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The mass of sugar in 1 bottle is 1.65kg.

The equation that represents the information in the question is:

Total kg of sugar bought = total kg of the bottes + sugar left over

Total kg of sugar bought = (number of bottles x mass of sugar in one bottles + sugar leftover

8.6 = (5 x s) + 0.35

8.6 = 5s + 0.35

In order to determine the value of s, take the following steps:

Combine and add similar terms together:

8.6 - 0.35 = 5s

8.25 = 5s

Divide both sides of the equation by 5

s = 8.25 / 5

s = 1.65 kg

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The two numbers are 3 and 12 when 15 is the result of sum two numbers. One to two are compared in a 4:1 ratio.

Given that,

15 is the result of adding two numbers. One to two are compared in a 4:1 ratio.

We have to find which two numbers are they.

We know that,

Let take x and y to denote the two numbers

We get

x + y = 15   ----->equation(1)

x = 4y        ----->equation(2)

Substitute the 4y in equation(1)

(4y) + y = 15

5y = 15

Divide both sides by 5

y = 3.

Substitute y=3 in equation(2)

x=4(3)

x = 12

Therefore, The two numbers are 3 and 12 when 15 is the result of adding two numbers. One to two are compared in a 4:1 ratio.

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The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Please refer below for the remaining answers.

We have,

Part A:

To rewrite the expression 2x³y + 18xy - 10x²y - 90y so that the greatest common factor (GCF) is factored completely, we can factor out the common terms.

GCF: 2y

\(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

Part B:

To completely factor the expression, we can further factor the quadratic term.

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Now,

Part A:

To determine the length of each side of the square given the area expression (9x² + 24x + 16), we need to factor it completely.

The area expression (9x² + 24x + 16) can be factored as (3x + 4)(3x + 4) or (3x + 4)².

Therefore, the length of each side of the square is 3x + 4.

Part B:

To determine the dimensions of the rectangle given the area expression (16x² - 25y²), we need to factor it completely.

The area expression (16x² - 25y²) is a difference of squares and can be factored as (4x - 5y)(4x + 5y).

Therefore, the dimensions of the rectangle are (4x - 5y) and (4x + 5y).

Now,

f(x) = 2x² - 5x + 3

Part A:

To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x² - 5x + 3 = 0

The quadratic equation can be factored as (2x - 1)(x - 3) = 0.

Setting each factor equal to zero:

2x - 1 = 0 --> x = 1/2

x - 3 = 0 --> x = 3

Therefore, the x-intercepts of the graph of f(x) are x = 1/2 and x = 3.

Part B:

To determine if the vertex of the graph of f(x) is maximum or minimum, we can examine the coefficient of the x^2 term.

The coefficient of the x² term in f(x) is positive (2x²), indicating that the parabola opens upward and the vertex is a minimum.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

For f(x),

a = 2 and b = -5.

x = -(-5) / (2 x 2) = 5/4

To find the corresponding y-coordinate, we substitute this x-value back into the equation f(x):

f(5/4) = 25/8 - 25/4 + 3 = 25/8 - 50/8 + 24/8 = -1/8

Therefore, the vertex of the graph of f(x) is at the coordinates (5/4, -1/8), and it is a minimum point.

Part C:

To graph f(x), we can start by plotting the x-intercepts, which we found to be x = 1/2 and x = 3.

These points represent where the graph intersects the x-axis.

Next,

We can plot the vertex at (5/4, -1/8), which represents the minimum point of the graph.

Since the coefficient of the x² term is positive, the parabola opens upward.

We can use the vertex and the symmetry of the parabola to draw the rest of the graph.

The parabola will be symmetric with respect to the line x = 5/4.

We can also plot additional points by substituting other x-values into the equation f(x) = 2x² - 5x + 3.

By connecting the plotted points, we can draw the graph of f(x).

The steps to graph f(x) involve plotting the x-intercepts, the vertex, and additional points, and then connecting them to form the parabolic curve.

The answer in part A (x-intercepts) and part B (vertex) are crucial in determining these key points on the graph.

Thus,

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

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Answer:225/8 in square

Step-by-step explanation:

No

Answer:

the length of each piece that i got was 3.5 or 3 1/2

Step-by-step explanation:

Answer:

16/20

Step-by-step explanation:

4:5

Multiply each side by 4

4*4: 5*4

16:20

16/20

Answer:

The answer is C. 16/20.

Step by step explanation:

This is because if you were to multiply 4 and 5 by 4, you would get 16/20. That means that both ratios are the same. Hope this helps! :)

Answer:C. (4,5)

Step-by-step explanation:

The first equation can be simplified to y=1/2x +3.

The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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The value of the integral over the region d is 0.

We want to evaluate the double integral:

∫∫d 7(r^2·sin(θ)) r dr dθ

where d={(r,θ)∣0≤r≤5cos(θ), 0≤θ≤π}.

We can integrate with respect to r first and then with respect to θ.

∫π0 ∫5cos(θ)0 7(r^2·sin(θ)) r dr dθ

= ∫π0 [7/3 · r^3 · sin(θ)]5cos(θ)0 dθ

= (7/3) · ∫π0 [125cos^3(θ)sin(θ)] dθ

We can solve this integral by substituting u = cos(θ), then du = -sin(θ) dθ:

(7/3) · ∫1-1 [125u^3(-du)]

= (7/3) · ∫-1^1 [125u^3 du]

= (7/3) · [125/4 · u^4]1-1

= 0

Therefore, the value of the integral over the region d is 0.

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Answer:

D.Mechanical energy produces an electric held.

Step-by-step explanation: its simple read it carefully

The high temperature for today using a 3-day moving average is 92 degrees.

To calculate the high temperature for today using a 3-day moving average, we take the average of the temperatures from the past three days, including today.

Given the daily high temperatures in St. Louis for the last week:

92, 92, 93, 95, 95, 86, 95 (yesterday)

To find the 3-day moving average for today's high temperature, we consider the temperatures from yesterday, the day before yesterday, and three days ago.

(95 + 86 + 95) / 3 = 92

Therefore, the high temperature for today, calculated using a 3-day moving average, is approximately 92 degrees Fahrenheit, rounded to one decimal place.

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Answer:

46.6

Step-by-step explanation:

375 rounds down the 6 to just 6 tenths

Answer:

46.64

Step-by-step explanation:

For example;

Say you wanted to round the number 838.274. Depending on which place value you'll round to, the final result will vary. Rounding 838.274:

Rounding to the nearest hundred is 800

Rounding to the nearest ten is 840

Rounding to the nearest one is 838

Rounding to the nearest tenth is 838.3

Rounding to the nearest hundredth is 838.27

An equation for this statement "The sum of seven times a number and 16 is 163," is 7n + 16 = 163.

The solution is 21.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

Based on the statement "The sum of seven times a number and 16 is 163," we can logically deduce the following algebraic equation;

7n + 16 = 163

7n = 163 - 16

7n = 147

n = 147/7

n = 21.

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The length of FD is 4.

In order to solve this problem, we need to use the Law of Cosines. The Law of Cosines states that in any triangle, the sum of the squares of the sides is equal to the square of the hypotenuse multiplied by two and minus twice the product of the sides multiplied by the cosine of the included angle.

Using the Law of Cosines, we can solve this problem as follows:

\(FD^2= EB^2 + CD^2 - 2*EB*CD*cos(mCD⏜)\\FD^2= 12^2 + 8^2 - 2*12*8*cos(90°)\\FD^2= 144 + 64 - 192FD^2= 16\\FD = √16\)

FD = 4

Therefore, FD = 4.

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The number of volunteers recruited for the first 5 weeks is; 486 people

A geometric sequence is defined as a sequence in which the result of the division of consecutive terms is always the same, called common ratio r.

The nth term of a geometric sequence is given by:

aₙ = a₁rⁿ⁻¹

where;

a₁ is the first term

r is the common ratio

In this question, on the first week there are 6 people, and since each new people involve three more, the common ratio is 3, hence the parameters for the geometric sequence are:

a₁ = 6

r = 3

Hence the number of people after n weeks is:

aₙ = 6(3)ⁿ⁻¹

Thus, the number of volunteers recruited for the first 5 weeks is;

a₅ = 6(3)⁵⁻¹

a₅ = 6 * 3⁴

a₅ = 486

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Answer:

Hey there!

The x-intercept is (6,0) meaning that if no children attend, 6 adults will attend.

The y-intercept is (0,14) meaning that if no adults attend, 14 children will attend.

Let me know if this helps :)

The x-intercept is (6,0) and y-intercept is (0,14).

x-intercept for "any curve is the value of x-coordinate at the point where the graph cuts the x-axis".

What is y-intercept?

y-intercept  for "any any curve is the value of y-coordinate at the point where the graph cuts the y-axis".

According to the question,

3.5x + 1.5y =21

Let 'x' is the number of adults and 'y' is the number of children.

To find  x-intercept put y=0.

3.5x + 1.5(0) = 21

             3.5x = 21

                  x = 21/3.5 =6.

To find y-intercept put x=0

3.5(0) + 1.5(y) = 21  

                  y = 21/1.5 = 14.

x-intercept (6,0) if no children attend the play then 6 adult attend the play. y - intercept (0,14) if no adult attend the play then 14 children attend the play.

Hence, The x-intercept is (6,0) and y-intercept is (0,14).

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In the field of astronomy, the ability to measure angles accurately and precisely enables us to calculate the position and relative movement of the stars and galaxies in relation to each other, to determine how far distant they are from us, and even to estimate their relative size.

The balanced chemical equation for the given reaction is:Fe2O3 + 3CO → 2Fe + 3CO2The molar mass of Fe2O3 is 159.69 g/mol. Mass of Fe2O3 = 50.7 g Moles of Fe2O3 = 50.7 g / 159.69 g/mol = 0.3179 mol According to the balanced chemical equation, 1 mole of Fe2O3 reacts with 3 moles of CO.

Hence, the number of moles of CO used = 3 × 0.3179 mol = 0.9538 mol. The molar mass of CO is 28.01 g/mol. Mass of CO used = 0.9538 mol × 28.01 g/mol = 26.7 g Hence, the mass of CO2 formed will be equal to the mass of CO used, i.e., 26.7 g. The molar mass of Fe is 55.85 g/mol. Mass of Fe formed = 0.3179 mol × 2 × 55.85 g/mol = 35.27 g

The number of grams of Fe and the number of grams of CO2 formed when 50.7 g of Fe2O3 reacts with excess CO are 35.27 g and 26.7 g, respectively.

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Answer:

Step-by-step explanation:

you hav to times it

The modeling process begins with the framing of a conceptual model that shows the relationships between the various parts of the problem being modeled. This model helps to identify the mathematical correlations between variables and provides a foundation for developing a more detailed and accurate mathematical model.

The modeling process begins with the framing of a mathematical model that shows the relationships between the various parts of the problem being modeled. This model is often based on data analysis and utilizes statistical techniques to establish correlations between the different variables in the problem. Ultimately, the goal of the modeling process is to create a predictive tool that can be used to make informed decisions about the problem at hand.

Process models involve graphically representing processes or functions that capture, manage, store, and distribute information between the system and its environment and physical objects. One type of process model is the flowchart (DFD). A data flow is a diagram that shows the movement of data between external sources and processes and the data stored in the system. While several different tools have been developed for modeling, we focus only on data streams as they are effective tools for modeling. While not all organizations use all analytical methods, including these methods such as data flow, they have a significant impact on the development process.

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If the equation y = 760+22t represents the total number of students who graduated from Andrea's school t years after 1998, then the number of students who graduated from Andrea's school each year is 22

The equation is

y = 760 + 22t

Where y is the number of students who graduated from Andrea's school

t is the number of years after 1998

We know

The slope intercept form is

y = mx + b

Where m is the slope of the line

Slope of the line is change in y coordinate with respect to the change in x coordinate.

Here the slope of the line is 22, that is the number of students graduated from Andrea's school each year

Hence, if the equation y = 760+22t represents the total number of students who graduated from Andrea's school t years after 1998, then the number of students who graduated from Andrea's school each year is 22

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Semiperimeter is used to find the area of various shapes including the equilateral triangle (False).

Semiperimeter is a term used in geometry to refer to half the perimeter of a polygon. It is generally used in formulas for triangles.

However, it is also part of calculations related to other geometric shapes. According to the above, it can be inferred that the semiperimeter can be used to find the area of various geometric figures.

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Answer:

f(x)=4/2x  

i dont have no explanation                                                

the solution of the given differential equation is:y = [16 ln |x| + 8x2 + C1]1/16

The given differential equation is y15 x dy/dx = 1 + x. Now, we will solve the given differential equation.

The given differential equation is y15 x dy/dx = 1 + x. Let's bring all y terms to the left and all x terms to the right. We will then have:

y15 dy = (1 + x) dx/x

Integrating both sides, we get:(1/16)y16 = ln |x| + (x/2)2 + C

where C is the arbitrary constant. Multiplying both sides by 16, we get:y16 = 16 ln |x| + 8x2 + C1where C1 = 16C.

Hence, the solution of the given differential equation is:y = [16 ln |x| + 8x2 + C1]1/16

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Answer:

b.......19/3...I. guess

Answer:

x =  \(\frac{9\sqrt{6} }{2}\)

Explanation:

using sohcahtoa method:

middle line: 9 ÷ sin(45) = 9√2

x = sin(60) * 9√2 = \(\frac{9\sqrt{6} }{2}\)

Answer:

P ( 3 ) = 16

the remainder is  

P ( a )

Answer:

12

Step-by-step explanation:

(5×6)-½(3×6 + 2×4 + 2×5)

=30 - ½(18+8+10)

= 30 - ½(36)

=30-18= 12