At Furnace Woods School, enrollment increased from 320 students in 2006 to 349 students in 2007. What is the percent increase in enrollment? 

x = 1 1/4 cups

x = 1.25 cup

Tonya poured 1 1/4 cups into each cup.

Tony poured a total of 2 1/2 cups of coffee into an unspecified number of cups.

To solve this problem, we first need to understand the different units of measurement being used and convert them appropriately. In the United States, 1 quart is equal to 4 cups. So, we will start by converting the coffee in the pot to cups.

The coffee pot originally contained 1 1/2 quarts of coffee. To find out how much this is in cups, we multiply by 4 (since there are 4 cups in 1 quart):

1 1/2 quarts = 1.5 quarts

1.5 quarts * 4 cups/quart = 6 cups

Thus, the coffee pot had 6 cups of coffee before Tony poured it into cups.

After pouring, 3 1/2 cups of coffee remain in the pot. To find out how much coffee was poured into the cups, we subtract the remaining coffee from the initial amount:

6 cups - 3 1/2 cups = 2 1/2 cups

This means that Tony poured a total of 2 1/2 cups of coffee into the cups. If we assume that he poured an equal amount into each cup, we would divide the total amount poured by the number of cups to find the amount per cup. However, since we don't know how many cups he filled, we can only conclude that Tony poured a total of 2 1/2 cups of coffee into an unspecified number of cups.

Option 2 is the correct answer because it shows the proper steps for constructing an angle bisector using a compass and a straightedge.

Steps:

Draw the angle to be bisected.

Place the compass point at the vertex of the angle and draw an arc that intersects both sides of the angle.

Without changing the compass radius, place the compass point at each of the arc intersection points and draw two more arcs that intersect each other.

Draw a line from the vertex of the angle through the point of intersection of the two arcs.

This line is the angle bisector.

The other options are incorrect because they do not show all of the necessary steps, or they show the steps in the wrong order.

For example, option 1 shows the steps for constructing an angle bisector using a protractor, but this is not the method that was asked for.

Option 3 shows the steps for constructing an angle bisector using a compass and a straightedge, but it does not show the step of drawing the arc through the vertex of the angle.

Option 4 is incorrect because it shows the steps for constructing an angle bisector using a ruler and a triangle, but this is not the method that was asked for.

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Sales for the first year were 2 millions of dollars

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

[tex]\large {\boxed {m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

[tex]\large {\boxed {y - y_1 = m ( x - x_1 )}}[/tex]

Let us tackle the problem!

Let:

Sales for the first year = s₁

Sales for the second year = s₂

Sales for the third year = s₃

Given:

s₂ = 6 + s₁

s₃ = 3s₂

s₃ = 24

Unknown:

s₁ = ?

Solution:

[tex]s_3 = 3s_2[/tex]

[tex]24 = 3s_2[/tex]

[tex]s_2 = 24 \div 3[/tex]

[tex]s_2 = 8[/tex]

[tex]s_2 = 6 + s_1[/tex]

[tex]8 = 6 + s_1[/tex]

[tex]s_1 = 8 - 6[/tex]

[tex]s_1 = 2[/tex]

Sales for the first year = 2 millions of dollars

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic

The sales in the first year is [tex]\boxed{2{\text{million of dollars}}}.[/tex]

Further explanation:

The linear equation with slope m and intercept c is given as follows.

[tex]\boxed{y = mx + c}[/tex]

The standard form of the linear equation can be expressed as follows,

[tex]\boxed{ax + by = c}[/tex]

The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left( {{x_2},{y_2}} \right)[/tex] can be expressed as,

[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]

Explanation:

Consider the sale in the first year as [tex]x[/tex].

Consider the sale in the second year as [tex]y[/tex].  

Consider the sale in the third year as [tex]z[/tex].

Sales for a company were 6 million dollars more the second year than the first.

[tex]y = 6 + x[/tex]

Sales for the third year were 24 million dollars.

[tex]z = 24[/tex]

Sales for the third year were tripled the sales for the second year.

[tex]z = 3y[/tex]

Substitute 24 for z in above equation.

[tex]\begin{aligned}24&= 3y\\\frac{{24}}{3} &= y\\8&= y\\\end{aligned}[/tex]

Substitute [tex]8[/tex] for [tex]\text{y}[/tex] in equation [tex]y = 6 + x[/tex]

[tex]\begin{aligned}8&= 6+ x\\8 - 6&= x\\2&= x\\\end{aligned}[/tex]

The sales in the first year is [tex]\boxed{2{\text{million of dollars}}}.[/tex]

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequality

Keywords: sales, company, 6 million, dollars, second year, first, sales for second, sales for third year, tripled, first year, 24 million, millions of dollars.

The decimal point should be to the left of the 6.

A division is a process of splitting a specific amount into equal parts.

A is INCORRECT because Lucita's estimate is about right and if the decimal point was to the left of 2, then the answer would be -0.26 which is still too small.

B is CORRECT because again Lucita's estimate is about right and if the decimal is to the left of six the number would be -2.6 which is close to her estimate (-3)

C is INCORRECT because it is saying that -0.026 is the correct answer and Lucita's estimate was just too small which is incorrect since we know -0.026 is actually what is too small.

D is INCORRECT because it is saying that -0.026 is correct and if her estimate (-3) was too high, it would be bigger than the number she got which was -0.026 and regardless of anything we know -3 is not bigger that -0.026.

Hence the decimal point should be to the left of the 6. Option C is correct.

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