To determine the number of ways Carmen can model the house using all 18 connecting cubes, considering them as distinguishable objects and applying permutations is essential.
Explanation:Carmen has 18 connecting cubes and wants to model a house shaped like a rectangle with a height of one connecting cube. To find the number of ways to model the house using all 18 cubes, we can approach it using combinatorics. One way to visualize this is by considering the cubes as distinguishable objects and applying permutations.
One approach could involve fixing the base of the rectangle, which will have a length of 16 cubes, leaving 2 cubes for the width. The 2 remaining cubes can be placed in 2! = 2 ways. So, the total number of ways to model the house would be 16!×2.
Answer:
There are 3 ways.
Step-by-step explanation:
Let each cube be 1 cm on the side.
The volume of each cube is 1 cm³.
volume = length × width × height
We are told the height is 1.
The volume is 18 cubes, so volume = 18 cm³.
length × width × height = 18 cm³
length × width × 1 cm = 18 cm³
length × width = 18 cm³
There are 3 ways to factor 18 into integer factors:
1, 18
2, 9
3, 6
Carmen can make the model 18 cubes long by 1 cube wide,
or 9 cubes long by 2 cubes wide, or 6 cubes long by 3 cubes wide.
Answer: There are 3 ways.
Choose among these options the one that results in a graph that shows exponential decay. A. f(x) = 0.6(2)x B. f(x) = 3(0.7)x C. f(x) = 0.4(1.6)x D. f(x) = 20(3)x
Arliss has two pieces of carpet runner. One is 2 1/3 yards long and the other is 3 1/3 yards long. She needs 10 yards of carpet runner altogether. How much more does she need to buy?
How do you solve this please help
Find the product 54×653
After the last stop on Mr. Tuttle’s route, the number of students on the bus is 3/4 of its full capacity. Once Mr. Tuttle has completed picking up all the students on his route, if no students have exited the bus, how many students could the remaining empty seats accommodate?
How do you solve the system of linear equation by multiplying?
5x - 2y = 11
3x + 5y = 19
The solution set for the system of equations is (3, 2).
What is system of equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought
Given is the system of equations -
5x - 2y = 11
3x + 5y = 19
Multiply Eq.{1} by 3 and Eq.{2} by 5, we get -
15x - 6y = 33
15x + 25y = 95
Now, performing Eq(2) - Eq(1), we get -
15x + 25y - 15x + 6y = 95 - 33
31y = 62
y = 2
x = 11 + 2y/5
x = 15/5
x = 3
Therefore, the solution set for the system of equations is (3, 2).
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Does anyone know how to do 9 and 10 ???
36,204+40,918 estimate then find the sum
the length of a cube is x centimeters. If x is an integer why can't the volume of the cube equal 15 cm cubed
The volume of a cube with a side length of x centimeters cannot equal 15 cm³ when x is an integer.
Explanation:The question asks why the volume of a cube with a length of x centimeters cannot equal 15 cm³ when x is an integer. In order to calculate the volume of a cube, we use the formula V = s³, where V represents the volume and s represents the length of a side. If x is an integer, the length of the cube can be any integer value.
However, when we substitute x = 15 into the formula, we find that the volume of the cube would be 15³ = 3375 cm³, which is not equal to 15 cm³. Therefore, the volume of a cube with a side length of x centimeters cannot equal 15 cm³ when x is an integer.
A store manager ordered 402 baseball caps and 122 ski caps estimate the total number of. Apps the manager ordered
ann picks a 4 digit number . The first digit is not a zero .The 4 digit number is a multiple of 5. how many different 4 digit numbers could she Pick?
Which number is bigger 2/3 or 66%
The equation of a line given two points needs to be found. Samuel claims that slope-intercept form will generate the equation and Helena claims that point-slope form will find the equation. Who is correct? Explain your reason by describing both forms.
Both Samuel and Helena are correct as the slope-intercept form and the point-slope form can be used to find the equation of a line given two points. The slope-intercept form is y = mx + b, while the point-slope form is y - y1 = m(x - x1). The methods vary but both are effective depending on the given information.
Explanation:Both Samuel and Helena are correct; they have mentioned different forms that can be used to find the equation of a line given two points. The slope-intercept form of a linear equation is commonly written as y = mx + b, where m represents the slope and b represents the y-intercept. The slope, m, describes the steepness of the line, and the y-intercept, b, is where the line crosses the y-axis. In contrast, the point-slope form is written as y - y1 = m(x - x1), where (x1, y1) is a specific point on the line and m is the slope. To find the slope, you take two points on the line, say, (x1, y1) and (x2, y2), and use the formula m = (y2 - y1)/(x2 - x1).
Either form will produce the equation of the line, but they require different approaches. The slope-intercept form immediately gives the y-intercept and is generally used when this information is valuable or when the graph will be drawn. Meanwhile, the point-slope form is particularly handy when you have one point on the line and the slope, as it can be used quickly without re-arranging the equation to solve for the y-intercept.
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Both Samuel and Helena's methods are valid for finding the equation of a line. The slope-intercept form (y = mx + b) requires finding the y-intercept, while the point-slope form (y - y1) = m(x - x1) uses a point on the line directly. Both forms yield the same final equation.
Both Samuel and Helena are correct, but they are using different methods to find the equation of a line. The slope-intercept form and the point-slope form can both lead to the same final equation of the line, which will be consistent after simplifying. Here's a step-by-step explanation of both forms:
Slope-Intercept Form (y = mx + b)Slope-Intercept Form is given by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.
First, find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1).Next, use one of the given points (x1, y1) and substitute in the found slope and coordinates to solve for b (the y-intercept).Substitute the slope and y-intercept back into the slope-intercept form.Example:
Given points (1, 2) and (3, 4):
Calculate the slope: m = (4 - 2) / (3 - 1) = 2 / 2 = 1.Use one of the points to find b: 2 = 1(1) + b; solving this, we get b = 1.Equation of the line: y = 1x + 1.Point-Slope Form (y - y1) = m(x - x1)The Point-Slope Form is given by the equation y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
First, find the slope (m) using the same formula: m = (y2 - y1) / (x2 - x1).Use one of the given points (x1, y1) and substitute in the found slope.Simplify the equation to convert it to slope-intercept form if needed.Example:
Given points (1, 2) and (3, 4):
Calculate the slope: m = (4 - 2) / (3 - 1) = 2 / 2 = 1.Select point (1, 2): y - 2 = 1(x - 1).Simplify: y - 2 = x - 1;y = x + 1.
Both forms ultimately lead to the same linear equation. Choosing which form to use depends on what information is given and personal preference.
The length of a rectangle is 5cm more than its width. The perimeter of the rectangle is 46cm. Find the width and the length
The width of the rectangle is 9 cm, and the length is 14 cm.
Explanation:To find the width and length of the rectangle:
Let's assume that the width of the rectangle is x cm. According to the problem, the length of the rectangle is 5 cm more than its width, so the length would be x + 5 cm.
The perimeter of the rectangle is 46 cm. The formula for the perimeter of a rectangle is P = 2(w + l), where P is the perimeter, w is the width, and l is the length.
So, we can set up the equation: 46 = 2(x + (x + 5)).
Simplifying the equation gives us: 46 = 2(2x + 5).
Expanding the equation further gives us: 46 = 4x + 10.
Subtracting 10 from both sides of the equation gives us: 36 = 4x.
Dividing both sides of the equation by 4 gives us: x = 9.
Therefore, the width of the rectangle is 9 cm, and the length is 9 + 5 = 14 cm.
To find the width and length of the rectangle, set up an equation using the given information and solve for x. The width is 9 cm and the length is 14 cm.
Explanation:To solve this problem, we can set up an equation using the information given. Let's assume the width of the rectangle is x cm. Since the length is 5cm more than the width, it will be x + 5 cm. The perimeter of a rectangle is found by adding all its sides, so we have:
2(x + x + 5) = 46
Simplifying this equation gives us:
4x + 10 = 46
Subtracting 10 from both sides:
4x = 36
Dividing both sides by 4:
x = 9
Therefore, the width of the rectangle is 9 cm and the length is 9 + 5 = 14 cm.
State whether the graph of each linear relationship is a solid line or set of unconnected points explain your reasoning the relationship between the number of $12 DVDs you buy and the total cost
Bella pays 7 payments of $5 each to a game store.she returns one game receives $20 back.what is the change of the about of money she has?
Answer:
$15 in total
Step-by-step explanation:
What is 0.8281 rounded to the nearest whole number?
When can you carve out time to study each month or each week
help !!! i dont understand !
solve for x 9x>-18 answer must be simplified
The number of the day is 936,165
Which is the other endpoint of a line segment with one endpoint at (-2, 5) and midpoint at (3, 1)?
A. (1/2, 3)
B. (1, 6)
C. (5/2, -2)
D. (5, -4)
E. (8, -3)
Combine the like terms to make a simpler expression:
3z+2+(-5z)+6
The correlation coefficient r between the size of a lake in square miles, x, and the yearly number of registered boaters, y, is 0.743. What percent of the variation in the number of yearly boaters can be explained by differences in lake sizes? A.74.3% B.55.2% C.44.8% D.37.2% Algebra
The variation in any sample group is simply the square of the correlation coefficient, that is:
variation = r^2
Therefore given an r value, we can simply directly calculate for variation percentage.
variation = (0.743)^2
variation = 0.552 or 55.2%
Answer:
B. 55.2%
How do you divided 14.28 /4.2
A rental company charges $15 plus $4 per hour to rent a bicycle. If Margie does not want to spend more than $27 for her rental, solve an inequality to determine how many hours she can rent the bicycle and not spend more than $27. Interpret the solution.
The number of hours she can rent the bicycle and not spend more than $27 is 3hours.
How to write an inequality equation?Total amount Maggie wants to spend = $27Fixed charge = $15Hourly charge = $4Number of hours = xThe inequality;
15 + 4x ≤ 27
4x ≤ 27 - 15
4x ≤ 12
x ≤ 12/4
x ≤ 3 hours
Therefore, the number of hours she can rent the bicycle and not spend more than $27 is 3hours
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Nina and her friends are going to the downtown rib festival. The festival organizers expect 10,000 people to attend the four-day festival. At the end of the festival the organizers say that they have exceed their expected attendance by 2000 people. What was the average number of people to attend the festival per day?
The average number of people attending the festival per day will be 3,000 per day.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
Nina and her friends are going to the downtown rib festival. The festival organizers expect 10,000 people to attend the four-day festival. At the end of the festival, the organizers say that they have exceeded their expected attendance by 2000 people.
The total number of people on four days will be given as,
⇒ 10,000 + 2,000
⇒ 12,000
The average will be given as,
⇒ 12,000 / 4
⇒ 3,000
The average number of people attending the festival per day will be 3,000 per day.
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write 3x+(2-4x) in standard form
I think the answer would be -1 + 2
2.654 2.564 2.065 2.465
greatest to least
A shopper purchased 4 tables and 2 chairs for $200 and 2 tables and 7 chairs for $400. What is the cost of each table and each chair? And can you please explain the process using substitution please? Thanks.