The Fundamental Counting Principle, choosing from 3 sizes of bottled water and from distilled, filtered, or spring water is 9 ways.
What is fundamental counting principle?The Basic Counting Principle is a technique used in mathematics, more especially in probability theory and combinatorics, to determine how many combinations of options, items, or outcomes are possible. The Rule of Multiplication, the Product Rule, the Multiplication Rule, and the Basic Counting Rule are some of its alternate names.
It has a connection to the Sum Rule, often known as the Rule of Sum, which is a fundamental counting method used to calculate probabilities.
According to the Basic Counting Principle, if a decision or event has a potential result or set of options, and a different decision or event has b possible outcomes or choices, then the sum of all the unique combinations of outcomes for the two is ab.
Using the fundamental counting principle, if an event occurs in m ways and another event occurs in n ways then the total occurrence is given as (m)(n).
Given that,
m = 3 for choosing between sizes.
n = 3 for distilled, filtered, or spring water.
Thus, the total number of occurrence is given as:
T = (3) (3) = 9
Hence, the Fundamental Counting Principle, choosing from 3 sizes of bottled water and from distilled, filtered, or spring water is 9 ways.
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A random sample of 20 seventh graders found that 14 participate in a local contest making duct-tape wallets. Complete parts a through c.
a. If there are 500 seventh graders, write a proportion to estimate the number of seventh graders, n, who participate in the contest.
The proportion
14 n
20 500
=
can be used to estimate the number of seventh graders who participate in the contest.
b. Solve the proportion to estimate the number of seventh graders who participate in the contest.
About seventh graders participate in the contest.
(Type a whole number.)
Answer:
350
Step-by-step explanation:
Using the proportion from part (a):
14/n = 20/500
Cross-multiplying, we get:
20n = 14 × 500
Dividing both sides by 20, we get:
n = 14 × 500 / 20 = 350
Therefore, about 350 seventh graders participate in the contest.
How many solutions does the equation have?
9x + 2 = 3x + 5
Answer:
it has 1 solution of 1/2 or decimal form of 0.5
help with this please
how much 60.5 kg in lbs?
The weight 60.5 kg is equal to approximately 133.38 pounds. This conversion was done using the formula 60.5 kg x 2.20462 lbs/kg = 133.37851 lbs.
We know that 1 kg is equivalent to 2.20462 pounds, which means that we can convert kilograms to pounds by multiplying the weight in kilograms by the conversion factor 2.20462.
So to convert 60.5 kg to pounds, we can use the following formula:
60.5 kg x 2.20462 lbs/kg = ? lbs
Multiplying 60.5 by 2.20462 gives us:
60.5 x 2.20462 = 133.37851
Therefore, 60.5 kg is equivalent to 133.37851 pounds.
Finally, we can round this result to two decimal places to get:
60.5 kg is approximately equal to 133.38 pounds.
So the final answer is that 60.5 kg is equivalent to approximately 133.38 lbs.
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a basketball court is 46 feet wide and 84 feet long. the court has a border that is 10 feet wide. the cost of a hardwood floor is $9 per square foot. how much will it cost to put a new floor on both the court and its border?
The total cost to put a new floor on both the court and its border is; $61776
How to solve Algebra Word problems?The parameters given are;
Initial length = 84 ft
Initial Width = 46 ft
Now, since the court has a border that is 10 ft wide, it means that we will add 20 ft to the initial length and width to get the new measurements. Thus;
New length = 84 + 20 = 104 ft
New Width = 46 + 20 = 66 ft
Thus;
Area = 104 * 66
Area = 6864 sq.ft
Thus;
Total Cost = 6864 * 9
= $61776
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2) Andrew brought packs of biscuit. Create a graph to determine if the
number of packs and price are proportional for each serving size listed in the
table. If the quantities are proportional, what is the constant of
proportionality or unit rate that defines the relationship? Explain how the
constant of proportionality was determined and how it relates to both the
table and graph.
The constant of proportionality of the graph is 8.
What is constant of proportionality?Constant of proportionality is the constant value of the ratio between two proportional quantities.
Given that, a table, of price of the number of pack of biscuits,
We are asked to find the constant of proportionality or unit rate that defines the relationship,
Unit rate is a rate for one of something.
Here, let us consider the number of packets be x and price be y,
x and y are proportional, therefore,
y = kx, here k is the constant of proportionality,
Put y = 8 and x = 1
8 = k
Similarly, if we check for other values we will get 8
[graph is attached]
Hence, the constant of proportionality of the graph is 8.
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let abc~def and the ratio of the respective altitude is 1:3. if the measure of the sides of abc are 3cm,5cm,and 7cm. Then find the measures of the sides of the larger triangle.
Answer:
Since the ratio of the altitudes of the two triangles ABC and DEF is 1:3, we can say that the altitude of triangle DEF is three times that of triangle ABC.
Let's assume the altitude of triangle ABC is h, then the altitude of triangle DEF is 3h.
Now, we know that the area of a triangle is given by the formula:
Area = (1/2) * base * height
Let's apply this formula to both triangles:
Area of triangle ABC = (1/2) * base * altitude
= (1/2) * 7cm * h
= 3.5h cm^2
Area of triangle DEF = (1/2) * base * altitude
= (1/2) * 7cm * 3h
= 10.5h cm^2
Since the two triangles are similar, their areas are proportional to the squares of their corresponding sides. That is:
Area of triangle ABC / Area of triangle DEF = (AB / DE)^2
Substituting the values, we get:
3.5h / 10.5h = (AB / DE)^2
1/3 = (AB / DE)^2
Taking the square root of both sides, we get:
AB / DE = 1 / sqrt(3)
AB = (1 / sqrt(3)) * DE
Now, we know that the sides of triangle ABC are 3cm, 5cm, and 7cm.
Let's assume that the sides of triangle DEF are a, b, and c.
Since the sides of the two triangles are proportional, we can write:
a / 3 = b / 5 = c / 7 = 1 / sqrt(3)
Solving for a, b, and c, we get:
a = 3 / sqrt(3) = sqrt(3) cm
b = 5 / sqrt(3) = (5 * sqrt(3)) / 3 cm
c = 7 / sqrt(3) = (7 * sqrt(3)) / sqrt(3) = 7 cm
Therefore, the measures of the sides of triangle DEF are sqrt(3) cm, (5 * sqrt(3)) / 3 cm, and 7 cm.
At the corner store, you can buy 5 super-size granola bars for $10. How much does a single super-size granola bar cost?
Answer:
3
Explanation:
Based on the given conditions, formulate: 3
Cross out the common factor: 3
get the result:3
Answer: 3
Answer:
2$
Step-by-step explanation:
10/5=2
expressions that are tested by the if statement are called ______
Expressions that are tested by the 'if' statement is called conditions.
A condition is an expression that evaluates to either 'True' or 'False', and it determines whether the code block within the 'if' statement is executed. The 'if' statement allows the program to make decisions and execute different codes based on whether the condition is 'true' or 'false'. For example, in Python, an 'if' statement might look like this:
if x > 10:
print("x is greater than 10")
In this example, the condition being tested is 'x > 10', which will evaluate as 'True' or 'False' depending on the value of x. If the condition is 'True', then the code block within the 'if' statement (in this case, the print statement) will be executed. If the condition is 'False', then the code block within the 'if' statement will be skipped.
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Select the correct phrase to make the statement about 96 multiplied by 11/8
is true.
The product is between 1/8 and 96
The statement that is true regarding "96 multiplied by 11/8" is: G. The product is greater than 96.
How to Find the Product of Two Numbers?To find the product of 96 and 11/8, we can multiply these two numbers:
96 x 11/8 = (96/1) x (11/8)
= 1056/8
= 132
So the product is 132.
Now we can check which statement is true:
F. The product is less than 11/8. This statement is false, since 132 is greater than 11/8.
G. The product is greater than 96. This statement is true, since 132 is greater than 96.
H. The product is between 11/8 and 96. This statement is false, since 132 is greater than both 11/8 and 96.
I. The product is equal to 96. This statement is false, since we have calculated that the product is actually 132.
The statement that is true is G. The product is greater than 96.
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100 points Your friend says the solution to 6x+14x-9=4(5x+1) is x=13. Solve 6x+14x-9=4(5x+1). What was your friend's likely error?
The equation 6x + 14x - 9 = 4( 5x + 1 ) has no solution.
What is the solution to the given equation?Given the equation in the question;
6x + 14x - 9 = 4( 5x + 1 )
To solve the equation, first apply distributive property to remove the parenthesis.
6x + 14x - 9 = 4( 5x + 1 )
6x + 14x - 9 = 4 × 5x + 4 × 1
Multiply 4 and 5x
6x + 14x - 9 = 20x + 4 × 1
Multiply 4 and 1
6x + 14x - 9 = 20x + 4
Next, collect and add like terms.
Subtarct 20x from both sides
6x + 14x - 20x - 9 = 20x - 20x + 4
6x + 14x - 20x - 9 = 4
Add 9 to both sides
6x + 14x - 20x - 9 + 9 = 4 + 9
6x + 14x - 20x = 4 + 9
20x - 20x = 4 + 9
20x - 20x = 13
0 = 13
Therefore, there is no solution to the equation.
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Suppose you grow, arrange, and sell flowers. If it costs $2,300 to arrange 500 bouquets,
and it costs $3,100 to arrange 600 bouquets, what is your marginal cost in this range?
Answer:
The marginal cost in this range is $0.50 per bouquet. This can be calculated by finding the difference in total cost of arranging 500 bouquets and 600 bouquets, which is $800, and dividing that by the difference in quantity of bouquets, which is 100. This gives a marginal cost of $0.50 per bouquet.
From tuesday to friday, noel, the supplier delivered 350 yards of ribbon per day. From saturday to monday, he delivered 700 yards of ribbon per day. What was the average length of ribbon that noel delivered per day?.
Noel delivered an average of 500 yards of ribbon per day from Tuesday to Monday.
The central value represents the typical or average value of all the numbers in the set.
From Tuesday to Friday, Noel delivered 350 yards of ribbon per day, a total of 4 days. So, the total length of ribbon that he delivered during this period is
=> 4 * 350 = 1400 yards.
From Saturday to Monday, he delivered 700 yards of ribbon per day, a total of 3 days. So, the total length of ribbon that he delivered during this period is
=> 3 * 700 = 2100 yards.
To find the average length of ribbon that Noel delivered per day, we need to find the total length of ribbon he delivered in both periods and divide it by the total number of days.
The total length of ribbon he delivered in both periods is
=> 1400 + 2100 = 3500 yards.
The total number of days is
=> 4 + 3 = 7 days.
So, the average length of ribbon that Noel delivered per day is
=> 3500/7 = 500 yards.
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Solve the problem bellow
How do you write an inequality in a word problem?
To indicate that one value is greater than, less than, or equal to another, an inequality in a word problem is written using mathematical symbols like, >, or.
Determine the values that the inequality will compare before using the correct mathematical symbol to express the relationship between them in a word problem. Once the values have been determined, represent the relationship between them using the proper mathematical symbol. For instance, the inequality would be phrased as "x > 5" if the problem stated that "x is greater than 5". Other possible symbols for inequalities are (less than), (less than or equal to), and (more than) (greater than or equal to). It is crucial to always use the appropriate mathematical symbols when creating an inequality since they are needed to indicate the direction of the comparison. Moreover, make sure to incorporate all essential components, including the values being compared, the mathematical symbol, and the equals sign, if required. These procedures can be used to effectively write an inequality in a word problem.
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Santiago’s total budget for the materials to build the ramp and the foam pit is 3,000. With his current design, will he be over budget or under budget, and by how much?
Total cost to build the ramp is $1467.4. Santiago’s has over budget to build the ramp.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Here,
Area of 2 rectangles is
2(Length×Width)
= 2(20×12)
= 480 square feet
Area of small rectangle = 12×8.5
= 102 square feet
Area of 2 triangles = 1/2×Base×Height
= 1/2 ×20×8.5
= 85 square feet
Total area = 480+102+85
= 667 square feet
Total cost to build the ramp = 667×2.20
= $1467.4
Santiago’s total budget for the materials to build the ramp and the foam pit is $3,000.
Hence, Santiago’s has over budget to build the ramp.
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"Your question is incomplete, probably the complete question/missing part is:"
The material Santiago will use to build the ramp cost $2.20 per square foot. Find the total cost of materials for the ramp? All sides are; 21.7, 20, 12 for perimeter and 8.5 for the height.
Santiago’s total budget for the materials to build the ramp and the foam pit is 3,000. With his current design, will he be over budget or under budget, and by how much?
Which of the following shows a correct method to calculate the surface area of the cylinder?
cylinder with diameter labeled 3.2 feet and height labeled 3.8 feet
SA = 2π(1.6)2 + 3.2π(3.8) square feet
SA = 2π(1.6)2 + 1.6π(3.8) square feet
SA = 2π(3.2)2 + 3.2π(3.8) square feet
SA = 2π(3.2)2 + 1.6π(3.8) square feet
The following equations should be used to calculate the cylinder's surface area = SA = 2πr² + 2πrh. As a result, the suggested options do not include the correct approach.
How to calculate the surface area of cylinder?Where h is the cylinder's height and r is the cylinder's radius.
The radius is equal to half of the diameter, or 1.6 feet, given that the diameter is 3.2 feet. And it stands 3.8 feet in height.
As a result, the following is the appropriate formula to get the cylinder's surface area:
SA is = 2.16 plus 2.16.3.8 square feet.
When we abbreviate the phrase, we get:
SA = 2.56 + 2.08 square feet
SA = 5.12 plus 12.16 square fee
SA = 17.28 square feet.
As a result, the suggested options do not include the correct approach.
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The surface area of the given cylinder is given by the equation:
SA = 2π (1.6)² + 3.2π(3.8) square feet
What is meant by a cylinder?
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.
The surface area of the cylinder is the sum of the area of the curvilinear surface and the areas of the top and bottom circular bases.
Now the area of the curved surface = 2πrh
Area of bases = πr² + πr² = 2πr²
where,
r = radius of the cylinder
h = height of the cylinder
Given,
r = 3.2 / 2 = 1.6 feet
h = 3.8 feet
Substituting,
Surface area SA = 2πrh + 2πr² = 2π * 1.6 * 3.8 + 2π (1.6)²
= 2π (1.6)² + 3.2π(3.8) square feet.
Therefore the surface area of the given cylinder is given by,
SA = 2π (1.6)² + 3.2π(3.8) square feet.
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What is the golden ratio of Fibonacci?
The golden ratio of Fibonacci, also known as the divine proportion, golden mean, or golden section, is a mathematical constant that is approximately equal to 1.618033988749895.
It is represented by the Greek letter phi (φ) and is found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part.
In mathematical terms, the golden ratio is expressed as:
φ = (1 + √5) / 2
The golden ratio is closely related to the Fibonacci sequence, which is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. The ratio of consecutive numbers in the Fibonacci sequence converges to the golden ratio as the sequence progresses.
For example, the first few numbers in the Fibonacci sequence are:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
As we divide each number by the one before it, we get closer and closer to the golden ratio:
1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.666...
8/5 = 1.6
13/8 = 1.625
21/13 = 1.615...
34/21 = 1.619...
55/34 = 1.617...
89/55 = 1.618...
144/89 = 1.618...
As you can see, the ratio of consecutive numbers in the Fibonacci sequence approaches the golden ratio as the sequence progresses. This is why the golden ratio is often referred to as the golden ratio of Fibonacci.
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please help me on this
Answer: 7/14
Step-by-step explanation:
first you have to find common denominators to do that the simplest way I can think of is to multiply the 7x2 to get 14 and what you have to do to the bottom is what you do to the top.then you get 12/14-5/14after that you subtract the numerators, and you get...7/14which is your final answer3/4 = 9/n solve for n please help
Answer:
Step-by-step explanation:
12
How do you find eigenvalues and eigenvectors on a calculator?
Eigenvalues and eigenvectors can be found using a calculator by solving the equation Ax = λx, where A is a matrix, x is the eigenvector, and λ is the eigenvalue.
To solve this equation, you first need to calculate the determinant of the matrix A, which is written as |A|. If the determinant is not equal to zero, then you can calculate the eigenvalue by dividing the trace of the matrix (the sum of the diagonal elements) by the number of rows or columns of the matrix. The eigenvalues can then be substituted into the equation to solve for the corresponding eigenvector. For example, for a 2x2 matrix A, the eigenvalues can be found by calculating |A| and then solving the equation λ^2 - (trace of A) * λ + |A| = 0. The eigenvectors can then be found by plugging the eigenvalues into the equation Ax = λx and solving for x.
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Write a quadratic equation with a vertical shrink of 1/3, shifts left 2 and down 5.
The quadratic function is y = 1/3(x + 2)^2 - 5
How to determine the quadratic functionThe parent function of a quadratic function is represented as
y = x^2
From the question, we have the following parameters that can be used in our computation:
vertical shrink of 1/3, shifts left 2 and down 5.
This means that
y = a(x + h)^2 + k
Where
a = 1/3
h = 2
k = -5
So, we have
y = 1/3(x + 2)^2 - 5
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S
A store sells a toy car for $1 less than twice what it costs to make the car.
1. Make a table to relate the selling price, s, to the cost of making the
car, c. Then graph the ordered pairs on the coordinate plane.
с
1
2
3
S
1
2. Write an equation that describes the relationship.
selling price = 2 times the cost minus $1
1
s=_2 x
3. What is the selling price of a toy car that costs $4
to make?
7
6
5
4
3
2
1
S
0
0 1 2 3 4
The appropriate values in the table will be:
Cost selling price
1. 1
2. 3
3. 5
How to calculate the priceFrom the information, the store sells a toy car for $1 less than twice what it costs to make the car.
It should be noted that the selling price when the cost price is $1 will be:
= (2 × $1) - $1
= $1
It should be noted that the selling price when the cost price is $2 will be:
= (2 × $2) - $1
= $3
It hould be noted that the selling price when the cost price is $3 will be:
= (2 × $3) - $1
= $5
The equation that shows the relationship will be:
Selling price = 2c - 1
The selling price when cost price is $4 will be:
=(2 × $4) - 1
= $7
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Can you help me answer this
Answer: C
Step-by-step explanation:
A restaurant serves pancakes that are made from a powdered pancake mix there is a proportional relationship between the number of scoops and powdered pancake mix and the amount of water needed to make them for every four scoops of mix 1/2 quart of water is needed in for every 10 scoops of mixed one and 1/4 quarts of water are needed per day find the constant of proportionality show every step of your work part be right in equation that represents the relationship show every step of your work part Siri describe how you would grab the relationship use complete sentences party how many quarts of water are needed for 12 scoops of pancake mix (I NEED HELP FAST!!)
Nvm. I got it wrong me self. Srry:(
Please i need hhelp tysm!!
Answer:
The answer is 4×7×8 units³
Step-by-step explanation:
This is a really easy question. All you have to do is take a look at the prism and you see the height of 4 units, the width of 8 units, and the length of 7 units. To find the volume of a cube you have to multiply the Length, Width, and Height. Therefore, 7×8×4. Also, it doesn't matter the order of the numbers to multiply. Hope this helps!!
Which of the following is equal to
The expression equal to 5¹/₃ is ∛5 (option B)
What is an expression?The definition of an expression in math is a statement composed of terms and operations. The terms may be constant (numbers), or variables with coefficients. The operations may be addition, subtraction, multiplication, or division.
Given is an expression, 5¹/₃,
Using indices rule,
b¹/ₐ = [tex]\sqrt[a]{b}[/tex]
Therefore,
5¹/₃, here b = 5, a = 3
Therefore,
5¹/₃ = ∛5
Hence, the expression equal to 5¹/₃ is ∛5 (option B)
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What’s the answer for this problem
Answer:-8
Step-by-step explanation:
f(x)=-3x-2
f(2)=-3(2)-2
-6 - 2=
-8
Solve the system of equations − 3 � + 7 � = − 18 −3x+7y=−18 and 4 � − 4 � = 8 4x−4y=8 by combining the equations.
The solution of the Equation is x=1 and y= -3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
-3x + 7y = -18...........(1)
4x - 4y = 8.................(2)
Solving equation (1) and (2) we get
-12x + 28y = -72
12x - 12y = 24
____________
16y = -48
y= -48/ 16
y = -3.
and, -3x + 7(-3) = -18
-3x = 3
x= -1
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Solve for x
Urgent help pleaseee
Show proofs
Using the geometric mean theorem, the value of x is approximately 8.2.
What is the Geometric Mean Theorem or Altitude of a Right Triangle Theorem?The right triangle altitude theorem, also known as the geometric mean theorem, is a basic concept in geometry that connects the altitude of a right triangle to the two line segments it creates on the hypotenuse. According to the theorem, the altitude is equal to the geometric mean of the two line segments.
Using the theorem, we have:
14 = √(x * 24)
14² = 24x
196 = 24x
x = 196/24
x ≈ 8.2
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