Find the unknown length. Round to the nearest tenth if necessary.

No, it is not it true that for any integer n ≤ 2, φ(n) has a 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:

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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The inequality that represents the constraint of the situation is x+y ≥ 400.

Inequality is defined as the mathematical expression in which both sides are not equal .

In inequalities the two vales are compared by "≤" , "≥" , "≠"  .

For Example : 2x+3y≥4 is an example of inequality .

In the given question

Part (a)

Given Kylie sell first oil painting in $x

and second oil painting in $y.

Kylie is trying to earn at least $400.

the term at least means she can earn $400 or greater than $400, so ≥ sign will  be used,

According to the question

we get , x+y ≥ 400    

So , x+y ≥ 400, is the inequality that represents the constraint of the situation.

Part (b)

The Graph of the inequality x+y ≥ 400 that represents the constraint on the sale is shown below .

Therefore , the inequality that represents the constraint of the situation is x+y ≥ 400.

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Answer:

A

Step-by-step explanation:

Multply = 24/105

Divide by 3

8/35

Answer:

22

Step-by-step explanation:

By the segment addition postulate, FH=8+14=22.

The equation will be,

→ FH = FG + GH

Then the value of FH will be,

→ FH = 8 + 14

→ [ FH = 22 ]

Hence, the value of FH is 22.

Answer:

x=2

Step-by-step explanation:

11-2x=5x-3

the first step, move the 3 over

14-2x=5x

In the second step moves 2x over

14=7x

finally, we just isolate the x from 7 by dividing 7

14/7=7x/7

simplify

2=x or x=2

Answer:

x=2

Step-by-step explanation:

*Shown two ways to solve.

11-2x=5x-3

 +2x +2x

11=7x-3

+3    +3

14=7x

Divide by 7.

2=x

11-2x=5x-3

-11          -11

-2x=5x-14

-5x -5x

-7x=-14

Divide by -7.

x=2

Check to see if you're right.

11-2(2)=5(2)-3

11-4=10-3

7=7

Yep, it's correct.

Hope this helps.

125 is greater than 23.

Given the question is to explain 125 > 23.

Here we have two numbers which are 125 and 23.

Inequalities:

Whenever we check the number which is greater or lesser by taking the difference between those two numbers we conclude which is greater or lesser.

If the difference between the numbers gets a positive number then the first number is greater than the second.

If the difference between the numbers gets a negative number then the first number is lesser than the second.

If the difference between the numbers gets zero value then the two numbers are equal.

So the difference between the given two numbers are

= 125 - 23

= 102

positive

So 125 is greater than 23.

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Your question is incomplete. Please find the complete question below

.Find 125 is greater than 23. Write about it in words.

Answer:

5x+12

-8

Step-by-step explanation:

i think you have the problem wrong

Answer:

Step-by-step explanation:

Bisects means that ∠RED will be divided in two parts by segment EB. This means that ∠REB = ∠BED. So,

5x-3 + 5x-3 = 8x+16

10x-6 = 8x+16

2x = 22

x = 11

Keep in mind that 11 is NOT the angle of ∠BED. You will plug it back into ∠REB to get

5(11)-3 = 52

Therefore, ∠BED = 52°

Answer:

5x - 6 ≤ 54

5x-6+6 ≤ 54+6

5x ≤ 60

divide by 5

x ≤ 12

Step-by-step explanation:

5,435,778 in scientific notation will be 5.435778×10⁶.

Scientific notation is the way to represents huge numbers in simple form. This ease understanding and calculation of the numbers. When written in a scientific notation, the number is called coefficient, the number to which power is raised is called base and raised power is called exponent. For instance, in the given answer, 5.435778 is coefficient, 10 is base and 6 is exponent.

While converting the numbers into scientific notation, we need to remember following points -

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The complete question is -

what is 5,435,778 expressed in scientific notation? a.5.435778 x 10⁷ b.5.435778 x 10³ c.5.435778 x 10⁶ d.5.435778 x 10⁵

The measure of an angle 2 is 85°.

Given that, ∠6=9x+13 and ∠2=11x-3.

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.

As we know, corresponding angles are congruent.

So, ∠6= ∠2

⇒ 9x+13=11x-3

⇒ 13+3=11x-9x

⇒ 16=2x

⇒ x=8

Now, ∠2=11x-3

=11×8-3=85°

Therefore, the measure of an angle 2 is 85°.

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Answer: The First game with 16/19 serves

Step-by-step explanation: Fraction also means division. So once you divide both fractions, you'll see that 16/19 > 13/16. That shows that she was more effective in the first game.

Answer:

20 1/16

Step-by-step explanation:

please give brilliantest pls

Answer:

You have the correct answer [tex]20 \frac{1}{16}[/tex]

Step-by-step explanation:

The value of the expression 10y²z is -750.

We are to calculate the expression 10y²z when y=−2 and z=−5.

This will be:

10y²z

= 10 × -5² × -3

= 10 × 25 × -3

= -750

The value of the expression 10y²z is -750.

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Answer:

[tex] \sf \large \: x=8a[/tex]

Step-by-step explanation:

Let's solve for x.

3/ax−4=20

Step 1: Multiply both sides by a.

−4a+3x=20a

Step 2: Add 4a to both sides.

−4a+3x+4a=20a+4a

3x=24a

Step 3: Divide both sides by 3.

3x/3 = 24a/3

x=8a

Answer: -3/4

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: −3/4

y-intercept: (0,0)

x    y

0    0

4   -3

The total cost is represented as C = $0.50x + $4300  and the average cost as avgC = $0.50 + $4300/x

We have been given that,

The variable cost for producing the game = $0.50 per unit

The fixed cost for producing the game = $4300

Let the total cost be denoted by C.

And let x be the number of games produced.

a) Total cost = variable cost + fixed cost

          C = $0.50x + $4300

b) Average cost = total cost/number of games produced

                        = C/x

                        = ($0.50x + $4300)/x

                        = $0.50 + $4300/x

Hence the total cost is C = $0.50x + $4300 and the average cost is $0.50 + $4300/x

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The number of days taken to complete the production of a batch of pens are 22, as calculated by basic algebra.

Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.

Now, According to the question, the factories used all 12 machines in the last days, Also, for the first 8 days, only 9 machines were in use.

Thus, If the factories used all 12 machines, the batch of pens took 20 days to be manufactured.

Hence, the equation formed from the given information by basic algebra is: 20 + 12 - 9(8) / 12

28 - (72/12)

=28 - 6 = 22

Hence, The number of days taken to complete the production of a batch of pens are 22, as calculated by basic algebra.

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Answer:

3/7

Step-by-step explanation:

12/28=3*4/4*7=3/7

Different letter arrangements that can be obtained from the letters of the word statistically, using all the letters= 6,48,64,800

Given,

Total number of arrangements obtained = 6,48,64,800

Given words = STATISTICALLY

Total word count = 13

Here we have repeated alphabets as -

"S"s = 2

"T"s = 3

"A"s = 2

"I"s = 2

"L" = 2

Total permutations we have here = 13! / 2!2!2!2!3!

= 6,22,70,20,800 / 96

= 6,48,64,800

A permutation of a set in mathematics is, broadly speaking, the rearranging of its components if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

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Answer:

Step-by-step explanation:

If you distribute 6 to the  numbers inside the parenthesis, it means that you multiply both number by 6
2 x 6 = 12
3 x 6 = 18
the expression can be rewritten like the following:

12 + 18 = 30

Answer:

-13

Step-by-step explanation:

(-21) - (-8) = -13

-21 - -8 = -13

Because of the two subtract signs next to each other before the number 8, they change to an addition sign.

From -21, move right 8 places along the number line because it is add 8.

-21  -20  -19  -18  -17  -16  -15  -14  -13

And you get to -13

Therefore, -21 + 8 = -13

Answer: Translation means you move a shape without rotating or flipping it and reflection is a mirror image of the shape. In the current example, the shape is translated right and down a noncalculable amount.

It will take 14.02 weeks for both the accounts to have the same balance

Bank account balance of Rhiannon = -$253.50

Money deposited by Rhiannon in the bank account each week = $35.80

Bank account balance of Sophie = -$78.25

Money deposited by Sophie in the bank account each week = $23.30

Let the number of weeks it takes to have the same account balance be x, therefore formulating the algebric equation we get:

Bank balance of Rhiannon + Money deposited by her each week*No of weeks it will take for the balance to be equal = Bank balance of Sophie + Money deposited by her each week*No of weeks it will take for the balance to be equal

= -253.5 + 35.8(x)  = -78.25 + 23.3(x)

= -175.25 = -12.5(x)

x =  14.02 weeks

Therefore, it will take 14.02 weeks for both the accounts to have the same balance

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The average rate of change of f(x) on the interval [1,1+h] is [1/(h + 6) - 1/6]/h

The function is given as

f(x) = 1/(x + 5)

The interval is given as

[1, 1 + h]

Calculate f(1) as follows

So, we have

f(1) = 1/(1 + 5)

f(1) = 1/6

Calculate f(1 + h) as follows

So, we have

f(1 + h) = 1/(1 + h + 5)

f(1 + h) = 1/(h + 6)

The average rate of change of f(x) on the interval [1,1+h] is then calculated as

Rate = [f(1 + h) - f(1)]/[1 + h - 1]

This gives

Rate = [1/(h + 6) - 1/6]/h

Hence, the average rate of change of f(x) on the interval [1,1+h] is [1/(h + 6) - 1/6]/h

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According to the solving Alyse buy 5/6lb pounds fraction of tea.

A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator as well as denominator of a complex fraction is a fraction.

A numerator, which is located above the line, and a denominator make up fractions (which is below the line). You may find out how many equally sized pieces are divided into something by looking at the denominator. How many of these equal components are taken into account is indicated by the numerator.

1/3lb of orange pekoe tea.

1/2lb of English cinnamon tea.

find the total pound of tea she buy:

So,

Adding these two fraction we get the total pounds:

= [tex]\frac{1}{3} + \frac{1}{2}[/tex]

= [tex]\frac{2 + 3}{6}[/tex]

= 5/6 lb

According to the solving Alyse buy 5/6lb pounds of tea.

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Answer:

1/-2

Step-by-step explanation:

Slope(m) = y2- y1/x2-x1

= -3-(-6)/-4-2

=+3/-6

=1/-2

Answer:

3.14159

Step-by-step explanation:

The value of π correct to 5 decimal places is 3.14159.

Decimal numbers are numbers which includes a whole number part and a fractional part.

The point separating both parts is the decimal point.

Pi, which is written as the Greek symbol π, is defined as the ratio of the circumference of any circle to the diameter of that circle.

We know that,

Circumference of a circle, C = 2 π r, where r is the radius.

2r will be the diameter.

π = C / 2r

The value of pi to 5 decimal places = 3.14159

Normally we use 3.14.

Hence the value of pi is 3.14159 to 5 decimal places.

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