.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's find the slope of the graph as follows:

using (0, -3)(6, 0)

Hence,

slope = m = 0 + 3 / 6 - 0

slope = 3 / 6

slope = 1 / 2

Therefore, let's find the y-intercept using (0, -3).

y = 1 / 2x + b

-3 = 1  /2 (0) + b

b = -3

Therefore, the equation is y =  1 / 2 x - 3

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So, 40% of the animals on the farm are cows, whereas 60% are pigs.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

Here,

(a) On the farm, the cow-to-pig ratio is 2:3, which means that for every 5 animals, there are 2 cows and 3 pigs. To get the percentage, divide the number of cows by the total number of animals and multiply by 100. As a result, the farm's cow proportion is:

(2 / (2 + 3)) * 100 = 40%

(b) To find the percentage of pigs on the farm, we can use the same method as for the cows. The percentage of pigs on the farm is:

(3 / (2 + 3)) * 100 = 60%

So, 40% of the animals on the farm are cows, and 60% of the animals are pigs.

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The complete steps to to Multiply Two Polynomials are listed below

From the question, we have the following parameters that can be used in our computation:

The steps with missing values

When completed, we have

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The probability that a student will complete the exam in more than 60 minutes but less than 90 minutes is 0.8099 (to 4 decimal places).

The probability of a student completing the exam in more than 60 minutes but less than 90 minutes can be calculated using the cumulative probability distribution formula. The cumulative probability of a random variable X is given by P(X≤x)=F(x).

In this case, let F(x) represent the cumulative probability of a student completing the exam in more than 60 minutes but less than 90 minutes.

F(x) = P(60<x<90) = P(X<90) - P(X<60)

Using the cumulative probability distribution formula, we can calculate P(X<90) and P(X<60).

P(X<90) = 0.9686

P(X<60) = 0.1587

Substituting these values in the equation:

F(x) = P(60<x<90) = 0.9686 - 0.1587 = 0.8099

Therefore, the probability that a student will complete the exam in more than 60 minutes but less than 90 minutes is 0.8099 (to 4 decimal places).

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Answer:

Since you know that 15 vases are worth 2,250 rupees, then to find how much 25 cost, you can first find how much each costs individually.

To find how much each vase cost, you can just divide the total cost of 15 vases, and the amount of vases:

2250/15 = 150

Each vase costs 150 rupees.

Now to find how much 25 vases cost, you can just multiply the cost per each flower vase, by the total amount of vases:

150 * 25 = 3,750

25 flower vases cost's 3,750 rupees.

Step-by-step explanation:

Hope it helps! =D

The slope of a fairly flat upward-sloping line will be a small positive number. (option c)

This is because a slope measures the change in the y value for a given change in the x value. As the line is fairly flat, the change in y value will be small. Since the line is upward-sloping, the change in the y value will be positive. Therefore, the slope of the line will be a small positive number.

To calculate the slope mathematically, we can use the formula

This formula gives us the slope of the line between two points (x1, y1) and (x2, y2). In our case, since the line is fairly flat, the difference in y values (y2-y1) will be small, resulting in a small positive number for the slope.

We can also visualize this mathematically. If we graphed the line, it would look like a flat line, because the difference in y values is small. Therefore, the slope of the line will be a small positive number.

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The value of x in the angle is 56 degrees

From the question, we have the following parameters that can be used in our computation:

The figure

On the figure, we have teh following equation

64 + x + 60 = 180

The above is by the angle on a straight line theorem

So, we have

124 + x = 180

Evaluate the like terms

x = 56

Hence, the value of x is 56

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Answer:

x = 56

Step-by-step explanation:

64 + x + 60 = 180

124 + x = 180

x = 56

One of the features of interactive model of communication is "Feedback where a recipient of communication such as a listener provides a response to a message, often to indicate understanding after a message has been received."

The Feedback is one of the key features that makes the Interactive Model of Communication different from the Linear Model  based on Shannon and Weaver's mathematical model .

The Feedback allow a reciprocal exchange of messages between the sender and receiver, making communication a dynamic and interactive process.

In the Interactive Model, the feedback enables the receiver to provide feedback to the sender, which allows clarification, confirmation, and correction of messages.

The given question is incomplete , the complete question is

One of the features of the interactive model of communication that is discussed by Turner and West which makes it different from the linear model that was based on Shannon and weaver's mathematical model of communication is ?

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The value of the exponential function is f ( x ) = 10ˣ - 4

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

f ( x ) = 10ˣ - 4   be equation (1)

Now , the exponential function is when it is raised to the power of x

So , the function is close to -4 because 4 is deducted from the function

Therefore , the value of A is 10ˣ - 4 and the graph is plotted

Hence , the exponential function is f ( x ) = 10ˣ - 4

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The time taken by the planes when they are 2000 miles apart is 2 hours.

We all know that formula of distance, speed and time is given by  distance = speed*time or time = distance/speed

Let x be the number of hours that the two planes will be 2000 miles apart.

Let 430x be the distance traveled by the first plane at 430 miles per hour

and 570x be the distance traveled by the second plane at 570 miles per hour.

here, 430x +570x =2000 is the total distance travelled by the first plane and the second plane

Solving yields the following steps:

1000x = 2000

Dividing 1000 to both sides of the above equation, we get

1000x/1000=2000/1000

So the value of x will be equivalent to 2

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The correct answer is) D.  Because on the graph you can see that it increases by 25 each day which follows the equation Y=25x.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.

Jacqueline reads 25 pages every night, as is given. After x days, Jacqueline has read the following number of pages, which is represented by y.

given that she starts with 0 pages and reads 25 pages every day.

As a result, there is a proportionate relationship between the total number of pages read and the number of days.

she reads 25 pages a night Meaning that the total number of pages Jacqueline has read (Variable Y) = 25 pages a night (x)

Therefore, On a coordinate plane, a graph titled Total Pages Jacqueline Has Read has days on the x-axis and Pages on the y-axis. A line goes through points (1, 25) and (2, 50).

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Answer:

d

Step-by-step explanation:

because

Answer:

It is :)

Step-by-step explanation:

We need -1.94 gallons of 18%-salt solution to be mixed with 7 gallons of 30%-salt solution to obtain a 25%-salt solution.

The formula used to calculate the number of gallons of 18%-salt solution needed to be mixed with 7 gallons of 30%-salt solution to obtain a 25%-salt solution is:

V1C1 + V2C2 = V3C3

Where:

V1 = Volume of 18%-salt solution

C1 = Concentration of 18%-salt solution

V2 = Volume of 30%-salt solution

C2 = Concentration of 30%-salt solution

V3 = Volume of 25%-salt solution

C3 = Concentration of 25%-salt solution

Plugging in the given values, we get:

V1C1 + 7(0.30) = V3(0.25)

Simplifying the equation, we get:

V1(0.18) + 2.1 = 0.25V3

Subtracting 2.1 from both sides, we get:

V1(0.18) = 0.25V3 - 2.1

Dividing both sides by 0.18, we get:

V1 = (0.25V3 - 2.1) / 0.18

Substituting V3 with 7, we get:

V1 = (1.75 - 2.1) / 0.18

Simplifying, we get:

V1 = -0.35 / 0.18

Therefore,

V1 = -1.94 gallons

Hence, we need -1.94 gallons of 18%-salt solution to be mixed with 7 gallons of 30%-salt solution to obtain a 25%-salt solution.

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Answer:

- 12(x + 2)

Step-by-step explanation:

- 12x - 24 ← factor out the common factor of - 12 from each term

= - 12(x + 2)

The value of the expression 11 - 14 using subtraction will be negative 3.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numbers are given below.

11 and 14

Then the difference between the numbers 11 and 14 will be given by putting a minus sign between them. Then we have

⇒ 11 - 14

⇒ - 3

The value of the expression 11 - 14 using subtraction will be negative 3.

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Answer:

Step-by-step explanation:

a + 3 1/4 = 5 2/9

     -3 1/4    -3 1/4

a = 1 35/36

The equation the line is, y = -3/2 *x -1

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have ,

from the given graph we get,

the line is passing through the points (0,-1)& ( -2,2)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

now, by solving we get,

-3x-2y=2

Hence, the required equation is, y = -3/2 *x -1

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The probability that at least one of them has received immunizations is 97.5611%.

Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes. The study of events susceptible to probability is known as statistics. Probability is a mathematical representation of the likelihood or potential that an event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%. Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes. The study of events susceptible to probability is known as statistics.

1 - P( no one was vaccinated).

1-71%=0.29

If you pick one person at random from the population, there is a [tex]29[/tex]% chance they are not immunized. There is therefore no chance that any of the three people you choose will be an unvaccinated person [tex]0.29 X 0.29 X 0.29 = 0.024389.[/tex] Your solution, calculated as a percentage by deducting from [tex]1[/tex], is [tex]97.5611[/tex]%.

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The probability of rolling an odd number or a multiple of 6 on a d20 is 0.6 (10/20 + 4/20 - 2/20). This can also be expressed as a probability of 60%.

The probability of rolling an odd number or a multiple of 6 on a d20 is calculated using the following formula:

P(odd or multiple of 6) = P(odd) + P(multiple of 6) - P(odd and multiple of 6)

P(odd) = 10/20 or 0.5

P(multiple of 6) = 4/20 or 0.2

P(odd and multiple of 6) = 2/20 or 0.1

Therefore, the probability of rolling an odd number or a multiple of 6 on a d20 is 0.6 (10/20 + 4/20 - 2/20). This can also be expressed as a probability of 60%.

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The radius of the spherical part is 3 inches and the length of the tube is 21 cm.

The capacity of a cylinder, which determines how much material it can hold, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, can be immersed in it uniformly.

Given that the volume when the water is fully dipped is 4554 / 7 cm³. The volume when the length is 9 cm empty is 396 cm³.

The two equations can be formed as below:-

4554 / 7 = πr²l + (2/3)πr³

396 = πr²( l - 9 ) + (2/3)πr³

Subtract the second equation from the first,

( 4554 / 7 ) - 396 = 9πr²

9πr² = 254.5

r² = 9

r = 3 cm

The length will be calculated as:-

4554 / 7 = πr²l + (2/3)πr³

4554 / 7 = π( 3 )²l + (2/3)π(3)³

l = 21 cm

Therefore, the tube's length is 21 cm, and the spherical part's radius is 3 inches.

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The probability of his then drawing a blue marble from his right pocket is

0.456 or 45.6 %  by using conditional probability theorem.

conditional probability, the probability that an event occurs given the knowledge that another event has occurred.

from the given information : considering for notations, let BL, BR, and WL denote drawing a blue marble from the left pocket, a blue marble from the right pocket, and a white marble from the left pocket, respectively. By the Law of Total Probability,

P(BR) = P(BL ∩ BR)+ P(WL ∩ BR)

= P(BL)P(BR|BL)+ P(WL)P(BR|WL)

= ( 5/9)(5/10) + (4/9)(4/10) = (41/90)

= 0.456

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The MP3 player cost is $109.05.

Two or more expressions with an Equal sign is called as Equation.\

Let us consider the cost of the MP3 player "x".

Terrell started with $135 and spent $25.95 on the Internet music subscription,

so he had 135 - 25.95 = $109.05 left to spend on the MP3 player.

The equation to solve for x is:

x + 25.95 = 135

Subtract 25.95 on both sides

x = 135 - 25.95

x = 109.05

Hence, the MP3 player cost is $109.05.

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