If six more than 3 times a number is equal to 12 less than double the same number. choose the equation you will use to solve for the unknown number and the number (solution).

Applying the rules of exponents, the value of n in the equation given is calculated as: n = 8.

The product rule of exponents says that when the base are the same, add their exponents together.

For example, m × m² = m^(1 + 2) = m³.

The exponents are 1 and 2. The expression has similar base of m. Therefore, to multiply m and m² together, we would simply add their exponents together while the final result will be the same base.

Also, the negative rule of exponents states that we subtract their exponents if they have he same base.

For example:

m³/m² = m³ ÷ m² = m^(3 - 2) = m.

Given the equation:

[tex]\frac{4^3 \times 8^2}{2^n} = 2^4[/tex]

Simplify the bases to make all equal

= [tex]\frac{2^{(2)(3)} \times 2^{(3)(2)}}{2^n} = 2^4[/tex]

= [tex]\frac{2^{6} \times 2^{6}}{2^n} = 2^4[/tex]

Apply the product rule and the negative rule of exponents to find the value of n in tye equation:

[tex]2^{(6 + 6 - n)} = 2^4\\\\2^{(12 - n)} = 2^4\\\\[/tex]

The bases will cancel each other:

12 - n = 4

Subtract 12 from both sides

12 - n - 12 = 4 - 12

-n = -8

Divide both sides by -1

n = 8

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Answer:

Hope the picture will help you

Answer:

164 cm

Step-by-step explanation:

(4x6) / 2= 12

12x2=24  because there are 2 triangles

10x6=60  for the rectangle

(4x10) x 2=80 for the sides

80+60=140

140+24=164

Answer:0.6

Step-by-step explanation:

20/3 is 6

[tex]5\sqrt{20} = 5\sqrt{4.5} = 5.2\sqrt{5} = 10\sqrt{5}[/tex]

[tex]10\sqrt{5} - 4\sqrt{5} = 6\sqrt{5}[/tex]

The amount of money would be $1115.45 the zoo makes selling the waste that day.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

They charge farmers $5 per pound for the daily feces from the elephants. If an elephant's daily waste production is at or below the 10th percentile for the distribution of waste which is given in the question.

To determine the amount of money would the zoo make selling the waste that day.

P(z ≤ z₀) = 0.1

z₀ = -1.28

⇒z₀ =(x₀ -μ ) / σ

Substitute the values and solve for x₀,

⇒ -1.28 =(x₀ -250 ) / 21

⇒x₀ = (-1.28)×21 - 250

⇒x₀ = 223.09

So the amount of money would be as :

⇒ 223.09 × 5

⇒ 1115.45

Therefore, the amount of money would be $1115.45 the zoo makes selling the waste that day.

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Step-by-step explanation:

when we put gasoline in a car that will depend on how much it will cost us, also for example if we are going to buy popcorn depending on how many we buy will be the price

Step-by-step explanation:

I hope this will be helpful for you.

[tex]2x(x+3)-(12x-4)\\=2x^{2} +6x-12x+4\\=2x^{2} -6x+4[/tex]

I hope this helps.

Based on the number of bushels that the farmer has to sell, the equation that represents the total change in the number of bushels after seven days is 220 - 15⁵/₈(7).

The farmer has a total of 220 bushels of wheat to sell and then sells about 15⁵/₈ every day.

After 7 days, the total change in the number of bushels would be:

= Total bushels to be sold - Bushels of wheat already sold

= Total bushels to be sold - (Number of bushels sold per day x Number of days)
= 220 - 15⁵/₈(7)

= 110 bushels of wheat

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Using the exterior angle of a polygon theorem, the value of the missing angle is 58°

From the question, we are to calculate the value of the missing angle.

From the given information, the missing angle is (3x -2)°.

To calculate the value of the missing angle,

First, we will determine the value of x

From the Exterior angle of a polygon theorem, we can write that

90° + (3x + 12)° + (4x - 10)° + (3x - 2)° + 70° = 360°

(3x + 12)° + (4x - 10)° + (3x - 2)° = 360° - 70° - 90°

3x° + 12° + 4x° - 10° + 3x° - 2° = 200°

10x° = 200° + 2° + 10° - 12°

10x° = 200°

x = 200/10

x = 20

The missing angle is (3x -2)°

Substitute the value of x

(3(20) -2)°

= (60 -2)°

= 58°

Thus,

The missing angle measure is 58°

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Answer: 60% of your teachers are female

Step-by-step explanation: 3 out of 5 is 60%

Based on the report that digital music had led to a global revenue of $6.85 billion, the option that describes the accuracy of this report is that B. The report is probably accurate because the number is not very specific.

Digital music revenue recognition might vary from country to country. This means that what constitutes revenue for one country, might not be revenue in another. For that reason, we cannot say that businesses measure revenue accurately.

The report can however be very accurate even if it isn't completely accurate. This shown by the number not being specific to the last cent.

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The time taken by Peter to arrange the chairs all by himself is 10/3 minutes.

Given that :-

Katrina can arrange the chairs in the classroom in 5 minutes.

One day peter helped her and took both of them 2 minutes to arrange the chairs.

We have to find the time taken by Peter to arrange the chairs all by himself.

LCM (5,2) = 10

Let the total work of arranging the chairs is of 10 units.

We know that,

Efficiency of a person = Total Work/Time taken by person

Hence,

Efficiency of Katrina = 10/5 = 2 units

Efficiency of Katrina + Efficiency of Peter = 10/2 = 5 units

Hence,

Efficiency of Peter = 5 - 2 = 3 units

Hence, time taken by Peter to arrange the chairs all by himself  = 10/3 minutes.

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The best description of the value of the expression 2x - 7, when x = 5 is B. The result is a prime number.

A prime number cannot be divided by another number except by itself or 1.

Common prime numbers include 2, 3, 5, 7, 11, 13, 17, and 19.

The value of 2x – 7, when x = 5 is 3.

3 is a prime number as well as a whole number, but it is not a composite number.

Thus, we can conclude that the result of solving the expression is the prime number 3.

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Answer:

the answer is -60........

Answer:

-60! 1560 divided by 26 is 60, but any negative divided by a positive is a negative, so the product will be negative as well.

Step-by-step explanation:

Hope it helps! =D

Step-by-step explanation:

equate the two small distances to the total distance and solve for x

perimeter of triangle is =  3 + 5 + 4 = 12 cm

perimeter of rectangle is = 2( 3 + 6 ) = 18 cm

perimeter of parallelogram is = 2 (5+7) = 24 cm

A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape. The circumference of a circle or an ellipse is referred to as its perimeter. Perimeter calculations have many practical applications.

perimeter of triangle is =  3 + 5 + 4 = 12 cm

perimeter of rectangle is = 2( 3 + 6 ) = 18 cm

perimeter of parallelogram is = 2 (5+7) = 24 cm

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The quadratic equation that has roots (-1 - √2)/3 and (-1 + √2)/3 is:

x² + (2/3)x - 1/9 = 0

We have been given the roots of quadratic equation.

(-1 - √2)/3 and (-1 + √2)/3

We need to find the quadratic equation.

Since (-1 - √2)/3 and (-1 + √2)/3 are roots, (x - (-1 - √2)/3) and (x - (-1 + √2)/3) must be the factors of the quadratic equation.

So, the required quadratic equation would be,

(x - (-1 - √2)/3) * (x - (-1 + √2)/3) = 0

x[x - (-1 + √2)/3) ] - ( (-1 - √2)/3) [x - (-1 + √2)/3] = 0

x² - x(-1 + √2)/3 - x(-1 - √2)/3 + [(-1 - √2)(-1 + √2)]/9 = 0

x² - x(-2/3) + (1 - 2)/9 = 0

x² + (2/3)x - 1/9 = 0

Therefore, the quadratic equation that has roots (-1 - √2)/3 and (-1 + √2)/3 is: x² + (2/3)x - 1/9 = 0

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Surface area of a cylinder= 2πr(h+r)

=2×22/7×5×(13+5)

=31.43×(18)

=565.74meter squared

The definition for the function is y = {-2x +1   x < 1 ; -x + 2   x ≥ 1. The correct option is b.

From the question, we are to determine the equation for the function

First, we will determine the equation for when x < 1

Picking the points (-1, 3) and (0, 1)

Using the formula,

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

(y - 3) / (x - -1) = (1 - 3) / (0 - -1)

(y - 3) / (x + 1) = -2 / (0 + 1)

(y - 3) / (x + 1) = -2 / 1

(y - 3) / (x + 1) = -2

y - 3 = -2(x + 1)

y - 3 = -2x - 2

y = -2x - 2 + 3

y = -2x + 1

Thus,

When x < 1, the function is y = -2x + 1

Now, determine the equation for when x ≥ 1

Picking the points (1, 1) and (2, 0)

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

(y - 1) / (x - 1) = (0 - 1) / (2 - 1)

(y - 1) / (x - 1) = -1 / 1

(y - 1) / (x - 1) = -1

y - 1 = -1(x - 1)

y - 1 = -x + 1

y = -x + 1 + 1

y = -x + 2

Thus,

When x ≥ 1, the function is y = -x + 2

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In this mathematical expression, the original number is 4.

We can use a mathematical equation to work out the original number.

A mathematical equation uses variables, numbers, and constants to show that two values are equal.

Mathematical equations connect two mathematical expressions using the equal sign (=).

Let the original number = x

According to the statement:

2x + 28 = {4}{9}

This implies that:

2x + 28 = 36

Subtracting 28 from both sides gives:

2x = 8

x = 4

Thus, the original number is 4.

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If the family’s monthly income is $3,286, Wren family budgets for entertainment each month is $328.60.

Income, which is typically stated in the monetary terms, is the spending and saving opportunity acquired by an entity within a given duration. Conceptually, income is hard to define, and different fields may have the distinct definitions. For instance, a person's income may differ from their income as defined by law and in an economic sense.

Haig-Simons income, which defines income as Consumption + Change in Net Worth and is commonly applied in economics, is a very significant definition of income.

Income is a total that includes any wages, salaries, profits, interest payments, rent, or other forms of earnings received in a calendar year for families and individuals in the United States, as defined by tax law. Gross income less taxes and other deductions (such as required pension payments) is a common definition of discretionary income and is frequently used as a benchmark to assess the wellbeing of taxpayers.

The idea may include the accumulation of both monetary and non-monetary consumption capacity, with the former (monetary) serving as a stand-in for total income in the field of public economics.

Gross income for a business is the total revenue less the cost of items sold. Costs are subtracted from revenue by cost of goods sold, expenses, depreciation, interest, and taxes to arrive at net income.

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Answer:

72,000 yards

Step-by-step explanation:

The scale factor can be found by doing:

[tex]240 \div 4 = 60[/tex]

This means that 60 is the scale factor. You can apply the scale factor to the length of the rectangular building, meaning that the length of the actual building is:

[tex]5 \cdot 60 = 300[/tex] yards

So, if the building is 240 yards wide, and 300 yards long. You can find the area of the actual building just like any other rectangle using:

[tex]A = l \cdot w[/tex]

(Area = length * width)

So, the final answer is:

[tex]A = 300 \cdot 240\\ A= 72,000[/tex]

This means that the area of the actual building is 72,000 yards.

The number of volunteers needed for each case is given as follows:

a. 0.4 miles: 5.

b. 2/7 miles: 7.

c. 0.125 miles: 16.

d. 6/45 miles: 15.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the unit rates of the context of the problem along with basic arithmetic operations, especially multiplication and division.

In this problem, a two mile section will be cleaned, hence the number of volunteers needed is calculated as follows:

n = 2/s.

In which s is the section cleaned by each volunteer.

In item a, the section is of 0.4 miles, hence the number of volunteers is given as follows:

n = 2/0.4 = 5 volunteers.

In item b, the section is of 2/7 miles, hence the number of volunteers is given as follows:

n = 2/(2/7) = 2 x 7/2 = 7 volunteers.

In item c, the section is of 0.125 miles, hence the number of volunteers is given as follows:

n = 2/0.125 = 2/(1/8) = 2 x 8 = 16 volunteers.

In item d, the section is of 6/45 miles, hence the number of volunteers is given as follows:

n = 2/(6/45) = 2 x 45/6 = 90/6 = 15 volunteers.

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The representation of the expression is 4 < x + 7

The mathematical statement is given as

"4 less than the sum of a number and 7"

Sum means Plus

So, we have the following representation

"4 less than the sum of a number and 7" ⇒  4 less than a number + 7"

Let the number be x

So, we have

"4 less than the sum of a number and 7" ⇒  4 less than x + 7"

Less than as used here means <

So, we have

"4 less than the sum of a number and 7" ⇒  4 < x + 7"

Hence, the expression represented by "4 less than the sum of a number and 7" is  4 < x + 7

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Answer:

0.635

Step-by-step explanation:

This is half way between 0.63 and 0.64.

Hope this helps!

Answer: 5.18 x 10^-3

Step-by-step explanation:

0.00518

**Move the decimal 3 spaces to the right**

5.18

**Since it goes like 0.00, you want to make sure the exponent is negative**

5.18 x 10^-3

Hope this helped <3