Step-by-step explanation:
For all the recent strides we’ve made in the math world, like how a supercomputer finally solved the Sum of Three Cubes problem that puzzled mathematicians for 65 years, we’re forever crunching calculations in pursuit of deeper numerical knowledge. Some math problems have been challenging us for centuries, and while brain-busters like the ones that follow may seem impossible, someone is bound to solve ‘em eventually. Maybe.
For now, take a crack at the toughest math problems known to man, woman, and machine.
1. The Collatz Conjecture

DAVE LINKLETTER
Earlier this month, news broke of progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao’s breakthrough is good news, the problem isn’t fully solved.
A refresher on the Collatz Conjecture: It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any natural number, apply f, then apply f again and again. You eventually land on 1, for every number we’ve ever checked. The Conjecture is that this is true for all natural numbers.
Tao’s recent work is a near-solution to the Collatz Conjecture in some subtle ways. But his methods most likely can’t be adapted to yield a complete solution to the problem, as he subsequently explained. So we might be working on it for decades longer.
The Conjecture is in the math discipline known as Dynamical Systems, or the study of situations that change over time in semi-predictable ways. It looks like a simple, innocuous question, but that’s what makes it special. Why is such a basic question so hard to answer? It serves as a benchmark for our understanding; once we solve it, then we can proceed to much more complicated matters.
The study of dynamical systems could become more robust than anyone today could imagine. But we’ll need to solve the Collatz Conjecture for the subject to flourish.
Answer:
Sorry brillant26 or whatever gave you a invalid answer. its actually A (25 employees on the company email list) and D (25 employees at a company wide assembly)
Hope this helps!!
Have a nice day!!
Step-by-step explanation:
Please help ! I don’t get it!
Answer:
PR = 16
SR = 12
Step-by-step explanation:
6/8 = (x-3)/(x+1)
8x-24 = 6x+6
simplify
2x = 30
x = 15
PR = 15 + 1 = 16
SR = 15 - 3 = 12
The charge for a bicycle repair was $9.28 for parts, 1/4 hour of labor at $18 per hour, and a $2 shop fee. What was the total cost (c) of the repair?
Answer:
15.78
Step-by-step explanation:
4 goes into 18 (4 quarters in 1 hour), 4.5 then 4.50+ 9.28+2= $15.78
Fred helped his mom make 40 dozen cupcakes for the last bake sale. For this sale, he is going to help make 20% more cupcakes. How many dozen cupcakes will Fred and his mom make?
Answer:
48 dozen cupcakes
Step-by-step explanation:
20 percent more is 120 percent overall, which as a decimal is 1.2. Multiply 40 by 1.2 and you have your answer.
1.2 * 40 = 48
Hopefully this helps- let me know if you have any questions
2/3 of a number is 8 what is the number?
Answer:
12
Step-by-step explanation:
8/ (2/3) = 12
The value of number is,
⇒ x = 12
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
2/3 of a number is 8
Let us assume that,
A number is, x
Hence, We can formulate;
⇒2/3 of x = 8
⇒ 2/3 × x = 8
⇒ 2x = 3 × 8
⇒ 2x = 24
⇒ x = 12
Thus, The value of number is,
⇒ x = 12
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If a punch bowl hold 216 ounces of punch how many 8 ounce glasses can be filled from the punch bowl
Answer:
27 glasses
Explanation:
216 divided by 8 is 27
What is the equation of the line with slope 13 and y intercept-6
Answer:
y = 13x - 6
Step-by-step explanation:
Hope This Helps ;)
Plz Mark Brainliest!!!
Problem
Evaluate 6 + x when x = 3
Answer:
9
Step-by-step explanation:
6+x x=3
6+3=9
What is the CIRCUMFERENCE of this pie?
Give an approximate answer by using 3.14 for π.
SHOW YOUR WORK!
I really need help on this!
hii! i just wanted to say hope you're having a fantastic day and hope that things are going well (: stay strong and stay safe!
Find the value of x.
Round to the nearest tenth.
16
30°
30
x = [?]
Answer:
X=18.0
Step-by-step explanation:
It says round to the nearest tenth, which is 1 digit after the . Even though 18.02 is correct it wants you to round so X= 18.0
Final answer is X=18.0
The value of x is 18.0 rounded to nearest tenth.
What is a cosine law?Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.
u² = s² + t² - 2(s)(t)·cos U
We are Given Triangle with sides, 16, 30, and x, and a measure of an angle corresponding to x = 30°
Required: Value of x to the nearest tenth
Using the Cosine rule:
c² = a² + b² - 2abcos(C)
Let c = x, a = 16, b = 30
C = 30°
Thus,
c² = 16² + 30² - 2 x 16 x 30 x cos 30°
c² = 256 + 900 - 960 x 0.8660
c² = 1,156 - 831.36
c² = 324.64
c = √324.64
c = 18.017769
x ≈ 18.0 (rounded to nearest tenth)
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A polynomial f (x) and one or more of its zeros are given.
f(x)=x4 - 6x° +52x² +36x – 348
3-7i is a zero
Part: 0/3
Part 1 of 3
(a) Find all the zeros. Write the answer in exact form.
If there is more than one answer, separate them with a comma.
Select "None" if applicable.
The zeros of f(x):
Answer:
+52
Step-by-step explanation:
True or False.
The expressions 3 + y and 1/3 (6 + y) are equivalent?
Answer:
false
Step-by-step explanation:
consider y = 3
its 6 for one and 3 for the other
What is the circumference of the circle with a radius of 31
Answer:
circumference = 194.68
Step-by-step explanation:
c = π2r
c = (3.14)(2)(31) = 194.68
2/3 times 21=
i need help again!!!
Answer:
14
Step-by-step explanation:
The series converges by the Limit Comparison Test. Each term is less than that of a convergent geometric series. The series converges by the Limit Comparison Test. The limit of the ratio of its terms and a convergent p-series is greater than 0. The series diverges by the Limit Comparison Test. Each term is greater than that of the divergent p-series. The series diverges by the Limit Comparison Test. The limit of the ratio of its terms and the harmonic series is greater than 0.
Answer:
hello your question has some missing information attached below is the complete question
answer : The series diverges by the Limit Comparison Test. The limit of the ratio of its terms and the harmonic series is greater than 0.
Step-by-step explanation:
steps to determine if the series converges
step 1 : apply series limit comparison test
step 2 : consider Cauchy's convergence condition ; which states that ∑an converges if and only if for every ∈ > 0 there is a natural number N
attached below is the detailed solution
Pls help ASAP math plsssss
Answer:
ASAP meaning as soon as possible
Answer:
y= 1.4x + 7
Step-by-step explanation:
y= mx + b
m = rise over run = 7/5 = 1.4
the y intercept is 7, this is our b
What is the value of pi to the hundred-thousands place. (Answer quickly going for 45 points)
Answer:
3.14159
Step-by-step explanation:
pi
Question 4
12 marks
4.1 a. In each case find the unit cost and then state which is the better buy.
4 marks
6kg of potatoes for $2.45 or
15 kg of potatoes for $5.9 or
10 kg of potatoes for $3.92?
Answer:
The better buy is to buy 10 kilograms of potatoes at $ 3.92, since each kilogram costs $ 0.392.
Step-by-step explanation:
To find the cost per unit in each case and then state which is the better buy, the following calculations must be performed:
6kg of potatoes for $ 2.45:
2.45 / 6 = 0.408
15 kg of potatoes for $ 5.9:
5.90 / 15 = 0.393
10 kg of potatoes for $ 3.92:
3.92 / 10 = 0.392
Thus, the better buy is to buy 10 kilograms of potatoes at $ 3.92, since each kilogram costs $ 0.392.
I’m confused on this one I have one more
Answer:
because the diagonals are congruent, you're going to set them equal.
2x+13=4x-1
13=2x-1
14= 2x
x=7
it's that easy
What is the problem 3/2 X h = 2
Answer:
h = 4/3
1/2 of 4/3 is 2/3
4/3 + 2/3= 6/3, or 2
A sketch of a new dog park in town is shown below. How many square feet will the dogs have to roam
and play?
Answer:
they will have 432 ft to play
a rectangular garden will be fenced on all four sides. If 120 ft. of fencing are available, what should be the dimensions of garden to maximize the area? What is the maximum area
Answer:
30 by 30. Area=900
Step-by-step explanation:
The dimensions of the garden to maximize the area are length + width = 60 and the maximum area is 900 ft².
A rectangular garden will be fenced on all four sides.
120 ft. of fencing is available, what should be the dimensions of the garden to maximize the area and What is the maximum area to be determined.
The rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.
The perimeter of the rectangle = 120
Perimeter = 2 (length + width)
120 =2(length + width)
length + width = 120/6
length + width = 60 - - - -(1)
So, the sum of the sides of the rectangle should not increase by 120.
Now, the Maximum area of a rectangle,
Let Length = width
Equation 1
Length + Length = 60
length = 60/2
length = 30 = width
Area of the rectangle = length * width
= 30 * 30
= 900 ft²
So the maximum area of the rectangle is 900ft²
Thus, the dimensions of the garden to maximize the area is length + width = 60 and maximum area is 900 ft².
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Which statement best describes the effect on a image when it is reflected over the x axis
Answer:
Vertical flip
Rocky pays a flat rate of $5 per month plus $0.10 per minute for
his long-distance phone plan. He wants his total monthly bill to be
less than $20.
Need Help
What solid would be created by rotating the figure above about line m?
Cone
Triangular Pyramid
A good ol' triangle
Triangular Prism
PLEASE HELP ILL GIVE BRAINLIEST!!
Answer:
Step-by-step explanation:
Since it is ROTATED about the vertical line a cone is formed.
PLSSSSS HELP I WILL GIVE BRAINLIEST TO CORRECT ANSWER
A: 49
B:45
C: 20.1
D:114
(3x-11)+(6x-10)+x=180
10x-21=180
10x=201
x=20.1
(I think I did that right)
8) A box of 12 light bulbs fell
and some are broken. If there
are 4 broken bulbs:
a) What fraction of the
bulb is broken? Write
answer in its lowest
term.
Answer: 2/3
Step-by-step explanation:
12 lightbulbs and 4 are broken
12-4=8
8/12
/2
4/6
/2
2/3
So I have a grade of 100.6 (an A+) and I had this assignment that was due a while ago (that was 15 points) and now I’m not allowed to turn it in. What would be my grade now that I didn’t do that assignment?
Answer:
maybe an 80 or 90
Step-by-step explanation:
Write an algebraic expression for each:
the sum of a number and 45
12 more than a number
the difference of 1 and a number
13 subtracted from a number
Answer:
X + 45
X + 12
1 - x
X - 13
Step-by-step explanation:
Using the keywords sum of, more than, and subtracted will help you. (You can also flip the expression since it didn't say how.
Pre calculus law of sines
Answer:
AB = 6.5
Step-by-step explanation:
C = 59°
AC = 7
CD = 6
AB = ?
Apply the Law of Cosines, which is AB² = AC² + CD² - 2(AC)(CD)*Cos(C)
AB² = 7² + 6² - 2(7)(6)*Cos(59)
AB² = 85 - 43.26
AB² = 41.74
AB = √41.74
AB = 6.5 (nearest tenth)