Answers
Answer:
you need to show the number is prime
Step-by-step explanation:
To show 2^7 -1 is prime, you have to show it is not divisible by any prime less than its square root. That root is approximately 2^(7/2) = 2^3×√2 ≈ 11.3.
The primes of in that range are 2, 3, 5, 7, 11. The prime we're testing is ...
2^7 -1 = 128 -1 = 127
The sum of digits is 10, which is not a multiple of 3: not divisible by 3.
The units digit is 7, not 0 or 5: not divisible by 5.
The test for divisibility by 7 is to subtract twice the units digit from the rest of the number: 12 -2(7) = -2. This is not 0 or a multiple of 7, so 127 is not divisible by 7.
We know that 11² = 121, so 127 is not divisible by 11.
All of the tests for primality pass, so 2^7 -1 is a Mersenne prime.
_____
Additional comment
It is known that 2^n -1 being prime requires n to be prime. (The converse is not true: 2^11 -1 = 2047 = 23×89 is not prime.) The discovery of Mersenne primes is an ongoing process involving thousands of computers around the world. Only about 50 such primes are known.
You will notice that we have made use of some divisibility rules in order to simplify the process of dividing by small numbers. These can be helpful in many situations, so can be useful to learn.
Related Questions
marlene is painting square tiles for a project.each tile has a perimeter of 16 in.what is the length of each side.
Answers
Answer:
64 i hope im right
Step-by-step explanation:
Answer: 4 in.
Step-by-step explanation:
A square has 4 equal sides for its perimeter.
Perimeter = 4x
16 = 4x
x = 4 in.
One whale sang to communicate with another whale. The song's sound wave traveled 2,100meters at a steady speed in 1.4seconds. What was the sound wave's speed?
Answers
Answer:
1500 meters / second
Step-by-step explanation:
Speed = the magnitude of distance / time
Distance = 2,100 meters
Time = 1.4 seconds
Speed = 2,100 meters / 1.4 seconds = 1500 meters / second
PLEASE ANSWER ASAP!! WORTH 20 POINTS
A cab company charges a $4 boarding rate in addition to its meter which is $1.50 for every mile. Write a linear equation which models this. Use the equation to determine the total fare for a trip that is 2 miles, 3 miles and 5 miles.
Answers
Answer:
y = 1.50x+4
if x = 2
y = 7
if x = 3
y = 8.5
if x = 5
y = 11.5
Step-by-step explanation:
every mile(x) add 1.50 dollars to 4 dollars
PLEASE help, I'm begging, this was due to all the way back at November 12th, please help!!! Finding the Inverse of a Function Algebraically Practice Pt. 2
Answers
Answer:
19
Step-by-step explanation:
Please help with this!!
Answers
Answer:
#1.---60% #2.---$12.60 per hour
Step-by-step explanation:
#1. Since It was originally $50 you have 50% already, so what I did was I multiplied 50 by 2. this got me 100 which is a simpler way to calculate by. 50 to 80 dollars is a $30 change, so multiply that by 2 and you get 60. 60 will be your percent of change. You can double check this by multiplying 50 by .60, the answer will be 30 and 50+30=80
#2 Since Tyler starts off with $12 per hour with a 5% increase you will need to multiply 12*.05 this will get you the answer of 0.6 you then need to add $12, since that was his original payment. 12+0.6=12.60, so his final payment would by $12.60 per hour
Write ratios in the form 1:n or n:1 6 : 14
Answers
Answer:
3/7 : 1 OR 1 : 7/3
Step-by-step explanation:
You can set up ratios as a fraction and solve for the missing piece. See images.
Answer:
1 : 2.33 aka 1: 2 1/3
Step-by-step explanation:
1) 6 : 14
2) divide both sides by 6
6/6=1
14/6=2 1/3
3) 1 : 2 1/3
(If someone is online)pls help me to answer this question
Answers
Answer:
The correct answer is yes.
Step-by-step explanation:
I can help you. What do you need? :)
esterday 5% of the 120 sixth graders at school were late. How many sixth graders were late?
Answers
Answer:6 six graders were late. 10% would be 12, and half of that is 6. You need to divide that in half because 5 is half of 10.
Answer:
6 sixth graders at school where late
Step-by-step explanation:
5% = 0.05
0.05(120) = 6
- Are the lines y = -1 and x = 1 parallel?
Answers
Answer:
No the lines are perpendicular.
Step-by-step explanation:
The lines are perpendicular because x and y meet up and make a perpendicular line. If you don't believe me plug it in a graphing calculator.
Given a ball with a diameter of 38 inches, how much fabric would be needed to cover the surface?
Answers
Answer:
[tex]27436\pi[/tex] square inches
Step-by-step explanation:
Since we are covering the surface of the ball, we need to determine the ball's surface area.
Assuming the ball to be a sphere, its surface area would be [tex]A=4\pi r^2[/tex] where [tex]r[/tex] is the radius.
Since the diameter is twice the radius, then the radius of the ball is 19 inches.
Therefore, the surface area of the ball is [tex]A=4\pi (19)^3=4\pi(6859)=27436\pi[/tex] square inches.
NO LINKS!!!
Help please ;-;
And please answer all 1, 2, 3, 4 questions!
Choose the inequality that describes the following
____ 1. The set of numbers {‐3, ‐2, ‐1, 0, 1, ...}
A. x > ‐4
B. x < ‐4
C. x ≥ ‐4
D. x ≤ ‐4
____ 2. The set of numbers {9, 8, 7, …}
A. x > 9
B. x < 9
C. x ≥ 9
D. x ≤ 9
____ 3. The set of numbers {0, -2, -4, -6, -8, ...}
A. x > 0
B. x < 0
C. x ≥ 0
D. x ≤ 0
____ 4. The set of numbers {-6, -4, -2, 0, 2, 4, 6, ...}
A. x > ‐6
B. x < ‐6
C. x ≥ ‐6
D. x ≤ ‐6
Answers
1. A
2. D
3. D
4. C
(IF YOU NEED A EXPLANATION, JUST ASK!)
Josephina lives on a farm with 3 sheep, 2 goats, 11 chickens, and 5 cows. She is going to randomly select an animal to take to the stock show. What is the probability of randomly selecting a cow or a goat
Answers
Answer:
7/21 or 1/3
Step-by-step explanation:
Adding all the animals together, we get 21. Then we add just the cows and the goats and get 7. Then we do 7/21 = 1/3 simplified
A line passes through the point ( -1,2 ) and has a slope of 6. Write an equation for this line.
Answers
Answer:
y = 6x+8
Step-by-step explanation:
y = mx+b
y = 6x + b
2 = 6(-1)+b
2 = -6+b
8 = b
y = 6x+8
Can someone help me ? :
Answers
Answer:
[tex]\huge\boxed{\sf y = 100.4}[/tex]
Step-by-step explanation:
Given equation is:
53 = y - 47.4
Add 47.4 to both sides
53 + 47.4 = y
100.4 = y
OR
y = 100.4
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Hello there!
Question:-[tex]\sf \longmapsto53=y - 47.4[/tex]
This is a equation. We need to find the value of variable y.
Solution:-[tex]\sf \longmapsto53=y- 47.4[/tex]
To Solve further,we need to overturn the equation.
That is :-
[tex]\sf \longmapsto \: y - 47.4 = 53[/tex]
Then, Add +47.4 to two sides:-
[tex]\sf \longmapsto \: y - 47.4 + 47.4 = 53 + 47.4[/tex]
On Simplification:-
Note that (-) and (+) equals to (-). So it would be 47.4 - 47.4 . Which results to 0.
[tex]\sf \longmapsto \: y - 0 = 100.4[/tex]
[tex]\sf \longmapsto \: y = 100.4( Ans.)[/tex]
Answer as a mixed fraction:-
[tex]\sf \longmapsto 100\dfrac{2}{5}[/tex]
Answer as a fraction:-
[tex]\sf\longmapsto 502/5[/tex]
______________________________________
Henceforth, the value of y is :-
[tex]\bf \: y = 100.4[/tex]
Or as a mixed fraction:-
[tex]\bf y = 100\dfrac{2}{5}[/tex]
Or as a fraction:-
[tex]\bf y = 502/5[/tex]
________________________________
I hope this helps!
Please let me know if you have any questions.
if x(square) plus y(square) is 8.and the froduvt is . what are x and y?
Answers
Given :-
x² + y² = 8Product of x and y is 4 .( say )To Find :-
The value of x and y .Answer :-
Here we are given that,
[tex]\red{\longrightarrow}[/tex] x² + y² = 8 .
And ,
[tex]\red{\longrightarrow}[/tex] xy = 4
[tex]\red{\longrightarrow}[/tex] y = 4/x
So that ,
[tex]\red{\longrightarrow}[/tex] x² + (4/x)² = 8
[tex]\red{\longrightarrow}[/tex] x² +16/x² = 8
[tex]\red{\longrightarrow}[/tex] x⁴ + 16 = 8x²
[tex]\red{\longrightarrow}[/tex] x⁴ - 8x² + 16 = 0
Assume k² = x⁴ and k = x²
[tex]\red{\longrightarrow}[/tex] k² - 8k + 16 = 0
[tex]\red{\longrightarrow}[/tex] k² -4k -4k +16 = 0
[tex]\red{\longrightarrow}[/tex] k(k-4) -4(k-4) = 0
[tex]\red{\longrightarrow}[/tex] (k-4)² = 0
[tex]\red{\longrightarrow}[/tex] k = 4
So ,
[tex]\red{\longrightarrow}[/tex] k = x²
[tex]\red{\longrightarrow}[/tex] 4 = x²
[tex]\red{\longrightarrow}[/tex] x = √4
[tex]\red{\longrightarrow}[/tex] x = ±2
Hence the required answer is ±2.
The values of x and y of the given function are; x = y = ±2
Roots of a Polynomial
We are given;
x² + y² = 8 -----(1)
Product of x and y = 4;
Thus; xy = 4
Now, making y the subject we have;
y = 4/x
Putting 4/x for y in eq 1 gives us;
x² + (4/x)² = 8
x² + (16/x²) = 8
Multiply through by by x² to get;
x⁴ + 16 = 8x²
⇒ x⁴ - 8x² + 16 = 0
using online polynomial root calculator, we have x = ±2
Thus, y will also be ±2
Complete question is;
If x² + y² = 8 and the product of x and y is 4, what are x and y?
Read more about roots of a polynomial at; https://brainly.com/question/10702726
Find the value of theta, to the nearest hundredth if cos they have is -0.7 and theta is in quadrant 2
Answers
Step-by-step explanation:
if I understand you correctly, then
cos(theta) = -0.7
then Theta = 134.427004...°
and that is rounded 134.43°
I need help plz
ASA
SSA
SAS
AAS
Answers
Answer:
SAS,
Step-by-step explanation:
2 sides and the included angle.
5) The Barnett triplets went to the school carnival. Henry rode on 5 rides, bought 2 drinks, 1 bag of popcorn and
spent $20.50. Mary spent $16.50 on 3 rides, 3 drinks and 1 bag of popcorn. While Tim rode on 6 rides only
purchased 1 drink and spent $20.00. How much did each ride cost?
a.
$12
b. $3
C. $2
d $4
PLEASE HURRY
2
Answers
Answer:
D
Step-by-step explanation:
Brady rode his bike 70 miles in 4 hours. He rode at an average speed of 17 mph for t hours and alah
respeed of 22 mph for the rest of the time. How long did Brady
ride at the slower speed? Use the variablet to
represent the time, in hours, Brady rode at 17 mph.
Answers
Answer:66 slower speed
Step-by-step explanation:
Find the greatest common factor and the least common multiple of 16 and 20. The prime factorizations of each number are given.
.
Answers
Answer:
GCF 4, LCM 80
Step-by-step explanation:
Since both 16 and 20 have two 2s as factor, their greatest common factor is 4.
The LCM is found by multiplying all of the remaining factors by the LCM:
16 still has (2 x 2), 20 still has (5), times the GCF (4) so 2 x 2 x 5 x 4 = 80.
a gardener makes a new circular flower bed. the bed is ten feet in diameter. calculate the circumference and the area of the circular flower bed
Answers
Answer:
10π
Step-by-step explanation:
First, remember the formula for the circumference of a circle is C= 2πr. Then remember that the diameter is twice the radius.
So here, when we have a diameter of 10ft, and we see the formula for circumference is C= 2πr, and because a Diameter is equal to 2 radii, I can also say C= Dπ. So in your case C= 10ft×π = 10ftπ
Can you plsssssssssssssssssssssssssssss help me with this.
Answers
Answer: (-1, 7) should be the answer
Step-by-step explanation:
why did you copy my profile picture hello......
please answer!!!!!!!!!
Answers
Answer:
C. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 5.
Step-by-step explanation:
I think this image demonstrates this concept the best.
Here’s a link to a site that has a better explanation: https://courses.lumenlearning.com/waymakercollegealgebra/chapter/compressions-and-stretches/
PLS ANSWER QUICK I HSVE EXAMS COMING UP VERY SOON у
42) Which equation best represents the line of best fit for this
scatter plot?
A. y = 4x - 4
B.y= 4x-2
C. y = x-4
D. y=x-2
-5-4-3-
Answers
If we drew a line of best fit, the gradient would be roughly equal to 1, and the y intercept would be at around -4
The graph shows a proportional relationship between the number of books sold at a yard sale and the amount of money collected from book sales.
Answers
Answer:
1.5
Step-by-step explanation:
6/4
school lunches cost 35.50 per week. About how much would 15.5 week of lunches cost?
Answers
Since you go to school for 5 days a week, the answer is going to be 550.25 for 15.5 weeks.
Hope that helped?
Answer:
15.5 weeks of school lunch would cost $550.25
Step-by-step explanation:
The unit rate is already given here, so all you need to do here is multiply the cost per week by the number of weeks. You can even think of it as canceling out the weeks:
[tex]\frac{cost}{week}\times week=cost[/tex]
[tex]35.50\times15.5=550.25[/tex]
15.5 weeks of school lunch would cost $550.25
You could also write this as a linear equation with a slope of 35.5 and a y-intercept of 0:
[tex]y=35.50x[/tex]
abebe is 12 years old and his sister aster is 2 years old. In how years abebe be exactly twice as old as aster
Answers
Answer:
8 years
Step-by-step explanation:
Currently
Abebe → 12 years old
Aster → 2 years
With every passing year, each of them will be 1 year older hence the difference between their ages will remain constant.
Difference in ages
= 12 -2
= 10
Let the age of Aster be x years old when Abebe is twice her age.
Abebe → 2x years old
Aster → x years old
Difference in age
= 2x -x
= x
x= 10
Aster is 10 years old when Abebe is twice her age.
Number of years passed
= 10 -2
= 8
Thus, Abebe will be twice as old as her sister in 8 years.
please help with my work
Answers
Answer:
F
Step-by-step explanation:
Domain is all x values that the graph passes through. Therefore, it starts at x=0 and ends at x=230 with no breaks so the domain is anywhere between 0 and 230.
I NEED HELP ON THIS MATH PROBLEM ASAP
Answers
Answer:
y= -5x +5
Step-by-step explanation:
what is -4(2x - 3) equal
Answers
Answer:
-8x + 12
Step-by-step explanation:
-4(2x - 3)
then -4*2x and -4*-3(an even number of negative signs multiplied equals to a positive sign)
therefore= -8x + 12