The area of a circle is a function equal to the product of pi (pi) and the square of the radius (r). Which of the following shows this function?
The function for the area of the circle if x is the radius of the circle and y is the area of the circle is y = πx².
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely cover the surface of a closed figure.
Given:
The area of a circle is a function equal to the product of pi (pi) and the square of the radius (r),
The area of the circle can be written as shown below,
Area of circle = π × R²
Here π is a constant, R is the radius of the circle,
When we put the value of the radius, we will get the value of the area,
Hence, the radius is an independent function and the area is dependent on the value of R (dependent function),
Replace y with area and radius with x as shown below,
y = πx²
Thus, y = πx² is the function for the area of the circle.
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In Andrew’s Furniture Shop, he builds bookshelves and tables. Each type of furniture takes him about the same time to make. He figures he has time to make at most 18 pieces of furniture by this Saturday. The materials for each bookshelf cost him $20.00 and the materials for each table cost him $45.00. He has $600.00 to spend on materials. Andrew makes a profit of $60.00 on each bookshelf and a profit of $100.00 for each table. How many of each piece of furniture should Andrew make to maximize profit?
Andrew should determine the number of bookshelves and tables to make by using linear programming to solve for the variables given the constraints of his time, material costs, and profits. The optimal solution lies where the constraints intersect within the feasible region.
The student inquired about how many bookshelves and tables Andrew should make in order to maximize profit, given the constraints of time, material cost, and the profit from each item sold. This is a typical problem that can be solved using linear programming, a method in mathematics to achieve the best outcome given a series of linear constraints.
First, let us define two variables: x for the number of bookshelves and y for the number of tables. The constraints given by Andrew's situation are:
x + y \<= 18 (time constraint to make the furniture)
20x + 45y \<= 600 (cost constraint for materials)
Profit function to maximize: P = 60x + 100y
To maximize the profit P, we need to solve for x and y within the given constraints. After setting up the equations, we can graph the constraints and find the feasible region. The solution will be at a vertex of the feasible region, given by the intersection of the constraints. Andrew can use methods like the graphical method, the simplex method, or an algebraic method to find the optimal numbers of bookshelves (x) and tables (y) to maximize his profit.
Please Help!! find the solution of this system of equations 2x - 2y= -38 -5x - 4y= 23
y = 72.
Solving the System of Equations
To find the solution of the system of equations given by 2x - 2y = -38 and -5x - 4y = 23, we can use the method of elimination or substitution. In the method of elimination, we can multiple the first equation by 2 to make the coefficients of y the same, which would give us 4x - 4y = -76. Then, we could add this new equation to the second given equation (-5x - 4y = 23) to eliminate the y variable:
4x - 4y = -76 (First equation multiplied by 2)
-5x - 4y = 23 (Second given equation)
Adding these equations together, we get:
-1x + 0y = -53
or simply
-x = -53, from which x = 53.
Next, we can substitute x back into either of the original equations to solve for y. For example, using 2x - 2y = -38:
2(53) - 2y = -38
106 - 2y = -38
-2y = -38 - 106
-2y = -144
y = 72
Therefore, the solution to the system of equations is x = 53 and y = 72.
NEED HELP FAST!!!
4.
Which of the following graphs shows a pair of lines that represent the equations with a solution (–2, 5)? (5 points)
8 - 14 + 95 - (-105) +(-111) - 63=? whats the answer?
Four more than half of a number is at least nine. What is the number ?
Consider the following set of equations:
Equation A: y = −x + 5
Equation B: y = 6x − 2
Which of the following is a step that can be used to find the solution to the set of equations?
−x = 6x + 2
−x − 2 = 6x + 5
−x + 5 = 6x – 2
−x + 5 = 5x
Answer:
C)
Step-by-step explanation:
both of the equations equal y so, the two equations equal eachother
The perimeter of a triangle is 133 inches. If one side of the triangle is five more than the shortest side, and the longest side is 14 more than the shortest side, find the lengths of the three sides?
133=x + (x+5) + (x+14)
133 = 3x+19
3x=114
x= 114/3 =38
5+38 =43
38+14 =52
check: 38 +43 +52 = 133
3 sides are : 38, 43 & 52
What is the quotient of 78,600 divided by 12
Martin earned the following scores on his last five tests. 98, 78, 84, 75, 91 What is the range of his scores?
7
20
23
84
The product of two consecutive even positive integers is 674 more than the sum of the two integers. Find the integers.
The equation is A ( A + 2 ) = 674 + ( A + ( A + 2 ) )
The first integer is A = 26
The second integer is B = 28
What is an 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.
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 data ,
Let the two numbers be A and B
where , the first integer is = A
The second integer is = B
B is the consecutive integer of A , so
The value of B = A + 2
Now , the equation will be
The product of two consecutive even positive integers is 674 more than the sum of the two integers
So , substituting the values in the equation , we get
A ( A + 2 ) = 674 + ( A + ( A + 2 ) )
On simplifying the equation , we get
A² + 2A = 674 + 2A + 2
Subtracting 2A on both sides of the equation , we get
A² = 674 + 2
A² = 676
Taking square roots on both sides of the equation , we get
A = 26
The value of B = A + 2
B = 28
Therefore , the value of A = 26
The value of B = 28
Hence ,
The first integer is A = 26
The second integer is B = 28
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how many three digit positive integers are there such that the three digits are 3, 4, and 8?
math question down below
what is pm/ pn equal to
To simplify a fraction by dividing both top and bottom by the same factor.
So, pm/ pn equals to m/n .
If any variable or factor is present in both numerator and denominator. Then, these variables or factor are cancelled out each other.
In expression pm/pn , we observed that variable p is present in both numerator and denominator. So, variable p is cancelled out to each other.
Therefore, pm/pn = m/n
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Find the equivalent 3/7=x/21
You want to get new carpet for a square room that has an area of 150 square feet. You can only order carpet using dimensions to the nearest whole foot. What would be the dimensions of the carpet so that the entire room is covered?
Write 4 3/7 as a decimal.
Enter your answer as a decimal rounded to the nearest hundredth, like this: 4.25
The decimal form of the number 4 3/7 is, 4.43
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The number is,
⇒ 4 3/7
Now, We can change in decimal form as;
⇒ 4 3/7
⇒ 31 / 7
⇒ 4.43
Thus, We get;
⇒ 4 3/7 = 4.43
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8 = x divided by 12.8
Which of the following statements is always true?
A All integers are counting numbers.
B All rational numbers are integers.
C All integers are whole numbers.
D All counting numbers are whole numbers.
D. All counting numbers are whole numbers.
All integers are counting numbers. This is not true. Counting numbers (also known as natural numbers) are positive whole numbers starting from 1, 2, 3, and so on. Integers include all positive and negative whole numbers, as well as zero. Thus, not all integers are counting numbers.
All rational numbers are integers. This is not true. Rational numbers include all fractions where the numerator and denominator are integers (denominator not zero). For example, 1/2 is a rational number but not an integer.
All integers are whole numbers. This is not true. Whole numbers include all non-negative integers (0, 1, 2, 3, ...), but integers also include negative numbers, which are not whole numbers.
Counting numbers (1, 2, 3, ...) are included in the set of whole numbers, which consists of all non-negative integers (0, 1, 2, 3, ...).
What does solution to the division mean and what does it tell you
364861210 what's the next number
The solution to m + (-38) = 15 is 53. True False
solve the equation 5.25x+6=74.25
What are the factors of 60a
Answer:
20
Step-by-step explanation:
Factor x^2 - 64 into two binomials
PLZ I need the answer ..IK IK but plzzz ;c
-2 (x-3) + 4 x - 6 need the answer soon
An item is regularly priced at $15. It is now priced at a discount of 55% off the regular price.
What are five pairs of integers with the sum of -6?
How can you use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages?
To fit data to a normal distribution and estimate population percentages, calculate the mean and standard deviation for the data set, use these values to construct a normal distribution, and apply the empirical rule and confidence intervals to estimate population percentages.
Explanation:To use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages, you will need to understand key statistical principles such as standard deviation, the mean, and the normal distribution curve.
Mean and Standard Deviation
The mean, which is an average of all the values in a data set, provides a central value. The standard deviation represents the spread of the data around this mean. A lower standard deviation indicates that the values are closer to the mean, while a higher standard deviation indicates a wider spread.
Fitting Data to a Normal Distribution
A normal distribution, also known as a bell curve, shows how values in a data set are dispersed around the mean. The properties of the normal distribution (68% of data within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations) are known as the empirical rule or the 68-95-99.7 rule.
Estimating Population Percentages
To estimate population percentages using the mean and standard deviation, you construct a confidence interval. This range provides an estimate of where you expect the true population parameter to lie with a certain level of confidence. For example, a 95% confidence interval means that you can be 95% confident that the true population mean lies within this interval.
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If 1/2 gallon of paint covers 1/6 of a wall then how much paint is needed for the entire wall
The number of gallons of paint to cover the entire wall will be 3 gallons of paint.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
If 1/2 gallon of paint covers 1/6 of a wall. Then the division of the numbers 1/2 and 1/6 will be given by putting a division sign between them. Then the number of gallons of paint is calculated as,
⇒ (1/2) / (1/6)
⇒ (1/2) x 6
⇒ 3
The number of gallons of paint to cover the whole wall will be 3 gallons of paint.
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