42 is the answer to x3 y3 z3 K in sum of cubes problem.
How can I solve the sum of cubes problem?In mathematics, completely by accident, there is a polynomial equation whose solution, 42, has similarly baffled mathematicians for decades. The "sum of cubes problem" refers to the equation x3+y3+z3=k.
The "sum of cubes problem" refers to the equation x3+y3+z3=k. The most brilliant mathematicians in the world have been baffled by a mathematical problem for decades. A Diophantine equation known as "summing of three cubes" is x3+y3+z3=k, where k is the sum of all the numbers between one and 100. ∴ 3xyz will be the necessary outcome.
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Does sine law only work for acute angles?.
Sine law work's for acute angles ,obtuse angles and right triangles.
What is sine law?Sine Law states that "When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C.It is given by :
[tex]\frac{a}{sin A}= \frac{b}{sin B}= \frac{c}{sin C}[/tex]
The Law of Sines is valid for obtuse triangles as well as acute and right triangles, because the value of the sine is positive in both the first and second quadrant—that is, for angles less than 180°. You can use this relationship to solve triangles given the length of a side and the measure of two angles, or given the lengths of two sides and one opposite angle.
Sine law work's for acute angles ,obtuse angles and right triangles.
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The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. What is the 99th percentile for the mean height of a random sample of 20 adult women?.
The 99th percentile for the mean height of a random sample of 20 adult women is approximately 68.7 inches, which is 3.7 inches above the mean of 65 inches.
The 99th percentile for the mean height of a random sample of 20 adult women can be calculated using the normal distribution. The normal distribution is a bell-shaped curve that describes the probability of a given event occurring. In this case, the mean and standard deviation of the height of adult women is used to calculate the probability of the mean height of a sample of 20 adult women being a certain value. For the 99th percentile, this means that the probability of the mean of the sample of 20 adult women being equal to or less than the value of 68.7 inches is 99%. This value is 3.7 inches above the mean of 65 inches, which is the expected mean height of adult women.
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What type of angle turns through 1 360 of a circle?.
An angle that turns through 1/360 of a circle is called a “one-degree angle” and can be used to measure angles.
A degree, generally represented by the symbol ° (the degree), is a unit of measurement for a plane angle, where one full revolution equals 360 degrees.
A degree is the name given to the mathematical unit of measurement for an angle. A protractor is a device used to determine the degree of an angle. Angles can be measured at different angles with different degrees, such as 30°, 45°, 60°, and so on. A complete circle rotates at 360°.
One-degree angles are used to measure angles because they turn around 1/360 of a circle; an angle is said to have an angle measure of n degrees if it turns through n one-degree angles.
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Does someone mind helping me with this problem? Thank you!
The larger number is x = 71 and the smaller number y is 17
How to solve the equations?An equation is a mathematical statement showing the equality of two things.
The equations are
x = 14 +3y and x+y = 90
To solve the equations, we substitute x = 14 + 3y in the equation x +y = 90
⇒14+3y+y = 90
Collecting like terms to have
4y = 90-14
4y = 76
Making y the subject
y=76/4
y=19
By substitution we have
x=14+3(19)
x=14+57
Therefore the value of x = 71
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How to find acceleration with velocity and distance?
a new car is purchased for 13,000 and over time it's value depreciates
It would take approximately 12.6 years for the value of the car to be $700.
To find out how long it would take for the value of the car to be $700, we can use the formula for exponential decay. The value of the car after t years is:
[tex]V(t) = V_0 \times (1/2)^{(t/k)}[/tex]
Where V₀ is the initial value of the car, t is the time in years, k is the time constant in years, and (1/2) is the decay constant.
Given:
V₀ = $13,000
V(t) = $700
k = 3
Now you can solve for t:
[tex]700 = 13,000 \times (1/2)^{(t/3)}[/tex]
Take the natural logarithm of both sides:
[tex]ln(700) = ln(13,000 \times (1/2))^{(t/3))}[/tex]
[tex]ln(700) = ln(13,000) + ln((1/2)^{(t/3)})[/tex]
ln(700) = ln(13,000) + (t/3) × ln(1/2)
t = 3 × (ln(700) - ln(13,000))/ln(1/2)
t = 12.6 years (rounded to the nearest tenth of a year)
Thus, it would take approximately 12.6 years.
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The question seems to be incomplete the correct question would be:
A new car is purchased for $13,000 and over time its value depreciates by one-half every 3 years. How long, to the nearest tenth of a year, would it take for the value of the car to be $700?
Hunter recorded the mass of each rock in his collection. A dot plot has a horizontal axis labeled, Mass, in grams, marked from 35 to 45, in increments of 1. The number of dots above each value is as follows: 35, 2; 38, 2; 39, 2; 41, 1; 42, 1; 43, 2; 44, 1; 45, 1. Find the median mass. \text{ g} gstart text, space, g, end text
The median mass is given as follows:
40 g.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.
The dot plot shows the number of times that each measure appears in the data-set, hence the data-set is given as follows:
35, 35, 38, 38, 39, 39, 41, 42, 43, 43, 44, 45.
The data-set is composed by 12 elements, which is an even cardinality, hence the median is the mean of the two middle elements, the 6th and the 7th elements, thus:
Median = (39 + 41)/2 = 40.
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What is the value of k for which the quadratic equation 3x2 KX 3 0 has equal roots?.
If a quadratic equation's discriminant is equal to zero, then its roots are all identical..The format for quadratic equations is as follows: axe? + bx + c=0, where a 0.
If a quadratic equation's discriminant is equal to zero, then its roots are all identical. The format for quadratic equations is as follows: axe? + bx + c=0, where a 0.The coefficients a, b, and c are used to calculate the discriminant of such equations.
D will act as the discriminator. D= b – 4ac first, let's figure out what our equation's coefficients a, b, and c are.When the discriminant (D) of the equation equals zero, the equation 3x2 + Kx-30 has equal roots. The quadratic equation discriminant is provided by the equation D = b2 - 4ac, where a = 3, b = K, and c = -30. We obtain the following formula by substituting these values: D= K2 - 4(3) (-30)
D=K2 + 360 K2 = -360, and K=V - 360) = 6V as a result (-5)
D =0
k- 128 = 0
→ k= 128
k=tv128
k=t V64 x 2
k=t8v2
|S-{-8V2, 8V2}
Complete question:
What is the value of k for which the quadratic equation 3x2 KX 3 0 has equal roots?. And also Find the value of k if the quadratic equation 4x2 - kx + 8 = 0 has equal roots
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The value of k for which the quadratic equation 3x² + kx + 3 = 0 has equal roots is -3.
The condition for a quadratic equation to have equal roots is that its discriminant, which is given by the expression b² - 4ac, must be equal to 0. In this case, a = 3, b = k, and c = 3. Substituting these values into the expression for the discriminant gives us:
k² - 4 * 3 * 3 = 0.
Solving for k gives us
k = ±√(4 * 3 * 3) = ±6.
Since the coefficient of x in the equation is positive, both roots are real and equal only if k = -6. Hence, the value of k for which the equation 3x² + kx + 3 = 0 has equal roots is -3.
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Complete Question:
What is the value of k for which the quadratic equation 3x² + kx + 3 = 0 has equal roots?
i need answer by today
The vertical portion of this plane's path is 81 degrees because it is travelling at a 90-degree angle of depression. She will have 393.3 yards remaining after multiplying 450 by 45 by 126.
What is the smallest angle of the plane ?The vertical component of this plane's angle of descent is 81 degrees, or 90 degrees. The landing field is no longer in this location. This is the landing area. I have 450 points and a 126-degree angle. Since this is not a right triangle, I will apply the law of sins.
I'm going to perform my x over my sin of 45, which is equivalent to my 450 yards over the 126 point. I'll multiply 126 times by 45 times to get 450 times. Divide both sides by 126 degrees; we'll do that. She will have 393.3 yards remaining after multiplying 450 by 45 by 126.
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Prove that (1+cotA+tanA) (sinA-cosA) /sec³A-cosec³A = sin²Acos²A
Hope it helps.
If you have any query, feel free to ask.
A plumber's old rate is $62 per hour. She
increases her fees by 12%.
What will her new hourly rate be?
Answer:
69.44
Step-by-step explanation:
now is 100%
100%=1
12%=0.12
1.12*62=69.44
For every 7 push-ups Dulce can do, Sara can do 6. If Ducle did 28 push-ups during gym class, how many push-ups did sara do?
The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.
How to solve ratio?Number of push ups Dulce can do : number of push ups Sara can do
Let
number of push ups Sara does = x
7 : 6 = 28 : x
7/6 = 28/x
cross product
7 × x = 28 × 6
7x = 168
divide both sides by 7
x = 168/7
x = 24
Therefore, Sara does 24 push ups during the gym class.
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How do you write limits?.
A limit is generally written as
[tex]lim _{x- > c} f(x) = L[/tex]
It is read as “the limit of f of x, as x approaches c equals L”
A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. It is employed in the analysis process and constantly considers how the function will behave at a specific point. The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in theory category. In general, there are two sorts of integrals: definite integrals and indefinite integrals. The upper limit and lower limit for definite integrals are correctly defined.
Let us consider a real-valued function “f” and the real number “c”, the limit is normally defined as:
[tex]lim _{x- > c} f(x) = L[/tex]
It is read as “the limit of f of x, as x approaches c equals L”. The “lim” shows limit, and fact that function f(x) approaches the limit L as x approaches c is described by the right arrow.
Let us take an example to fully understand how to write limits.
[tex]lim_{x- > 2} 2x + 2[/tex]
= 2(2) + 2 = 6
This is how to write and represent limits.
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A TV wa priced at 250 euro before VAT of 20% wa added on. What wa the elling price of the TV
The selling price of the TV is 300 euro (250 euro original price + 20% VAT).
What is VAT(Value Added Tax) ?
VAT stands for Value Added Tax, it is a consumption tax that is added to the price of goods and services. VAT is imposed on most goods and services in many countries around the world, and it is usually a percentage of the sale price. The percentage can vary depending on the country and the type of goods or services being sold.
To calculate the VAT, we can use the formula:
VAT = (original price x VAT percentage) / 100
So, in this case:
VAT = (250 x 20) / 100 = 50
Now we add the VAT to the original price to find the selling price:
selling price = original price + VAT
250 + 50 = 300 euro.
Therefore , The selling price of the TV is 300 euro (250 euro original price + 20% VAT).
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VAT = (original price x VAT percentage) / 100
So, in this case:
VAT = (250 x 20) / 100 = 50
Now we add the VAT to the original price to find the selling price:
selling price = original price + VAT
250 + 50 = 300 euro.
Therefore , The selling price of the TV is 300 euro (250 euro original price + 20% VAT).
The monthly income of Ram i R. 40,000. If he pend 30% on food, 20% on education and
20% on clothing find:
i. Hi expenditure
ii. Hi monthly aving
iii. Hi yearly aving
All the parts of the given problem have been solved using the concepts of the percentage below.
It is given that the principal amount that Ram has, as his income is 40,000.
i) Ram spends 30% of his income on food
that will be,
40,000×30/100
=40,000×0.3
=12,000
ii) Ram spends 20% of his income on his education
that will be,
40,000×20/100
=40,000×0.2
=8,000
iii) Ram spends 20% of his income to buy his clothes
that will be,
40,000×20/100
=40,000×0.2
=8,000
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Solve for g.
156 = 13g
Answer:
[tex] \sf \: g = 12[/tex]
Step-by-step explanation:
Given equation,
→ 156 = 13g
Now the value of g will be,
→ 156 = 13g
→ 13g = 156
→ g = 156 ÷ 13
→ [ g = 12 ]
Hence, the value of g is 12.
How do you write a quadratic equation from roots Class 10?.
We are aware that x2(a+b)x+ab=0 is one such equation if a and b are the roots of a quadratic equation.
How can you tell whether or not an equation is quadratic?In other words, if a times the square of the phrase after b plus b times the same expression not squared plus c equals 0, then you have an equation with the quadratic form. The original equation will change to a quadratic equation if the value in the () is replaced with a variable like t.
What are the four approaches for locating a quadratic equation's roots?Factoring, using square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic problem.
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Vince wrote the following equation, where C is the circumference in inches, to represent the value of π
for a circle that he drew.
π=C10
The length the diameter of the circle will be 10 units. And the graph of the circle is given below.
What is the circumference of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let d be the diameter of the circle. The circumference of the circle will be
C = πd units
Vince wrote the following equation, where C is the circumference in inches, to represent the value of π for a circle that he drew. Then the diameter of the circle is calculated as,
π = C / 10
C = π x 10
πd = 10π
d = 10
The length the diameter of the circle will be 10 units. And the graph of the circle is given below.
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What is the answer to this question? (4x) + (x-5)
The answer is to the problem is 5x-5
How do you find the sum of a number?.
The sum is an Arithmetic operation that results in the addition of 2 values to get the final value. Let the first number be X and the second be Y. Adding X and Y, we get the resultant as, X + Y = Z.
Sum most commonly means the whole of two or greater numbers delivered collectively; see addition. A summation additionally known as a sum is the result of arithmetically adding numbers or portions. A summation constantly includes a whole range of terms. There can be as few as two terms, or as many as one hundred, a thousand, or one million. some summations include infinitely many terms.
In arithmetic, the summation is the addition of a chain of any form of numbers, called addends or summands; the result is their sum or general. the combination of two or extra numbers, magnitudes, portions, or details as decided via or as if via the mathematical technique of addition: The sum of 6 and 8 is 14. a selected combination or overall, specifically with regards to money: The fees came to a giant sum.
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Complete Question:
How do you find the sum of two numbers?
What is the GCF of 20z and 30z?
Answer:
10z
Step-by-step explanation:
20z=2*2*5*z
30z=2*3*5*z
common ones are 2, 5, z
2*5*z=10z
what is the slope of the line
Answer: 3/2
Step-by-step explanation:
To find the slope of the line, we are going to look at that change in rise (meaning the change of the y values) over the change in the run (meaning the change of the x values). The easiest way to do this is to pick two points on the line and use the slope equation: (y2-y1)/(x2-x1). I will pick two points at random, though multiple can work to find the slope.
point one: (1,-3) *it is easiest to make the first point to the left of point two*
point two: (3,0)
now, use the equation to solve.
(0 - -3)/(3-1) = (0+3)/(3-1) = 3/2
Hope this helps!
sketch the solution to each system of inequalities
The solution to the system of inequalities y ≤ 2x + 2 and y < -2x - 3 can be represented by a graph. The inequality y ≤ 2x + 2 represents a line with a slope of 2 and y-intercept of 2. The inequality y < -2x - 3 represents a line with a slope of -2 and y-intercept of -3. ( The graph attached)
SYSTEM OF INEQUALITIESThe inequality y ≤ 2x + 2 represents a line in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2 and the y-intercept is 2. To graph this inequality, we can first plot the line by using the y-intercept, which is the point (0,2) on the graph. Then, we can use the slope to find additional points that fall on the line, such as (1,4) or (-1,0). Once we have plotted several points, we can connect them to form the line.
The inequality y < -2x - 3 represents a similar line, but with a different slope and y-intercept. In this case, the slope is -2 and the y-intercept is -3. To graph this inequality, we can use the same process as before by first plotting the y-intercept (0,-3), and then using the slope to find additional points that fall on the line.
The solution to the system of inequalities is the area that lies on one side of the first line and the opposite side of the second line, which is the area between the two lines. This area can be represented by shading the region below the first line and above the second line on the graph. It is important to note that the solution region is not including the lines themselves, because the inequalities are strict inequalities.
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2(4+3(x-5))
Answer: 6x-22
-3(9-2(k+3)+5k)
Answer: -9k-9
Explain how you get the answer
Answer:
After that, the 3X + 1 problem has appeared in various forms. It is one of the most infamous unsolved puzzles in the word. Prizes have been offered for its solution for more than forty years, but no one has completely and successfully solved it [5].
Step-by-step explanation:
Angela check out 12 library book and Inola check out 1/3v le than that. How many book doe Inola check out?
Angela check out 12 library book and Inola check out 1/3v then Inola checked out 12 - 3 = 9 books.
What is algebra ?
Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a way to represent mathematical relations and to reason about them. Algebraic concepts include using variables (such as x or y) to represent unknown values, using operations such as addition, subtraction, multiplication and division.
We know that ,
Angela = 12 books
Inola = 1/3v less than Angela
To find the value of v, we can set up the proportion ,
12 = v + 1/3v
We can then solve for v by multiplying both sides by 3 ,
12*3 = 3v + v
36 = 4v
So, v = 9
Inola checked out 1/3v less than Angela, which is ,
1/3 * 9 = 3
So, Angela check out 12 library book and Inola check out 1/3v then Inola checked out 12 - 3 = 9 books.
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A line goes through (2,4) and has a slope of 1/2. Find a second point on the line
Answer:
(0,3)
Step-by-step explanation:
y = mx + b
[tex]y=\frac{1}{2}x+b[/tex]
[tex]4=\frac{1}{2}(2)+b[/tex]
4 = 1 + b
b = 3
[tex]y=\frac{1}{2}x+3[/tex]
'b' represents the y-intercept in slope-intercept form. Another point is (0,3)
Box A contain only green and purple counter. Box B contain only green, purple and orange counter. Juan pick one counter from box A and one counter from box B. How many poible way are there for Juan to pick exactly one purple counter
The number of possible ways in which Juan can pick exactly one purple counter from Box A and Box B is 3.
Given,
We know that, Box A contains only green and purple counters.
We also know that, Box B contains only green, purple, and orange counters.
According to question ,
Juan picked one counter from Box A and one counter from Box B
Possible ways to pick exactly one purple counter :
Box A Box B
one purple counter one orange counter
one purple counter one green counter
one green counter one purple counter
Hence, there are 3 ways in which Juan can pick exactly one purple counter.
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Logical Reasoning-
You have blue pants, green pants and a blue shirt, red shirt and an orange shirt so How many outfits can you make?
Using fundamental counting principle, the total total number of outfits that can be worn is 6.
A way for keeping track of all the possible outcomes in a circumstance is the fundamental counting principle.
If there are n ways to carry out one activity and m ways to carry out another activity after that, then there are n m n times n methods to carry out both of these activities, according to this assertion.
The Fundamental Principle of Counting dictates how choices are made depending on options.
The Fundamental Principle of Counting makes it easier to apply the selection method, which considers all feasible alternatives and their combinations for calculating the probability.
Total number of pants = 2
Total number of shirts = 3
Total number of outfits that can be worn = 3 × 2
= 6
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How many solutions does the following equation have − 15y 7 17y 2y 70?.
There is no solution for the given equation "-15y + 7 + 17y = 2y + 70".
We are given an equation.
"-15y + 7 + 17y = 2y + 70"
We have to calculate the number of solutions to the given equation.
"-15y + 7 + 17y = 2y + 70"
Rearrange the terms
-15y + 17y + 7 = 2y + 70
Combine like terms
2y + 7 = 2y + 70
Subtraction property of equality
2y - 2y = 70 - 7
Combine like terms
0 = 61
But it is not possible.
Thus, there is no solution for the given equation -15y + 7 + 17y = 2y + 70.
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Find the root of the equation D^2=36
Answer:
D = 6
Step-by-step explanation:
We can find D by:
[tex]D^{2*\frac{1}{2}} = 36^{\frac{1}{2}}[/tex]
We can multiply the square root of 1/2 to cancel out the 2 and put 36 into square root form, giving us:
D = [tex]\sqrt[2]{36}[/tex]
= 6
