.For any positive integer n, prove that n^3 - n is divisible by 6.
Answers
Answer:
Step-by-step explanation:
Related Questions
Only 0.6% of the students at a high school did not attend the first football game. Write 0.6% as a fraction and as a decimal
Answers
Answer:
here my answer
Step-by-step explanation:
hope this helps
A path is made of red tiles and blue tiles.
1/5 of the tiles are red.
a) Write down the ratio of red tiles to blue tiles in its simplest form.
Answers
Answer:
The ratio of red tiles to blue tiles is 1 to 4.
Step-by-step explanation:
Since 1/5 of the tiles are red, 4/5 of the tiles are blue, giving the ratio of red tiles to blue tiles as 1 to 4.
Which of the following choices simplifies -(-x + 1)?
-x − 1
x − 1
-x + 1
x + 1
Answers
Answer:
x-1 is ur answer :)
Step-by-step explanation:
I WILL GIVE 100 PRECENT BRAINLIEST. PLS ANSWER THIS CORRECTLY,DUE IN A DAY.
[tex]x^{2} =3x-1 , x^{2} +\frac{1}{x^{2} }= what[/tex].
pls answer correctly,will mark brainliest for 100 percent real.
Answers
Answer:
7
Step-by-step explanation:
1. Solve for x in [tex]x^2 = 3x - 1[/tex].
[tex]x=\frac{3+ \sqrt{5}}{2} ,\frac{3- \sqrt{5}}{2}[/tex]
2. Substitute [tex]x=\frac{3+ \sqrt{5}}{2} ,\frac{3- \sqrt{5}}{2}[/tex] into [tex]x^2 + \frac{1}{x^2} = y[/tex].
[tex]\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2} = y[/tex]
3. Solve for y in [tex]\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2} = y[/tex]
[tex]y=\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2}[/tex]
4. Therefore,
[tex]x=\frac{3 + \sqrt{5} }{2}, \frac{3-\sqrt{5}}{2}\\y=\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2}[/tex]
............
[tex]x= \frac{3-\sqrt{5}}{2}[/tex]≈[tex]0.381966011, y=7[/tex]
[tex]x= \frac{\sqrt{5}+3}{2}[/tex]≈[tex]2.618033989, y=7[/tex]
Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Please rate and click the Thanks button if it helped you out. Brainliest would be MUCH appreciated. Have a great day!
Stay Brainy!
−Kallmekrish
The best way to predict the future is to create it.
- Abraham Lincoln, Past U.S. President
Answer:
7
Step-by-step explanation:
Given equation: [tex]x^2=3x-1[/tex]
Rearrange so that it is equal to zero:
[tex]\implies x^2-3x+1=0[/tex]
Quadratic formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
Using the quadratic formula to solve the given equation:
[tex]\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(1)} }{2(1)}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{5}}{2}[/tex]
[tex]\implies x^2=\dfrac{7 \pm 3\sqrt{5}}{2}[/tex]
Substituting this into [tex]x^2+\dfrac{1}{x^2}[/tex]
[tex]\implies \dfrac{7\pm3\sqrt{5}}{2}+\dfrac{1}{\dfrac{7\pm3\sqrt{5}}{2}}[/tex]
[tex]\implies \dfrac{7\pm3\sqrt{5}}{2}+\dfrac{2}{7\pm3\sqrt{5}}[/tex]
[tex]\implies \dfrac{(7\pm3\sqrt{5})(7\pm3\sqrt{5})}{2(7\pm3\sqrt{5})}+\dfrac{4}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{(7\pm3\sqrt{5})(7\pm3\sqrt{5})+4}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{49\pm42\sqrt{5}+45+4}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{98\pm42\sqrt{5}}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{14(7\pm3\sqrt{5})}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{14}{2}[/tex]
[tex]\implies 7[/tex]
Based on data from two very large independent samples, two students tested a hypothesis about equality of population means using α = 0. 2. One student used a one-tail test and rejected the null hypothesis, but the other used a two-tail test and failed to reject the null. Which of these might have been their calculated value of t?
Answers
Based on the calculations, the most likely value of t is equal to 2.2.
Given the following data:
[tex]\alpha =0.2[/tex]What is a null hypothesis?A null hypothesis ([tex]H_0[/tex]) can be defined the opposite of an alternate hypothesis ([tex]H_a[/tex]) and it asserts that two (2) possibilities are the same.
For the one-tail test, we would reject the null hypothesis ([tex]H_0[/tex]) when the p-value is lesser than the value of [tex]\alpha[/tex];
[tex]H_o: P(Z > |\delta|) < 0.02[/tex]
For the two-tail test, we would fail to reject the null hypothesis ([tex]H_0[/tex]) when the p-value is greater than the value of [tex]\alpha[/tex];
[tex]H_o: 2P(Z > |z|) > 0.02\\\\H_o: P(Z > |z|) > 0.01[/tex]
Next, we would determine the positive value of z-score that satisfies this expression;
[tex]0.01 < P(Z < z) < 0.02\\\\[/tex]
From the z-table, we have:
[tex]P(Z > 2.326)\;and\; P(Z > 2.054)\\\\2.054 < z < 2.326[/tex]
Therefore, t = 2.2.
Read more on null hypothesis here: https://brainly.com/question/14913351
NEED ANSWERS QUICKLY, CORRECT ANSWER GETS BRAINLIEST!
Answers
Answer:1.25
Step-by-step explanation:5/1/4=1.25
3a+2(4a-b)
please simplify this equation with processing
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[tex]\bf \colorbox{black} {\bf {\textcolor{blue}{topic= }{ \bf { \textcolor{orange}{mathematics= }{ \bf{ \textcolor{cyan}{answer = }}}}}}}[/tex]
3a+2(4a-b)=
3a+8a-2b=
[tex] \bf \textcolor{green}{ \underbrace{11a - 2b}}[/tex]
xLasersx✨There are 30 students in Mrs. Jones class. 20% of the students received an A on the last math test. How many students received an A?
Answers
Answer:
20% of 30
= 20/100 * 30
= 6
hence 6 students recieved A grade
pls help i’ll reward brainliest
Answers
Answer:
A. y = 2x + 2
Step-by-step explanation:
For this function....
f(0) = 2
f(1) = 4
f(2) = 6
f(3) = 8
I hope this helps!
The sum of 3 consecutive numbers is 240 what are the 3 numbers?
Answers
Answer:
79, 80, 81
Step-by-step explanation:
Creating an equation.
let a = first number , a + 1 = second number and a + 2 = third number
the sum of these three consecutive numbers is 240
this means that , a + ( a + 1 ) + ( a + 2 ) = 240
Solving for x using the equation created.
a + ( a + 1 ) + ( a + 2 ) = 240
==> remove parenthesis
a + a + 1 + a + 2 = 240
==> combine like terms
3a + 3 = 240
==> subtract 3 from both sides
3a = 237
==> divide both sides by 3
a = 79
Finding the 3 numbers
First number = a
a = 79 so first = 79
Second number = a + 1
a = 79 so second number = 79 + 1 = 80
Third number = a + 2
a = 79 so third number = 79 + 2 = 81
The three numbers are 79, 80 and 81
Answer:
79+80+81=240
Step-by-step explanation:
240/3=80
take 1 away from 80 and add 1 to 80
1. What is the algebraic expression for the following word phrase:
a. the sum of 4x and 3
b. the quotient of 5 and the sum of 9 and y
C.
the quotient of 7 and y
Answers
Answer & Step-by-step explanation:
a. 4x + 3 {sum means add the numbers together}
b. [tex]\frac{5}{9 + y}[/tex] {quotient means divided by}
c. [tex]\frac{7}{y}[/tex]
4
Elijah is given a birthday cake. He is rather selfish and does not share this cake with anyone
else. On the first day he eats 2/5 of the cake and on the second day he eats 3/7 of the cake. What
fraction of the cake is now left?
Answers
Answer:
6/35
Step-by-step explanation:
so he ate 2/5 first day, and the 3/7 the other day, so we need to add the 3/7 to 2/5.
they had to have the same number as their denominator.
so we gonna multiply (5) (3) and (5) (7) and also (7) (2) and (7) (5)
then we have 14/35 and 15/35 so we can add them together to find out 29/35
then we minus it from 35/35 to find out how much is left
35/35 - 29/35 is 6/35 , which is our answer
There are 10 students in Class 1 and 40 students in Class 2.
All 50 students sit a test.
The mean score for the students in Class 1 was 80%
The mean score for the students in Class 2 was 70%
Find the mean score of all the students.
Answers
Answer:
72%
Step-by-step explanation:
We have 10 sudents in class 1 and 40 in the other for a total of 50 students.
The 10 in class 1 had a mean of 80 so we do 80x10=800
The mean of the class of 40 is 70, so we do 40x70=2800
we add both of those together to get 3600 then we divide that by 50 because there are 50 students in total.
3600/50=72.
In a survey of some tourists, 80% of the tourists have been to India and 35% of the tourists have been to china.If all the tourists who have been to china also been to India and 260 have not been either of the countries, find the number of tourists who have been india but not china.
Answers
Answer:
585
Step-by-step explanation:
This sort of problem can be solved using a 2-way table that categorizes tourists by combination of destinations. Of the four possible combinations, one is ruled out (China, but not India). We can determine percentages and numbers for the combinations of interest using the given data.
__
80% have been to India, so 20% have not. All of those have also not been to China. Since tourists in that category number 260, there must be ...
260/20% = 1300 . . . tourists surveyed
Of the 80% who have been to India, 35% have been to China. That leaves 45% who have been to India, but not China. This number is ...
45% × 1300 = 585
The number of tourists who have been to India, but not China, is 585.
one of the two equal sides of an isosceles triangle is 5.4 CM. if the perimeter of the triangle is 15.4 cm, find the length of the remaining sides of the triangle.
Answers
Answer:
4.6cm
Step-by-step explanation:
5.4 is the length of one side and if you have 2 sides that are equal you double that
5.4 x 2 = 10.8
15.4 - 10.8 = 4.6cm
Since the triangle is isosceles then two sides will be equal
Perimeter =length +length+ length
Since the two sides are equal then
P=5.4+5.4+L=15.4
10.8+L=15.4
L=15.4-10.8
L=4.6
Cooper is throwing a dinner party. He says about 67 people are coming to the party. He is paying a company to make the food, and they said each person would cost about $15. To add drinks, each person would cost $3. How much money will Cooper be spending for food and drinks at his party if you round the number of people to the nearest tenth digit? What is a way you can solve this estimation problem? Select all that apply.
Round the $15 to $20, the $3 to $5 and the 67 to 70 before you do anything else.
Round the 67 to 70, add the $15 and the $3 and then multiply the 2 answers.
Round 67 to 70. Multiply 70 by 15 and 70 by 3 and then add the answers.
Add the amount for food and drinks then multiply by how many people there are.
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Answer:
Round the 67 to 70, add the $15 and the $3 and then multiply the 2 answers.
Round 67 to 70. Multiply 70 by 15 and 70 by 3 and then add the answers.
Step-by-step explanation:
you get the same answer both ways.
I tried this but couldn't figure it out I hope ya'll can but it's this
1/3x1/6
Answers
1/18
Step-by-step explanation:
[tex] \frac{1}{3} \times \frac{1}{6} = \frac{1}{18} [/tex]
Brooke has a box of crayons. 5 are yellow, 2 are green, 6 are blue, and 7 are red If Brooke randomly selects a green crayon and doesn’t put it back, what is the probability that she will choose a red crayon next?
Answers
Explanation: The total amount of crayons is 20 (the 100% in probability). Since there are 2 green crayons, the proportion will be 2/20. The question is asking what is the probability if she will choose a red crayon next, so we have to set up a fraction multiplication for the red crayon as well. Since she doesn’t put the green crayon back, the total will be 19 crayons, and the final fraction multiplication will be 2/20 x 7/19, which is equal to 7/190.
Solve the following equation for x 13x2 - 5 =0
Answers
Step-by-step explanation:
if its x13^2-5=0 then 5/169
but if its x13*2-5=0 then 1.07
8/4 x 3/4. I know it is 1.5 but can someone show step by step? I am having trouble.
Answers
[tex]\dfrac 84 \times \dfrac 34\\\\\\=2 \times \dfrac 34\\\\\\=\dfrac 32\\\\\\=1.5[/tex]
Step-by-step explanation:
First divide 8 by 4 and 3 by 4
it will be 2×0.75=1.5
Help please extra points
Answers
Answer:
The answers would be Kendrick and Cardi.
Step-by-step explanation:
J. Cole is wrong since it's impossible to tell if any cities got exactly 30 inches of rainfall, and Nas is wrong because only 10/25 of the cities received over 34 inches of rainfall.
Kendrick is right because there were exactly 15 cities with rainfall of 33 inches or less, and Cardi is right because 8% (2) of the cities recieved 25-27 inches of rainfall.
Answer:Kendrick and Cardi
Step-by-step explanation:
2+3+10=15
2 is 8% of 25
A bag contains 6 different colored chips. If 2 chips are selected at random, how many different combinations of colors are
possible?
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Answer:
I think the answer is 4 or am I wrong please I don't understand
Please help me with this please and thank you
Answers
Answer:
so i wrote the steps but not the answers, if you want i can write the answers too
Step-by-step explanation:
hello! so here all you have to do is substitute the given points of x to the equation. then you put two points on the graph. (two points on each graph) i can write the answers if you want, but please try first! if you cant ill help some more and show how to do it.
round to the nearest hundredth
(please help picture inculded)
Answers
Answer:
AB ≈ 6.53
Step-by-step explanation:
using the cosine ratio in the right triangle
cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{5}{AB}[/tex] ( multiply both sides by AB )
AB × cos40° = 5 ( divide both sides by cos40° )
AB = [tex]\frac{5}{cos40}[/tex] ≈ 6.53 ( to the nearest hundredth )
I need help with this question pls help
Answers
Answer:
y = - 4
Step-by-step explanation:
x = - 2
3x - 2y = 2
substitute x = - 2 into 3x - 2y = 2
3(- 2) - 2y = 2 ← step 1
- 6 - 2y = 2 ( add 6 to both sides ) ← step 2
- 2y = 8 ( divide both sides by - 2 )
y = - 4
Hong has a bookcase with 8 shelves. There are k books on each shelf. Using , write an expression for the total number of books.
Answers
Answer: total books = 8k
Step-by-step explanation:
k = books on each shelf
total books = bookcases * shelves per bookcase * books per shelf (k)
total books = 1 * 8 * k
total books = 8k
Answer:
8k
Step-by-step explanation:
To find the total number of books, take the number of shelves and multiply by the number of books on each shelf
8*k
The total number of books is 8k
A ________ is a set of points that extends infinitely in both directions.
Answers
Answer:
line
Step-by-step explanation:
A line is a set of points that extends infinitely in both directions.
Regan measured a neighborhood park and made a scale drawing. the scale she used was 7 inches = 5 yards. what is the scale factor of the drawing?
Answers
Answer:
fgy8errrbtthy333eeeee[tex]x^{2} 33\pi \sqrt[n]{x} \int\limits^a_b {x} \, dx[/tex]r4g344myngívr3vh57744kpuiv2224gpo48
Step-by-step explanation:
uyrooou
If QR=x+29 and PS=x–16, what is the value of x?
Answers
Answer:
61
Step-by-step explanation:
By the triangle midsegment theorem, 2(SP)=RQ.
So, 2(x-16)=x+29, meaning x=61.
How many solutions are there to the equation below?
6x+ 33 = 6(x+6)
A. Infinitely many solutions
B. No solution
C. One solution
Answers
NO SOLUTION.