I NEED HELP PLEASE, THANKS! :)

I NEED HELP PLEASE, THANKS! :)

Answers

Answer 1

Answer:

Assume that Sk is valid for n=k and prove that Sn is valid for n= k+ 1

Step-by-step explanation:

This is Principle of Mathematical Induction ---PMI

Step 1: Verify that Sn is valid for n =1

Step 2:Assume that Sk is valid for n=k and prove that Sn is valid for n= k+ 1


Related Questions

Write the equation of each line in slope intercept form (If possible please show work)

Answers

Hope it make sense now :)

A box is filled with 3 yellow cards , 4 green cards. A card is chosen at random from the box. What is the probability that the card is not green?

Answers

Answer:

3/7

Step-by-step explanation:

total cards 3+4 = 7

Not green = 7-4 = 3 cards

P ( not green )= not green cards / total = 3/7

Answer:

3/7.

Step-by-step explanation:

There are seven cards in total, four of them being green.

The knowledge of the color of the other cards aren't really nessesary, so you can just subtract four from seven, which is three.

Hope this helped!

choose the function that has domain x ≠ -3 range y ≠ 2.

Answers

The function is f(x)= 2x+1/x+3.

How to find the domain of a function?

A work domain is a set of all possible inputs for a job. For example, the domain f (x) = x² is all real numbers, and the domain g (x) = 1 / x is all real numbers except x = 0. And we can define the special functions of its most limited domains.

Which function has the domain and range?

The function domain f (x) is a set of all values ​​defined by the function, and the scope of the function is a set of all values ​​taken by f. (In grammar school, you probably call the domain a set of substitutes and a set of solutions.

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Answer:

B

Step-by-step explanation:

i got it right! :)

Which expression correctly represents “six more than the product of five and a number, decreased by one”?

Answers

Answer:

Step-by-step explanation:

Product of 5 and a number:  5n

Six more than that would be 5n + 6

Finally, "six more than the product of 5 and a number, decreased by one" would be

5n + 6 - 1, or 5n + 5

Answer: A) 6 + 5n - 1

Step-by-step explanation: edge. 2022

Do 2b+ b and 3b have the same value for all values of b? explain your reason

Answers

Answer:

Yes

Step-by-step explanation:

b is as in 1b so. . .

2 + 1 = 3

We can plug in b or as "b"

2b + b = 3b

So yes in whatever case 2b + b's value  will always equal 3b's value

Answer:

yes

Step-by-step explanation:

because you can use any number to put for B and they will have the same value as an example we will use 3 for b so 2b = 6 + b = 9 and 3b = 9

Two similar biscuit tins hold the same type of biscuits. The net mass of biscuits in the smaller tin is 1 kg. Find the net mass of biscuits in the larger tin. Net mass of biscuits in larger tin = __?_ kg

Answers

Answer:

1.5 kg

Step-by-step explanation:

Assuming it scales linearly: the higher tin holds 9/6 as many biscuits, so:

9/6 · 1 kg = 1.5 kg

Vickie buys a pack of 30 folders. She keeps 15 for herself and divides the rest between three of her friends. Which equation will help us find the number of folders each friend gets? *

Answers

Answer: 30 folders - 15 folders which she keeps = 15 folders; 15 folders / 3 friends = 5 folders per firend.

Step-by-step explanation:

Answer:

x= (30 -15)/3

Step-by-step explanation:

Number of folders = 30Kept for herself = 15 foldersDivided = the reminderNumber of friends= 3Each friend gets= ?

If we call x the number each friend gets, then the equation is:

x= (30 -15)/3

Solving this we get:

x= 5

Each friend gets 5 folders

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)∫414√lnxdx,n=6

Answers

Answer:

trapezoidal rule: 14.559027midpoint rule: 14.587831Simpson's rule: 14.577542

Step-by-step explanation:

We assume you want the integral ...

  [tex]\displaystyle\int_4^{14}{\sqrt{\ln{x}}}\,dx[/tex]

The width of each interval is 1/6 of the difference between the limits, so is ...

  interval width = (14 -4)/6 = 10/6 = 5/3

Then the point p[n] at the left end of each interval is ...

  p[n] = 4 +(5/3)n

__

Trapezoidal Rule

The area of a trapezoid is the product of its average base length multiplied by the width of the trapezoid. Here, the "bases" are the function values at each end of the interval. The integral according to the trapezoidal rule can be figured as ...

  [tex]\dfrac{5}{3}\sum\limits_{n=0}^{5}\left(\dfrac{f(p[n])+f(p[n+1])}{2}\right)[/tex]

  integral ≈ 14.559027

If you're doing this on a spreadsheet, you can avoid evaluating the function twice at the same point by using a weighted sum. Weights are 1, 2, 2, ..., 2, 1.

__

Midpoint Rule

This rule uses the area of the rectangle whose height is the function value at the midpoint of the interval.

  [tex]\dfrac{5}{3}\sum\limits_{n=0}^{5}{f(p[n+\frac{1}{2}])}[/tex]

  integral ≈ 14.587831

__

Simpson's Rule

This rule gives the result of approximating the function over each double-interval by a parabola. It is like the trapezoidal rule in that the sum is a weighted sum of function values. However, the weights are different. Again, multiple evaluations of the function can be avoided by using a weighted sum in a spreadsheet. Weights for 6 intervals are 1, 4, 2, 4, 2, 4, 1. The sum of areas is ...

  [tex]\dfrac{10}{3}\sum\limits_{n=0}^{2}{\left(\dfrac{f(p[2n])+4f(p[2n+1])+f(p[2n+2])}{6}\right)}[/tex]

  integral ≈ 14.577542

A flagpole is casting a 20 feet shadow. the flagpole measures 16 feet find the angle of elevation of the sun

Answers

Answer:

39°

Step-by-step explanation:

==>Given:

Shadow length = 20ft

Flag height = 16ft

==>Required:

Angle of elevation of sun (θ)

==>Solution:

To calculate the angle of elevation of the sun, recall the trigonometry formula SOHCAHTOA.

We are given adjacent side = 20ft, and opposite side = 16ft

Therefore, we would use TOA, which is:

tan θ = Opposite/Adjacent

tan θ = 16/20

tan θ = 0.8

θ = 38.6598083 ≈ 39°

Angle of elevation of the sun = 39°

The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the letters of the alphabet do not appear as the first letter of a surname If more than one surname begins with a letter besides A and O, how may surnames begin with that letter?

Answers

Step-by-step explanation:

40children - 23 (with A, O) = 17left

26 letter in alphabet- ( A, O) = 24 letter left

24 letters left - 14 (not used for 1st letters) = 10

10 letters left to use/ 17 children left

10÷17 = 0.5882352941 x 10 =5.8 or as close to 6 I can get

There are six surnames that start with each letter other than A and O when more than one surname does.

What are permutation and combination?

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given, The surnames of 40 children in a class are arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A.

Since, 14, of the letters of the alphabet do not appear as the first letter of a surname

14 of the letters of the alphabet do not appear as the first letter of the surname

∴ the no. of letters that appeared = 26-14 = 12 alphabets

15 surnames begin with 10 letters beside O and A

∴ 6 surnames begin with a letter

Therefore, If more than one surname begins with a letter besides A and O, 6 surnames begin with that letter.

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PLEASE ANSWER FAST!! THANK YOU :)

Answers

Answer:

option 1 both statements are true

Step-by-step explanation:

Prove by PMI -- Principle of Mathematical  Induction

1) n³ + 2n

n= 1 , 1³ +2*1 = 1+2 = 3 = 3*1   ---->divisible by 3

n = 2 ; 2³ + 2*2 = 8+4 = 12  = 3*4  ----> is divisible by 3

Assume that It is valid for n = k ;  

[tex]k^{3}+2k[/tex] = 3*m -----(I) , for all m ∈ N

We have to prove for n =k +1 , the statement is true.

n = k+1, [tex](k+1)^{3}+2(k +1) =k^{3}+3k^{2}+3k +1 +2k +2[/tex]

                                           = k³ + 3k² + 3k + 3 + 2k

                                           =  k³ +  2k + 3k² + 3k + 3

                                           = 3m + 3 (k² + k + 1)

                                          = 3(3 + [k² + k + 1] ) is divisible by 3

Therefore, this statement is true

2) [tex]5^{2n}-1\\[/tex]

[tex]n=1 ; 5^{2}-1 = 25 -1 = 24 divisible by 24\\\\n = 2 ; 5^{2*2}-1 = 5^{4}-1 = 625 - 1 = 624 divisible by 24[/tex]

This statement is also true

PLEASE HELP!!(PIC INCLUDED)
Which of the following steps were applied to ABCD to obtain A'B'C'D?

A. shifted 3 units right and 2 units down

B. shifted 4 units right and 2 units down

C. shifted 2 units right and 3 units down

D. shifted 3 units right and 1 unit down

Answers

Answer:

A. Shifted 3 unit right and 2 unit down

Step-by-step explanation:

Let's determine the reason for the answer.

We will use a reference point, only one point to determine the reason.

Because the both shape are identical.

Let's use point A

The position of A is 2 on the y axis and 1 on the x axis

While the position of A' is 0 on the y axis and 4 on the X asis

Let's know how many units where moved from the position.

A' -A

For X axis

4-1= 3

For y axis

0-2= 2(we need only the magnitude)

So its 2 units Down and 3 unit right

Try it
Evaluate the function g(x) = -2x² + 3x – 5 for the input values -2, 0, and 3.
g(-2) = -2(-2)2 + 3(-2) - 5
g(-2) = -2(4) - 6-5
g(-2) = ?
g(0) =?
g(3) =?

Answers

Answer:

g(-2) = -19g(0) = -5g(3) = -14

Step-by-step explanation:

When you have several evaluations to do, it is often convenient to put the formula into a graphing calculator or spreadsheet.

__

If you must evaluate a polynomial by hand, it is often easier if the expression is written in "Horner form":

  g(x) = (-2x +3)x -5

Then we have ...

  g(-2) = (-2(-2) +3)(-2) -5 = 7(-2) -5 = -19

  g(0) = (-2(0) +3)(0) -5 = -5

  g(3) = (-2(3) +3)(3) -5 = (-3)(3) -5 = -14

The amount of time t(in minutes) that it takes to put out a fire varies inversely with G, the volume of water used (in hundreds of gallons). When G is 2, t is 20. Find how long it takes to put out a fire when 500 gallons of water (G = 5) are used.

Answers

Answer:

50 minutes.

Step-by-step explanation:

You can use a ratio to solve:

    [tex]t[/tex]     :     [tex]G[/tex]

  20    :     2

   10    :     1

    [tex]x[/tex]     :     5

[tex]x[/tex] must be 50 minutes since 100 gallons of water takes 10 minutes.

PLEASE HELP!!! How many 2-digit numbers are among the terms of the arithmetic sequence 2, 7, 12, 17, ...?

Answers

Step-by-step explanation:

The difference between. Each numbers is 5 so, it's answer is 22 and 27

1. The graph of yf(x) is translated 3 units right and 4 units down. What is the equation of the translation
image in terms of the function ?
A. Y-3 = f(x+4)
B. y + 4 = f(x-3)
C. y + 3 = f(x-4)
D. y - 4 = f(x + 3)

Answers

Answer:

D.y-4=f(x+3)

Step-by-step explanation:

The correct translation would be y-4 because the y-coordinate moves down 4 units and f(x+3) because the x-coordinate would move 3 spaces to the right.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

The equation of the translation image of the function is  y - 4 = f(x + 3).

which is the correct answer would be an option (D).

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.

For example, If shift up by 1 unit,  add 1 to the function

If shift down by 4 units, subtract 4 from the function

To determine the graph of y (x) is translated as 3 units right and 4 units down.

The x-coordinate will increase by 3 if we move it to the right.

If we shift it downward, it will become negative and read as y - 4.

So y - 4 = f(x + 3)

Therefore, the equation of the translation image of the function is  y - 4 = f(x + 3).

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7. Factor by grouping.
6p2 - 17p - 45
A (2p - 9)(3p + 5)
B (2p + 9)(3p + 5)
7096
Oc
C (2p - 9)(3p - 5)
90%
D (2p + 9)(3p - 5)
ping​

Answers

Answer:

Step-by-step explanation: 4

Given: a concave polygon Conjecture: It can be regular or irregular

Answers

Answer:

[tex]false[/tex]

Step-by-step explanation:

A concave polygon can never be regular (all sides and angles must be congruent). Hope this helps..

A farmer is enclosing a rectangular area for a pigpen. He wants the length of the pen to be 20 ft longer than the width. The farmer can use no more than 100 ft of fencing. What is the pen’s greatest possible length? Let w represent the width of the pen. What expression represents the length?

Answers

Answer:

Width is 15, length is 35.We can check our answer by multiplying the length by 2 and the width by two in order for the perimeter to be equal to 200.15 times 2 is 30 and 35 times two equals 70.70+30=100 so our solution satisfies our problem.

Step-by-step explanation:

Let the width be x.Then the length should be x+20.The farmer can’t use more than 100 ft of fencing and by mentioning enclosing a rectangle area for a pigpen, we can tell that 100 is the perimeter.So 2(x+20) + 2(x)=100.2x+ 40 + 2x=100.4x+40=100.4x=60.X is 15 which is the width so then the length is 35.

1/4 ÷ 3/8 simplest form

Answers

Answer:

2/3

Step-by-step explanation:

divide by a fraction = multiply by reciprocal

1/4 * 8/3

2/3

Answer:

Step-by-step explanation:

= ¼ ÷ ⅜

= ¼ × ⁸/3

= ⅔

Have a great day !

please help. Find the value of x

Answers

Answer:

x  =24

Step-by-step explanation:

Call the angle in the lower right corner y

The outside angles add to 180 degrees for the large triangle

41+ 94+ y = 180

135 + y = 180

y = 180-136

y =45

The small triangle in the lower right also has angles that add to 180

y+ 111+x = 180

45+111+x = 180

156 + x = 180

x = 180-156

x =24

Answer:

x = 24

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

a + 111 = 180

180 - 111 = a

a = 69

Angles in a quadrilateral add up to 360 degrees.

69 + 41 + 94 + c = 360

204 + c = 360

c = 360 - 204

c = 156

Angles on a straight line add up to 180 degrees.

x + 156 = 180

x = 180 - 156

x = 24

If a carton contains 6 eggs, how many eggs are there in 13 cartons? would it be 6x13?? which is equal to 78 I'm not sure.

Answers

Answer:

78 eggs

Step-by-step explanation:

13 × 6 = 78 eggs

Hope this helps! :)

Answer:

Yes it would be 6x13=78

Step-by-step explanation:

cross multiplication and divide:

1 cartoon = 6 eggs

13 cartoons = x

Find the missing side and round the answer to the nearest tenth. Thanks.

Answers

Answer:

22.2

Step-by-step explanation:

The missing side is x

cos19° = 21/x      switch x and cos19° x = 21/cos 19°

x = 22.21≈ 22.2

Write the function whose graph is the graph of y= Vx, but is translated 5 units downward.

Answers

Answer:

y = Vx - 5

Step-by-step explanation:

shift down is -5

y = Vx - 5 is the function whose graph is the graph of y= Vx, but is translated 5 units downward.

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The function y = Vx represents the square root function, which is a graph of a half of a parabola opening upwards and passing through the point (0, 0).

To translate this function 5 units downward, we need to subtract 5 from the function. Therefore, the function we need is:

y = Vx - 5

This is the square root function shifted downward by 5 units.

The graph of this function will be the same as the graph of y = Vx, but shifted 5 units downward.

Hence, y = Vx - 5 is the function whose graph is the graph of y= Vx, but is translated 5 units downward.

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Lindsey made an error while solving this equation. 143.5 = 2 - (7(x+3). What line has the error?

(Refer to image)

A: Step 1
B: Step 2
C: Step 3
D: Step 4

Answers

Answer:

Step 1

Step-by-step explanation:

She didn't distribute the negative while she distributed 7. It should be -7x - 21, not 7x - 21.

Which statement explains if a dilation was applied? A dilation was applied to the fabric because the width of the fabric was preserved. A dilation was applied to the fabric because the angle measures were preserved. A dilation was not applied to the fabric because the angle measures are the same. A dilation was not applied to the fabric because the length was changed, not the width.

Answers

Answer:

A dilation was not applied to the fabric because the length was changed, not the width.

Step-by-step explanation: B was not the answer it was D.          

Answer:

D.

Step-by-step explanation:

Edge 2022.

A director of the library calculates that 10% of the library's collection is checked out. If the director is right, what is the probability that the proportion of books checked out in a sample of 899 books would be less than 11%? Round your answer to four decimal places.

Answers

Answer:

0.8413

Step-by-step explanation:

p = 0.10

σ = √(pq/n) = 0.01

z = (x − μ) / σ

z = (0.11 − 0.10) / 0.01

z = 1

P(Z < 1) = 0.8413

The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.

We have,

We can use the normal approximation to the binomial distribution to find the probability that the proportion of books checked out in a sample of 899 books would be less than 11%.

First, we need to calculate the mean and standard deviation of the binomial distribution:

Mean:

np = 899 × 0.1 = 89.9

Standard deviation:

√(np(1-p)) = √(899 × 0.1 × 0.9) = 9.427

Next, we need to standardize the sample proportion of 11% using the formula:

z = (x - μ) / σ

where x is the sample proportion, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Substituting the values we have, we get:

z = (0.11 - 0.1) / 0.9427 = 0.1059

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 0.1059 is 0.5425.

Therefore,

The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.

Rounded to four decimal places, the answer is 0.5425.

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PLZ I need Help the Question is: 5+13·18+85÷17−11

Answers

Answer:

233

Step-by-step explanation:

The distance d of a particle moving in a straight line is given by d(t) = 2t3 + 5t – 2, where t is given in seconds and d is measured in meters. Find an expression for the instantaneous velocity v(t) of the particle at any given point in time. Question 1 options: 6t3 – 5 5t3 + 6 6t2 + 5 5t2 – 6

Answers

Answer:

(C)[tex]6t^2+5[/tex]

Step-by-step explanation:

Given the distance, d(t) of a particle moving in a straight line at any time t is:

[tex]d(t) = 2t^3 + 5t - 2, $ where t is given in seconds and d is measured in meters.[/tex]

To find an expression for the instantaneous velocity v(t) of the particle at any given point in time, we take the derivative of d(t).

[tex]v(t)=\dfrac{d}{dt}\\\\v(t) =\dfrac{d}{dt}(2t^3 + 5t - 2) =3(2)t^{3-1}+5t^{1-1}\\\\v(t)=6t^2+5[/tex]

The correct option is C.

Answer:

6t2+5

Step-by-step explanation:

Solve by completing the square: 5x2 + 20x + 32 = 0

Answers

your answer is no solution (because a negative square root doesn't exist)
first, you divide all sides by five and then take b, half it then square it
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(1 point)reciborecibarecibirecibi Entre 1908 e 1912, foi proposta pelo gelogo alemo Alfred Lothar Wegener a teoria da deriva continental. Nesta teoria, ele afirma que as placas continentais se rompem, separam-se e chocam-se, criando posteriormente cadeias de montanhas.Um dos argumentos mais fortes de Wegener para justificar a deriva continental era que as bordas dos continentes tm formas que se encaixam. Para defender sua teoria, mostrou que as formaes rochosas de dois lados do oceano Atlntico - no Brasil e na Africa Ocidental - coincidem em idade, tipo e estrutura.Alm disso, costuma conter fsseis de criaturas terrestres que no poderiam ter nadado de um continente ao outro. Sobre a expanso do fundo do mar, na dcada de 20, o estudo dos leitos dos mares trouxe evidncias de que as dorsais ocenicas so zonas onde se cria a nova crosta ocenica.(Certo ou Errado) What should be done following health violations from an inspection? a cat went from a to b a distance of 20 kilometres in one 1/2 hours but return in one hour calculate the average speed for the whole journey What could a dog living now and a cat living thousands of years ago have incommon?O A. They have some of the same matter.O B. They have the exact same DNA.O C. They have the same bone structure.O D. They have the same amount of energy. earning a 6% pay increase to current $62,900 annual salary Footsteps Co. has a bond outstanding with a coupon rate of 5.4 percent and annual payments. The bond currently sells for $1,007.49, matures in 18 years, and has a par value of $1,000. What is the YTM of the bond Ujalakhan01! Please help me! ASAP ONLY UJALAKHAN01. What's (x-1)(x-1)? When there are lower prices, but waiting lines customers will often be drawn to the competing location of a Monopolistic Competitor with greater customer service and better atmosphere.A. TrueB. False Please answer this correctly Pericles was a leader and lawmaker in ancient Athens. While Athens was fighting the Peloponnesian War, he gave a famous speech called the Funeral Oration. In his speech, he talked about Athenian democracy. Read the following excerpt from Pericless speech: Our constitution does not copy the laws of neighboring states; we are rather a pattern to others than imitators ourselves. Its administration favors the many instead of the few. . . . If we look to the laws, they afford equal justice to all in their private differencesclass considerations not being allowed to interfere with merit; nor again does poverty bar the way, if a man is able to serve the state, he is not hindered by the obscurity of his condition. Based on the excerpt above, how does Pericles feel about Athenian democracy?