No, it is not it true that for any integer n ≤ 2, φ(n) has a primitive root
What is primitive root?In modular arithmetic, a number g is called a primitive root modulo n if every number coprime to n is congruent to a power of modulo . Mathematically, g is a primitive root modulo n if and only if for any integer a such that gcd(a, n)=1 , there exists an integer k such that:
.[tex]g^{k}[/tex]≡ a (mod n)
Now,
Existence of Primitive root modulo n exists if and only if:
n is 1, 2, 4, orn is power of an odd prime number , orn is twice power of an odd prime number .So,
if n be a positive integer. A primitive root mod n is an integer g such that every integer relatively prime to n is congruent to a power of g mod n.
For example,
As ϕ(11)=10, the order of 2(mod11) must divide 10.
So we check 22≡4(mod11) and 25≡10(mod11).
Since neither of these are 1, and
we know 2ϕ(11)=210≡1(mod11) by Euler's Theorem,
ord112=ϕ(11), making 2 a primitive root modulo 11.
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HELP ME QUICK!!
Joe wants to wallpaper the back wall of his bedroom. The wall is in the shape of a rectangle its length of 17 feet and its width is 13 feet suppose wallpaper cost five dollars for each square foot how much will paper cost for the wall
Based on the shape of the back wall of Joe's bedroom and the dimensions of the rectangle, and the cost per square foot, the paper cost of the wall would be $1,105
What is the paper cost of the wall?First, find the area of the back wall of Joe's bedroom because this is the area that would need to be covered by the wall paper:
Area of rectangle = Length x Width
Solving gives:
= 17 x 13
= 221 square foot
The cost to cover the wall based on the cost in dollars of each square foot is:
= Number of square feet x Cost per square foot
= 221 x 5
= $1,105
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are there any points with integer coordinates on a line if a line passes through (5,-8.5) and (13.8, 6.9)?
please provide a yes or no and examples.
There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).
Does a line contain coordinates with only integers?
In this problem we have a line that passes through two points on a Cartesian plane and herein we must check if that line contains at least one point with integer coordinates. First, determine the equation of the line:
Slope
m = [6.9 - (- 8.5)] / (13.8 - 5)
m = 7 / 4
Intercept
b = - 8.5 - (7 / 4) · 5
b = - 69 / 4
The equation of the line is y = (7 / 4) · x - 69 / 4.
Second, evaluate the equation of the line at different integers:
x= 6
y = (7 / 4) · 6 - 69 / 4
y = - 27 / 4
x = 7
y = (7 / 4) · 7 - 69 / 4
y = - 5
x = 8
y = (7 / 4) · 8 - 69 / 4
y = - 13 / 4
x = 9
y = (7 / 4) · 9 - 69 / 4
y = - 3 / 2
x = 10
y = (7 / 4) · 10 - 69 / 4
y = 1 / 4
x = 11
y = (7 / 4) · 11 - 69 / 4
y = 2
x = 12
y = (7 / 4) · 12 - 69 / 4
y = 15 / 4
x = 13
y = (7 / 4) · 13 - 69 / 4
y = 11 / 2
There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).
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Multiply and simplify completely
√6 x 3√54
Answer:
54
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] and [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a , then
[tex]\sqrt{6}[/tex] × 3[tex]\sqrt{54}[/tex]
= [tex]\sqrt{6}[/tex] × 3 × [tex]\sqrt{9(6)}[/tex]
= [tex]\sqrt{6}[/tex] × 3 × [tex]\sqrt{9}[/tex] × [tex]\sqrt{6}[/tex]
= [tex]\sqrt{6}[/tex] × [tex]\sqrt{6}[/tex] × 3 × 3
= 6 × 9
= 54
[tex]{ \qquad\qquad\huge\underline{\boxed{\sf Answer}}} [/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{6} \times 3 \sqrt{54} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{2 \times 3} \times \sqrt{2 \times {3}^{3} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {2}^{2} \times {3}^{4} } [/tex]
[tex]\qquad \sf \dashrightarrow \:2 \times {3}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:2 \times 9[/tex]
[tex]\qquad \sf \dashrightarrow \:18[/tex]
What value of "x" makes the equation -4x+7=2x+13 true?
OA. -4
OB. -1
OC. 2
OD. O
Answer:
B. -1
Step-by-step explanation:
Let's solve your equation step-by-step.
−4x+7=2x+13
Step 1: Subtract 2x from both sides.
−4x+7−2x=2x+13−2x
−6x+7=13
Step 2: Subtract 7 from both sides.
−6x+7−7=13−7
−6x=6
Step 3: Divide both sides by -6.
−6x/−6 = 6/−6
x=−1
Solve: 1 1/8 - 3/4
pls answer in fraction!!
Answer:
3/8
change to an improper fraction
1 1/8=9/8
3/4 times 2 equals
6/8
9/8-6/8
3/8
Answer: I think the answer is 3/8 or it can be 5/8.
explanation: I hope this helps.
suppose a survey of 979 business owners found that more than % bought . which part of the survey represents the descriptive branch of statistics? make an inference based on the results of the survey.
In this problem, descriptive statistics is used because the survey percentage is used to make inference for all business owners.
What is descriptive statistics?
Descriptive statistics is used when data from a sample, which is a sub-set of a population, is used to make inferences about the entire population.
In this problem, the data 979 business owners sampled is used to make inference about the population, which is composed by all business owners, hence descriptive statistics is used.
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Which table has a constant of proportionality between y and az of 0.6?
Choose 1 answer:
(G
z
Y
47
6
8
-8
4
9
14
H
10
13
y
2.4
5.4
8.4
y
3
2
9 6
15 10
Answer:
C
Step-by-step explanation:
if you divide the y by x, the answer it will give you will be 2/3 or .6
Please help me with this geometry question. Answer should be entered like this (answer, answer) thank you
Answer:
Q is the point (3, 4).
Step-by-step explanation:
The formulae for the coordinates of a point (h, k) which divides a line joining the points (x1, y1) and (x2, y2) in the ratio m : n is:
h = (mx2 + nx1) / (m + n), k = (my2 + my1)/(m+n)
Now we have S = (x1, y1) = (-2, -6) and T = (x2, y2) = (5, 8) and
m = 5 and n = 2.
So here, for point Q:
h = (5*5) + 2*-2)/(2+5)
= 21/7
= 3.
k = (5*8 + (-6*2) / 7
= 28/7
= 4.
10. Sam earns a salary of $25,000 while Charlie earns a salary of $30,000. They each receive
a $2000 raise. Which of the following is true?
(a) Sam's raise is larger than Charlie's in both absolute and relative terms.
(b) The raises are the same in absolute terms, but Sam's is larger in relative terms.
(c) The raises are the same in relative terms, but Sam's is larger in absolute terms.
(d) The raises are the same in absolute terms, but Charlie's is larger in relative terms.
If the salary of Sam is $25000 and Charlie earns $30000 and each get a raise of $2000 then the statement "The raises are the same in absolute terms, but Charlie's is larger in relative terms" is true.
Salary of Sam = $25000
Raise in Sam's Salary = $2000
New Total Salary = $25000 + $2000 = $27000
Salary of Charlie = $30000
Raise in Charlie's Salary = $2000
New Total Salary = $30000 + $2000 = $32000
Hence the absolute value of their salaries are same but Charlie will get more in relative terms.
Hence, option d is correct.
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Jenna can't wait to play in her new sandbox! Her mom fills the sandbox with seven 50-pound bags of sand. Then, Jenna uses her bucket to dump out sand 10 times. If she dumps out 8 ounces of sand each time, how many pounds of sand are left in the sandbox?
Answer:
345 pounds
Step-by-step explanation:
Each bucket dumps out 8 ounces of sand
8 ounces = 1/2 pound
So total sand dumped 10 times = 1/2 x 10 = 5 pounds
Originally sandbox had 7 x 50 = 350 pounds of sand
Sand left in box = 350 - 5 = 345 pounds
the jazz band has b members. to raise money for a tour, each member sold 12 raffle tickets. write an expression that shows the number of raffle tickets sold. submit
The term or expression 12b represents the number of raffle tickets sold by the members of the band.
Expression: An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
There are b number of members in a jazz band. The jazz band wants to take a tour.
Each of the members sold 12 raffle tickets to raise money for the tour.
Therefore, the number of raffle tickets sold will be the product of the number of jazz members and the number of raffle tickets sold by each member.
So, the expression for the number of raffle tickets sold by the members of the jazz band will be:
= 12 × b
= 12b
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if f(x) = x and g(x) = 2, what is (f.g) (x)?
The value of (f.g) (x) is 2. Option B
What is a function?A function can be defined as an expression or rule that explains the relationship between an independent and dependent variable.
Given the functions;
f(x) = xg(x) = 2To determine (f.g) (x), we need to know that it is a composite function
We substitute the value of g(x) = 2 as x in f(x)
But we have f(x) = x
Then,
(f.g) (x) = 2
Thus, the value of (f.g) (x) is 2. Option B
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Sarah had a balance of $162 in her bank account at the start of the week. She withdrew $63.50 on Monday, $23.25 on Wednesday, and $26.45 on Thursday. On Friday, she deposited $87.30.At the end of the week, Sarah had ___(less or more) money in her savings account than she had at the beginning of the week.
How much more or less? $_______
Answer:
Less; $25.90 less than at the beginning of the week
Step-by-step explanation:
162-(63.50+23.25+26.45)=162-113.20=48.80
48.80+87.30=136.10; 162>136.10
162-136.10=Δ$25.90
$25.90 less
Write a linear function f(x)=mx+b for the table
The standard form the linear function is f(x)= -3x-3.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+3. Where:
m= the slope. It can be calculated for Δy/Δx .
b= the constant term that represents the y-intercept.
For the given example: m=5 and b=3.
You should replace in the minimum two given values for x and y in the standard form for a linear equation mx+b . Thus, you will write a system linear where from it, you can find the coefficients m and b. See below.
For x=0 and y=-3y=mx+b
-3=0*m+b
-3=b
For x=-2 and y=3y=mx+b
3= -2*m+b
Now, you find b=-3, then
3= -2*m-3
3+3= -2m
6=-2m
m= -3
Thus, you can write f(x)= -3x-3.
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you're given a fair coin. you flip the coin until either heads heads tails (hht) or heads tails tails (htt) appears. is one more likely to appear first? if so, which one and with what probability?
The HHT is more likely to appear first with a probability of 2/3.
What is probability?The probability is an estimation of the likelihood that an event will occur. It assesses the event's certainty.
The formula for probability is given as;
P(E) = Number of Favourable Outcomes/Number of total outcomes.
Now according to the given question;
Only the second and third flips in the sequence matter. We understand the first flip is an H, and we're not interested in sequences that begin with T.
Lets start with the given format;
H _ _
If we get an HH_, the game is over and HHT will surely win (regardless of the number of heads we get, the next T is an automatic win). If we get an HTT, the game is over.
If we get an HTH, the game is a tie, and we must restart it.
Thus,
P(HHT) = 1/2
P(HTT) = 1/4
P(Draw) = 1/4
P(HHT wins) = P(HHT) / [1-P(Draw)]
= (1/2) / (1-1/4)
P(HHT wins) = 2/3
Thus, the probability of occurrence of HHT has more chances with 2/3.
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Help I have no clue what are the answers I tried 30 times!
The correct options for the linear combinations of the vectors are given by:
A, B, C, D, E and F.
What is a span between two vectors?The span between two vectors is the set that contains all linear combinations between these two vectors.
Supposing we have two vectors u1 and u2, as is the case in this problem, the infinitely many linear combinations have the following format:
k1u1 + k2u2
In which k1 and k2 are real numbers.
With k1 = 4 and k2 = -7, we get that option A is correct.
For option B, we have to see if it is possible to solve the following system.
k1 + 4k2 = 0.5k1 + 22k2 = 0.-4k1 - 11k2 = 0.The solution is k1 = k2 = 0, which are real numbers, hence option B is correct.
Both vectors u1 and u2 are part of the span, hence options D and F are correct. The size of the span is of infinity, hence option E is correct while option G is not.
The dimension of the span is of 3, as the vectors have 3 elements, hence option C is correct.
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b. Parallel lines are lines that will never intersect. Do parallel lines exist in spherical geometry? Explain your answer.
Yes parallel line exist in spherical geometry. The radius or diameter and the tangent can be a pair of parallel line in spherical geometry
How parallel can exist in spherical geometryThe tangent of the sphere refers to a line that make contact with only a point in the sphere. The tangent is perpendicular to the center and the radius can be drawn to be parallel to the tangent.
The radius refers to a line running from the center to an end of the circle. Two radius can be drawn say radius A and radius B. Radius A will be drawn perpendicular to the tangent and radius B drawn perpendicular to radius A.
The pair of lines tangent and radius B will be parallel to each other.
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What reasoning shows correctly how to rewrite 4 to the power of 3 over 2 end exponent?
The reasoning which shows the given statement correctly is [tex]4^{\frac{3}{2}}[/tex].
Given the statement is "4 to the power of 3 over 2 end exponent".
In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.
In the given statement 3 over 2 means, 3 is divisible by 2 and it can be written as 3/2.
And it is also given that 4 to the power of 3 over 2 that means we have to write 3/2 in the power of 4 and it can be written as
[tex]4^{\frac{3}{2}}[/tex]
Hence, the reasoning which shows the given statement "4 to the power of 3 over 2" correctly is [tex]4^{\frac{3}{2}}[/tex].
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HELP PLEASEEE
If g (x) = x² + 6 and ƒ (x) = 2x − 4, find g (ƒ (x))
Step-by-step explanation:
Plug in 2x-4 in the function g(x)
[tex]g(f(x)) = {(2x - 4)}^{2} + 6 \\ \\ g(f(x)) = (2x - 4)(2x - 4) + 6 \\ = 4 {x}^{2} - 8x - 8x + 16 + 6 \\ g(f(x)) = 4 {x}^{2} - 16x + 22[/tex]
HOPE THIS HELPS
two years ago, paul was 7 times as old as matt was. two year from now, paul will be five times as old as matt will be. find the present age of each
The present age of Paul is 52 years and the present age of Matt is 10 years.
We are given that two years ago, Paul = 7 times as Matt
Let the current age of Matt be x and of Paul be y
2 years ago, we will have that:
Age of Matt = x - 2
So, we get the equation as:
Age of Paul = 7 ( x - 2) = 7 x - 14
y - 2 = 7 x - 14
y = 7 x - 14 + 2
y = 7 x - 12
Also, we are given that to year from now, Paul = five times Matt
We get that:
y + 2 = 5 ( x + 2)
y + 2 = 5 x + 10
y = 5 x + 10 - 2
y = 5 x + 8
So, we get:
7 x - 12 = 5 x + 8
7 x - 5 x = 8 + 12
2 x = 20
x = 20 / 2
x = 10
y = 5 (10) + 2
y = 50 + 2
y = 52
Therefore, the present age of Paul is 52 years and the present age of Matt is 10 years.
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What is the answer rounded to the
hundredths
place?
9.3478 m
+2.73 m
12.0778 m
➜>>
→ [?] m
Answer:12.8
Step-by-step explanation: u just round it
Solve the inequality -5/2 (3x-2)<6-2x. For full credit, you will need to show and explain every step. You may add more lines if you need them.
The solution to the inequality, -5/2(3x - 2) < 6 - 2x is: x > -2/11.
How to Solve an Inequality?To find the solution to the inequality given, follow the steps explained below:
-5/2(3x - 2) < 6 - 2x [given]
-5/2(3x) -5/2(-2) < 6 - 2x [distribution property]
-15x/2 + 5 < 6 - 2x [simplify]
-15x/2 + 5 - 5 < 6 - 2x - 5 [subtraction property]
-15x/2 < 1 - 2x
-15x/2 + 2x < 1 - 2x + 2x [addition property]
-11x/2 < 1 [simplify]
-11x/2 × 2 < 1 × 2 [multiplication property]
-11x < 2
-11x/-11 > -2/11 [division property]
x > -2/11
Note: the inequality sign would change if we are dividing both sides by a negative number.
Therefore, the solution to the inequality, -5/2(3x - 2) < 6 - 2x is: x > -2/11.
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A sum of £350 is invested at simple interest and amounts to £476 after 3 years. Calculate
(a) the total interest
(b) the rate per cent per annum.
Answer:
(a) $126
(b) .453333%
Step-by-step explanation:
(a) 476 - 350 = $126
(b)
[tex]si = p \times r\times t \\ 476 = 350 \times r\times 3 \\ 476 = 1050r \\ \frac{476}{1050} = r \\ r = 0.453333\%[/tex]
What is the answer to
|x+8|=|2x+1| ?
Answer:
[tex] \sf \large \: x=7 or x=−3[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
|x+8|=|2x+1|
Solve Absolute Value.
|x+8|=|2x+1|
We know eitherx+8=2x+1orx+8=−(2x+1)
x+8=2x+1(Possibility 1)
x+8−2x=2x+1−2x(Subtract 2x from both sides)
−x+8=1
−x+8−8=1−8(Subtract 8 from both sides)
−x=−7
−x/−1 = −7/−1
(Divide both sides by -1)
x=7
x+8=−(2x+1)(Possibility 2)
x+8=−2x−1(Simplify both sides of the equation)
x+8+2x=−2x−1+2x(Add 2x to both sides)
3x+8=−1
3x+8−8=−1−8(Subtract 8 from both sides)
3x=−9
3x/3 = −9/3
(Divide both sides by 3)
x=−3
Check answers. (Plug them in to make sure they work.)
x=7(Works in original equation)
x=−3(Works in original equation)
Answer:
7
Step-by-step explanation:
x+8=2x+1
Subtract x on both sides. Subtract 1 on both sides
x=7
Describe a real-world situation that can be modeled by the equation y = 1/20x be sure to describe which each variable represents
The equation can be modelled to a real scenario where every purchase can be use to calculate sales tax.
How to find a real world situation that models an equation?The equation to be modelled is as follows:
y = 1 / 20x
let
x = The total price of purchases
y = The amount of sales tax
This simply means a person pays 1 / 20 or 5% of every purchase he/she makes.
The total price of the purchase(including tax) is x while the actual amount of tax paid is y.
Let's say you buy a goods worth 400 dollars. Let's calculated the tax as follows:
x = $400
Therefore,
y = 1 / 20 × 400
y = 1 / 20 × 400
y = $20
Hence, the tax for a purchase of 400 dollars is 20 dollars.
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You start at (6,4) and move 4 units left and 2 units down what point will you end up on?
Answer:(2,2)
Step-by-step explanation:
because if you follow the steps you will end up there
19. The football game was attended by 237 people, down 40% from last week. How many
people attended last week's game?
(a) 332
(b) 395
(c) 142
(d) 379
Answer:
(a) 332
Step-by-step explanation:
Find 40% of 237
94.8, Round to 95
237 + 95 = 332
find the value of x:
Answer:
The answer to the question is 35 degrees
What is the quotient?
StartFraction (negative 7) squared Over (negative 7) Superscript negative 1 EndFraction
Negative 343
Negative 7
7
343
The quotient of the given division operation is -343. and The correct option is the first option -343.
According to the statement
We have to find that the value of the quotient.
So, For this purpose, we know that the
Quotient can be defined as the result of the division of a number by any divisor.
In other words, The result of the division is the quotient.
From the given information:
we are to determine the quotient of the given division operation
And
The statement become is:
[tex]\frac{-7^{2} }{-7^{-1} }[/tex]
Then we have to solve this
Then
[tex]\frac{49}{-7^{-1} }[/tex]
Then
49*-7
-343.
the quotient of the given division operation is -343.
So, The quotient of the given division operation is -343. and The correct option is the first option -343.
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Answer:
-343
Step-by-step explanation:
Edge
alysha is at a local library with her best friend. they've noticed a lot of cute boys in the library, and alysha bets that of the next twenty people to enter the library, exactly 12 will be cute boys. assuming there is a 50% chance that the next person to walk into the library is a cute boy, what is the probability that alysha will win the bet?
The probability that Alysha will win the bet is 0.12013
Let ‘x’ be the number of cute boys from next 20 persons that enter the library
And assume x be the integral values from 0 to 20
Given, the probability is 50% that the next person that enters the library is a cute boy,
total number of trials n=20 and probability of success p=50% = 0.5 = 1/2.
Hence, the p.m.f of X is given by
fX(x) = 20Cx(1/2)x(1−1/2)20−x
=20Cx(1/2)x(1/2)20−x
=20Cx(1/2)20
=20!(20−x)!x!⋅ 1220
=0,1,2,…,19,20
and the probability that X=x,
thus
P(X=x)=20!(20−x)!x!⋅1220
x=0,1,2,…,19,20
P(X=x)=20!(20−x)!x!⋅1220
x=0,1,2,…,19,20.
In particular, for X=x=12
P(X=12)=20!(20−12)!12!⋅1220
=20!8!12!⋅1220
≈0.12013
Hence, the probability that exactly 12 persons of the next 20 persons that walk into the library are cute boys is only approximately 0.12013.
Therefore, 0.1203 is less than 0.5, then it is more probable that Alysha will lose the bet than win it.
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