The ratio of the number of red balls to blue balls to green balls is 3:2:5. There are 60 balls altogether? (1) How many balls are red? (2) How many balls are blue? (3)Write in fraction form,the ratio of green balls to red balls​

The first statement, "Commutative states that the grouping of three terms being added does not affect the result" is referring to the commutative property of addition.

The first statement, "Commutative states that the grouping of three terms being added does not affect the result" is referring to the commutative property of addition.

The second statement, "Distributive states that the order of two terms being added may be switched which does not affect the result" is referring to the commutative property of multiplication.

The third statement, "Associative states that the multiplying a sum by a number is the same as multiplying each addend by that number and then adding the two products" is referring to the associative property of multiplication.

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Answer:

Step-by-step explanation:

Question 1 :

The statement that best describes the solutions of a two-variable equation is (1) The ordered pairs must lie on the graphed equation. This means that any ordered pair (x,y) that satisfies the equation will corresponds to a point on the graph of the equation. In other words, if we plot all the points (x,y) that make the equation true, we will obtain the graph of the equation. Any points that do not lie on the graph is not a solution to the equation. Therefore, when solving a two-variable equation, we need to find the values of x and y that make the equation true and plot those points on the graph to visualize the solutions.

Question 2 :

To use the arithmetic sequence formula, we need to know the first term (a1), the common difference (d), and the desired term (an). In this case, we are given the first term as 4 and the common difference as 3 (since each term is increasing by 3). To find the 10th term, we would replace the variable "n" with 10 in the formula. Therefore, to determine the 10th term of this sequence, we would use the formula:

a10 = a1 + (n-1)d

a10 = 4 + (10-1)*3

a10 = 4 + 27

a10 = 31

Thus, the 10th term of the given sequence is 31.

Question 3 :

The formula an = al + (n-1)d is used to determine the nth term in an arithmetic sequence, where "a" represents the first term in the sequence, "n" represents the term number being solved for, and "d" is the common difference between terms. The formula essentially states that to find any term in an arithmetic sequence, one must add the common difference between terms multiplied by the number of terms-1 to the value of the first term. This formula can be applied to various situations, such as determining the total cost of goods sold in a business with a constant markup percentage, or calculating the number of days it will take to save a given amount of money with a fixed monthly contribution. By understanding the principles behind the formula, individuals can successfully solve problems involving arithmetic sequences in a variety of contexts.

Answer: b

Step-by-step explanation:

I didnt get it  but thats the correct answer when i guessed on it

Answer:

The answer is the skin est one there

Step-by-step explanation:

I got the question wrong so I don't know how but this is the correct one

Answer:

Sam balance was -10 and the ending balance was $70

=80+(-10)

=$70

Answer:

y=1/2x+4

Step-by-step explanation:

The point of intersection is 4, and it goes up one, right 2 so the rise over run is 1/2

The percentage increase of Seraphina's speed would be = 12.3%

The speed she travelled in the first hour = 57miles/hr

The speed she travelled in the second hour = 73miles/jr

The increase in speed = 73-57 = 16

Therefore the percentage increase;

= 16/130×100/1

= 1600/130

= 12.3%

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Answer:

19,322 cubic feet.

Step-by-step explanation:

Volume = Length × Width × Height

Given the measurements provided:

Length = 24 1/2 feet

Width = 14 feet

Height = 11 feet

We need to convert the mixed number for the length, 24 1/2 feet, into a single fraction.

24 1/2 feet = 24 + 1/2 feet = 48/2 + 1/2 feet = 49/2 feet

Now we can substitute the given values into the formula for volume:

Volume = (Length) × (Width) × (Height)

= (49/2 feet) × (14 feet) × (11 feet)

Next, we can multiply the lengths, widths, and heights together:

Volume = (49/2 feet) × (14 feet) × (11 feet)

= 49 × 14 × 11 cubic feet / 2

Finally, we can calculate the volume by dividing the product by 2:

Volume = 49 × 14 × 11 cubic feet / 2

= 19,322 cubic feet

There seems to be an error in the expression for P3(x). It appears to be missing an exponent for the second term.

Assuming that the correct expression is P3(x) = x^4 - 21x^2 + 20x, we can analyze its properties.

The degree of the polynomial P3(x) is 4, which means its graph will have at most 4 x-intercepts and at most 3 turning points.

To find the x-intercepts, we set P3(x) equal to zero and solve for x:

x^4 - 21x^2 + 20x = 0

x(x^3 - 21x + 20) = 0

Using the factor theorem or synthetic division, we can find that x = 0 is a root of the polynomial, so (x-0) is a factor. The remaining cubic factor can be factored as (x-1)(x-4)(x+5).

Therefore, the x-intercepts of the graph of P3(x) are x = 0, x = 1, x = 4, and x = -5.

As for the y-intercept, we can find it by setting x = 0:

P3(0) = 0^4 - 21(0)^2 + 20(0) = 0

So the y-intercept is (0,0).

To determine the turning points, we can find the critical points by taking the derivative of P3(x) and setting it equal to zero:

P3'(x) = 4x^3 - 42x + 20

4x^3 - 42x + 20 = 0

Solving this equation yields three critical points: x ≈ -1.23, x ≈ 0.58, and x ≈ 2.65.

We can use the second derivative test to determine the nature of these critical points. The second derivative is:

P3''(x) = 12x^2 - 42

At x ≈ -1.23 and x ≈ 2.65, the second derivative is negative, indicating that these are local maxima. At x ≈ 0.58, the second derivative is positive, indicating that this is a local minimum.

Therefore, the graph of P3(x) has a local maximum at (approximately) (-1.23, P3(-1.23)), a local minimum at (approximately) (0.58, P3(0.58)), and a local maximum at (approximately) (2.65, P3(2.65)).

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In linear equation, Roger and Trish can finish 11x/30 of the homework if they work together for x hours.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

In one hour, Roger can finish 1/6 of the work, and Trish can finish 1/5 of the work. So, working together for one hour, they can finish:

(1/6) + (1/5)

= (5/30) + (6/30)

= 11/30 of the work.

If they work together for x hours, then they will finish:

x × (11/30) = 11x/30

of the work in x hours.

Therefore, Roger and Trish can finish 11x/30 of the homework if they work together for x hours.

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The equation of the line is y=5x+17.

What is slope intercept form of the equation?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).   It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.

Here the given the point [tex](x_1,y_1)=(-4,-3)[/tex] and slope m = 5.

Now using equation formula then,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y -(-3)=5(x-(-4))

=> y+3 = 5(x+4)

=> y+3 = 5x+20

=> y = 5x+20-3

=> y = 5x+17

Hence the slope intercept form of the equation is y = 5x+17.

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The estimate of the annual snowfall in 78th year is 29.88 inches. The Option C.

Using the given information, we can use the linear equation y = mx + b, where y represents the annual snowfall and x represents the number of years since 1920.

The initial measurement in 1920 was 48.6 inches, so b = 48.6.

The decrease in annual snowfall is 0.24 inches per year, so m = -0.24.

The equation is y = -0.24x + 48.6.

We will plug in x = 78 into the equation and solve for y:

y = -0.24(78) + 48.6

y = -18.72 + 48.6

y = 29.88.

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The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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Answer:

  181.875 cm³

Step-by-step explanation:

You want to know the amount of additional material Jessica needs to make a prism with a volume of 35 cm³ and one that is dilated by a factor of 2.5, given that she has 400 cm³ of material.

The dilation factor for volume is the cube of the linear dilation factor:

  2.5³ = 15.625

so the volume of the scaled-up prism will be ...

  (35 cm³) × 15.625 = 546.875 cm³

The total volume of material Jessica needs for the two prisms is ...

  35 cm³ + 546.875 cm³ = 581.875 cm³

Since Jessica has 400 cm³ of material, the amount she needs is ...

  581.875 cm³ - 400 cm³ = 181.875 cm³

Jessica needs 181.875 cm³ more material to make the second prism.

The probability of getting a multiple of 2 or a multiple of 3s:

P = 0.67

The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes, which in this case are 12.

The multiples of 2 and the multiples of 3 are

{2, 3, 4, 6, 8, 9, 10, 12}

So 8 out of the total of 12 outcomes make the event true, then the probability we want to get is the quotient between these numbers:

P = 8/12 = 0.67

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The correct vocab in written as;

DC = semi-circle

<ECD = minor arc

<ECF = point of tangency

CF = chord

To determine the corresponding terms, we need to take note of the following definitions;

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In this scenario, the researcher is interested in comparing the effectiveness of three different doses of a new medication in treating panic attacks. To analyze the data, the researcher can use a hypothesis testing technique called analysis of variance (ANOVA).

ANOVA is a statistical technique used to compare the means of three or more groups to determine if there are significant differences between them. In this case, the means being compared are the number of panic attacks experienced by each group after 30 days on the medication.

The null hypothesis in this study would be that there is no significant difference in the mean number of panic attacks between the three dosage groups, and the alternative hypothesis would be that there is a significant difference in the mean number of panic attacks between at least two of the dosage groups.

The researcher can use a one-way ANOVA test to analyze the data, which will calculate the F-statistic and associated p-value. If the p-value is less than the chosen significance level (usually 0.05), the researcher can reject the null hypothesis and conclude that there is a significant difference in the mean number of panic attacks between at least two of the dosage groups.

If a significant difference is found, post-hoc tests such as Tukey's HSD can be used to determine which specific groups have significantly different means.

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System developers can initiate a formal project as early as the preliminary investigation stage, or later on, as analysis, design, and implementation activities occur. True.

System developers can initiate a formal project as early as the preliminary investigation stage or at any point in the analysis, design, and implementation activities.

The decision to initiate a formal project depends on various factors, including the scope of the project, the availability of resources, the complexity of the system, and the stakeholders' needs and requirements. A formal project may involve a team of developers, analysts, and other experts who work collaboratively to design and implement a system that meets the stakeholders' requirements and objectives.

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True. System developers can initiate a formal project as early as the preliminary investigation stage or later on as

analysis, design, and implementation activities occur.

The initiation stage is when the need for a new system is identified, and preliminary investigations are conducted to

determine the feasibility of the project.

If the project is deemed feasible, the formal project can be initiated at this stage.

However, if the project is initiated later on, the analysis, design, and implementation activities will have already begun.

System developers can initiate a formal project as early as the preliminary investigation stage or later on as

analysis, design, and implementation activities occur. therefore, the given statement is true.

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Answer:

This is a geometric series with first term 1/4 and common ratio 1/4. So the sum of this series is:

[tex] \frac{ \frac{1}{4} }{1 - \frac{1}{4} } = \frac{1}{4} \div \frac{3}{4} = \frac{1}{4} \times \frac{4}{3} = \frac{1}{3} [/tex]

Given statement "3-2 Roof area can be broken down into three basic shapes: rectangle, triangle, and trapezoid"

Given statement is True.
Because: When calculating the roof area, we can generally break it down into three basic shapes:

The term "roof area" typically refers to the total surface area of a roof. This can be calculated by measuring the length and width of each section of the roof, and multiplying those measurements together to get the area of each section.

Then, the areas of all the sections can be added together to get the total roof area.

It's important to accurately measure the roof area when planning for construction or repairs, as it will affect the amount of materials needed and the cost of the project.

Roof area can also be used to calculate the amount of insulation needed or to estimate the potential energy savings of installing solar panels.

Rectangle:

A four-sided polygon with opposite sides parallel and equal in length.
Triangle:

A three-sided polygon with three vertices and three angles.
Trapezoid:

A four-sided polygon with one pair of parallel sides.
By dividing a roof's surface into these shapes, you can calculate the total area more easily.

Hence statement is True.

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The height above the bottom of the canyon at the end of his jump is 385 feet.

we have,

Canyon depth = 400 feet

Trevor's height= 6 feet

cord length = 9 feet

So, Trevor height to end of jump is

= 400 - (9+6)

= 400 - 15

= 385 feet

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The standard form of the polynomial 2m-3m²+4m⁵+21 is 4m⁵ - 3m² + 2m + 21.

The standard form of a polynomial is when the polynomial is written with the terms in descending order of degree, with each term having a coefficient and an exponent. To convert the given polynomial 2m-3m²+4m⁵+21 to standard form, we need to rearrange the terms in descending order of degree.

The degree of a term is the exponent of the variable in that term. For example, the degree of the term 4m⁵ is 5, and the degree of the term -3m² is 2.

So, we start by arranging the terms in descending order of degree:

4m⁵ - 3m² + 2m + 21

Next, we can simplify the coefficients of each term if possible. In this case, all of the coefficients are already simplified, so we leave them as they are.

In summary, to convert a polynomial to standard form, we arrange the terms in descending order of degree and simplify the coefficients of each term if possible. This makes it easier to compare and manipulate polynomials, and is often required when solving equations or finding roots of polynomials.

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From the given information about the vertices of the quadrilateral, the point at which the PQRS quadrilateral will be made a rectangle is S(17/14, -1/7).

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The answer is option c.) S(-8,2).

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

For PQRS to be a rectangle, its opposite sides must be parallel and have equal length. We can find the length of PQ and RS using the distance formula:

PQ = √[(Qx - Px)² + (Qy - Py)²]

  = √[(-3 - (-5))² + (6 - 7)²]

  = √[4 + 1]

  = √[5]

RS = √[(Sx - Rx)² + (Sy - Ry)²]

  = √[(-8 - (-6))² + (2 - 0)²]

  = √[4 + 4]

  = √[8]

Since PQ and RS are not equal, we need to find a point S such that PQRS has equal sides. Moreover, the diagonals of a rectangle bisect each other. Hence, we can use the midpoint formula to find a point that bisects PR:

M = [(-5 - 6)/2, (7 + 0)/2]

 = (-11/2, 7/2)

Let's consider each option:

a.) S(-4,-1)

The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-8 + 6) = 1, so S(-4, -1) cannot be a point of RS.

b.) S(-7,2)

The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-7 + 6) = -2, so S(-7, 2) cannot be a point of RS.

c.) S(-8,2)

The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-8 + 6) = 1, so S(-8, 2) could be a point of RS. Moreover, the distance from S to the midpoint of PR is:

√[(-11/2 - (-8))² + (7/2 - 2)²]

= √[25/4 + 9/4]

= √[34]/2

This is equal to the length of PQ, so PQRS could be a rectangle with S(-8, 2).

d.) S(-8,1)

The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (1 - 0)/(-8 + 6) = -1, so S(-8, 1) cannot be a point of RS.

Therefore, the answer is option c.) S(-8,2).

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Answer:

31.97⁰ to the nearest hundredth.

Step-by-step explanation:

sin x = opposite side / hypotenuse

        = 9/17

x = 31.9657

the earned interest after 3 years is $1,608.75.

What is simple interest?

Before delving further into the concept of simple interest, it is worth noting that it is a straightforward method for calculating interest on money, whereby interest is added at a constant rate for each time period and always to the initial principal amount. When we deposit our money into a bank, we can earn interest on our investment. Simple interest is one type of interest that banks may offer.

The formula for simple interest is:

I = P * r * t

where:

I = interest earned

P = principal (initial amount)

r = interest rate per year (as a decimal)

t = time (in years)

Substituting the given values, we have:

P = $9,750

r = 0.055 (since the interest rate is 5.5%)

t = 3

I = $9,750 * 0.055 * 3

I = $1,608.75

Therefore, the earned interest after 3 years is $1,608.75.

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The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      [tex]A_L=\frac{\theta}{360\textdegree}2\pi r[/tex]

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length [tex]A_L=\frac{\theta}{360\textdegree}2\pi r[/tex]

=> [tex]A_L=\frac{60}{360} \times2\times3.14\times3[/tex]

=> [tex]A_L=\frac{1}{6}\times2\times3.14\times3[/tex]

=> [tex]A_L[/tex] = 3.14 m.

Hence the arc length is D) 3.14 meters.

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The area of a triangle is equal to half the product of the triangle's base and height. The triangular box has a height of 6 inches.

The area of a right-angle triangle is half of the product of the triangle's base and height.

Area of triangle = [tex]\frac{1}{2} * base * height[/tex]

As stated previously, the lengths of the triangle's altitude and base are 3.5 inches and 5.2 inches, respectively. As a result, the volume of the triangular box is 54.6 cubic inches, and the height of the box must be determined in inches.

The volume of the triangular box =

[tex](\frac{1}{2} * base *height) * Height\\54.6 = (\frac{1}{2} * 5.2 * 3.5) * Height\\Height = \frac{54.6}{2.6 * 3.5} \\Height = 6 inches[/tex]

Therefore the height of the box of sticky notes is 6 inches.

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Answer: parabolic curve

Step-by-step explanation:

Answer: parabolic curve

Step-by-step explanation: