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The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3)

The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).

The commutative property of addition states that the order of the numbers does not matter when adding them together.

In this equation, the numbers are rearranged but the result is still the same. This is because the commutative property of addition allows for the numbers to be added in any order and still have the same result.

Here is the step-by-step explanation:

Identify the commutative property of addition, which states that a+b=b+a.

Look at the given equations and see which one follows the commutative property of addition.

The equation (1+2)+3=1+(2+3) follows the commutative property of addition because the numbers are rearranged but the result is still the same.

Therefore, the equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).

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The number of students who voted for each mascot is given as follows:

Then the difference is given as follows:

nT - nC.

The difference between the two amounts is obtained applying the proportions in the context of the problem.

The circle graph gives the percentage of each type of vote.

Hence the amounts relative to each type of vote are given as follows:

In which:

The problem is incomplete, hence the general procedure is given to solve the problem.

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The polynomial in factored form whose solutions are x = -3, 5/2, and -5i is 2(x + 3)(2x - 5)(x² + 25).

Given the solutions;

To have the solutions at x = -3 and x = 5/2, the polynomial must have factors of (x + 3) and (2x - 5), respectively.

Also, to have a solution at x = -5i, there must be a factor of (x+5i) and its complex conjugate (x-5i):

Hence;

(x + 3)(2x - 5)(x + 5i)(x - 5i)

Multiplying out these factors gives:

(x + 3)(2x - 5)(x + 5i)(x - 5i)

(x + 3)(2x - 5)(x² + 25)

= (2x² + x - 15)(x² + 25)

= 2x⁴ + x³ - 15x² + 50x² + 25x - 375

= 2x⁴ + x³ + 35x² + 25x - 375

So the polynomial in factored form is:

= 2(x + 3)(2x - 5)(x + 5i)(x - 5i)

= 2(x + 3)(2x - 5)(x² + 25)

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The equation for the graph that passes through (4,-5) and (7,10) is: y = 5x - 25

What is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It contains an equal sign (=) between two expressions, one on each side. An equation can contain variables, constants, numbers, and mathematical operations like addition, subtraction, multiplication, and division

To write an equation for the graph that passes through the points (4,-5) and (7,10), we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

To find the slope of the line passing through the two points, we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (4,-5) and (x2, y2) = (7,10).

m = (10 - (-5)) / (7 - 4)

m = 15 / 3

m = 5

Now that we know the slope of the line, we can use either point to solve for the y-intercept, b. Let's use the point (4,-5):

y = mx + b

-5 = 5(4) + b

-5 = 20 + b

b = -25

Therefore, the equation for the graph that passes through (4,-5) and (7,10) is: y = 5x - 25

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The sample space for choosing one card from the set of eight cards labeled m, u, t, i, p, l, y is 8.

An assortment or set of potential results from a random experiment make up a sample space. With the letter "S," the sample space is denoted. Events are a subset of the possible results of an experiment. Depending on the experiment, a sample space could have several different outcomes. Discrete sample spaces, often known as finite sample spaces, are those that have a finite number of outcomes.

The sample space for choosing 1 card is given as:

Sample space = 8C1 = 8! / (1!)(8 - 1)!

Sample space = 8.

Hence, the sample space for choosing one card from the set of eight cards labeled m, u, t, i, p, l, y is 8.

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For each of the given , we need to use the Law of Sines to determine whether the given information results in two triangles, one triangle, or no triangles. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of the opposite angle is the same for all three sides:

a/sin A = b/sin B = c/sin C

Let's look at each scenario and apply the Law of Sines:

Scenario 1: a = 7, b = 10, A = 50°

Using the Law of Sines, we can find the value of angle B:

7/sin 50° = 10/sin B

sin B = 10*sin 50°/7

sin B = 0.918

B = sin^-1(0.918) = 66.4°

Since the sum of the angles in a triangle must equal 180°, we can find the value of angle C:

C = 180° - 50° - 66.4° = 63.6°

Since all three angles add up to 180° and are positive, we can conclude that this scenario results in one triangle.

Scenario 2: a = 5, b = 7, A = 120°

Using the Law of Sines, we can find the value of angle B:

5/sin 120° = 7/sin B

sin B = 7*sin 120°/5

sin B = 1.209

Since the sine of an angle cannot be greater than 1, this scenario does not result in a triangle.

Scenario 3: a = 9, b = 12, A = 30°

Using the Law of Sines, we can find the value of angle B:

9/sin 30° = 12/sin B

sin B = 12*sin 30°/9

sin B = 0.667

B = sin^-1(0.667) = 41.8°

Since the sum of the angles in a triangle must equal 180°, we can find the value of angle C:

C = 180° - 30° - 41.8° = 108.2°

Since all three angles add up to 180° and are positive, we can conclude that this scenario results in one triangle.

In conclusion, scenario 1 and scenario 3 result in one triangle, while scenario 2 does not result in a triangle. We can determine this by using the Law of Sines and checking whether the values of the angles are valid and add up to 180°.

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Answer:

see explanation

Step-by-step explanation:

the x- intercepts are the values of x on the x- axis where the graph crosses the x- axis.

On the x- axis the y- coordinate of any point is zero.

Set the factored form of the polynomial to zero and solve for x

x(x - 3)(x + 3)(x - 2) = 0

equate each factor to zero and solve for x

x = 0

x - 3 = 0 ⇒ x = 3

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

the x-intercepts are then x = - 3, x = 0, x = 2, x = 3

these can be confirmed from the graph of the polynomial

The answers are (a) (fog)(4) = 6√2, (b) (gof)(2) = 6√2, (c) (f of)(1) = 3√3, and (d) (gog)(0) = 0.

The given expressions are f(x) = 3√x and g(x) = 2x. We need to find the following expressions: (a) (fog)(4) (b) (gof)(2) (c) (f of)(1) (d) (gog)(0)

(a) (fog)(4) = f(g(4)) = f(2(4)) = f(8) = 3√8 = 3√(4*2) = 3√4 * √2 = 3*2*√2 = 6√2

(b) (gof)(2) = g(f(2)) = g(3√2) = 2(3√2) = 6√2

(c) (f of)(1) = f(f(1)) = f(3√1) = f(3) = 3√3

(d) (gog)(0) = g(g(0)) = g(2(0)) = g(0) = 2(0) = 0

Therefore, the answers are (a) (fog)(4) = 6√2, (b) (gof)(2) = 6√2, (c) (f of)(1) = 3√3, and (d) (gog)(0) = 0.

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Based on the information, we can infer that the surface area of the pyramid is: 105 inches²

To find the surface area of the pyramids we must perform the following procedure:

We must find the surface of each of the faces and the base.

According to this procedure, each face of the pyramid measures 20 inches². Then we must multiply this value by the number of faces of the pyramid (4).

We must add the surfaces of the faces and the base.

According to the above, the surface area of the pyramid would be 105 inches².

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The simplified expression is (3x^(4)-12x^(3)-26x^(2)+21x-44)/((x^(2)+1x-6)*(2x^(2)-5x+2)), or (f(x))/(g(x)), where f(x)=3x^(4)-12x^(3)-26x^(2)+21x-44 and g(x)=(x^(2)+1x-6)*(2x^(2)-5x+2).

To simplify the expression (2x^(2)+5x+2)/(x^(2)+1x-6)-:(x^(2)+6x+8)/(2x^(2)-5x+2), we need to find a common denominator and then subtract the numerators. The common denominator in this case is (x^(2)+1x-6)*(2x^(2)-5x+2).

So, the expression becomes:

((2x^(2)+5x+2)*(2x^(2)-5x+2)-(x^(2)+6x+8)*(x^(2)+1x-6))/((x^(2)+1x-6)*(2x^(2)-5x+2))

Simplifying the numerator, we get:

(4x^(4)-5x^(3)-4x^(2)+27x+4-1x^(4)-7x^(3)-14x^(2)-6x-8x^(2)-48x-48)/((x^(2)+1x-6)*(2x^(2)-5x+2))

Combining like terms, we get:

(3x^(4)-12x^(3)-26x^(2)+21x-44)/((x^(2)+1x-6)*(2x^(2)-5x+2))

So, the simplified expression is (3x^(4)-12x^(3)-26x^(2)+21x-44)/((x^(2)+1x-6)*(2x^(2)-5x+2)), or (f(x))/(g(x)), where f(x)=3x^(4)-12x^(3)-26x^(2)+21x-44 and g(x)=(x^(2)+1x-6)*(2x^(2)-5x+2).

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The number of lbs in 15. oz is 9 3/8 lb

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

lb and oz are both units of weight of a substance.

1 oz = 0.0625 lb

therefore 1 oz = 625/1000

= 25/40 lb

15 oz = 25/40 × 15

= 75/8 lb

= 9 3/8 lb

therefore the number of lbs in 15 oz is 9 3/8 lb

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cost = 3/√34,  csct = √34/5, sect =√34/3 , and cott = 3/5

explanation:-

The given equation is: tant = 5/3, so, cot t = 3/5 as cot t= 1/tan t

we know sec² t - tan² t = 1

or, sec²t= 1 + tan²t = 1+(25/9) = 34/9

or, sect = √(34/9) = √34/3

or, cos t=√(9/34) = 3/√34 as cos t= 1/sec t

now, also, csc²t - cot²t = 1

or, csc²t = 1+cot²t = 1+ 9/25 = 34/25

or, csc t= √34/5

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The two variables that vary the most across these countries are "Animal Protein" and "Vegetable Protein."

The variable that varies the least is "Total Protein." The profile plot tells us that Denmark has the highest amount of animal protein, followed by Norway and then Sweden. However, Sweden has the highest amount of vegetable protein, followed by Denmark and then Norway. Overall, Denmark has the highest total protein, followed by Norway and then Sweden.

This suggests that Denmark relies more heavily on animal protein sources, while Sweden relies more heavily on vegetable protein sources. Norway falls somewhere in the middle, with a more balanced mix of animal and vegetable protein sources.

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The ratio of strawberries to bananas in the basket is 12:18 or 2:3. To find this ratio, you simply take the number of strawberries and place it over the number of bananas. In this case, there are 12 strawberries and 18 bananas, so the ratio is 12:18.

However, this ratio can be simplified by dividing both numbers by their greatest common factor, which is 6. So, the simplified ratio of strawberries to bananas is 2:3. This means that for every 2 strawberries, there are 3 bananas in the basket.

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Answer:₹14.40

Step-by-step explanation:

36x2=72

24x2=48

72+48=120x12=1440/100 =14.40

Using dilation, the scale factor here is 2,

X' = (2,2)

Y' = (4,4)

Z' = (6,0)

A thing must be scaled down or altered during the dilation process. It is a transformation that reduces or enlarges the objects using the supplied scale factor. The pre-image is the original figure, while the image is the new figure that emerges via dilatation. Two types of dilation exist:

Expansion describes an increase in an object's size.

Reduction in size is referred to as contraction.

In the given question,

The scale factor here is 2.

So, the new dilated triangle will be:

X' = (2,2)

Y' = (4,4)

Z' = (6,0)

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Step-by-step explanation:

Let L and W be the length and width of the rectangle, respectively.

We know that the perimeter, P, of a rectangle is given by:

P = 2L + 2W

In this case, P = 16 cm, so we have:

16 = 2L + 2W

Simplifying, we get:

8 = L + W

To find the greatest area of the rectangle, we need to maximize the product of L and W, which is the formula for the area, A:

A = L * W

We can solve for one variable in terms of the other using the equation we found earlier:

L = 8 - W

Substituting this into the formula for the area, we get:

A = (8 - W) * W

Expanding and simplifying, we get:

A = 8W - W^2

To find the maximum value of A, we can use calculus or complete the square. Completing the square, we get:

A = -(W - 4)^2 + 16

Since the square of a real number is always nonnegative, the maximum value of A occurs when (W - 4)^2 = 0, which is when W = 4.

Substituting this value back into the equation for the perimeter, we get:

8 = L + 4

L = 4

Therefore, the rectangle with a perimeter of 16 cm and the greatest area is a square with sides of length 4 cm, and its area is:

A = L * W = 4 * 4 = 16 square centimeters.

The zeros of the polynomial are -5i, √5i, -√5i.

The given polynomial is: f(x)=x⁴+16x²-225.

Zeros of a polynomial are the values of x that make the polynomial equal to zero. These will be the x-intercepts of the polynomial's graph. To find the zeros of a polynomial, use the factored form of the polynomial and set each factor equal to zero. The solutions of this equation are the zeros of the polynomial.

The given zero is: -5i

To find the remaining zeros of the polynomial, we need to factor the polynomial.

We can factorize the polynomial as:

f(x) = (x² + 5i)(x² - 5i)

Finding Zeros:

Therefore, the remaining zeros of the polynomial are:

x = ±√5i

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A package that weighs 5 pounds will cost $15 for both options.

The equation can be used to symbolize the price, y: Y is equal to 5 plus 2 times the weight of the package, x.

Another choice is for the buyer to pay a one-time price of $15, which is represented by the equation y = 15, in order to send the package.

We'll compare the equation as a whole.

In this case,

5 + 2x = 15

Compile similar terms,

2x = 15 - 5

2x = 10

x = 10 / 2

x = 5

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Answer:

not a function

Step-by-step explanation:

Answer:

not a function

Step-by-step explanation:

The expressions that are equivalent to 2x - 3y = 12 are B and D.

We can modify the equation algebraically and simplify 2x - 3y = 12 to find the expressions that are equal to that number:

2x - 3y = 12

2x - 12 = 3y (subtract 12 from both sides) (subtract 12 from both sides)

(2/3)x - 4 = y (divide both sides by 3) (divide both sides by 3)

As a result, the equation can also be written as y = (2/3)x – 4.

We can now determine which expressions have the same meaning as this form:

A. y = 4 - (2/3)x

This expression is simplified to give y = (-2/3)x + 4. This isn't the same as y = (2/3)x – 4.

B. y = (2/3)x - 4

This formula already equals y = (2/3)x - 4 in terms of value.

C. 2x - 3y = -12

2x - 3y + 12 = 0 is the result of adding 12 to both sides of the equation. y = (2/3)x - 4 is not the same form as this.

D. y = (3/2)x - 6

This expression can be simplified to y = (2/3)x - 4 by doing so. The formula for this is y = (2/3)x – 4.

Hence, the formulas B and D are the same as 2x - 3y = 12.

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The annual interest rate.

To find the annual interest rate r that will allow your balance to reach $2000 in 10 years, we need to use the formula for continuously compounded interest: A = Pert, where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.

We are given that P = $1000, A = $2000, and t = 10 years. Plugging these values into the formula, we get:

$2000 = $1000e10r

Dividing both sides by $1000, we get:

2 = e10r

Taking the natural logarithm of both sides, we get:

ln(2) = 10r

Dividing both sides by 10, we get:

r = ln(2)/10 ≈ 0.0693

Therefore, the annual interest rate r that will allow your balance to reach $2000 in 10 years is approximately 6.93%.

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Moving the ladder 1 foot towards the building will not be enough to raise it by 1 foot, and moving it 2 feet away from the building will not be enough to lower it by 2 feet.

The relationship between the distance the ladder is moved along the ground (run) and the resulting change in height (rise) is determined by the ladder's angle of inclination, which is constant. This angle can be calculated using trigonometry, specifically the tangent function:

[tex]angle = arctan(rise/run)[/tex]

For a 20-foot ladder, the angle of inclination is approximately 75.96 degrees. If the painter moves the ladder 1 foot towards the building, the run will decrease from 20 feet to 19 feet, which means the rise will decrease proportionally according to the tangent function:

[tex]new rise = tan(angle) * new run[/tex]

[tex]new rise = tan(75.96) * 19[/tex]

new rise ≈ 18.7 feet

So, moving the ladder 1 foot towards the building will only raise it by about 0.3 feet, not enough to achieve the desired 1-foot increase. Similarly, moving the ladder 2 feet away from the building will increase the run from 20 feet to 22 feet, causing the rise to increase proportionally according to the tangent function:

new rise = tan(angle) x new run

new rise = tan(75.96) x 22

new rise ≈ 21.3 feet

Therefore, moving the ladder 2 feet away from the building will only lower it by about 1.3 feet, not enough to achieve the desired 2-foot decrease.

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Answer:

20000

Step-by-step explanation:

1.4 divided by 0.007%

1.4 - 0.0007%

x - 100%

0.0007x = 1.4

x = 2000

∴ 1.4 is 0.0007% of 2000.

NO, the ordered pair (9,2) is not the solution to the system 8x-4y=64 3y=6x-47.

The given ordered pair is (9,2) and the system of equations is:

8x-4y=64
3y=6x-47

To determine whether the given ordered pair is a solution to the system, we can substitute the values of x and y into the equations and see if they are true.

For the first equation:

8(9)-4(2)=64
72-8=64
64=64

For the second equation:

3(2)=6(9)-47
6=54-47
6=7

The first equation is true, but the second equation is not true. Therefore, the given ordered pair is not a solution to the system.

The final answer is: No, the given ordered pair is not a solution to the system.

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Answer:

To determine who has a greater mean, we need to calculate the mean (average) number of miles ridden by Liz and Sara and compare them.

Day Liz Sara

1 7 6

2 12 8

3 10 5

4 8 10

5 5 7

To find the mean for Liz, we add up the miles she rode and divide by the number of days:

Mean for Liz = (7 + 12 + 10 + 8 + 5) / 5 = 8.4 miles per day

To find the mean for Sara, we add up the miles she rode and divide by the number of days:

Mean for Sara = (6 + 8 + 5 + 10 + 7) / 5 = 7.2 miles per day

Therefore, Liz has a greater mean than Sara by 1.2 miles per day (8.4 - 7.2 = 1.2).

The mass of the solid copper cuboid with dimensions length = 10cm, breadth = 5cm, and height = 3cm, is 1.479 kg.

A cuboid is a three-dimensional geometric shape that has six rectangular faces. It is also known as a rectangular parallelepiped. A cuboid has six rectangular faces, where opposite faces are congruent and parallel. The cuboid has eight vertices, twelve edges, and six rectangular faces.

To calculate the mass of a cuboid, you need to know its volume and density. The volume of a cuboid is the product of its length, width, and height. The density of a material is its mass per unit volume. Once you have these values, you can use the following formula to calculate the mass of the cuboid:

Mass = Density x Volume

where Mass is the mass of the cuboid, Density is the density of the material of which the cuboid is made, and Volume is the volume of the cuboid.

In the given question,

Using the given values, we can now calculate the mass of the solid copper cuboid in kg.

The volume of the copper cuboid is:

Volume = Length × Breadth × Height = 10 cm × 5 cm × 3 cm = 150 cm³

The mass of the copper cuboid can be calculated by multiplying its volume with its density. We are given that the density of copper is 9.86 g/cm³. Therefore, we have:

Mass = Volume × Density = 150 cm³ × 9.86 g/cm³ = 1479 g

To convert the mass in grams (g) to kilograms (kg), we need to divide the mass by 1000. Therefore:

Mass in kg = Mass in g / 1000 = 1479 g / 1000 = 1.479 kg

Therefore, the mass of the solid copper cuboid with dimensions length = 10cm, breadth = 5cm, and height = 3cm, is 1.479 kg.

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The best forecast is the one with the lowest MSE level. In this case, the "3 Month Moving Average" has the lowest MSE level of 2.1, making it the best forecast. Therefore, the correct answer is B. 3 Month Moving Average.

One common metric used to compare forecasting methods is the Mean Squared Error (MSE). The MSE measures the average squared difference between the actual values and the forecasted values, so a lower MSE indicates a better fit.

In this case, we have four different forecasting methods and their respective MSE values. The 3 Month Moving Average has the lowest MSE of 2.1, which suggests it is the best forecasting method among the four options.

Thus, the answer is B. 3 Month Moving Average.

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