Let un be the nth Fibonacci number. Prove that the Euclidean algorithm takes precisely n steps to prove that gcd(un+1, un) = 1.

Answer:

irrational

Step-by-step explanation:

A = s^2

s^2 = 24,200

[tex] s = \sqrt{24200} [/tex]

[tex] s = \sqrt{242 \times 100} [/tex]

[tex] s = \sqrt{100 \times 121 \times 2} [/tex]

[tex] s = 10 \times 11\sqrt{2} [/tex]

[tex] s = 110\sqrt{2} [/tex]

P = 4s

[tex] P = 4 \times 100 \sqrt{2} [/tex]

[tex] P = 440 \sqrt{2} [/tex]

The perimeter is irrational.

Derrick's value = 0

Ari's value = 0.5

Wesley's value = 2.1

============================

Explanation:

Derrick doesn't shade anything, so his value is 0.

Ari shades half of one model, so 1/2 = 0.5 is his value

Wesley shades 2 full models, plus 1/10 = 0.1 of another one, leading to 2+0.1 = 2.1 as his value.

The fractional amount of the model shaded by each of the boys are :

The size of each model cut out = 1/100 = 0.01

DERRICK :

ARI :

WESLEY

Therefore, the amount shaded by each of the boys represented as a decimal are :

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Answer:

68.5

Step-by-step explanation:

Subtract 4 from 73.

You get 69.

Then, subtract 0.5 more.

Your answer is 68.5.

Hope it helps!

Answer:

Number = 14

Step-by-step explanation:

It is given that,

Twice the sum of a number and seven is three times the number

Let the number be x. Twice of the number is 2x. Three times of the number is 3x.

So,

2(x+7)=3x is the equation that models the given scenario

Opening brackets on LHS,

2x+14=3x

Subtracting 2x on both the sides

2x-2x+14=3x-2x

14=x

So, the number is 14.

The number is 14.

The calculation is as follows:

Based on the above information, the calculation is as follows:

2(x+7)=3x  

2x+14=3x

x = 14

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Hello, when x tends to [tex]\infty[/tex] the term with the highest degree will lead the behaviour.

In other words.

[tex]\displaystyle \lim_{x\rightarrow+\infty} {x^4+3x^3-2x+7}\\\\=\lim_{x\rightarrow+\infty} {x^4}\\\\=+\infty\\\\\\\displaystyle \lim_{x\rightarrow-\infty} {x^4+3x^3-2x+7}\\\\=\lim_{x\rightarrow-\infty} {x^4}\\\\=+\infty[/tex]

So, the answer B is correct.

Thank you.

As x → - ∞, then y → ∞ and x → ∞, then y → ∞. Then the correct option is B.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = x⁴ + 3x³ - 2x + 7

If the value of x approaches the negative infinity, then the value of the function will be

f(x) = x⁴ + 3x³ - 2x + 7

We know that the value of (x⁴ - 2x) is greater than the value of 3x³. Then the value of the function will approach the positive infinity.

If the value of x approaches the positive infinity, then the value of the function will be

f(x) = x⁴ + 3x³ - 2x + 7

We know that the value of (x⁴ + 3x³) is greater than the value of 2x. Then the value of the function will approach the positive infinity.

Thus, As x → - ∞, then y → ∞ and x → ∞, then y → ∞.

Then the correct option is B.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

equation is y = 8x

=============================================

Explanation:

Divide each x and y pair like so: y/x

If we get the same result each time, then we have a direct proportion.

y/x = 32/4 = 8

y/x = 56/7 = 8

y/x = 96/12 = 8

Each time we get the same result 8, which is the constant of proportionality. The table does show a direct proportional relationship. The equation is y = 8x which is in the form y = kx. The k value is the constant of proportionality. So k = y/x.

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the line parallel to 3x - y = 14 we must first find the slope of 3x - y = 14.

So we have

y = 3x - 14

Comparing with the general equation above

Slope / m = 3

Since the lines are parallel their slope are also the same

So slope of parallel line = 3

Equation of the line using point ( - 4 , -7) and slope 3 is

We have the final answer as

Hope this helps you

Answer:

You can make 64 different sums (which includes a sum of $0 using none of the coins).

Step-by-step explanation:

The number of sums you can make is equal to:

⁶C₀ + ⁶C₁ + ⁶C₂ + ⁶C₃ + ⁶C₄ + ⁶C₅ +⁶C₆ = 1 + 6 + 15 + 20 + 15 + 6 + 1 = 64

Answer:

Hey there!

I would prefer method two.

Both methods give the right solution, but method two is more straightforward. Instead of distributing, you simply divide and don't need to do as much work.

Let me know if this helps :)

Answer:

This is  called a mid segment theorem in which the al ine segment (DE) joining the midpoints of two sides of a triangle is parallel to the third side.

Step-by-step explanation:

Suppose we have a triangle ABC. Then the midpoints can be located as D, E and F. If we join D , E and F another triangle is formed.

From the figure we can see that

AE≅ CE

AD≅DB

BF≅CF  

BECAUSE  all the given points are the midpoints which divide the lines into two equal halves.

If we increase the line DE to a point L we find out that DL is parallel to BC i.e. it does not meet at any point with BC. ( the two lines do not meet)

(1)

If we join C with L we find out that the the line DE is half in length to the line BC.

AS

AE= CE  (midpoints dividing into equal line segements.)

LE= DE

Triangle CEL= Triangle DEF

so

DL= BC

But DE = 1/2 DL

therefore

DE= 1/2 BC (2)

Therefore from 1 and 2 we find that a line segment (DE) joining the midpoints of two sides of a triangle is parallel to the third side

Answer: 200

Step-by-step explanation:

given data:

In a sample 76 people or 38% voted  the mayor to be prosecuted.

solution:

how many people were in that sample

if 38% = 76 people

therefore;

let

p = total number of people

76/p = 38/100

cross multiply both sides

38p = 7600

divide both sides by 38

38p /38 = 7600 /38

p = 200

the number of people in the sample original was 200.

Answer:

The next number going up or down?

Step-by-step explanation:

Down

20

5

Up

180

Answer:

60

Step-by-step explanation:

The sequence is to first add 20 and then divide by 2. To find the next number in the sequence, add 20. This means the next number in the sequence is 40+20=60.

Answer:

a. Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are

b. Theoretical Probability. Experimental Probability.

Use theoretical probability by counting the favorable outcomes and put that in a fraction above all possible outcomes.

Use experimental probability by comparing the number of times the event occurs to the total number of trials.

Step-by-step explanation:

I don't really know what to explain.  :v

Answer:

The brainliest!

Step-by-step explanation:

c= 7/6k- 17(7/6)

6/7c = k - 17

k = 6/7c+17

Answer:

$0.14

Step-by-step explanation:

Hello!

To find the price per ounce you divide the total cost by the number of ounces

11.99/84 = 0.1427

Round to nearest hundredth

0.14

The answer is $0.14

Hope this helps!

Answer:

13 and 14.

Step-by-step explanation:

So we have two consecutive integers.

Let's call the first integer a.

Since the integers are consecutive, the other integer must be (a+1) (one more than the last one).

We know that the sum of the greatest integer (or a+1) and twice the lesser integer (a) is 40. Therefore, we can write the following equation:

[tex](a+1)+2(a)=40[/tex]

The first term represents the greatest integer. The second term represents 2 times the lesser integer. And together, they equal 40.

Solve for a. Combine like terms:

[tex]a+1+2a=40\\3a+1=40[/tex]

Subtract 1 from both sides. The 1s on the left cancel:

[tex](3a+1)-1=(40)-1\\3a=39[/tex]

Divide both sides by 3:

[tex]\frac{3a}{3}=\frac{39}{3}\\a=13[/tex]

Therefore, a or the first integer is 13.

And the second integer is 14.

And we can check:

14+2(13)=14+26=40

Let the two consecutive integers be x and x + 1.

According to the question,

★ Greatest integer = x + 1

★ Lesser integer = x

The sum of the greatest integer and twice the lesser integer is 40. [ Given ]

⇒ ( x + 1 ) + 2 ( x ) = 40

⇒ x + 1 + 2x = 40

⇒ 3x + 1 = 40

⇒ 3x = 40 - 1

⇒ 3x = 39

⇒ x = 39/3

⇒ x = 13

★ x + 1 = 13 + 1 = 14

Hello, let's note a this positive real number.

The sum of the square is

[tex]a^2+(a-4)^2[/tex]

right?

So, we need to solve

[tex]a^2+(a-4)^2=72[/tex]

We will develop, simplify.

Let's do it!

[tex]a^2+(a-4)^2=72\\\\a^2+a^2-8a+16=72\\\\2a^2-8a+16-72=0\\\\2(a^2-4a-28)=0\\\\a^2-4a-28=0[/tex]

Now, we can use several methods to move forward. Let's complete the square.

[tex]a^2-4a=a^2-2*2*a=(a-2)^2-2^2=(a-2)^2-4[/tex]

So,

[tex]a^2-4a-28=0\\\\(a-2)^2-4-28=0\\\\(a-2)^2=32=4^2*2\\\\a-2=\pm4\sqrt{2}\\\\a = 2(1+2\sqrt{2}) \ \ or \ \ a = 2(1-2\sqrt{2})[/tex]

As a should be positive, the solution is

[tex]\Large \boxed{\sf \bf \ \ a = 2(1+2\sqrt{2}) \ \ }[/tex]

and the other number is

[tex]2(1+2\sqrt{2})-4=2(2\sqrt{2}-1)[/tex]

Thank you.

Answer:

x = 15

Step-by-step explanation:

angles 2 and 4 are supplementary so they add up to 180

2x + 10 + 4x + 80 = 180

6x + 90 = 180

6x = 90

x = 15

Answer:

x=15

Step-by-step explanation:

Angles 2 and 4 are same-side interior angles. This means that if they are supplementary angles, then the lines A and B are parallel.

Supplementary angles, when added together, will equal a total of 180°. Set up an equation in which the angles are added and are equal to 180:

[tex](2x+10)+(4x+80)=180[/tex]

Solve for x. Remove the parentheses and combine like terms:

[tex]2x+10+4x+80=180\\\\2x+4x+10+80=180\\\\6x+90=180[/tex]

Work to isolate the variable, x. Subtract 90 from both sides:

[tex]6x+90-90=180-90\\\\6x=90[/tex]

Isolate x. Divide both sides by 6:

[tex]\frac{6x}{6}=\frac{90}{6} \\\\x=15[/tex]

The value of x is 15.

:Done

If you want to check your work, insert the value of x into the angles, and add them. If the answer is 180, then the value of x is true:

[tex]2x+10\\\\2(15)+10\\\\30+10\\\\40[/tex]

∠2=40

[tex]4x+80\\\\4(15)+80\\\\60+80\\\\140[/tex]

∠4=140

∠2+∠4=180

40+140=180

The value of x is true.

Answer:

2,267.9g

Step-by-step explanation:

2,267.9g is more precise than 2,268 g becasue it is providng the actual number, with decimals.  It is providind the most accurate weight, showing that it's just a tiny bit less than 2,268 g, but still has the exact weight.  2,268g on the other hand, is rounded up which is also good in some scenarios, but it's not as accuracte/precise as the exact amount of something.

Answer:

29 years

Step-by-step explanation:

The population of the Chinese people is 1.3 bn, and they grow at a rate of 0.49% per year. To get the number of years it requires to reach 1.5 bn, we use this method

after x years, the population will be

1.3 * 1.0049^x

so you just need to solve

1.3 * 1.0049^x = 1.5

1.0049^x = 1.5/1.3

x log 1.0049 = log(1.5/1.3)

x = log(1.5/1.3)/log(1.0049)

x = 0.062 / 0.002122

x = 29.25 years

Therefore, at the rate of 0.49%, the Chinese population of 1.3bn needs 29 years to clock 1.5 bn

Answer:

[see below]

Step-by-step explanation:

Reflection across the x-axis is: [tex](x,y)\rightarrow(x,-y)[/tex]

Apply that to the point: [tex](4,-6.5)\rightarrow(4,6.5)[/tex].

Reflection across the y axis: [tex](x,y)\rightarrow(-x,y)[/tex]

Apply that to the point: [tex](4,-6.5)\rightarrow(-4,-6.5)[/tex]

Hope this helps.

Answer:

1.0000

Step-by-step explanation:

It is know that 20% of air bags produced by the manufacturing plant are defective.

20% of x

Therefore, the probability that two are defective will be

20/100 × 5

0.2×5=1.0000

Hello, let's note A the matrix, we need to find [tex]\lambda[/tex] such that A[tex]\lambda[/tex]=[tex]\lambda[/tex] I, where I is the identity matrix, so the determinant is 0, giving us the characteristic equation as

[tex]\left|\begin{array}{cc}1-\lambda&3\\-3&1-\lambda\end{array}\right|\\\\=(1-\lambda)^2+9\\\\=\lambda^2-2\lambda+10\\\\=0[/tex]

We just need to solve this equation using the discriminant.

[tex]\Delta=b^2-4ac=2^2-40=-36=(6i)^2[/tex]

And then the eigenvalues are.

[tex]\lambda_1=\dfrac{2-6i}{2}=\boxed{1-3i}\\\\\lambda_2=\boxed{1+3i}[/tex]

To find the basis, we have to solve the system of equations.

[tex]A\lambda_1-\lambda_1 I=\left[\begin{array}{cc}3i&3\\-3&3i\end{array}\right] \\\\=3\left[\begin{array}{cc}i&1\\-1&i\end{array}\right] \\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}ai+b=0\\-a+bi=0\end{cases}\\\\\text{(1,-i) is a base of this space, as i-i=0 and -1-}i^2\text{=-1+1=0.}[/tex]

[tex]A\lambda_2-\lambda_2 I=\left[\begin{array}{cc}-3i&3\\-3&-3i\end{array}\right] \\\\=3\left[\begin{array}{cc}-i&1\\-1&-i\end{array}\right]\\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}-ai+b=0\\-a-bi=0\end{cases}\\\\\text{(1,i) is a base of this space as -i+i=0 and -1-i*i=0.}[/tex]

Thank you

Answer:

108 skittles

Step-by-step explanation:

If she divides a bag of 324 skittles between 3 people, then we want to find a third of 324 - aka [tex]324\div3[/tex].

324 divided by 3 is 108, so each person will get 108 skittles.

Hope this helped!

Answer:

Standard deviation of the binomial distribution

                               = [tex]\sqrt{n p q} = \sqrt{192} = 13.856[/tex]

Step-by-step explanation:

Explanation:-

Given size 'n' = 800

The population proportion 'p'=0.6

Let 'X' be the random variable of the binomial distribution

a)  mean of the binomial distribution  = n p = 800 ×0.6

                                                             μ  = 480

b)  variance of the binomial distribution

                                                                      = n p q

                                                                      =  800 X 0.6 ×0.4

                                                                 σ²  = 192

Standard deviation of the binomial distribution

                                                             σ    = [tex]\sqrt{n p q} = \sqrt{192} = 13.856[/tex]

Answer:

80?

Step-by-step explanation:

i counted the numbers on the first domino and that would be the first number, counted on the second one that would be the second number but since c had a two digit number they added the first number of the two digit number to the first domino number and that is what i did with d

hope it's correct:)

Answer:

80

Step-by-step explanation:

Basically, the first domino represents the tens place of the number and the second domino represents the units place. For a, we see that there are 3 dots on the first domino and 4 dots on the second domino so the number is 30 + 4 = 34. The same goes for b. For c, there are 6 tens and 11 ones so the number is 60 + 11 = 71. For d, there are 7 tens and 10 ones so the number is 70 + 10 = 80.

Answer:

Yes, the triangles are simirar with a scale factor of 3/2.

Step-by-step explanation:

We find the scale factor by dividing corresponding sides:

12/8=3/2

18/12=3/2

24/16=3/2

Answer:

It is over then 749mm. so 800mm.

If it is less or same as 749mm, It is 700mm.

Answer:

[tex]\huge \boxed{\mathrm{800 \ mm}}[/tex]

Step-by-step explanation:

765 mm to nearest 100 mm would be to round up 765 to nearest hundred.

765 rounded up to nearest hundred’s place would be 800.

The place after 7 is 6, which is higher or equal to 5, so we add 1 to the hundred’s place followed by zeros.

Answer:

Step-by-step explanation:

First of all transform the expression using trigonometric identities

That's

[tex] \sec(x) = \frac{1}{ \cos(x) } [/tex]

[tex] \csc(x ) = \frac{1}{ \sin(x) } [/tex]

[tex] \cot(x) = \frac{1}{ \tan(x) } [/tex]

So we have

[tex] \frac{1}{ \cos(x) } \times \tan(x) \times \frac{1}{ \sin(x) } \times \frac{1}{ \tan(x) } \times \sin(x) \times \cos(x) [/tex]

Reduce the expression with tan x

We have

[tex] \frac{1}{ \cos(x) } \times \cos(x) \times \frac{1}{ \sin(x) } \times \sin(x) [/tex]

Reduce the expression with cos x

That's

[tex]1 \times \frac{1}{ \sin(x) } \times \sin(x) [/tex]

Reduce the expression with sin x

We have

[tex]1 \times 1[/tex]

We have the final answer as

Hope this helps you

Answer:

1. 1435

2. 4235

3. WEAR

4. 6512

5. 3265

6. TERM

Step-by-step explanation:

In the first 3 questions, the number codes are:

1 = D

2 = E

3 = A

4 = R

5 = M

6 = W

In the last 3 questions, the number codes are:

1 = T

2 = E

3 = S

4 = R

5 = I

6 = M