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The average distance a planet is from the Sun is 9.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given;

Sun can be modeled by d=t^2/3, where t is the number of Earth years that it takes for the planet to orbit the Sun.

The planet has an orbit of 27 Earth years.

Now,

d=27^2/3

d^3=27^2

d=9

Therefore, by unitary method the answer will be 9.

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The proofing of the triangle is shown below.

A triangle is a shape which has three sides and the sum of the three angles is equal to 180 degrees.

We have, Triangle ABC and Triangle CDE

Both triangles are equilateral. This means, three sides are equal and the angle opposite to the side is also equal.

Now, ∠ACB and ∠DCE are vertical angles.

Vertical angles are equal. If ∠ACB and ∠DCE are equal.

The sides opposite ∠ACB and ∠DCE are also equal.

This means, AB = DE

Now, If AB = DE

We can say that, AB is parallel to DE

Thus, AB // DE

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Answer:

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

If the slope of the line is 6 and the y-intercept is -4, the equation of the line is y = 6x - 4. This equation describes a line with a slope of 6 that intercepts the y-axis at the point (0, -4).

The results of the multiplication of the binomials (x - 6)(x + 3) is x² - 3x - 28

The multiplication of binomials is the results of the products of two or more binomials.

(x - 6)(x + 3)

open parenthesis

= x² + 3x - 6x - 28

= x² - 3x - 28

Ultimately, the multiplication of the given binomials is x² - 3x - 28.

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Answer:

Below

Step-by-step explanation:

Here is a sample:

Answer:

V=whl=3.25·2.5·4.5=36.5625 cm

Step-by-step explanation:

Formula: V=whl

Width and base are interchangeable words so all you do is plug the base into (w).

Turn the fractions into decimals and multiply.

3 1/4 = 3.25

2 1/2 = 2.5

4 1/2 = 4.5

3.25*2.5*4.5 = V

V = 36.5625 cm

The required ratio of the areas of the two similar figures is 16:9

What is the area?

The space found inside a 2D shape's perimeter is known as the area. It is expressed as square units like [tex]cm^2[/tex], [tex]m^2[/tex], etc. The area is the quantity of space an object takes up in a plane.

For the given similar figures,

The square of the ratio of the corresponding sides is equal to the ratio of the areas of two comparable figures.

The ratio of the areas of these rectangles would be

= [tex]\frac{(6+2)^2}{6^2} = \frac{64}{36} = \frac{16}{9}[/tex]

= 16:9

Hence, the required ratio is 16:9.

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The integers are 12 & 4

The difference , the sum and the product of two positive integers are in the ratio 1:2:6.Find the integers.

Let x = first integer

     y = second integer

Finding x and y;

(x - y): (x + y) : xy = 1:2:6

for : (x-y)/(x+y) = 1/2

cross multiply

       2(x-y) = x+y (equation 1)

for: (x+y)/ xy = 2/6 = 1/3

cross multiply

       3(x+y) = xy    (equation 2)

solve for x and y using equation 1 and equation 2

equation 2: xy= 3(x+y)

                   xy = 3x + 3y

                    xy -3y = 3x

                    y(x-3) =3x

              divide both sides by (x-3):

                     y= 3x/(x-3)         (equation 3)

substitute equation 3 to equation 1:

2(x-y) =x+y

2[x-(3x/(x-3))] = (3x/(x-3)) +x

solve for x:

x = 12

using equation 3, solve for y:

y = 3(12)/ (12-3)

y = 4

Check:

difference: 12-4 =8

sum: 12+4 =16

product: 12(4) =48

8:16:48 (when reduce to lowest term; dive by 8)

1: 2: 6 (same with the given ratio of the difference, sum and product)

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An expression that represents the total area of Meiling's new deck is  4.3x + 29.67.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.

Given:
An architect plans to build an extension to Meiling's rectangular deck.

Let x represent the increase, in meters, of her deck's length.

The expression 4.3(x+ 6.9) represents the area of the deck,

where 4.3 is the width in meters and (x + 6.9) represents the extended length in meters.

Using the Distributive Property to write an expression that represents the total area of Meiling's new deck.

A = 4.3(x+ 6.9)

A = 4.3x + 29.67

An expression that represents the total area of Meiling's new deck is  4.3x + 29.67.

Hence, area is 4.3x + 29.67 square meters.

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The engine operates for 7 mins at 35% of the full power.

As we know that, full power of the engine refers to 100% capacity.

A/Q,

∵ 100% power of the engine operates for 20 mins

∴ 1% power of the engine operates for  [tex]\frac{20}{100}[/tex] mins

∴ 35% power of the engine will operate for  [tex]\frac{20}{100}[/tex] × [tex]35[/tex] mins

                                                                       [tex]=\frac{1}{5}[/tex] × [tex]35[/tex] = 7 minutes (Ans.)

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After the hole is cut, 248  square feet of blue feet of blue surface remain.

What is the surface area of the given cube?

The formula for surface area is equal to six times of square of the length of the sides of the cube. It is represented by 6a², where a is the side length of the cube. It is basically the total surface area.

We have given,

the cube of side length 6 ft,

the shape of a 2-by-4-by-6-foot rectangular prism is cut out of the cube,

to find: After the hole is cut, how many square feet of blue feet of blue surface remain?

area of an original cube is:

= 8 * 6 * 6

= 288 ft²

the area of the cube, after the hole, is cut.

remaining area = original cube area - 2 * 4 *4

= 288 -  32 ft²

= 248 ft²

Hence, After the hole is cut, 248  square feet of blue feet of blue surface remain.

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Answer:The appropriate number in the cage for the first equation is:

(5²)³ = 5³

The evaluation for log₃9 is:

log₃9 = 2

Step-by-step explanation:

The value of f(0) is 5.

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

Given;

The graph

From the graph we can observe the value of function for various values.

When, x=0

y=5

Therefore, the answer of f(0) from the graph is 5.

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The number of students who were wearing spirit wear at the assembly is = 120.

As given in Question that 3 out of 10 students were wearing spirit were.

if we have these type of Question then we will find the fraction part for 1 student as given 3 out of 10 then  the fraction part for 1 will be = 3/10 = 0.3

for 1 student there  is 0.3 fraction of students has wear spirit wear

so for 400 students were at the assembly

for 1 fraction is 0.3

for 400 = 400*(0.3 )= 120

Here 120 students were wear spirit wear in assembly

as like type we can solve for any number of students who were in assembly . like if there is 500 student the we can do like 500*.03 = 150 students.

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The total area formed by the two congruent trapezoids in this problem is given as follows:

48 m².

The area of a trapezoid is obtained adding the bases, multiplying by the height, and dividing by 2.

For the two congruent trapezoids in this problem, the parameters are given as follows:

Considering that there are two trapezoids, teh total area is given as follows:

A = 2 x 1/2 x (3 + 9) x 4

A = 12 x 4

A = 48 m².

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The division of the polynomial 2x⁴ - 3x³ - 6x² + 11x + 8 by x - 2 will give a quotient of  2x³ + x² - 4x + 3 +(14 / x - 2)

The quotient of polynomials is the result of dividing one polynomial by another. It is a mathematical expression representing the ratio of two polynomials, often written as a fraction. The numerator of the fraction is the dividend polynomial, and the denominator is the divisor polynomial. The quotient of polynomials can be found using long division or synthetic division methods.

In the polynomial division between 2x⁴ - 3x³ - 6x² + 11x + 8 and x - 2

2x⁴ - 3x³ - 6x² + 11x + 8 ÷ x - 2 = 2x³ + x² - 4x + 3 +(14 / x - 2)

The quotient of the division is 2x³ + x² - 4x + 3 +(14 / x - 2) while the divisor is x - 2.

The remainder of the polynomial division is 14

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From 390 grams to 28 grams, Element X would decompose in about 4.4 minutes.

The formula y = a(0.5)t, where y is the final amount, a is the initial amount, and t is the time in half-lives, can be used to calculate this. Since Element X has a half-life of six minutes, we can add t = six minutes to the equation. We can solve for t by rearranging the data so that

t = ln(a/y) / ln(0.5).

We obtain

t = ln(390/28) / ln(0.5) = 4.4 minutes by putting in the values for a and y.

This is how long it would take for Element X's weight to drop from 390 grams to 28 grams through decay.

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Answer:

[tex]\boxed{0} < x < \boxed{4}[/tex]

Step-by-step explanation:

The graph is y = x² - 4x

For  x² - 4x < 0 find out the interval of x
Factor x² - 4x ==> x(x - 4)

x² - 4x < 0 ==> x(x-4) < 0

Find the x-intercepts where x(x - 4) = 0

x(x - 4) = 0 means
x = 0 or x - 4 = 0
x - 4 = 0 ==> x = 4
These are critical points where the function changes sign

From the graph we see that the function has a value of 0 at x = 0 and x = 4 and is negative between 0 and 4

So the range of values for x where x² - 4x < 0 is

[tex]\boxed{0} < x < \boxed{4}[/tex]

Hope that makes sense. If not, please ask questions

The current value of Pablo's car in pesos corresponds to 15,750,000 pesos.

This is calculated by multiplying the original price of 35,000,000 by the discount percentage of 45%, which corresponds to 15,750,000. To calculate the current price, the discount percentage (45%) is first determined and then multiplied by the original price (35,000,000). This is done to determine the discount in pesos (15,750,000) and is then subtracted from the original price to get the current price of 15,750,000.

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Complete Question:

When Pablo buys his car, it cost him 3,500,000 pesos. If it is now worth 45% of its original price, then what is its current value in pesos?

The correct answer is (a) Yes, because  we cannot use the binomial probability the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent

The probability of at least 30 adults out of 100 being left-handed can be calculated using the binomial probability formula with x counting the number who are left-handed. However, option (b) is not correct because the trials can still be considered independent even if the number of successes is greater than 5% of the sample size. The condition that the number of trials should be less than 5% of the population size is used to ensure that the sampling distribution can be approximated by a normal distribution.

Option (c) is also not correct because even though the sample was selected without replacement, the size of the population is much larger than the sample size, so the effect of the sampling without replacement is negligible.

Option (d) is not correct because we are interested in finding the probability of at least 30 left-handed adults, not the number of right-handed adults.

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Answer:

2.4 lb

Step-by-step explanation:

We know

Alicia paid 1.32 for a bag of pinto beans

The beans cost .55 per lb

How much did the bag of pinto beans weigh?

1.32 / .55 = 2.4 lb

So, the bag of pinto beans weighs 2.4 lb.

The detail that best supports the inference that the auto manufacturing industry supports green solutions is -

"Pyrolysis generates low-cost energy that can be used in the automobile manufacturing industry".

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

Given is a graph as shown in the image attached.

We can write -

{ 1 } -

f{g(x)} = (x - 2)² - 2(x - 2) - 3

{ 2 } -

g{f(x)} = (x² - 2x - 3) - 2

Therefore, we can calculate f{g(x)} and g{f{x}) as -

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Variables:  A = Adult tickets, C = Children tickets, S = Senior tickets

Expression for number of adult tickets sold: A = 15 + 3C

Expression for number of children's tickets sold: C = S/3

Let's define our variables:

A = Adult tickets

C = Children tickets

S = Senior tickets

We know that Joey sold 15 more adult tickets than children tickets. This means that the number of adult tickets (A) is 15 more than the number of children tickets (C). We can write this as an expression: A = 15 + C

We also know that Joey sold 3 times as many senior tickets as children tickets. This means that the number of senior tickets (S) is 3 times the number of children tickets (C). We can write this as an expression: S = 3C

Now, we can combine these two expressions to solve for the number of adult tickets sold. We can substitute the expression for S (3C) into the expression for A (15 + C) and solve for C.

Substituting 3C for S in A = 15 + C, we get: A = 15 + 3C

This expression tells us that the number of adult tickets sold (A) is equal to 15 plus 3 times the number of children tickets sold (C).

To solve for the number of children tickets sold (C), we can use the expression for S (3C). We can divide both sides of the equation by 3 to solve for C.

Dividing both sides by 3, we get: C = S/3

This expression tells us that the number of children tickets sold (C) is equal to the number of senior tickets sold (S) divided by 3.

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Define the variables: Let x be the number of children's tickets sold.

Write an expression to represent the number of adult tickets sold: The number of adult tickets sold can be represented as x + 15.

Write an expression to represent the number of children's tickets sold: The number of children's tickets sold can be represented as x.

In this problem, we are asked to represent the number of adult and children's tickets sold in terms of a single variable, x. The given information is that Joey sold 15 more adult tickets than children's tickets, and he sold 3 times as many senior tickets as children's tickets. Hence, we can represent the number of adult tickets sold as x + 15 and the number of children's tickets sold as x.

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Anna's total earnings in a week with $2400 in sales would be $810. Her total earnings in a week with $x in sales would be $450 + ($x * 0.15).

Anna makes a guaranteed salary of $450 per week, and she earns a commission of 15% on her total sales. To calculate her total earnings in a week when she made $2400 in sales, we need to find her commission and add it to her base salary. The commission can be calculated by multiplying her total sales by 15%, which is $2400 * 0.15 = $360. Therefore, Anna's total earnings for that week would be $450 + $360 = $810.

To calculate Anna's total earnings in a week when she made $x in sales, we would follow the same process. The commission would be $x * 0.15, and this amount would be added to the base salary of $450 to determine her total earnings.

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Answer:

The answer is a ( 1 5/6 )

Step-by-step explanation:

.................

If the tax rate at this restaurant is 9. 5% and some other person’s sales tax is $1. 61 then their subtotal is $18.56

Here, some other person’s sales tax is $1. 61

Let us assume that for the amount of 'p' dollars, the sales tax is  is $1. 61

Here, the tax rate at this restaurant is 9. 5%

This means, 9.5 percent of m dollars is $1.61

Using percentage formula,

m × (9.5 / 100) = 1.61

m × 9.5 = 1.61 × 100

m × 9.5 = 161

m = 16.95 dollars

So, their subtotal would be,

m + sales tax

= 16.95 + 1.61

= 18.56 dollars

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The complete question is:

The tax rate at this restaurant is 9. 5%. Some other person’s sales tax is $1. 61. How much was their subtotal?

the value of x in the isosceles triangle will be 36°.

What is an isosceles triangle ??

An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception. The faces of bipyramids, the golden triangle, the isosceles right triangle, and some Catalan solids are all examples of isosceles triangles.

in this figure, it is an isosceles triangle as two sides of the triangle are equal.

a) In the given triangle Δ the angles which are same given 72°

So the other angle will be 180 - 2(72) = 36°

Hence the value of x in the isosceles triangle will be 36°.

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The number of units produced does not affect net operating income when using absorption costing.

All production expenses, including direct materials, direct labour, and both variable and fixed overhead costs, are included in the cost of each unit produced in absorption costing. This means that as more units are manufactured, the total manufacturing cost is distributed over a greater number of units, resulting in a reduced cost per unit.

Variable costing, on the other hand, includes only variable production expenses, such as direct materials, direct labor, and variable overhead costs, in the cost of each unit produced. Fixed manufacturing overhead costs are considered period expenses and are not included in the product cost.

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Answer:

Step-by-step explanation:

(0,8)

With examples

in the photo