4 • 2 - 3 = -2 • 2 + 9

12/17 as a decimal, rounded to the nearest thousandth, is 0.706, obtained by dividing 12 by 17 and rounding up due to the fourth decimal place being greater than 5.

To convert the fraction 12/17 to a decimal, divide 12 by 17. Upon doing this calculation, we get approximately 0.7058823529411765. Now, to round this to the nearest thousandth, we look at the fourth decimal place, which in this case is an '8'. Therefore, we round up the third decimal place from '5' to '6', giving us 0.706 as the final answer, rounded to the nearest thousandth.

The phrase for the algebraic expression 8y is 'eight times the variable y'. It represents a multiplication of the variable y by 8.

The algebraic expression 8y can be represented by the phrase 'eight times the variable y'. This type of question involves translating algebraic expressions into verbal phrases, which is important in understanding and communicating mathematical concepts clearly. The expression consists of a constant multiplier, 8, and a variable, y, indicating that y is to be multiplied by 8.

The inequality represents this sentence "Six plus two is less than nine plus three" is B. 6 + 2 < 9 + 3.

When the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Then values are called solution to that equation or inequality.

Thus we have set of such values is called solution set to the considered equation or inequality.

We are given that Six plus two is less than nine plus three.

So here six plus two = 6 + 2

It is less than 9 + 3

Means

6 + 2 < 9 + 3

Therefore, the correct option is B.

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An equation that gives the city's population p (in thousands of people) x years after 2010 will be D. p = 4x + 15.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this situation, the population of a city increases by 4000 people each year. In 2025, the population is projected to be 450,000 people.

p = 450

4x + 15 = 450

4x = 435

Divide.

x = 108.75

Substituting the answer to check will be:

p = 4(108.75) + 15

p = 450

The correct option is D.

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The equation that gives the city's population x years after 2010 is p = 4x + 390.

To find an equation for the city's population x years after 2010, we need to determine the initial population in 2010 and the rate at which the population is increasing. Since the population is increasing by 4000 people each year, that means the population will increase by 4 people for every 1 year. We can represent this with the equation p = 4x + p0, where p is the population x years after 2010 and p0 is the population in 2010. Given that the population in 2025 is projected to be 450,000 people, we can substitute x = 15 into the equation and solve for p0:

p = 4(15) + p0
450 = 60 + p0
p0 = 450 - 60
p0 = 390

Therefore, the equation that gives the city's population p (in thousands of people) x years after 2010 is p = 4x + 390. So, the correct answer is option A: p = 4x + 390.

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The correct equation that gives the city's population 'p' (in thousands of people) 'x' years after 2010 is 'p-450 = 4(x - 15)', option B.

The problem can be solved by understanding the concept of linear equations. Since the population is growing steadily by 4000 each year, we can say that the rate of change is constant, which implies linear growth. The population in 2010 forms the base value and the annual increase forms the slope.

The year 2025 corresponds to 15 years after 2010 and at that point the population is projected to be 450,000 (or 450 based on the problem's notation of thousands of people). Therefore, for each year after 2010, the population increases by 4 (thousands of people). Consequently, the equation which represents this situation would be:

p = 4x + 450

But, since the question has given options that are in the format of p in terms of (x-15), we subtract 15 from each side to put the equation in the given format:

p-450 = 4(x - 15)

So, the correct answer is B.

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The area of a rectangle is calculated by multiplying the number of rows by the number of squares in each row, which represents the length and breadth respectively.

The area of a rectangle can be calculated by multiplying the number of rows by the number of squares in each row. This corresponds to the multiplication of the length (number of squares in each row) and the breadth (number of rows). For example, if you have a rectangle made up of 4 rows and each row consists of 5 squares, the area would be 4 rows * 5 squares per row = 20 squares.

In real-life applications, for instance, if calculating the area of a floor that is 12.0 m², and the uncertainty is 3 percent (expressed as an area this is 0.36 m² - rounded to 0.4 m² assuming measured to a tenth of a square meter). Therefore, understanding the concept of calculating area is highly important.

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Bonnie can make a frame with sides measuring 20 tiles and 2 tiles, using all of her 40 tiles.

To find the largest frame size that Bonnie can make with her 40 tiles, we need to determine the factors of 40. A factor is a number that divides evenly into another number. The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, and 40.

To create a frame, Bonnie needs two sides with lengths that multiply to give 40. The largest frame size will have sides of length 20 and 2, which can be achieved by placing the tiles in a rectangular shape.

Therefore, Bonnie can make a frame with sides measuring 20 tiles and 2 tiles, using all of her 40 tiles.

Answer

[tex]Lola=\frac{203}{537}[/tex]

[tex]Ahmed=\frac{154}{537}[/tex]

[tex]Tommy=\frac{60}{179}[/tex]

Explanation

To find fraction of the total sales for each salesperson, we just need to divide the amount sold by each person by the total sales.

First, we are going to find the total sales:

$2030 + $1540 + $1800 = $5370

Now we can divide the amount sold by each salesperson by $5370:

[tex]Lola=\frac{2030}{5370} =\frac{203}{537}[/tex]

[tex]Ahmed =\frac{1540}{5370} =\frac{154}{537}[/tex]

[tex]Tommy=\frac{1800}{5370} =\frac{60}{179}[/tex]

We can conclude that Lola sold [tex]\frac{203}{537}[/tex] of the total sales, Ahmed sold [tex]\frac{154}{537}[/tex] of the total sales, and Tommy sold [tex]\frac{60}{179}[/tex] of the total sales.

Answer

Lola = $37.80

Ahmed = $28.68

Tommy = $33.52

Explanation

We need to divide $100 bonus according of the fraction of the total sales sold by each salesperson; to do so, we need to multiply $100 by the fraction of the total sales for each salesperson:

[tex]Lola=\frac{203}{537}*100=37.8026[/tex]

And rounded to the nearest cent:

Lola = $37.80

[tex]Ahmed=\frac{154}{537}*100=28.6778[/tex]

And rounded to the nearest cent:

Ahmed = $28.68

[tex]Tommy=\frac{60}{179}*100=33.5195[/tex]

And rounded to the nearest cent:

Tommy = $33.52

We can conclude that of the $100 bones, Lola received $37.80, Ahmed $28.68, and Tommy $33.52

Answer:

The answer is c.

Step-by-step explanation:

The total elevation change from the bottom of the lake to the top of the mountain is 760 feet. This calculation comes from multiples and subtraction.

You've got a neat problem here involving subtraction and multiplication. It's all to do with altitude and elevation change. You have climbed one-third of the way up the mountain and are currently 220 feet above lake level. This means that a third of the mountain's height from the lake's surface is 220 feet. To find the total height from the lake to the top of the mountain, we can do a simple multiplication:

1. 3 (representing the whole mountain) × 220 feet (one-third of it) = 660 feet.

However, you asked for the elevation change from the bottom of the lake to the top of the mountain. The lake is 100 feet deep, so we add this to our total:

2. 660 feet (mountain height) + 100 feet (lake depth) = 760 feet.

So, the elevation change from the bottom of the lake to the top of the mountain is 760 feet.

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The total elevation change from the bottom of the lake to the top of the mountain is 760 feet.

To answer the question, we need to understand that if the student is already 220 feet above the lake, and this represents one third of the way up the mountain, we can use this information to find the total elevation change from the lake bottom to the top of the mountain. We first need to calculate how high the mountain is above the lake by dividing 220 feet by one third (or 0.33), which gives approximately 660 feet. However, this does not include the depth of the lake. As the lake is 100 feet deep, we need to add this to our previous value to get the total elevation change. This gives us an elevation change of 660 feet + 100 feet = 760 feet from the bottom of the lake to the top of the mountain.

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Let us call the frames A and B

The two sides of A are Ax and Ay

The two sides of B are Bx and By

Bx 4

---- = ----

Ax 5

Bx = (4*Ax)/5

As they are similar: By = (4*Ay)/5

Area of A = Ax*Bx

Area of B = Ay*By = (16*Ax*Ay)/25

Area of B 16

----------- = -------

Area of A 25