Which property is used in the following expression ? (a x b) x c = a x (b x c)

Associative Property of Multiplication
Associative Property of Multiplication

Commutative Property of Addition
Commutative Property of Addition

Associative Property of Addition
Associative Property of Addition

Distributive Property

Answer:

the second one, 280/32

Step-by-step explanation:

i did the calculating

sorry if wrong

Answer:

The answer is D. Multiply 3 1/8 and 2 3/4 in order to get something close to that. Since there are no answers involving the max amount of space, this is the most likely answer.

The unit rate of Zoe for watching the video series is  15 minutes/ episode.

For the stated question;

Total time = 90 minutes = 1.5  hours

Number of episodes = 6.

So,

unit rate = 1.5 hours / 6 episodes

unit rate  =  1.5 / 6  hour/episode

unit rate  =  1/4 hour per episode  

unit rate  = 15 minutes/ episode

Thus, unit rate of Zoe for watching the video series is  15 minutes/ episode.

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Answer:

It is not a solution.

Step-by-step explanation:

First, as we know what x is equal to, substitute the second equation into the first:

3x + 2y = 27

3(y + 1) + 2y = 27

3y + 3 + 2y = 27

5y + 3 = 27

Subtract 3 from both sides:

5y + 3 - 3 = 27 - 3

5y = 24

Divide both sides by 5:

\(\frac{5y}{5} = \frac{24}{5}\)

So \(y= \frac{24}{5}\)

At this point we know that (5, 6) is not a solution to the system because this should be the y value (6). To confirm this we will calculate x by substituting in the known y in the second equation:

x = y + 1

x = \(\frac{24}{5} + 1\)

\(x = \frac{29}{5}\)

Further proving that (5,6) is not a solution.

Hope this helps!

Answer:

The answer is 4,761

the probabilities for each event are Red ball: 1/5, White ball: 7/20, Yellow ball: 9/20 by using formula of  probability =possible outcome /total outcomes

To find the probability of a given event, we need to determine the number of successful outcomes and divide that by the total number of possible outcomes.

In this case, the event we want to find the probability for is not specified, so I will provide the probabilities for each color:

1. Probability of drawing a red ball:

Number of successful outcomes: 4 red balls
Total number of outcomes: 4 red + 7 white + 9 yellow = 20 balls

Probability of drawing a red ball = (Number of red balls) / (Total number of balls) = 4/20 = 1/5

2. Probability of drawing a white ball:

Number of successful outcomes: 7 white balls

Probability of drawing a white ball = (Number of white balls) / (Total number of balls) = 7/20

3. Probability of drawing a yellow ball:

Number of successful outcomes: 9 yellow balls

Probability of drawing a yellow ball = (Number of yellow balls) / (Total number of balls) = 9/20

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If 828 cm² of wrapping paper is needed to cover the smaller box, then the larger box would require more wrapping paper. The exact amount can be determined by comparing the surface areas of the two boxes.

To find the amount of wrapping paper needed to cover the larger box, we can use the concept of ratios between the lengths of the boxes and their corresponding surface areas. The ratio of the lengths of the two boxes is 28 cm (larger box) to 24 cm (smaller box).

Since the boxes have the same shape, the ratio of their surface areas will be the square of the ratio of their lengths. Therefore, the ratio of the surface areas is (28/24)² = (7/6)² = 49/36.

If we know that 828 cm² of wrapping paper is needed to cover the smaller box, we can calculate the amount needed for the larger box by multiplying the surface area of the smaller box by the ratio of surface areas:

828 cm² * (49/36) = 1134 cm².

Thus, approximately 1134 cm² of wrapping paper would be needed to cover the larger box.

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Answer

\(C=2.5\pi\)

Step-by-step explanation:

Radius is always half of the diameter so, \(\frac{2.5}{2} \\\) is equal to \(1.25\).

The Formula for Circumference is \(C=2\pi r\)

Since we found out the radius, we need to basically substitute (or insert) it into the radius spot so the next step will be: \(C=2\pi (1.25)\)

Then we multiply (2)(1.25) to get an answer of 2.5 (which we already know)

So our answer is going to be \(C=2.5\pi\)

Hope this helped and answers your question! Have a great rest of your day/night!

Answer:

8cm

Step-by-step explanation:

the ratio of cm to km is 1 cm on the map equals 40 km. or 1/40 so you have to find what is x/320 using the ratio of 1/40 you gt that x equals 8

In a simple regression model, the unexplained variation in the response variable is determined by summing the squares of errors. This method, known as residual sum of squares (RSS), quantifies the discrepancy between the observed values and the predicted values by the regression model.

In a simple regression model, the goal is to find a line that best fits the relationship between a single predictor variable (X) and a response variable (Y). However, due to various factors and sources of variability, the observed values of the response variable may not perfectly align with the predicted values based on the regression line.

The errors, or residuals, are the differences between the observed values and the predicted values. To quantify the unexplained variation, the errors are squared to eliminate negative values and emphasize larger deviations. These squared errors are then summed up, resulting in the residual sum of squares (RSS).

By calculating the RSS, one can assess the amount of unexplained variation or "error" in the regression model. A smaller RSS indicates that the model provides a better fit to the data, as it suggests less unexplained variation. On the other hand, a larger RSS implies a less accurate fit, with more unexplained variation in the model.

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Answer:

3 3/4

Step-by-step explanation:

First: 1/4 x 15/1 = 15/4

Second is to simplify: 15/4 equals 3 3/4

Fraction:-

Turn to mixed

\(y = (1/6)^{(1/3)} x^{(1/3)} - (1/36)^{(1/3)} x^{(-1/3)} + C x^{(-1/3)}\).

where we have also absorbed the constant \((1/6)^{(1/3)}\) into C for simplicity.

The Bernoulli equation is a mathematical equation that describes the conservation of energy in a fluid flowing through a pipe or conduit. It is named after the Swiss mathematician Daniel Bernoulli, who derived the equation in the 18th century.

The Bernoulli equation relates the pressure, velocity, and height of a fluid at two different points along a streamline. It assumes that the fluid is incompressible, inviscid, and steady, and that there are no external forces acting on the fluid.

The general form of the Bernoulli equation is:

P + (1/2)ρ\(v^2\) + ρgh = constant

where P is the pressure of the fluid, ρ is its density, v is its velocity, h is its height above a reference level, and g is the acceleration due to gravity. The constant on the right-hand side of the equation represents the total energy of the fluid, which is conserved along a streamline.

To begin, we substitute\(v=y^3\) into equation (1), then differentiate both sides with respect to x using the chain rule:

\(dv/dx = d/dx (y^3)\)

\(dv/dx = 3y^2 (dy/dx)\)

We can then substitute this expression into equation (1) to obtain:

\(3y^2 (dy/dx) + 2y = x(y^-2)\)

\(3(dy/dx) + 2/y = x/y^3\)

\(3(dy/dx)/y^3 + 2/y^4 = x/y^4\)

\(3(dy/dx)/v + 2/v = x/v\)

where the last line follows from the substitution \(v=y^3.\) This is now a first-order linear differential equation, which we can solve using the integrating factor method.

We first multiply both sides by the integrating factor. \(e^{(6x)}\)

\(e^{(6x)} (dv/dx) + 6e^{(6x)} v = 3xe^{(6x)}\)

Next, we recognize that the left-hand side can be written as the product rule of \((e^{(6x)v)})\):

\((d/dx) (e^{(6x)} v) = 3xe^{(6x)}\)

Integrating both sides with respect to x, we obtain:

\(e^{(6x)}\) v = ∫ \(3xe^{(6x)}\) dx = \((1/6)xe^{(6x)}\) - \((1/36)e^{(6x)} + C\)

where C is the constant of integration. Dividing both sides by e^(6x), we obtain the solution for v:

\(v = (1/6)x - (1/36)e^{(-6x)} + Ce^{(-6x)}\)

where we have absorbed the constant of integration into a new constant C.

Substituting back. \(v=y^3\), we have the final solution for y:

\(y = (1/6)^{(1/3)} x^{(1/3}) - (1/36)^{(1/3)} x^{(-1/3)} + C x^{(-1/3)}\)

where we have also absorbed the constant  \((1/6)^{(1/3)}\)into C for simplicity.

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Answer:

9 : 25

Step-by-step explanation:

Given the ratio of the sides of 2 similar equilateral triangles = a : b , then

the ratio of their areas = a² : b²

Given ratio of sides = 3 : 5 , then

ratio of areas = 3² : 5² = 9 : 25

Step-by-step explanation:

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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Answer:

So, 5, 20, 45, 80,...5N2

Step-by-step explanation:

Divide the sequence by 5 and the answer becomes very obvious:

EX: 1, 4, 9, 16,...N2

Answer:

Step-by-step explanation:

interval in mathematics stands for a set of real numbers,

denoted by [a,b] where a and b are the starting and ending real numbers both inclusive respectively.

thus, interval [a,b] is the set of real numbers starting from a to b both are real numbers and are included.

Answer:

900 outfits

Step-by-step explanation:

You just have to multiply them all together :)

Answer:

y = (7/4)x + 3

Step-by-step explanation:

(isolate the y variable by moving 7x) 4y = 7x + 12

(divide by 4 to get y by itself) y = (7/4)x + 3

Answer:

Volume of the given pyramid = 1122.37 cubic feet

Step-by-step explanation:

Volume of the regular hexagonal pyramid = \(\frac{1}{3}(\text{Area of the base})(\text{Base})\)

Measure of internal angle of a polygon = \(\frac{(n-2)\times 180}{n}\)

Here, n = number of sides of the polygon

For a hexagon, n = 6

Measure of interior ∠C = \(\frac{(6-2)\times 180}{6}\)

                                       = 120°

Measure of ∠BCD = \(\frac{120}{2}\)

                              = 60°

By applying tangent rule in ΔCED,

tan(∠ECD) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(60°) = \(\frac{DE}{CE}\)

\(\sqrt{3}=\frac{DE}{6}\)

DE = \(6\sqrt{3}\) feet

And cos(60°) = \(\frac{EC}{CD}\)

\(\frac{1}{2}=\frac{6}{CD}\)

CD = 12 feet

Area of ΔBCD = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                        =  \(\frac{1}{2}(6\sqrt{3})(12)\)

                        = \(36\sqrt{3}\) feet

Area of hexagonal Base of the pyramid = \(6(36\sqrt{3})\)

                                                                  = 216√3 square feet

Since, lateral height of the pyramid (AC) = 15 feet

By applying Pythagoras theorem in ΔADC,

AC² = AD² + CD²

(15)² = AD² + (12)²

AD = \(\sqrt{225-144}\)

AD = 9 feet

Volume of the given pyramid = \(\frac{1}{3}(216\sqrt{3})(9)\)

                                                 = 648√3 cubic feet

                                                 = 1122.37 cubic feet

The given equation, y = -1.7x + 8.5, is not in standard form with integer coefficients. The standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A is positive.

To convert the given equation to standard form, we need to eliminate the decimal coefficient. We can do this by multiplying both sides of the equation by 10 to clear the decimal: 10y = -17x + 85 Next, we want the coefficient of x to be positive, so we can multiply both sides of the equation by -1: -10y = 17x - 85

Now, we can rearrange the terms to match the standard form: 17x - 10y = 85 So, the equation of the given line in standard form with integer coefficients is 17x - 10y = 85. To convert the given equation to standard form, we need to eliminate the decimal coefficient.

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Answer:

A

Step-by-step explanation:

the rock lands when it reaches height 0.

so, for what t is h(t) = 0 ?

16t² - 100 = 0

16t² = 100

now we pull the square root on both sides (we can ignore the negative solutions, as negative seconds don't make any sense in our scenario)

4t = 10

t = 10/4 = 5/2 = 2.5 seconds

so, A is correct.

Answer:

D

Step-by-step explanation:

As the counter clockwise rule is A(x,y) becomes A'(-y,x).

So (1, -6) becomes (6, 1)

Hope it helps you

Answer:

See explanation

Step-by-step explanation:

The hypotenuse is the longest side of a triangle.

You could either add a point at (3,2) or (6,9) to make a right triangle and get the same answer, but for the sake of looking at it right-side-up, I'd use (3,2).

Now, you can use the distance vertically (y coordinate) from the top point to the bottom point ( 9 to 2 ) as your first side length. 9-2= 7, so 7 is that side length.

Then, you can use the distance horizontally (x coordinate) from the bottom left point (3,2) to the bottom right point (6,2). 6-3= 3, so 3 is that side length.

Now for the Pythagorean Theorem (a^2 + b^2 =c^2)

7^2 + 3^2 = c^2

49+9=c^2

58=c^2

c= \(\sqrt{58\\\\}\) is the distance between points

Answer: 8.4 cm

Step-by-step explanation:

The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle.

In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.

Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.

A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm.

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Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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Answer:

12

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos 60 = 6/hyp

hyp = 6 / cos 60

hyp = 6 / (1/2)

htp = 12

Answer:

$205.00

Step-by-step explanation:

$615÷3 =205

205 × 3= 205

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