Compute 41, 42, 43, 44, 45, 46, 47, and 48. Make a conjecture about the units digit of 4n where n is a positive integer. Use strong mathematical induction to prove your conjecture.

Answers

Answer 1

Answer:

The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even

Step-by-step explanation:

[tex]4^1 = 4\\4^2 = 16\\4^3 = 64\\4^4 = 256 \\4^5 = 1024\\4^6 = 4096\\4^7 = 16384\\4^8 = 65536[/tex]

The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even

To prove this conjecture

[tex]4^1 = 4\\4^2 = 16[/tex] unit digit = 6

hence the property is true for ; n = 1 and n = 2 and also for every odd and even number ( i.e. from 1  to 8 )


Related Questions

Use the inequality below to find the value of r .
150 - 5 r ≥ 87.5

a. r ≥ 12.5
b. r ≤ 12.5
c. r ≥ -(12.5)
d. r ≤ -(12.5)

Answers

.....the answer is d

Given the point and slope write the equation of the line (6, -6); slope = 5/6

Answers

Answer:

y=5/6x-11

Step-by-step explanation:

Slope intercept form: y=mx+b

With slope: y=5/6x+b

Replace x with 6 and y with -6

[To figure out which one is x or y remember (x,y) so if you compare (6,-6) then you will find that 6 is x and -6 is y]

-6=5/6(6)+b

Simplify:

-6=5+b

Subtract 5 on both sides:

-11=b or b=-11

Answer:y=5/6x-11 (Replace the b in y=5/6x+b with -11 since -11 is equal to b)

Hope this helps!

Brita has a monthly budget of x dollars. She spends $1,425 on her mortgage every month. One-third of her remaining budget is spent on recreational activities. Which equation below can be used to determine the amount, in dollars, spent on recreational activities?

Answers

Answer:

y = ⅓(x - 1425)

Step-by-step explanation:

Given

Budget = x

Mortgage = 1425

Required

Determine the amount spent on recreational activities.

First, we need to get the balance after she pays her mortgage.

Balance = Budget - Mortgage

Balance = x - 1425

From the question, we understand that she spends ⅓ of the balance on recreational activities.

Represent this with y.

y is calculated as thus:

y = ⅓ of Balance

y = ⅓ * (x - 1425)

y = ⅓(x - 1425)

Hence, the above equation y = ⅓(x - 1425) can be used to calculate the amount spent on recreational activities

Jessica has an account with a credit union. Her account earns 2.6% simple interest yearly. Exactly a year and a half ago, she opened her account with $900.

How much interest has she earned so far?

Answers

35.1

(2.6*900*1.5)/100

Answer:

$35.1

Step-by-step explanation:

2.6% of 900 = 23.4

Since it's a year and a half you might want to divide by two.

2.6/2 = 1.3

1.3% of 900 = 11.7

add them up,

23.4 + 11.7 = 35.1

It's asking for how much she EARNED not HAS in her bank account in 1.5 years. So include what she earned with interest, do not include the 900 dollars because she didn't earn it with interest, she already had that.

Help please! I’ll give brainliest if correct!

Answers

Answer:

The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation.

Step-by-step explanation:

Hope  his helps!

It’s B because the input 8 has more than 1 output

write -90 in simplest radical form
please help or i’ll failll

Answers


Search Results
Featured snippet from the web

Simplest radical form means simplifying the radical such that there are no square roots ,cube roots ,etc to find. When simplifying a fraction, if there is a radical, should it always be a numerator?

2.2.PS-16

Challenge Schools A and B are competing in an academic contest. Correct answers earn 9 points.

Incorrect answers lose 2 points. In the final round, School A gives the same number of correct and

incorrect answers. School B gives no incorrect answers and the same number of correct answers as

School A. School A started the final round with 62 points. School B started with 24. The game ends

with the two schools tied. Let x represent the number of correct answers given by School A in the final

round. Write an equation that models the outcome of the contest. Then find the number of answers

that each school got correct in the final round.

Which equation models the scoring in the final round and the outcome of the contest?

OA. 9x + 2x - 62 = - 9x + 24

OB. 2x-9x + 62 = 9x + 24

OC. 9x - 2x - 62 = 9x + 24

OD. 9x - 2x + 62 = 9x + 24

Answers

Answer:

9x - 2x + 62 = 9x + 24

Number of correct answer each obtained = 19

Step-by-step explanation:

Given that:

Number of correct answers = x

POINTS for correct answers = 9

POINTS for incorrect answers = - 2

SCHOOL A:

Number of correct answers = x

Number of incorrect answers = x

Initial point = 62

Initial point + 9(number of correct answers) + - 2(number of incorrect answers)

62 + 9x - 2x

SCHOOL B :

Number of correct answers = x

Number of incorrect answers = 0

Initial point = 24

Initial point + 9(number of correct answers) + - 2(number of incorrect answers

24 + 9x

Since they end up tied :

School A = School B

62 + 9x - 2x = 24 + 9x

9x - 2x + 62 = 9x + 24

Number of correct answers gotten :

9x - 2x + 62 = 9x + 24

7x + 62 = 9x + 24

7x - 9x = 24 - 62

-2x = - 38

x = 19

Hence, Number of correct answers each obtained = 19

What are the answers and explain

Answers

Answer:

Step-by-step explanation:

answers to what

?ummm can you rephrase this because I don’t understand

Complete the following statements to prove that ∠IKL and ∠JLD are supplementary angles.

Answers

Answer:

Is there a picture?

Step-by-step explanation:

What does 0.05 x 300 represent?

Answers

Answer:

15

Step-by-step explanation:

Your friend and her parents are visiting colleges. They leave their home in Enid, Oklahoma, and drive to Tulsa, which is 107 mi east and 18 mi south of Enid. From Tulsa, they go to Norman, 83 mi west and 63 mi south of Tulsa. Where is Norman in relation to Enid?


Answers

That question is hard try google that always helps me
They went 107 miles east and 83 miles west, subtract those to get 24 miles east. They went 18 miles south and 63 miles south, add those to get 81 miles south.

24 miles east and 81 miles south.

Brainliest Answer
(has to be right for brainliest)

Answers

Answer:

it is 0.7x0.4=0.28

Step-by-step explanation:

Answer:

3627514

Step-by-step explanation:

3)m I really need help

Answers

Answer:  angle ULM = 120 degrees.

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

Explanation:

We'll use the angle addition postulate. This is basically the idea where we can break any angle into smaller parts, or go in reverse to build up larger angles based on smaller pieces.

In this case, we can see that the smaller angles KLU and ULM combine to form the largest angle KLM. Think of it like puzzle pieces.

Let x be the measure of angle ULM

We can say the following

(angle KLU) + (angle ULM) = angle KLM

(36) + (x) = 156

36 + x = 156

To solve for x, we subtract 36 from both sides

36+x-36 = 156-36

x = 120

Angle ULM is 120 degrees.

-------------------

As a check,

(angle KLU) + (angle ULM) = 36 + 120 = 156

which matches with angle KLM, so the answer is confirmed.

ULM = KLM - KLU

ULM = 156 - 36

ULM = 120 degrees


17 times the sum of a number, n, and 31 is 300. Write as an equation.

Answers

Answer:

17(n+31)=300

Step-by-step explanation:

17 times the sum of a number, n and 31 is 17(n+31)

and then set that equal to 300

What is the value of k in the equation k/3-5=34

Answers

Answer: What is the value of k in the equation k/3-5=34

Step-by-step explanation: Solution for k/3-5=34 equation: k in (-oo:+oo) k/3-5 = 34 // - 34 k/3-34-5 = 0 1/3*k-39 = 0 // + 39 1/3*k = 39 // : 1/3 k = 39/1/3 k = 117 k = 117

Answer:

k = 117

Step-by-step explanation:

I was just learning this in class...

So basically you need to get the variable k by itself so you add 5 to -5 in the equation and leave k/3 alone and then you add 5 to the other side of the equation also so you add 34+5 and you get 37 so you get k/3=37 and now you multiply 3 by 3 to cancel it out and then you once again do it on the other side of the equation 37 x 3=117 soo that leads you too k=117 YAYYY!!

the pic the pic this is it​

Answers

Answer:

yes I agree with you

Step-by-step explanation:

thanks for the free question

Answer: mmmmmm Otae?

Step-by-step explanation:

Erasers cost 45 cents a piece. Notebooks cost 90 cents a piece . Karla spent $18 for a total of 28 erasers and notebooks . How many did she buy ?​

Answers

Answer:

12 Notebooks And 16 Erasers

Step-by-step explanation:

Let x represent the number of notebooks and y represent the number of erasers. (x+y=28) Then, input the cent numbers into the equation. (90x+45y=1800) The 1800 represents the amount of dollars spent. Then simplfy the equation, which gives you 12 notebooks and 16 erasers.

Problem
What is the constant of proportionality in the equation y=3xy

Answers

Answer:

-3

Step-by-step explanation:

y=3xy and subtract y on both sides that gives u -1 and then you have -1=3x and then divide 3 on both sides you are left with -3 =x

An ice cream factory makes 310 quarts of ice cream in 5 hours. How many quarts can they make per hour?

Answers

62 quarts of ice cream can be made in 1 hour. brainliest?

Celeste wants to have her hair cut and
permed and also go to lunch. She knows
she will need $95. The perm costs twice
as much as her haircut and she needs $5
for lunch.
How much does the perm cost?

Answers

Answer:

the perm will cost $60

Step-by-step explanation:

take away $5 from the total because Its a set amount that's already known

which leaves 90 which if you  take 30 away you are left with 60 its twice the amount of the haircut, I didn't really do any math techniques so I'm sorry that my explanation is weird, I hope this helped

Write the letters of the expressions that are equivalent to the given expression.
5(2x + 3)
a. 10x + 15
b. 5x + 15x + 5x
c. 10x + 8

Answers

Answer: A.) 10x + 15

Step-by-step explanation:

You would distribute (multiply) the 5 to the 2x which would then make it 10x and you would distribute (multiply) the 5 to the 3 which would then make it 15. Because the 5 is a positive number the sign stays the same.

Therefore, 10x + 15 is your answer.

Please help someone last one

Answers

Answer:

a in table → b on number line

b in table → c on number line

c in table → a on number line

Step-by-step explanation:

Here, we see the points are square roots. A square root of a number is a value, that when multiplied by itself, gives the number. For example, 4 × 4 = 16, so the square root of 16 is 4.

We can apply this logic easily by simplifying the square root, or multiplying integers with each other (aka "squaring" the integers) and seeing which result is closest to the value inside the square root.

Simplifying the square root won't help here, if we don't know basic values such as √3 or √2. So, we can just multiply an integer with itself and see if that value is closer to the value inside the square root.

For point a, we see the number inside the root is 27. We can start multiplying:

1×1 = 12×2 = 43×3 = 94×4 = 165×5 = 256×6 = 36

25 is the closest value to 27 here. So, we know the point is somewhere around 5, and since 27 is slightly larger than 25, the point is slightly larger than 5. So, point a in the table is most likely point b on the number line.

For point b, we see the number inside the root is 32. We can start multiplying:

1×1 = 12×2 = 43×3 = 94×4 = 165×5 = 256×6 = 36

36 is the closest value to 32 here. So, we know the point is somewhere around 6, and since 32 is smaller than 36, the point is lesser than 6. So, point b in the table is most likely point c on the number line.

For point c, we see the number inside the root is 16. We can start multiplying:

1×1 = 12×2 = 43×3 = 94×4 = 16

16 is right on the dot! That means that the square root of 16 is 4, which leaves us with point a on the number line.

In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonable) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).

In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 27% with a margin of error of 1.6%. Describe the conclusion about p using an absolute value inequality.

The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in < and then =, the symbolic entry option will automatically convert that too ≤ . In the same way, if you type in > and then =, the symbolic entry option will automatically convert that to ≥.

Be sure to use decimal numbers in your answer (such as using 0.40 for 40%).

Answers

Answer:

|0.254 ≤ p ≤ 0.286|

Step-by-step explanation:

Given that:

In a made up poll :

Proportion of people who like dark chocolate than milk chocolate (p) = 27%

Margin of Error = 1.6%

Hence,

p ± margin of error

27% ± 1.6%

(27 - 1.6)% ; (27 + 1.6)%

25.4% ; 28.6%

0.254 ; 0.286

Therefore ;

Lower bound = 0.254

Upper bound = 0.286

Expressing p as an absolute value Inequality ;

|0.254 ≤ p ≤ 0.286|

both the domain and range of the graph shown above is all real numbers.

true or false

Answers

Lol the answer is true

DUE IN 10 MINUTES!!!!!!!!!!!!!!!!!!!!!!!!!!

What is the slope?

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Should be 1/4 I think

Answer:

1/4

Step-by-step explanation:

Solve this 2 step equation 3x-7=20

Answers

Answer:

x=9 if thats what your asking

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

3x-7=20

3x=20+7

3x=27

X=27/3

X=9

So the value of X is 9

What is the first step needed to solve 2 over 5 multiplied by x minus 6 equals negative 16?

Subtract 16 from both sides
Add 6 to both sides
Divide both sides by 5
Multiply both sides by 2

Answers

Answer:

The correct answer is D.

Step-by-step explanation:

A linear function contains the following points. (-2,8) (0,6) What are the slope and y-intercept of this function?​

Answers

Answer:

slope= -1

y-intercept is 6

Step-by-step explanation:

slope = y2-y1/ x2-x1

slope = 6-8/ 0-(-2) = -1

y-intercept is 6 because of (0,6), where the points cross y-axis

Use the equation m=y2-y1/x2-x1 to find the slope
6-8/0-(-2)
-2/2
M=-1
Plug inyour slope one set of coordinates into y=mx+b. I’ll use the ordered pair (0,6)
6=-1(0)+b
6=b
Equation: y=-x+6

A box that measures 15 inches by 5 inches by 3 inches.
What are the units of the volume of the figure?

square inches
cubic inches
square centimeters
cubic centimeters

Answers

Answer: cubic inches.

Step-by-step explanation: When calculating volume, all of the units must be cubed. And all of the measurements are in inches.

Find the midpoint of the segment with the following endpoints.
(-4,-9) and (4, -1)

Answers

Answer:

[tex](0,-5)[/tex]

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS

Alg I

Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Step-by-step explanation:

Step 1: Define

Point (-4, -9)

Point (4, -1)

Step 2: Find midpoint

Substitute:                    [tex](\frac{-4+4}{2},\frac{-9-1}{2})[/tex]Add/Subtract:               [tex](\frac{0}{2},\frac{-10}{2})[/tex]Divide:                          [tex](0,-5)[/tex]
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