Mathematics High School

## Answers

**Answer 1**

The **equation** x + (60 + 70)° = 180° is used to solve for the measure of the **vertical** **angle** x = 50°

What are vertically opposite angles

**Vertical** angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite **angles** and are equal to each other.

The **angle** y and x form **vertical** angles, so x = y

Angle y form a straight line with 60° and 70° so we have the **equation** to solve for x as:

x + 60° + 70° = 180° {sum of **angles** on a straight line}

x + 130° = 180°

x = 180° - 130° {subtract 139° from both sides}

x = 50°

Therefore, the measure of the vertical **angle** x is equal to 50° derived with the **equation** x + (60° + 70°) = 180°.

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## Related Questions

At a local play, student tickets cost $5 each and adult tickets cost $11 each. if ticket sales were $3,000 for 300 tickets, how many students attended the play? a. 50 b. 150 c. 250d. 300

### Answers

This problem can be solved used **linear** **equations**. Here there are two **variables**, number of students and number of adults. After calculations we get the number of students attended the play is 50.

Lets consider the number of students is x and number of adults is y.

Total tickets sold = 300

x + y = 300 ------------ equation 1

The **amount** of total tickets sold is 3000.

Amount sold to students = 5x

Amount sold to adults = 11y

So, 5x+11y =3000 ----------- equation 2

Equating the x term for equation 1

Multiplying both sides with 5

5 (x+y) = 5 × 300

5x + 5y = 1500 ---------- equation 3

Subtracting equation 3 from equation 2

5x + 11y = 3000

- ( 5x + 5y = 1500)

6y = 1500

y = 1500/6 = 250

Number of adult attended = 250

From equation 1, x+y = 300

Substituting the value of y

x + 250 = 300

x = 300-250 = 50

So number of students attended is 50

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**Answer: 50**

**Step-by-step explanation: i got it right on my quiz**

Take care to properly set up your equations. The $3,000 is the sum of total money from student tickets and total money from the adult tickets.

A rectangle has an area of 174. 8m2

One of the sides is 3. 8m in length.

Work out the perimeter of the rectangle.

### Answers

The **perimeter **of the** rectangle** with area 174.8m² and side-length 3.8m is equal to** 99.6 meters.**

**Area** of the rectangle is equal to 174.8 m².

Length of the rectangle is equal to 3.8 m

let us consider 'w' be the width of the rectangle.

area of the rectangle = length × width

⇒ 174.8 = 3.8 × w

⇒ w = 174.8 / 3.8

⇒ w = 46 m

**Perimeter **of the rectangle = 2 ( length + width )

⇒ Perimeter of the rectangle = 2 ( 3.8 + 46 )

⇒ Perimeter of the rectangle = 2 ( 49.8 )

⇒Perimeter of the rectangle = 99.6 meter.

Therefore, the **perimeter** of the rectangle with length 3.8m and width 46m is equal to 99.6m.

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Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their HCF is 101. Show your steps.

Please give answer immediately

### Answers

Based on the information provided, the two **numbers** whose **HCF** is 101 are 1010 and 1313.

What is the HCF?

The **HCF** is the highest common factor or in other words, the highest **number** by which two numbers can be divided. Let's start by listing the four digits **numbers** that can be the **HCF** related to 101.

101 x 10 = 1010

101 x 11 = 1111

101 x 12 = 1212

101 x 13 = 1313

Now, from these **numbers**, there are two **numbers** whose difference is 303.

1313 - 1010 = 303

Based on this, the two **numbers** are 1010 and 1313

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Scott has a blue front of the new deck his building with dimension 7.5” x 4.5”. The actual deck will have dimensions 20’ x 12’. What is the scale

### Answers

The **scale of the drawing** is given as follows:

1 : 4.5.

How to obtain the scale of the drawing?

The scale of the drawing is obtained applying the **proportions **in the context of this problem.

The scale is defined as the **division **of the drawn length by the actual length.

The lengths are given as follows:

Drawn length: 20 inches.Actual length: 7.5 feet = 7.5 x 12 = 90 inches.

90/20 = 4.5, hence the **scale **of the drawing is given as follows:

1 : 4.5.

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Some fireworks are fired vertically into the air from the ground at an initial speed of 80 feet per second. The equation for this object's height h at time t seconds after launch is h(t) = -16(t)^2 +80t. Find the domain of the function.

### Answers

The **domain **of the function h(t) = -16(t)² + 80t is,

⇒ (- ∞, ∞)

**What is Quadratic equation?**

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The **equation **for this object's height h at time t seconds after launch is,

⇒ h(t) = -16(t)² + 80t

Now, The function is shown a Quadratic equation.

Hence, The **domain **of the function h(t) = -16(t)² + 80t is,

⇒ (- ∞, ∞)

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write an equation:

an addition equation with one variable that has a solution of 3

### Answers

**Answer:**

x + 5 = 8

**Step-by-step explanation:**

x + 5 = 8

Subtract 5 from both sides.

x + 5 - 5 = 8 - 3

x = 3

**Answer: x+5=8**

**Step-by-step explanation:**

Which inequality matches the graph? -2x + 3y > 7 02x-3y

### Answers

**the inequality model.** 5x-6y <0 is attached below.

What is **inequality**?

**Inequalities** are mathematical **expressions **where neither side is **equal**. In **inequality**, as **opposed **to **equations**, we compare two values. Less than (or **less **than or equal to), **greater **than (or **greater **than or equal to), or not equal to signs are used in place of the equal **sign **in between. Sometimes it can be about a "not equal to" **relationship**, where one thing is more than the other or less. In **mathematics**, an **inequality **is a relationship that results in a non-equal **comparison **between two numbers or other **mathematical expressions**.

2x + 3y > 7x-3y

5x-6y <0

So we have to plot this **inequality**.

Hence, the **inequality **model. 5x-6y <0 is attached below.

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Help meeeee please i need help with this

### Answers

**Answer: I believe the answer would be y = 3x. **

**Step-by-step explanation: I like to start by counting the x-values, then the y-values. Since the y-values are increasing by a constant of 3 and the x-values are increasing by 1, that would technically make the equation y = 3x + 0, but you don't need the 0 in this case. So it's just y = 3x. I hope this helps! :)**

generally, all stakeholders agree that there is a problem and on what the problem is before beginning the dmaic process. state of true of false.1. true2. false

### Answers

The given statement about the **stake holders **of **DMAIC **is **false**.

The term **DMAIC **stands for Define, **Measure**, Analyze, Improve, and Control and it represents the **five phases** that make the process,

Here we have given that generally, all **stakeholders **agree that there is a problem and on what the problem is before beginning the DMAIC process.

And we need to check whether the statement is true or not.

Here we know that in **DMAIC **process we have to follow the following steps they are listed as,

=> Define the **problem**

=> Improve activity

=> To determine **opportunities **for improvement

=> Identify the project goals

=> To analyze **project goals** and customer requirements.

Hence through this we have identified that the main purpose of DMAIC is to improve the effectiveness and **efficiency **of an organization's existing processes.

And here we have also know that DMAIC is a core data-driven improvement methodology of** Six Sigma.**

So, here the given statement is false.

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Please help me w this!!!

### Answers

Answer:

Step-by-step explanation:

X =90

solve 3x≤-5/4 as a inequality

### Answers

**Answer:**

Inequality Form:

**x ≤ −5/12**

Interval Notation:

**(−∞, −5/12]**

**Step-by-step explanation:**

5. Write the negation of each of the following statements:

a. R: Ron went to school.

b. S: A triangle has 3 sides.

c. T: x=9

d. U: 20 is a multiple of 3.

### Answers

The **negation** of the following statements are a. R: Ron did not go to school. b. S: A **triangle** does not have 3 sides. c. T: x ≠ 9 d. U: 20 is not a multiple of 3.

What is negation?

It's vital to know the **opposite** of a particular mathematical statement from time to time in mathematics. This practice is known as "negating" a claim. Remember that if a claim is **true**, then the negation must be false.

The negation of the following statements is:

a. R: Ron did not go to school.

b. S: A triangle does not have 3 sides.

c. T: x ≠ 9

d. U: 20 is not a multiple of 3.

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if a lawyer charges $120 an hour (or any fraction of an hour), how much is a bill for 3 hours and 20 minutes? what is the equation for this problem?

### Answers

**Answer: If a lawyer charges $120 an hour (or any fraction of an hour), how much is a bill for 3 hours and 20 minutes? What is the equation for this problem? answer choices l (x) = 120x l (x) = 120 [x-1] l (x) = 120 [x] l (x) = 120 [x+1] **

**Thank me later.**

solve these proportion for the variable x. Use the reasoning of scalling to solve

### Answers

The value of x from the given **proportion** is given as x = 10 after scalling both side of the equation.

**What is Ratio and Proportion ?**

A** ratio** is a divisional comparison of two quantities, and a proportion is the equality of two ratios. A ratio is often read as "x is to y" but may also be written as "x: y" or "x/y." The proportion equation, on the other hand, states that two ratios are equal.

The equality of two ratios is referred to as **proportion.** There is never a difference between two comparable ratios. The ratio sign (::) is used to express proportions, which aid in solving problems with ambiguous amounts. To put it another way, a percentage is an equation or a claim that shows the equality of two ratios or fractions. If a: b = c: d, then four non-zero values, a, b, c, are said to be in proportion. Let's now compare the two ratios, 3:5 and 15:25. In this case, 3:5 and 15:25 may both be written as 3:5 = 3/5 and 0.6, respectively. We may argue that these two ratios are proportionate because they are both equal.

There are two types of proportions :

Direct ProportionInverse Proportion

The proportion is given by ,

x/12 = 15/18

⇒ multipling both side with 12 we get ,

x = (12*15)/18

⇒ x = 5 * 2 = 10

The value of x from the given proportion is given as x = 10.

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The value of x from the given proportion is given as x = 10 after scalling both side of the **equation**.

**What is meant by** **equation?**

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more **components** must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.An equation that expresses a significant **relationship** between two or more variables is called a formula.

There are two types of proportions :

==>Direct Proportion

==>Inverse Proportion

The proportion is given by ,

x/12 = 15/18

⇒ multipling both side with 12 we get ,

x = (12*15)/18

⇒ x = 5 * 2 = 10

The value of x from the given proportion is given as x = 10.

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Solve the equation ax + b = c for x.

x =

### Answers

**Answer:**

X = C - B

--------

A

**Step-by-step explanation:**

Solving for X is pretty much getting X alone on one side of the equal sign. That's when we would do the "opposite" of what the original equation is showing. And we do that to both sides.

For example, we see +b. The opposite of addition is subtraction, so we do just that. We do -b on BOTH sides of the equal sign. b -b = 0. It cancels it out. c-b is just as it says. So now we have ax = c-b.

Now we see ax are right next to each other with no symbol, which means they are being multiplied. The opposite of multiplication is division. So we'll do that exactly. We will divide A on both sides. ax/a gets rid of that a and leaves the x alone. Dividing c-b/a gives you just that, making the answer X = C-B/A

Which descriptions and equations could be the function rule? Select all that apply.

The table in the attached image shows some of the input and output values for a function rule.

### Answers

For the given table of values the** equation **that could be the** function rule** is option 4: y = 3x - 2.

**What is a function?**

In mathematics, a **function** is a unique arrangement of the **inputs** (also referred to as the **domain**) and their **outputs** (sometimes referred to as the **codomain**), where each **input** has exactly one **output** and the **output **can be linked to its** input**.

The table of** input** and **output **values are given for the** function**.

The **slope-intercept **form of an **equation/function** is - y = mx + b

To find the** slope **m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the **equation** -

[-2 - (-11)]/[0 - (-3)]

(-2 + 11)/(0 + 3)

9/3

3

So, the **slope** point is obtained as m = 3.

The **equation** becomes - y =3x + b

To find the value of b substitute the values of x and y in the **equation** -

-11 = 3(-3) + b

-11 = -9 + b

b = -11 + 9

b = -2

So, the value for b is -2.

Now, the **equation** becomes -

y = 3x - 2

The graph is plotted for the **function**.

Therefore, the **equation** is y = y = 3x - 2.

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One bank account pays 6% interest and another pays 12%. If $6,000 was invested for a year and the interest earned was $540, how much was invested at 6%?

### Answers

**Answer:**

360

**Step-by-step explanation:**

0.06x6000=360 also that 6% equal 6/100 wich is 0.06

Two cars leave the same parking lot, with one heading north and the other heading east. After several minutes, the northbound car has traveled 4 kilometers, and the eastbound car has traveled 4 kilometers. Measured in a straight line, how far apart are the two cars? If necessary, round to the nearest tenth

### Answers

The straight line **distance** between the northbound and eastbound **cars** is 5.7 kilometres.

The movement of cars and straight line connecting them forms a **right angled triangle**. The straight line will be hypotenuse will the eastbound and northbound distance will be perpendicular and base of the triangle. Thus, using Pythagoras theorem to find the distance between the two cars.

Distance between the two cars = ✓4² + 4²

Taking square of the numbers

Distance between the two cars = ✓16 + 16

Performing addition

Distance between the two cars = ✓32

Taking square root

Distance between the two cars = 5.66

Round to nearest tenth = 5.7

Thus, the distance is 5.7 kilometres.

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The equation m = 40g gives the distance in miles, m, that a car can travel using g gallons of gas.

a. If the car has gone 140 miles, how much gas was used? Show your thinking.

b. Write an equation that represents the inverse function: the gallons of gas as a function of distance in miles

### Answers

a)

g = m / 40

g = 140 /40

g = 3.5

b)

m = 40g

m / 40 = g

a survey for kindergartners asked about their favorite color. the children were asked to check the box corresponding to blue, red, green, yellow, or orange. what is the scale of measurement for this question? group of answer choices ordinal interval nominal ratio

### Answers

**Nominal scale**- A nominal scale is a discrete classification of data, in which data are neither measured nor ordered but subjects are **merely **allocated to distinct categories.

Measurements on an** interval** scale have substantial differences between the values. In other words, the disparities between the scale's points are exact and measurable.

Ratio scales are interval scales where lengths are expressed in relation to a **rational **zero.

**Ordinal scale**: a scale where data is presented merely in terms of order of magnitude because there is no accepted method for determining differences.

Since there are 5 categories: Blue, Red, Green, Yellow, Orange, so by the above definition we can say that for this question we would use Nominal scale for measurement.

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Let f(x) = 4x + 3 and g(x)=x²-x+1. Perform the function operation and then find the domain.

g(x)-f(x)

g(x)-f(x) = (Simplify your answer.)

### Answers

The **domain** of g(x) - f(x) is all** real numbers**, or (-∞, ∞).

**What is the domain?**

The **domain** of a **function** is the set of all possible **input values** (x-values) for which the **function** is defined and produces a valid **output (y-value)**. In other words, it is the set of values for which the function is valid and can be used without producing any errors or undefined results.

To perform the function operation g(x) - f(x), we need to subtract the function f(x) from the function g(x).

g(x) = x² - x + 1

f(x) = 4x + 3

g(x) - f(x) = x² - x + 1 - (4x + 3)

g(x) - f(x) = x² - 5x - 2

The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value).

For the function g(x) - f(x) = x² - 5x - 2, there are no restrictions on the input values, meaning that any value of x can be plugged into the function to produce a valid output.

Therefore, the **domain** of g(x) - f(x) is all** real numbers**, or (-∞, ∞).

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Solve for x to the nearest tenth.

### Answers

By **calculating **, The **value **of x is 5√5.

**What is triangle?**

Triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always** 180 degrees.**

From the given figure,

When we draw a line inside the figure than it becomes into rectangle and one another **triangle.**

so,

In the **right angled triangle,**

with** base 10** and** opposite side 5**

We have to find the hypothenuse **that is x . **

so,

from** pythagorean theorem**

we can say that

Sum of squares of two sides is** equal **to square of hypothenuse

so,

**10*10 + 5*5 = x*x**

100+25 = x*x

x*x = 125

**x = 5√5 . **

Hence, The value of x is **5√5 **

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(e) (i) Using a scale of 2cm to represent 5 units on each axes, show, by shading the unwanted regions, the set of points satisfying the three inequalities in parts (b), (c) and (d). [3] (ii) Calculate the maximum number of rabbits the farmer can buy. [2]

### Answers

**Answer: (e) (i) To represent the inequalities graphically on a coordinate plane, you can use a scale of 2cm to represent 5 units on each axis. To shade the unwanted regions, you can start by drawing the coordinate plane and labeling the x and y axes. Then, you can graph the inequalities by plotting the lines and shading the regions that do not satisfy the inequalities.**

**(b) 2x + 3y ≤ 30**

**This inequality represents a line with the equation 2x + 3y = 30. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or below the line satisfy the inequality.**

**(c) x - 2y ≥ -10**

**This inequality represents a line with the equation x - 2y = -10. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or above the line satisfy the inequality.**

**(d) y ≤ -2x + 10**

**This inequality represents a line with the equation y = -2x + 10. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or below the line satisfy the inequality.**

**The set of points that satisfy all three inequalities is the area that is not shaded in the graph.**

**(ii) To find the maximum number of rabbits the farmer can buy, we need to find the coordinates of the vertex of the feasible region.**

**The coordinates of the vertex of the feasible region is (x,y) the point where the line 2x+3y=30 and x-2y=-10 intersects.**

**We can substitute the x-2y=-10 into the 2x+3y=30 equation**

**2x+3y=30**

**2x+3y+2y=-10**

**2x+5y=-10**

**x=-5y+10**

**substituting this into one of the equation we have**

**2(-5y+10)+3y=30**

**-10y+20+3y=30**

**-7y=10**

**y= -10/7**

**substituting this into x = -5y+10 we have**

**x = -5(-10/7)+10 = 15**

**the maximum number of rabbits the farmer can buy is 15**

**Step-by-step explanation:**

Trina is buying favors for a birthday party. All of the party favors cost more than $13. What is the least expensive the party favors could be?

### Answers

The least** **expensive will be the **lowest** **cost** among the cost greater than $13.

i.e $13.5

If the **cost** of the **favors** is:

$13.5 < $14 < $15 < $20

What is inequality?

It shows a relationship between two numbers or two **expressions**.

There are commonly used four **inequalities**:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

All of the party favors cost **more** **than** $13.

This means,

Cost = x

x > 13

Now,

If the following are the **cost** of the **favors**:

$13.5, $14, $15, and $20

The least** **expensive will be the **lowest** **cost** among the cost greater than $13.

i.e $13.5

13.5 < 14 < 15 < 20

Thus,

The **least** **expensive** will be the lowest cost among the cost greater than $13.

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jennifer takes 2 hours to make a loaf of bread and 1 hour to make a dozen cookies. janet takes 3 hours to make a loaf of bread and 3/4 hours to make a dozen cookies. who, if either, has an absolute advantage baking bread? who, if either, has an absolute advantage making cookies?

### Answers

When it comes to baking **bread**, **Jennifer** has an **absolute** advantage. But when it comes to making **cookies**, **Janet **has an absolute advantage.

**Absolute** advantage is used when there is efficient production. It is used to describe the ability of a person, place, business, or nation to produce a lot of goods or services with the same amount of inputs in a given amount of time.

Here, a **loaf** of bread baked by Jennifer takes about 2 hours but it takes about 3 hours for Janet to bake a loaf of bread. So, **Jennifer **has an absolute advantage in baking a loaf of bread.

Also, Jennifer takes about 1 hour to bake 12** cookies** but it only takes 3/4 hours or 45 minutes for Janet to bake cookies 12 cookies. So, **Janet** has an absolute advantage in baking a dozen cookies.

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Select one or more expressions that together represent all solutions to the equation. Your answer should be in degrees.

Assume

�

nn is any integer.

7

cos

(

9

�

)

−

1

=

1

7cos(9x)−1=17, cosine, left parenthesis, 9, x, right parenthesis, minus, 1, equals, 1

### Answers

The trigonometric equation 7cos(9x) - 1 = 17 has an **undefined **solution.

How to solve the trigonometric equation?

The trigonometric equation for this problem is **defined **as follows:

7cos(9x) - 1 = 17

Isolating the **cosine**, we have that:

7cos(9x) = 18

cos(9x) = 18/7

Now we isolate x applying the** arc cosine**, which is the inverse of the cosine, as follows:

9x = arccos(18/7)

9x = undefined.

The solution is **undefined **because the arccosine only exists for values between -1 and 1, as the cosine of an angle is always going to assume a value between -1 and 1.

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mj supply distubutes bags of dog food to pet stores its markup rate is 28% which eqaution represents the new price of a bag of dog food y given an orignal price x?

### Answers

**Answer:**

**Step-by-step explanation:**

You didn't post any answer choices, but the answer should be:

y = x + (0.28)x = 1.28x

If the number of tickets sold is 125, what will be the total sales?

### Answers

**Answer:**

I don't know????????....................

The graph of y = In(x) was transformed by shifting 8 units left and 12 units up. Write an equation

### Answers

The equation of the** translated function** for this problem is given as follows:

y = ln(x + 8) + 12.

What are the translation rules?

The **four **translation rules are defined as follows:

Left a units: g(x) = f(x + a).Right a units: g(x) = f(x - a).Up a units: g(x) = f(x) + a.Down a units: g(x) = f(x) - a.

The **parent **function in this problem is given as follows:

y = ln(x).

The **translations **in this problem, and their effects, are given as follows:

8 units left: x -> x + 8.12 units up: y -> y + 12.

Hence the **translated **function is defined as follows:

y = ln(x + 8) + 12.

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Volume of Composed Figures What is the volume of this container?

15 cm 4,000 cm3 20 cm 6,000 cm3 10 cm 10 cm 900 cm3 20 cm 3,000 cm3 15 cm

### Answers

The **volume** of the container is 4,500 cm3.

Calculate the volume of the two cubes that make up the container.

For the **cube** on the left, the volume can be found by multiplying the length (15 cm) by the width (10 cm) by the height (10 cm).

15 cm × 10 cm × 10 cm = 1,500 cm3

For the cube on the right, the volume can be found by **multiplying** the length (20 cm) by the width (15 cm) by the height (10 cm).

20 cm × 15 cm × 10 cm = 3,000 cm3

Add the two volumes together to find the total volume of the container.

1,500 cm3 + 3,000 cm3 = 4,500 cm3

Therefore, the volume of the **container** is 4,500 cm3.

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