The circumference of the table is 9.42 feet
What is circumference?The circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.
For a example a circular ball with diameter 7 cm will have a circumference of 44cm
The circumference of a circle is expressed as:
C = πd
C = 3.14 ×3
C = 9.42 feet
Therefore the circumference of the table is 9.42 feet.
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factor each polynomial by grouping
^(3)+4x^(2)+2x+8
4b^(3)-6b^(2)+10b-15
2m^(3)+4m^(2)+6m+12
7r^(3)-35r^(2)+6r-30
10a^(3)+4a^(2)+5a+2
The required factor each polynomial by grouping are factored.
What are polynomials?A polynomial is an algebraic expression in which the operators "+" and "-" are used to separate terms, and the exponents of the variables are consistently non-negative integers. Polynomials include, for instance, x² + x + 5, y² + 1, and 3x³ - 7x + 2.
According to question:1)1) [tex]x^3+4x^2+2x+8[/tex]
can be factored by grouping as:
[tex]x^3 + 2x + 4x^2 + 8[/tex]
= [tex]x(x^2+2) + 4(x^2+2)[/tex]
= [tex](x+4)(x^2+2)[/tex]
2) [tex]4b^3-6b^2+10b-15[/tex]
can be factored by grouping as:
[tex]2b^2(2b-3)+5(2b-3)[/tex]
=[tex](2b-3)(2b^2+5)[/tex]
3)[tex]2m^3+4m^2+6m+12[/tex]
can be factored by grouping as:
[tex]2m^2(m+2) + 6(m+2)[/tex]
= [tex](2m^2+6)(m+2)[/tex]
= [tex]2(m^2+3)(m+2)[/tex]
4) [tex]7r^3-35r^2+6r-30[/tex]
can be factored by grouping as:
[tex]7r^2(r-5)+6(r-5)[/tex]
=[tex](7r^2+6)(r-5)[/tex]
[tex]10a^3+4a^2+5a+2[/tex]
can be factored by grouping as:
[tex]2a^2(5a+2)+1(5a+2) = (2a^2+1)(5a+2)[/tex]
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Suppose ABC is a right triangle, and cos (B) =a/c, which of the following much also be true ?
Answer:
option 1 --> sec A = c/a
option 3 --> sin(b) = b/c
option 4 --> Sin(A) = a/c
Step-by-step explanation:
Since cos is adjacent, we know the legs are a and b and the hypotenuse is c
For angle B
sin (opposite over hypotenuse) = b/ctan (opposite over adjacent) = b/acsc (hypotenuse over opposite) = c/bsec (hypotenuse over adjacent) = c/bcot (adjacent over opposite) = a/bFor Angle A
sin = a/ccos = b/ctan = a/bcsc = c/asec = c/bcot = b/aThe volume of the cone is 471 cubic yards and the radius is 5. What is the height of the cone?
ues 13.4 for π
Answer:
Step-by-step explanation:
The formula for the volume of a cone is given by:
V = (1/3)πr^2h
where V is the volume of the cone, r is the radius of the base, h is the height of the cone, and π is the mathematical constant pi (approximately equal to 3.14159).
Substituting the given values, we get:
471 = (1/3) x 13.4 x 5^2 x h
Multiplying both sides by 3 and dividing by 13.4 x 25, we get:
h = 471 x 3 / (13.4 x 25)
h ≈ 6.98 yards (rounded to two decimal places)
Therefore, the height of the cone is approximately 6.98 yards.
what is the meaning of permutations and combinations?
Answer:
Step-by-step explanation:
Permutations and combinations are mathematical concepts that deal with counting the number of different arrangements or selections of objects from a set.
Permutations:
A permutation is an arrangement of objects in a specific order. For example, consider a set of three letters: A, B, and C. There are 3! = 6 possible permutations of these letters, which are ABC, ACB, BAC, BCA, CAB, and CBA. The notation "3!" is the factorial notation, which means 3 × 2 × 1.
Combinations:
A combination is a selection of objects, where the order does not matter. For example, consider a set of three letters: A, B, and C. There are 3 C 2 = 3 possible combinations of two letters from this set, which are AB, AC, and BC. The notation "3 C 2" is the combination notation, which means the number of ways to choose k objects from a set of n objects.
In summary, permutations deal with the arrangement of objects in a specific order, while combinations deal with the selection of objects without regard to the order.
what is the product?
The product is ( 2) option (B)
( 0)
What is scalar product?A scalar is a physical quantity that is completely defined by its magnitude. Dot Product: A dot product is the product of two vectors by taking the component of the second vector in the direction of the first vector. In the above diagram, there are two vectors A → and B → .
The scalar product is obtained by multiplying 2 by other value
2 × -1 = -2
2 × 0 = 0
therefore the scalar product is {2}
{0}
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two trains, train a and train b weigh a total of 537 tons. train a is heavier than train b. the difference if their weights is 421 tons. what is the weight of each train?
Answer:
Let the weight of Train A be x tons. Then the weight of Train B is 537 - x tons. We know that the difference between their weights is 421 tons, so we can set up an equation to solve for x:
x - (537 - x) = 421
Expanding the right side:
x - 537 + x = 421
Combining like terms:
2x = 958
Dividing both sides by 2:
x = 479
So Train A weighs 479 tons and Train B weighs 537 - 479 = 58 tons.
Step-by-step explanation:
To raise money for charity, Carmen and her friends start the Pampered Pooch Pet Wash. The first day they are open, they forget to put up posters and only raise a little money. The next day, they hang posters all over the neighborhood and raise $55.50. In all, Carmen and her friends raise $65.50 on the first two days they are open.
Julie will reach her goal 21 days before Mary.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
Mary and Julie both have a goal of raising $1000 for charity.
Mary raises money in every 4 days = $12.
In one day Mary raises money = 12/4
= $3
Mary needs time to reach her goal = 1000/3
= 333.33 ≈ 334 days
Julie raises money in every 6 days = $19
In one day Julie raises money = 19/6
= $3.1666 ≈ $3.2
Julie needs time to reach her goal = 1000/ 3.2
= 312.5 ≈ 313 days
Difference of the days between both of them to reach their goal
= 334 - 313 = 21 days
Julie will reach her goal first, 21 days before Mary.
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Camden just accepted a job at a new company where he will make an annual salary of $43000. Camden was told that for each year he stays with the company, he will be given a salary raise of $2000. How much would Camden make as a salary after 7 years working for the company? What would be his salary after
t years?
Answer:
Step-by-step explanation:
His salary after 7 years would be $57000 per year
Answer:
Step-by-step explanation:
the answer for this question would be $57,000.
What value for x makes the equation −13(x + 11) + 12x = -26 true
Answer:
x= -177
Step-by-step explanation:
−13(x + 11) + 12x =-26
x=-177
In many classes, a passing test grade is 60 (A = 60). Using the formula A = 10 R,
what raw score (R) would a student need to get a passing grade after her score is
adjusted?
A student need a raw score of 36.
How to determine the raw score (R) of the student?
We can find the raw score (R) of the student by substituting A = 60 into the the formula and then solve for R. That is:
A = 10√R
√R = 60/10
√R = 6
R = 6²
R = 36
Thus, a student need a raw score of 36 to get a passing grade after her score is adjusted.
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The average temperatures for two of the world's hottest places are given. Determine which location has the warmer average temperature and by how many degrees Fahrenheit
Location A: 85.3°F and Location B: 29.3°C
The location with the warmer average temperature is
(Round to the nearest tenth of a degree as needed.)
which is warmer by about F
Location A has the warmer average temperature, by about 0.6°F (rounded to one decimal place).
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To compare the temperatures of Location A and Location B, we need to convert the temperature of Location B from Celsius to Fahrenheit. We can use the formula:
°F = (°C × 9/5) + 32
Substituting the given temperature of Location B, we get:
°F = (29.3 × 9/5) + 32 = 84.74°F (rounded to two decimal places)
So, the average temperature of Location A is 85.3°F and the average temperature of Location B is 84.74°F (rounded to two decimal places).
Therefore, Location A has the warmer average temperature, by about 0.6°F (rounded to one decimal place).
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Find the measure of the missing angle
Answer:
a = 149 degrees
Step-by-step explanation:
Angles must add up to 180 degrees so,
180 - 31 = 149.
f(3/4) If f(x) =2x-1/4
If the given function is f(3/4), then evaluation of function (3/4) = 5/4.
What is expression ?
An expression is a mathematical phrase that can contain numbers, variables, and operators such as addition, subtraction, multiplication, and division. It can also contain functions, exponents, and other mathematical symbols.
Expressions can be used to represent a wide range of mathematical concepts, such as equations, inequalities, and formulas. They can be as simple as a single number or variable, or they can be more complex, involving multiple operations and variables.
What is function ?
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. In other words, a function is a rule or mapping that assigns a unique output to each input.
Functions can be expressed using a variety of mathematical expressions, such as algebraic formulas, graphs, and tables. They are used to model relationships between variables in many areas of mathematics, science, engineering, and other fields.
According t o given condition :
To find f(3/4), we simply substitute 3/4 in place of x in the given function f(x):
f(3/4) = 2(3/4) - 1/4
Simplifying the expression, we get:
f(3/4) = 6/4 - 1/4
f(3/4) = 5/4
Therefore, if the given function is f(3/4), then evaluation of function (3/4) = 5/4.
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find the sum. use your answer in the simplest terms, using the slash ( / ) as the fraction bar.
1/4 + 2/5
Answer:
Step-by-step explanation:
= 1/4 + 2/5
= 5/20 + 8/20
= 13/20
How do you make a transfer function in Matlab?
With MATLAB 's "t f" function, you may build a transfer function. A transfer function object is created by the "t f" function and can be used to manipulate transfer functions
So, you can create a transfer function with the aid of MATLAB's "t f" function. The "t f" function generates a transfer function object that can be used to manipulate transfer functions in a variety of ways, such as multiplying, adding, and inverting them. The MATLAB "t f" function can produce transfer functions using the following syntax. The numerator and denominator coefficients of the transfer function are "num" and "den", respectively and they are used to compute the system equation: sys = t f(num, den). The coefficients of "num" and "den" can be visualised as vectors, with "s" serving as the Laplace variable and the coefficients as descending powers of "s." Consider using the transfer function equation below as an example to create
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50 POINTS, Which statements describe the solutions to the inequality x less-than negative 20? Check all that apply.
There are infinite solutions.
Each solution is negative.
Each solution is positive.
The solutions are both positive and negative.
The solutions contain only integer values.
The solutions contain rational number values.
A little help is required please. I choose A, C, and E, Is this right?
The solutions can be any rational number less than -20. They do not have to be integers.
What is rational number?Real numbers are the set of all rational and irrational numbers, which include numbers such as integers, fractions, decimals, square roots, and transcendental numbers like pi and e. Real numbers can be represented on a number line, where each point corresponds to a unique real number. The set of real numbers is denoted by the symbol R. Real numbers are used in various branches of mathematics, including algebra, calculus, and geometry, and have applications in various fields such as physics, engineering, and economics.
Given to the question: -
No, your choices are not correct.
The correct choices are:
There are infinite solutions.
Each solution is less than negative 20.
Each solution is a real number.
The solutions contain rational number values.
To explain further:
The inequality x < -20 means that any value of x that is less than -20 is a solution. There are an infinite number of values less than -20, so there are infinite solutions.
Each solution is less than -20. Therefore, each solution is negative.
The solutions can be any real number less than -20, so they can be positive, negative or zero, but they must be less than -20.
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Can somebody help with number 8 find the value of each variable using the properties of a Parallelogram p
Answer: (9,8) A
Step-by-step explanation: how the mandle 10 30 6 150 144
solve this problem pls a question of inequality
Answer:
x > - 6
Step-by-step explanation:
[tex]\frac{x}{2}[/tex] > - 3 ( multiply both sides by 2 to clear the fraction )
x > - 6
If the measure of each central angle of a regular polygon is 60degree. What is the measure of each interior angle
The measure of each interior angle is 120 degrees.
In conclusion, the measure of each interior angle of a regular polygon with central angles measuring 60 degrees is 120 degrees.
Measure of each interior angleThe measure of each interior angle of a regular polygon with central angles measuring 60 degrees can be found using the formula (n-2)180/n, where n is the number of sides of the polygon.
First, we need to find the number of sides of the polygon. Since the measure of each central angle is 60 degrees, we can use the formula 360/n = 60 to find the number of sides.
Solving for n, we get: 360/n = 60 360 = 60n n = 360/60 n = 6 So the polygon has 6 sides.
Now we can use the formula (n-2)180/n to find the measure of each interior angle:
(6-2)180/6 = (4)180/6 = 720/6 = 120 degrees
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An antique dresser was $115, but is on sale for
30% off. If there is a 10% tax added to the sale
price, how much will the dresser cost?
Answer:
$88.55
Step-by-step explanation:
First find how much the 30% off discount will be.
115 x 0.30 = 34.5
Subtract it from original price
$115 - 34.5 = $80.5
Now find the 10% tax
80.5 x 0.10 = 8.05
Add that to the price
$80.5 + 8.05 = 88.55
The dresser's final sale price is $88.55
factor the following:
(a-b)*z+3(b-a)^2
The factored expression of (a-b) * 2 + 3(b-a)^2 is (-2 + 3(b - a))(b - a)
How to factor the expressionFrom the question, we have the following parameters that can be used in our computation:
(a-b)*z+3(b-a)^2
Express properly
So, we have
(a-b) * 2 + 3(b-a)^2
Rewrite as
-2(b - a) + 3(b - a)^2
Factor out b - a from the expression
So, we have
(-2 + 3(b - a))(b - a)
Hence, the factored expression is (-2 + 3(b - a))(b - a)
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Sydney and two of her friends want to
go to a concert by one of their favorite
bands. Sydney found a deal that was
$102.51 for three tickets. How much
does each ticket cost?
The cost of each ticket is $34.17
How to determine the cost of each ticketTo find the cost of each ticket, we need to divide the total cost of the tickets by the number of tickets.
In this case, the total cost of the tickets is $102.51 for three tickets.
So, to find the cost of one ticket,
We can divide $102.51 by 3:
Using the above as a guide, we have the following:
$102.51 ÷ 3 = $34.17
Hence, each ticket costs $34.17.
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in which situation would an accountant prepare a variance analysis?
Variance analysis is the quantitative investigation of the difference between actual and planned behavior. This analysis is used to maintain control over a business through the investigation of areas in which performance was unexpectedly poor.
Variance analysis is the study of deviations of actual behaviour versus forecasted or planned behaviour in budgeting or management accounting. This is essentially concerned with how the difference of actual and planned behaviors indicates how business performance is being impacted.
Comparing Budget with Actual: Variance analysis helps in managing the annual budgets by monitoring the budgeted figures and comparing it with the actual revenue/cost. In case of companies which are project or program driven, the financial data are evaluated at key intervals such as month close, quarter end, etc.
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Examine the graph.
How many times does Marc increase his speed during his drive to work?
A. Marc never increases his speed.
B. Marc increases his speed 3 times.
C. Marc increases his speed 2 times.
D. Marc increases his speed 1 time.
The required speed of the object increase only one time.
Explain about change in motion in graph?We can see how far an object has moved over time by looking at a distance-time graph. The motion is faster when the graph is steeper. A horizontal line indicates that an object is at rest and not altering position. A downward sloping line indicates that the thing is going back to the beginning.
According to question:As we can see that upwards and downwards in the graph, which says about the increase and decrease in speed of the object.
First speed of object increase, then constant for some time.After that it decreases and then constant, at last it was decrease.
So, the speed of car is increase only one time.
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Janice is at her favorite store checking out. She wants to buy a few shirts (s) that cost $14 each and a pair of jeans that cost $32. She wants to spend less than $88. How many shirts can she buy without going over her limit? Write an inequality to represent the scenario. Then, solve.
The number of shirts that Janice can buy without going over her limit is; 3 shirts
How to solve Inequality word problems?The number of shirts she can buy is denoted as s.
Cost of each shirt = $14
Cost of a pair of jeans = $32
She wants to spend less than $88.
Thus, the inequality that depicts this problem is;
14s + 32 < 88
Subtract 32 from both sides to get;
14s < 56
Divide both sides by 14 to get;
s < 4
Thus, maximum number of shirts will be 3 shirts
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La semana pasada Pedro y Pablo fueron al doctor a una consulta de rutina si Pedro pesa 43 kg y Pablo pesaba 94 libras quien pesa más ?
Pedro weighs slightly more than Pablo.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Examples:
1 hour = 60 minutes
1 minute = 60 seconds
1 km = 1000 m
We have,
Pedro weighs = 43 kg
Pablo weighs = 94 pounds.
Now,
1 kg = 2.205 pounds
Multiply 43 on both sides.
43 kg = 43 x 2.205 pounds
43 kg = 94.815 pounds
94.815 pounds > 94 pounds
We can see that Pedro weighs slightly more than Pablo.
Thus,
Pedro weighs slightly more than Pablo.
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The complete question in English.
Last week, Pedro and Pablo went to the doctor for a routine checkup. If Pedro weighs 43 kg and Pablo weighs 94 pounds, compare their weights to the same unit of measurement.
Who weights more?
ABCD is a parallelogram.
The diagonals of ABCD intersect at O.
OA = a and OB = b
a) Express the vector CA in terms of a.
b) Express the vector AB in terms of a and b.
c) Express the vector BC in terms of a and b.
Answer:
[tex]\textsf{a)} \quad \overrightarrow{CA} =2\textbf{a}[/tex]
[tex]\textsf{b)} \quad \overrightarrow{AB} =\textbf{b}-\textbf{a}[/tex]
[tex]\textsf{c)} \quad \overrightarrow{BC} =-\textbf{a}-\textbf{b}[/tex]
Step-by-step explanation:
A parallelogram is a quadrilateral where opposite sides are equal in length and parallel to each other.
The diagonals of a parallelogram are not equal in length, but they bisect each other (divide into two equal parts).
Therefore, if OA = a then CO = a.
Similarly, if OB = b then DO = b.
Part (a)
Express the vector CA in terms of a:
[tex]\begin{aligned}\overrightarrow{CA} &= \overrightarrow{CO} + \overrightarrow{OA}\\&=\textbf{a}+\textbf{a}\\&=2\textbf{a}\end{aligned}[/tex]
Part (b)
Express the vector AB in terms of a and b:
[tex]\begin{aligned}\overrightarrow{AB} &= \overrightarrow{AO} + \overrightarrow{OB}\\&= -\overrightarrow{OA} + \overrightarrow{OB}\\&= \overrightarrow{OB}-\overrightarrow{OA}\\&=\textbf{b}-\textbf{a}\end{aligned}[/tex]
Part (c)
Express the vector BC in terms of a and b:
[tex]\begin{aligned}\overrightarrow{BC} &= \overrightarrow{BO} + \overrightarrow{OC}\\&= -\overrightarrow{OB} - \overrightarrow{CO}\\&= -\overrightarrow{CO}-\overrightarrow{OB}\\&=-\textbf{a}-\textbf{b}\end{aligned}[/tex]
What is the value of the following function when x = 0?
y=-5
y=-2
Y=-1
Y= 0
The numeric value of the function when x = 0 is found replacing each instance of x by zero in the definition of the function.
If a graph is given, then the numeric value is given as the value of y when the function crosses the y-axis.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
Supposing we have a function definition, then the numeric value at x = 0 is found replacing each instance of x by zero.
On graph, x = 0 is when the graph of the function touches or crosses the y-axis.
Missing InformationThe problem is incomplete, hence the general procedure to obtain the numeric value at x = 0 was presented.
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What is the value of 50g in tbsp?
The conversion rate for grams to tablespoons is 1 gram is equal to 0.2 tablespoons. This conversion is useful for both converting small amounts of ingredients in recipes and converting larger amounts of ingredients in recipes.50 grams is equal to 10 tablespoons."
This means that 50 grams is equal to 10 tablespoons. To calculate the value of 50 grams in tablespoons, we can use the following formula:50 grams x 0.2 tablespoons = 10 tablespoons.The value of 50 grams in tablespoons is 10 tablespoons.To convert from grams to tablespoons, the basic formula is to multiply the weight in grams by 0.2. This conversion is useful for converting small amounts of ingredients in recipes, as many recipes call for weights in grams rather than tablespoons. For example, if a recipe calls for 20 grams of butter, this would be equal to 4 tablespoons. To convert from tablespoons to grams, the basic formula is to multiply the weight in tablespoons by 5. This conversion is useful for converting larger amounts of ingredients in recipes, as many recipes call for weights in tablespoons rather than grams. For example, if a recipe calls for 8 tablespoons of sugar, this would be equal to 40 grams. To summarize, the value of 50 grams in tablespoons is 10 tablespoons. This conversion is useful for both converting small amounts of ingredients in recipes and converting larger amounts of ingredients in recipes.
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Help with geometry. Given ABC is congruent to MNO. m < A = 51 , m < N = 67 , and m < B = (2x + 7) What is the value of x?
The value of x is given as follows:
x = 30.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.For the two similar triangles, we have that B and N are equivalent angles, hence they are congruent and the value of x is given as follows:
2x + 7 = 67
2x = 60
x = 60/2
x = 30.
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