If the product is positive integers is 32118, then the king's age is 53, his number of children is 6 and is length of boat is 101m.
What is integer?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
The puzzle demands for three numbers - x, y, z which represent the king's number of children, age and length of boat respectively.
It will be advantageous to conceive the problem thus: We have but one unknown; this unknown, however, is not a number but a tripartite unknown, a triplet (x, y, z) of numbers.
It is very important to split the condition that is expressed by the statement of the problem into appropriate clauses. This needs careful con-sideration of details and considerable regrouping. After several trials (which we skip to save space) we may arrive at the following two clauses:
(r1), x, y, and z are positive integers different from 1 and such that -
xyz = 32118
(r2) 4 ≤ x < y < 100
Begin with (r1) which leaves only a finite number of possibilities, whereas (r2), which does not restrict z at all, leaves an infinite number.
Therefore, we examine (r1). Now, 32118 is divisible by 6, and so we easily decompose it into prime factors:
32118 = 2 × 3 × 53 × 101
For a decomposition into three factors we have to combine two of the four primes. Therefore, there are only six different ways to decompose the number 32118 into a product of three factors all different from 1:
6 × 53 × 101
3 × 101 × 106
3 × 53 × 202
2 × 101 × 159
2 × 53 × 303
2 × 3 × 5353
Of these six possibilities, the remaining requirement (r2) rejects all except the first one, and so we obtain -
x = 6 , y = 53 and z = 101.
Therefore, the values of x, y and z are 6, 53 and 101 respectively.
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I need help please. I would like someone to make sure I have the right answer .
3 /4 + 1 /6 − 2/ 3 =
Answer:
Step-by-step explanation:
Answer: 1/4
Add: 3/4 + 1/6 = 3 · 3 / 4 · 3 + 1 · 2 / 6 · 2 = 9/12 + 2/12 = 9 + 2/12 = 11/12
Subtract: 1 - 2/3 = 11/12 - 2/3 = 11/12 - 2 · 4 / 3 · 4 = 11/12 - 8/12 = 11 - 8/12 = 3/12 = 3 · 1 / 3 · 4 = 1/4
Is the solution of the equation 2x y 5 and 3x 2y 11 *?.
The value of x=3 and y=1 is the solution.
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.
given equations are,
2x-y=5 and 3x+2y=11
Let 2x-y=5 ----[1]
, 3x+2y=11 ----[2]
Now, solving [1] and [2] by substitution method,
Substitute the value of x from [1] in [2],
x= [tex](\frac{5+y}{2})[/tex]
3x+2y=11
3[tex](\frac{5+y}{2})[/tex] + 2y = 11
[tex](\frac{15+3y}{2})[/tex] + 2y = 11
[tex](\frac{15+3y+4y}{2})[/tex] = 11
15 + 7y = 22
7y = 22 - 15
7y = 7
y = 1
Substitute the value of y=1 in [1],
2x - y = 5
2x - 1 = 5
2x = 6
x = 6 / 2
x = 3
Therefore, The value of x=3 and y=1.
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A sculptor begins work on a block of granite that has a mass of 400 kg. What is the density of the granite?
The method for density is d = M/V, where d is density, M is mass, and V is extent. Density is usually expressed in devices of grams in keeping with cubic centi meter.
what's the density of the granite?The common density of granite is between 2.65 and 2.75 g/cm3 (one hundred sixty five and 172 lb/cu feet), its compressive energy usually lies above hundred MPa (29,000 psi), and its viscosity close to STP is 3–6·1020 Pa·s.
GRN = GL * GW * GT/12 * a hundred seventy five
GRN is the Granite Weight (lb)
GL is the granite period (ft)
GW is the granite width (feet)
GT is the granite thickness (in)
The density of granite is high and tiers from 2.sixty three to two.75 g according to cm3. Its resistance to strain is between 1.000 and 1.4 hundred good enough in step with cm2.
Rock density can be very sensitive to the minerals that compose a particular rock kind. Sedimentary rocks (and granite), which can be rich in quartz and feldspar, have a tendency to be less dense than volcanic rocks.
Therefore, The method for density is d = M/V, where d is density, M is mass, and V is extent.
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What percentage of scores must fall within 4 standard deviations of the mean according to Chebyshev's theorem?.
Percentage of scores must fall within 4 standard deviations of the mean according to Chebyshev's theorem is 93.75%
Chebyshev's theorem states that the proportion of the data set that lies between k standard deviations from the mean be calculated with the formula below.
1 − 1/k²
which in this case is,
=1 − 1/4²
= 1− 1/16
=15/16
=0.9375
which is 93.75%.
According to probability theory, Chebyshev's inequality ensures that no more than a specific percentage of values can deviate significantly from the mean given a large class of probability distributions.
The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied with this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.
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For each rhombus, find each angle measure or segment length.
Answer:34xt25
Step-by-step explanation:
Please help me I am struggling ;((((
Answer:
X
[tex] \frac{y2 - y1}{x2 - x1} - \frac{y - y1}{x - x1} [/tex]
Step-by-step explanation:
in every point given put one as (x1, y1) and the other is (x2, y2)
simplify the formula and you'll get you linear equation
The ratio of consonants to vowels in a word is 7:5.Are there more vowels or consonants in the word?
Answer:
constants because
7 > 57>5
There u go
If consonants to vowels has a ratio of 7:5, this means there are 7 consonants for every 5 vowels. There are more consonants in the word.
don’t really understand can someone help me. how do you turn this into radical form
Answer :
The first one
Step-by-step explanation:
A cube root is a number that, when cubed, is equal to the given number.
It is denoted with an exponent of "1/3".
Example, the cube root of 27 is 27^1/3 = 3.
Now,
[tex]24^{ \frac{1}{3} } \: is \: the \: same \: as \: \sqrt[3]{24} [/tex]
From there, we can simplify
[tex] \sqrt[3]{24} \\ \sqrt[3]{2 \times 2 \times 2 \times 3} \\ \sqrt[3]{ {2}^{3} \times 3} \\ 2 \sqrt[3]{3} [/tex]
What is range in math class 8?.
The range in statistics for a given data set is the difference between the highest and lowest values.
As a result, the range can also be defined as the difference between the highest and lowest observations. The range of observation is the name given to the outcome. In statistics, the range indicates the dispersion of observations.
To find the range in statistics, we need to arrange the given values or set of data or set of observations in ascending order.
For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.
Thus, The range in statistics for a given data set is the difference between the highest and lowest values.
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What is 7 8 equivalent to in fractions?.
Equivalent 7/8 is equals to 56/64 in fractions.
In mathematics, equivalent fractions are those with the same denominator but different numerators. For instance, since they both equal 1, 2/4 and 3/6 are comparable fractions. An element of the whole is a fraction. To represent identical components of the total, equivalent fractions are utilized.
The numerator and denominator of each fraction can be multiplied by the same integer to determine the equivalent fraction. Equivalent fractions are those that, despite visible differences, signify the same value. For instance, if you take a piece of cake, divide it into two equal pieces, and then eat one of them, you will have consumed half of the cake.
= 7/8 is equivalent to:
= 7/8 * 8/8
= 56/64
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Correct Question:
What is 7/8 equivalent to in fractions?.
9x2+4y÷z 9 x 2 + 4 y ÷ z when x=23, x = 2 3 , y=3, y = 3 , and z=6?
The solution of the given expression 9x² + ( 4y / z ) will be 4763.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 9x² + ( 4y / z ) and the values are x=23, y=3, and z=6.
The expression will be solved as below,
E = 9x² + ( 4y / z )
E = 9 x ( 23 ²) + ( 4 x 3 ) / ( 6 )
E = 4761 + 2
E = 4763
Hence, the solution will be 4763.
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In 3 1/2 hours a car moving at 40 miles per hours (mph) will travel
miles
Answer: 140 mph
Step-by-step explanation:
3 1/2+40=140 mph
The number of miles traveled in 3(1/2) hours is 140 miles.
We have,
Speed is the ratio of the given distance and time.
It shows how fast an object is moving at a given time.
The formula of speed is used.
Speed = Distance / Time
From the given statement, make an expression.
1 hour = 40 miles
Multiply 3(1/2) on both sides.
3(1/2) hours = 3(1/2) x 40 miles
Simplify the mix fraction.
3(1/2) hours = 7/2 x 40 miles
Simplify the fraction.
3(1/2) hours = 7 x 20 miles
3(1/2) hours = 140 miles
Thus,
The number of miles traveled in 3(1/2) hours is 140 miles.
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if point A is (2,0) and point B is (2,12) What point divides the directed line segment AB¯¯¯¯¯ into a 3:1 ratio?
The coordinates of the point dividing the segment in the ratio 3:1 will be ( 38 / 4, 6 / 4).
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that point A is (2,0) and point B is (2,12) and the line is divided in the ratio of 3:1. the coordinate of the point will be calculated as,
Point = { ( mx₂ + nx₁ ) / ( m + n ) }, { ( my₂ + ny₁ ) / ( m + n ) }
Point = { ( 3 x 12 0 + ( 1 x 2 ) / ( 3 + 1 )], { ( 3 x 2 ) + 0 ) / ( 3 + 1) }
Point = { 38 / 4, 6 / 4 }
Hence, the coordinates of the point dividing the segment by a factor of three will be (38 / 4, 6 / 4).
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Alyson deposits $500 in the bank for 12 years. The bank offers her a 4% interest rate compounded monthly. How much money will be in her account at the end
of the 12 years? (Remember to round your answer to the nearest cent.)
A-$ type your answer.....
Answer:$917.58.
Step-by-step explanation:
The formula for compound interest is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the initial deposit is $500, the annual interest rate is 4%, the number of times compounded per year is 12 (monthly), and the number of years is 12.
So, we can plug in the values into the formula:
A = $500(1 + 0.04/12)^(12*12) = $500(1.003333333)^(144) = $500(1.835170816) = $917.585
The final amount in her account after 12 years is $917.58
To round to the nearest cent, we can use the following method:
If the digit in the thousandths place is less than 5, we keep the hundredths digit as is.
If the digit in the thousandths place is greater than 5, we round up the hundredths digit.
In this case the digit in the thousandths is 5 so, we have to round up the hundredths digit of $917.58.
So, the final amount in her account after 12 years is $917.59.
Answer: $800.516
Step-by-step explanation:
We use the equation
A = P(1 + )^nt
P = principal
r = rate of interest
t = times
Now let's solve
P = $500
r = 4% = 0.04
t = 12 years
A = $500(1 +[tex]\frac{0.04}{12}[/tex] ) ^12 = $800.516
Dylan is hosting a party she buys pumpkins 20 dollars each and balloons 2 dollars each she has a budget of 250 if x represents pumpkins and y represents balloons write an inequality that represents all possible ways she could buy a pumpkin and balloons what is the max number of ballons she could buy
Answer:
Dylan's budget is $250, and she is buying pumpkins for $20 each and balloons for $2 each. We can represent the total cost of the pumpkins as 20x and the total cost of the balloons as 2y. The inequality that represents all possible ways she could buy pumpkins and balloons within her budget is:
20x + 2y <= 250
To find the maximum number of balloons she could buy, we can use the equation above and set x = 0, and then solve for y.
20(0) + 2y <= 250
2y <= 250
y <= 125
The maximum number of balloons she could buy is 125.
How do you use the 3 4 5 triangle method?.
To get the sides of the right-angle triangle, we employ the 3 4 5 triangle method.
A right triangle is a particular kind of triangle that only has one right (90°) angle.A mathematical formula for determining the length of the third side of a right triangle given the lengths of the other two sides was developed by the Greek mathematician Pythagoras.
The sides of variables a and b make up the right angle of the triangle. Any side may make use of any variable. The variable c stands for the left side, or the side that leans away from the right angle. The longest side, or side c, is always present and is known as the hypotenuse.
Therefore, to determine the sides of the right-angle triangle, we employ the 3 4 5 triangle method.
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1) Evaluate.
8²=?
2) Evaluate.
5²=?
3) Evaluate.
13²=?
8² = 64 , 5² = 25 and 13² = 169 . A number that has been multiplied by itself produces a square number.
What is the squares of the given numbers ?8² = 8 × 8 = 64 , 5² = 5 × 5 = 25 and 13² = 13 × 13 = 169 . Informally: A square number, perfect square, or simply "a square" is what is produced when you multiply an integer (a "whole" number), positive, negative, or zero, times itself. So all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so forth.
Similar to numbers like 2, 3, 5, 6, 24, 13, 125, etc., 12, however, is not a square. Consequently, its simplicity is somewhat usual. nevertheless, are 4, 16, 25, 81, 121, and other numbers. It is incorrect to say that the number 14 is a perfect square because it cannot be written as the product of two equal numbers. If n is a number, then n2 stands in for n.
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Jackie’s pizzeria made 50 pizzas. 3 of the pizzas had thin crust and the rest had thick crust. What is the ratio of the number of thick-crust pizzas to the number of thin-crust pizza?
Answer:
47:3
Step-by-step explanation:
47 pizzas had thick crust and 3 had thin crust
You're planning on making 7 meatloafs for a party. You go to the store to buy breadcrumbs, and see they are sold by the canister. How many canisters do you need to buy?
First, determine what information you need to answer this question, then click here to display that info (along with other info).
You will need ___ canisters.
Give your answer accurate to at least one decimal place (You can only buy whole canisters, but this way you'll know how much you'll have left over)
You will need 2.8 canisters.
To determine this, you need to know the quantity of breadcrumbs required for one meatloaf and how many meatloafs you are planning to make. Since the breadcrumbs are sold by the canister, you will also need to know the quantity of breadcrumbs in one canister. With this information, you can calculate the total quantity of breadcrumbs required for all the meatloafs and divide it by the quantity of breadcrumbs in one canister to find out how many canisters you need to buy.
Write a sentence describing a situation that could be represented by the equation.
4 ÷ 1 1/3
The sentence which describes a situation which can be represented by the equation 4 ÷ 1 1/3 is, "4 divided by the fraction number 11 by 3"
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
An equation,
⇒ 4 ÷ 1 1/3
Mathematically, it represents that,
4 is divided by fraction number 11 by 3
or
Product of 4 and reciprocal of 11 divided by 3
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i need answer by today
What is the product of X+ a and x b )?.
The product of expressions ( x + a ) and (x + b ) is equals to the x² + (a - b)x - ab.
Product is an important arithmetic operation. The multiplication or product of algebraic expressions is a method of multiplying two expressions consisting of variables and constants. The product of two factors with the same signs will be positive, and the outcome of multiplying two terms with two, unlike signs, will be negative. We have two algebraic expressions as ( x + a) and ( x - b) and we have to calculate their product.
=> (x + a) ( x - b) = x( x- b) + a(x - b)
=> (x + a) ( x - b) = x² - xb + ax - ab
=> (x + a) ( x - b) = x² + (a - b)x - ab
Hence, required product is x² + (a - b)x - ab .
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Complete question:
What is the product of (x + a )and (x - b )?.
the graph of a sinusoidal function has a maximum point at (0,5) and then has a minimum point at (2pi,-5). write the formula of the function, where x is entered in radians
The equation of the function is y = 10 * sin(x/2pi) + 5.
What is the sinusoidal function?
The period of a sinusoidal function is the time it takes for the sinusoidal function to complete one cycle of revolution.
The graph of a sinusoidal function can be represented by the equation:
y = A * sin(B(x - C)) + D
where A is the amplitude, B is the frequency, C is the horizontal shift, and D is the vertical shift.
From the information given, we know that the maximum point is at (0,5) and the minimum point is at (2pi,-5). We can use this information to find the values of A, B, C, and D.
The amplitude is the distance between the maximum and minimum points. In this case, it is 5 - (-5) = 10. So A = 10.
The period of the function is the distance between two consecutive maximum or minimum points. In this case, it is 2π.
So the frequency is 1/2π.
The horizontal shift is the amount by which the function is shifted along the x-axis. In this case, the maximum point is at x = 0, so the function is not shifted horizontally. So C = 0.
The vertical shift is the amount by which the function is shifted along the y-axis. In this case, the maximum point is at y = 5, so the function is shifted upward by 5. So D = 5.
So the equation of the function is:
y = 10 * sin(1/2pi (x - 0)) + 5
y = 10 * sin(x/2pi) + 5
where x is entered in radians.
Hence, the equation of the function is y = 10 * sin(x/2pi) + 5.
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How do you change the base of a logarithm?.
To change the base of a logarithm, for example from base a to base c, we use the formula [tex]log_{a} (b)[/tex] = [tex]log_{c} (b)[/tex] / [tex]log_{c} (a)[/tex].
In order to change the base of a logarithm the following basic formula is used,
[tex]log_{a} (b)[/tex] = [tex]log_{c} (b)[/tex] / [tex]log_{c} (a)[/tex]
For example,
If we have to change the base of log₃(81) to base 5,
It will be written as
log₃(81) = log₅(81) / log₅(3)
The change of base rule is able to covert a logarithm in a given base to a logarithm in a new base. The result will be a quotient, which is a fraction, with the new logarithm as both the numerator as well as a denominator.
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what is 2 and 2/13 of 52
Answer:
the answer 112
Step-by-step explanation:
hope this helps
[Real world example] A sewage treatment centre fills a cylindrical silo with waste. The diameter is 20m and the height 5m. It is full to the top with 1300kg of waste. Find the density of the waste.
Step-by-step explanation:
density is mass/volume.
usually it is expressed as grams/cm³.
the question does not give us the information about the dimensions for density. so, I am going with my assumption.
the volume of a cylinder is
ground area × height
the ground area is a circle, so this is
pi×r²×height
r is the radius and therefore half of the diameter.
so, we have in our case as volume :
pi×(20/2)²×5 = pi×100×5 = 500pi = 1,570.796326... m³
1 m = 100 cm
1 m³ = 100×100×100 = 1,000,000 cm³
so, the volume of our cylinder is then also
1,570,796,326.7948966192... cm³
1 kg = 1000 g ("kilo" means 1000)
1300 kg = 1,300,000 g
so the standard density is
1,300,000/1,570,796,326.7948966192... g/cm³ =
= 0.000827606... g/cm3
The density of the waste is approximately 0.827 kg/m³.
What is density?A physical property is known as density gauges a substance's mass per unit volume. It is referred to as the mass-to-volume ratio.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base of the cylinder and h is the height.
Since the diameter of the silo is 20m, the radius is 10m. Therefore, the volume of the silo is:
V = π(10m)²(5m) = 500π m³
Since the silo is full to the top with 1300kg of waste, the density of the waste is:
density = mass/volume
density = 1300kg/(500π m³)
density ≈ 0.827 kg/m³
Therefore, the density of the waste is approximately 0.827 kg/m³.
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Can a linear system only have 2 solutions?.
Most linear systems will have exactly one solution. Nevertheless, it is possible that there are no solutions or infinitely many. (but It is not possible that there are exactly two solutions of a linear system.)
Let's assume a system of two linear equations, then, there are three possibilities of solutions.
The possibilities are:
Two parallel lines
e.g. y = 3x + 1
y = 3x − 2 (with the same slope, different intercepts)
Two (distinct) intersecting lines
As we know two straight lines cannot meet at two points. Two points determine only one line (not two lines).
e.g. y = 3x + 1
y = 5x − 2 (different slopes)
These equations have the same line as their graphs
If two lines do have two points in common, then "the lines coincide" (which really means "there is only one line".) In this case, we say, "the two lines are the same".
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Sorry for the markings but I need help ASAP. Please help!!
Answer: 72 + 2x = 180
Step-by-step explanation:
4x-8=3x+72
please answer in linear equations
By calculating, The sides of the given triangle 5x+1 , 2x+3 and 5x+2 are 51,23,52 respectively.
What is triangle ?
Triangle can be defined in which it consists of three sides, three angles and the sum of three angles is always 180 degrees
Given expression ,
4x-8 = 3x+2
4x-3x = 2 + 8
x = 10
So the sides given in the triangle are 5x+1 , 2x+3 and 5x+2
So put x=10 in the give sides
we get,
5x+1 = 5*10 + 1 = 51
2x+3 = 2*10 + 3 = 20 + 3 =23
5x+2 = 5*10 + 2 = 50 + 2 = 52
The sides of the given triangle 5x+1 , 2x+3 and 5x+2 are 51,23,52 respectively.
Hence, By calculating, The sides of the given triangle 5x+1 , 2x+3 and 5x+2 are 51,23,52 respectively.
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