Answer: A
Step-by-step explanation: 2.5 inches = 63.5 millimeters
Fractional index
Without using mathematical table simplify the following
(16/81)^-3/4
Answer:
[tex]\frac{27}{8}[/tex]
Step-by-step explanation:
using the rules of exponents/ radicals
• [tex](\frac{a}{b}) ^{-m}[/tex] = [tex](\frac{b}{a}) ^{m}[/tex]
• [tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a}) ^{n}[/tex]
then
[tex](\frac{16}{81}) ^{-\frac{3}{4} }[/tex]
= [tex](\frac{81}{16}) ^{\frac{3}{4} }[/tex]
= [tex]\frac{(\sqrt[4]{81})^3 }{(\sqrt[4]{16})^3 }[/tex]
= [tex]\frac{3^3}{2^3}[/tex]
= [tex]\frac{27}{8}[/tex]
any help please — Put the fractions 12,38 and 34 in order from smallest to largest. Find the value of 113+256.
The value of 113+256 is determined by the above fractional formulae. Is 369
Why are fractional equations difficult to solve?An exact number that shows a percentage of a total is called a fraction. You may figure it out by dividing a sum by the quantity of parts. As an example, the number 12 represents one-half of a whole number or an object. Simple subtraction of the smaller numerator from the larger numerator will yield the solution to the problem. To solve, for instance, 6/8 - 2/8, just take 2 out of the answer. The answer, which can be abbreviated to "4/8," is 12, or 12.
Making a fraction simpler by reducing or simplifying it is our goal. In order to do this, we divide the denominator and numerator by the largest integer that can be divided into both integers precisely. That is to say,
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What is the solution of the system of equations? Show your work.
4x - 2y = 10
2x + y = -3
Answer:
no solutions
Step-by-step explanation:
you have to divide the whole first equation by 2 and you would get
2x+y=5
2x+y=-3
That is not true the same thing can’t have different outcomes.
it is no solution
Which property of equality illustrates the statement "If AC = 14, then BD + AC = BD + 14?"
A. Transitive Property of Equality
B. Symmetric Property of Equality
C. Division Property of Equality
D. Substitution Property of Equality
'Substitution Property of Equality' illustrates the statement "If AC = 14, then BD + AC = BD + 14" from the question.
What is property of equality?
The equality characteristics define the relationship between two equal quantities. If a mathematical operation is applied to one side of an equation, it must also be applied to the opposing side to keep the equation balanced.
The Substitution Property of Equality states that if we know that two expressions are equal, we can substitute one of them for the other in any equation.
In this statement, it is stated that "If AC = 14, then BD + AC = BD + 14." Here we substitute 14 for AC in BD + AC = BD + 14. Which means that if we know that AC = 14, we can substitute 14 for AC in any equation, and the equation will still be true.
Therefore, given statement illustrates the Substitution Property of Equality.
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Frank does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at least 6 hours. He spends at most 12
hours on weight training. He spends at most 3 hours doing cardiovascular work. Letx denote the time (in hours) that Frank spends doing cardiovascular work.
Let y denote the time (in hours) that he spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.
The expression can be written as x ≤ 3 + y ≤ 12 ≥ 6. which is an inequality.
What is inequality?
A mathematical operator that expresses the inequal comparison between different numbers or different variables and numbers. There are various types of inequalities such as greater than >, less than <, greater than or equal ≥ and less than or equal ≤
How to express the inequality as per given statement?
Frank participates in exercise program at least 6 hours in each week.
He spends at most 12 hours on weight training
y denotes the time in hours that he spends on weight training.
Frank spends at most 3 hours doing cardiovascular works
x denotes the time in hours that he spends doing cardiovascular works
The expression that can represent the above statement.
can be written as
x ≤ 3 and y≤ 12
x ≤ 3 + y ≤ 12 ≥ 6
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the set {...,-2,-1,0,1,2...} is called what?
Answer: Set of integers
Integers are positive and negative whole numbers, with 0 included.
Answer: Set of Integers
Step-by-step explanation:
{...,-2,-1,0,1,2...}
since we can see that here is a zero as well as positive and negative numbers, therefore, we call this set, a set of integers.
hope that helps...
Here are two number machines that always give the same number for any input. Use the machines expressions to explain why both machines will produce the same outputs for any input.
The sum of any three different even numbers is odd.
Which of the following statements must be true based on the diagram below?
Select all that apply. (Diagram is not to scale.)
As a result, after studying the diagram below of triangle and considering the reasons that follow, the appropriate answers are 1, 2, 3, and 4.
Define triangle.Any three points in a plane can be connected to create triangles, which are polygonal (shapes) with three sides and three angles. They are among the first shapes in geometry that are explored. Since each polygon (with 4, 5, 6, or n sides) may be divided into triangles, triangles are particularly significant.
Here,
A segment bisector in this case is 1)OP.
Since segment LKMN is not divided into two equal sections, NO OP is not a segment bisector.
A perpendicular bisector is
2)OP.
NO,Because a perpendicular bisector creates an angle to the normal and divides a segment into two equal halves, OP is not a perpendicular bisector.
The angle bisector NO is OP.
Due to the fact that OP they do not divide any angles into two equal pieces.
4) The diagram's vertex of a pair of congruent angles is O.
YES Since O lines connect two angles with the same degree ()
5)O is the right angle's vertex.
NO
As a result of things not being at a straight angle.
6) A segment's midway in the diagram
By drawing diagonals across the four vertices LMNK, it is possible to determine where this segment's midpoint lies.
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Please I need help also please explain your answer and show the work
1. The degree form of 4π/9 is approximately 228.6°.
2. A positive coterminal angle to -123° that is between 500° and 750° is 677°. A negative coterminal angle to -123° that is between -300° and -500° is -243°.
3. The terminal side of 215° lies in the second quadrant.
4. The radius of the circle is approximately 15.7.
1. The degree form of 4π/9 is approximately 228.6°. To express an angle in degrees, we multiply its radian measure by 180°/π.
2. A positive coterminal angle to -123° that is between 500° and 750° is 677°. A negative coterminal angle to -123° that is between -300° and -500° is -243°. To find a coterminal angle, we can add or subtract 360° as many times as necessary to bring the angle into the desired range.
3.
In the standard position, an angle is measured counterclockwise from the positive x-axis. The positive x-axis corresponds to the 0° angle, the positive y-axis corresponds to the 90° angle, the negative x-axis corresponds to the 180° angle, and the negative y-axis corresponds to the 270° angle. Angles in the first quadrant are between 0° and 90°, angles in the second quadrant are between 90° and 180°, angles in the third quadrant are between 180° and 270°, and angles in the fourth quadrant are between 270° and 360°.
So, the terminal side of 215° lies in the second quadrant.
4.
We can set up the equation l = Cθ/2π and solve for r.
Substituting the given values, we have 56π = (2πr)(120°/180°), which simplifies to r = 56π/(2π) = 28.
Dividing this value by 2, we get the radius of the circle as approximately 15.7.
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The fourth term of an arithmetic sequence is 20. The common difference is -1/5 times the first term. What is the first term? Graph the sequence.
As a result, the first term of the answer to the given arithmetic mean problem is 14.
What does arithmetic mean?The Arithmetic Mean or Average of the Group is the product of the sum of all the numbers in a group and the amount of items in that list, divided by both. The Geometric progression is also same as this .This average of the numbers 5, 7, and 9 is, for instance, 4, as 5 + 7 + 9 is 21, and 21 split by 3 [there really are three numbers] equals 7.
Here,
In this case, t(n) = (a + ((n — 1) * d)),
The value of the nth term is t(n),
The first term of the AS is a.
The position of a value in the A.S. is represented by the positive whole integer n, and
The constant common difference among A.S. words is d.
In light of the question, we can say:
11 = (5 + ((4 — 1) * d)),
Take 5 away from both sides.
11 — 5 = (5 + ((4 — 1) * d)) — 5,
On the RHS, the fives cancel one another out.
6 = 3d,
d = 2.
In summary, the common distinction is: 2.
=> 20 = a + 3d
=> 20 - 6
=> a =14
As a result, the first term of the answer to the given arithmetic mean problem is 14.
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Now you will write an informative paragraph that will help Frankie to understand his financial options and formulate best practices for spending and saving.
Answer:
Strategies that Frankie should consider:
1.) What he needs vs what he wants (does Frankie need new shoes?)
2.) Opportunity cost (savings Frankie would have to give up if he buys new shoes)
3.) Short-term and long-term goals (Does Frankie needs shoes now, or can he wait?)
Frankie should think about a number of options before purchasing a new pair of shoes. He should first consider whether he actually needs or wants these shoes. He should then think about opportunity cost. How else could he have used that money if he had not purchased the shoes? Could he have utilized his resources more effectively? He must also think about the issue of setting goals. He needs to decide if this is a task for the present or the future.
Also I dont understand how this is math
find the volume of the following solids:
The volume of the solid is 104 cubic centimeters.
What is cuboid?A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.
Given:
We have the cuboid.
And the height of the cuboid is 2 centimeters.
Length = 9 centimeters.
Width = 8 centimeters.
The volume of a cuboid is,
= Length × Width × Height Cubic units.
= 9 x 8 x 2
= 144 cubic centimeters.
And we have missing part of the cuboid.
And the height of the missing cuboid is 2 centimeters.
Length = 9-4 = 5 centimeters.
Width = 8 - 4 = 4 centimeters.
The volume of the missing cuboid is,
= Length × Width × Height Cubic units.
= 5 x 4 x 2
= 40 cubic centimeters.
So, the required volume,
= Total volume - missing volume
= 144 - 40
= 104 cubic centimeters.
Therefore, the required volume is 104 cubic centimeters.
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The table at the right shows data representing a polynomial function. Answer A, B, and C.
a) The degree of the polynomial is 5.
b) The second difference is -726 -126 -6 114 714
c) The difference when they are constant is 480.
What is a polynomial?
A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.
y values: -999 -140 -7 0 1 116 945
1st difference 859 133 7 1 115 829
2nd difference -726 -126 -6 114 714
3rd difference 600 120 120 600
4th difference -480 0 480
5th difference 480 480
The degree of a polynomial is the number of difference where it is constant.
The degree of the polynomial function is 5.
The constant is the 5th difference which is 480.
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Timothy bought a house for $360,000. He paid 20% down, and agreed to pay $1,375.69 per month for 30 years. His payment of $1,375.69 does not include property tax and insurance. How much interest will Timothy pay in 30 years?
INTREST-300000
Step-by-step explanation:
36000000
with a 5% sale discount the price of an item is $38 what was the original price
Answer:
[tex]38 \div5 \\ [/tex]
A question on a test asks students to find the speed at which a car travels. The graph shows a proportional relationship between the distance traveled in miles and time in hours. billy incorrectly says that the speed of the car is 1/68 mile per hour. What is the speed of the car? What error might have billy made?
The car travels at the speed of 68 miles per hour.
Billy made error on substitution process.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
The graph shows a proportional relationship between the distance traveled in miles and time in hours.
That means,
distance traveled in miles/ time in hours = k,
where k is a proportional constant.
Here, k is the speed.
The incorrect speed is,
1/68 miles per hour.
k = 1/68.
From the graph,
distance = 272 miles
And the corresponding time is 4 hours.
So, the speed,
= distance / time
The speed = 272 / 4
The speed = 68 miles per hour.
Billy made the error of not substituting the right values to the formula.
Therefore, the speed of the car is 68 miles per hour.
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The complete question is given in the attached image.
Identify the quotient and the remainder
(24x^3 - 14x^2 + 20x +6)÷(4x^2 - 3x +5)
The quotient is (6x + 1) and the remainder is (-7x + 1).
What is a factor of a polynomial?
We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given A cubic polynomial 24x³ - 14x² + 20x + 6 divided by 4x² - 3x + 5.
So, (24x³ - 14x² + 20x + 6)/(4x² - 3x + 5).
= (4x² - 3x + 5)(6x + 1) + (-7x + 1)/(4x² - 3x + 5) in rhe form N = DQ + R.
The same applies to the division of polynomials.
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YZ ≅ VW, WX ≅ UV, and XY ≅ UZ. Complete the proof that △UVZ ≅ △XWY.
Evaluate fraction with negative 3 raised to the seventh power times negative 3 squared in the numerator and negative 3 raised to the fifth power in the denominator.
−81
−27
27
81
Answer:
Last option, 81.
Step-by-step explanation:
Evaluate, [tex]\frac{(-3)^{7}(-3)^{2} }{\ (-3)^{5} }[/tex]
[tex]\frac{(-3)^{7}(-3)^{2} }{\ (-3)^{5} }[/tex] => [tex]\frac{(-3)^{7+2} }{\ (-3)^{5} }[/tex] => [tex]\frac{(-3)^{9} }{\ (-3)^{5} }[/tex] => [tex](-3)^{9-5}[/tex] => [tex](-3)^{4}[/tex] => [tex](-3)(-3)(-3)(-3)[/tex] => [tex]81[/tex]
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Let C be the number of children who used the public swimming pool and A be the number of adults.
The total number of people at the pool is given by the equation: C + A = 660
The total cost of admission for all the people at the pool is given by the equation: 1.5C + 2.5A = 1279
Solving the system of equations using substitution, we get:
A = 289 and C = 371
There were 371 children and 289 adults at the public pool on the hot summer's day.
a book cost $36 is on 25% discount sale how much does the customer needs to pay for the discounted book
Given,
The cost of the book is $36 There is a 25% discount on all itemTo Find : Amount the customer needs to pay for the discounted book
In order to convert Discount % to Discount we use the formula
[tex]D = \frac{25}{100} X36\\D = 9[/tex]
SP = 36 - 9
SP = $27
2. A number m is less than -3 or greater than or equal to 1.
The absolute value of m is equal to the positive distance between m and 0.
What is value?Value is an important concept in economics, finance, and accounting. It is the worth of a thing, such as a product, service, or currency. Value can be determined by the amount of goods or services it can exchange for, or the amount of money it can produce. Value is subjective, so it is up to the individual to decide what is valuable to them. Value is also a measure of the relative worth of a good or service, and it can have an effect on the price of a good or service. Value is an important concept to understand in economics, finance, and accounting.
The absolute value of m can be calculated by taking the distance between m and 0, regardless of whether m is negative or positive. For example, if m is -7, the absolute value of m is 7, since the distance between -7 and 0 is 7. If m is 3, then the absolute value of m is also 3, since the distance between 3 and 0 is also 3.
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The absolute value of m is equal to the positive distance between m and 0.
What is value?Value is an important concept in economics, finance, and accounting. It is the worth of a thing, such as a product, service, or currency. Value can be determined by the amount of goods or services it can exchange for, or the amount of money it can produce. Value is subjective, so it is up to the individual to decide what is valuable to them. Value is also a measure of the relative worth of a good or service, and it can have an effect on the price of a good or service. Value is an important concept to understand in economics, finance, and accounting.
The absolute value of m can be calculated by taking the distance between m and 0, regardless of whether m is negative or positive. For example, if m is -7, the absolute value of m is 7, since the distance between -7 and 0 is 7. If m is 3, then the absolute value of m is also 3, since the distance between 3 and 0 is also 3.
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Need help solving this please
Answer:
30 students
Step-by-step explanation:
First, we need to find exactly how many students went to school by car and how many went on the bus.
To do this, we simply multiply the fraction of students that used each transportation method by the total number of students.
[tex]\# \textrm{ of students by car} = \dfrac{3}{8} \times 240 = \dfrac{3 \times 240}{8} = \dfrac{720}{8} = 90 \textrm{ students}[/tex]
So, 90 students went to school by car.
[tex]\# \textrm{ of students on bus} = \dfrac{6}{12} \times 240 = \dfrac{1}{2} \times 240 = \dfrac{240}{2} = 120 \textrm{ students}[/tex]
So, 120 students went to school on the bus.
The number of students that walked to school is the same as the number of students who didn't go in a car or on the bus, so to find the number of students that walked to school, we can subtract the number of students that went by car and on the bus from the total number of students.
[tex]\# \textrm{ of students that walked} = 240 - 90 - 120 = 30 \textrm{ students}[/tex]
Rounded to the nearest inch what is the circumference of a circle with a radius of 15 inches
Answer:
95.25 or 95
Step-by-step explanation:
[tex]C=2\pi r[/tex]
C = 2 x [tex]\pi[/tex] x 15 = 94.24778in = 94.25 or 95
Hope I helped you my dear friend.
how many times does 6 go into 137
Answer: 22 times
Step-by-step explanation: divide 137 by 6
when a fraction has a small numerator and a bigger denominator what you notice about the percent
when a fraction has a small numerator and a bigger denominator, the percent would be a proper fraction.
What is percent?A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100.
As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol “%” represents it.
Therefore, When a fraction has a small numerator and a large denominator, it is a proper fraction.
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Shaikha types at a rate of 34 words per minute. How many words does she type in 2 minutes?
Answer:
68 words
Step-by-step explanation:
If 34 words are typed in a minute what about two minutes hence take 34×2
Answer:
68
Step-by-step explanation:
What is a rate?A rate can be a quantity, or frequency, measured against a different quantity or amount.
If we know that Shaikha can type at a rate of 34 words per minute, and we need to figure out how many words she can type in 2 minutes, we can use an equation that looks like this:
Let m = minutes, w = words per minute and t = total words
m × w = t
Simply just insert your numbers into the equation.
2 × 34 = 68
Therefore, the number of words, or rate, that Shaikha types in 2 minutes is 68.
Write the expression d-7 / 2 in words
Answer:
The expression "d-7 / 2" can be written in words as
Step-by-step explanation:
The expression "d-7 / 2" can be written in words as "the quotient of d minus 7, divided by 2".
This is the operation of subtracting 7 from d and then dividing the result by 2.
A growing amusement park is able to sell 7 times as many tickets each year as it did the year before. If you list the number of tickets sold over time, what kind of sequence will you see?
tysm ;-;
The kind of sequence that you will obtain when you list the number of tickets sold over time is given as follows:
A geometric sequence.
How to classify the sequence?A sequence can be classified as either arithmetic or geometric, as follows:
Arithmetic sequence: the difference between consecutive terms is constant.Geometric sequence: the ratio between consecutive terms is constant.If none of these statements is true, then the function is neither arithmetic or geometric.
A growing amusement park is able to sell 7 times as many tickets each year as it did the year before, which means that there is a constant ratio of 7 between the amounts of tickets sold each year, and thus this sequence is a geometric sequence.
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