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

If 200 men can make a road 5 km long in 25 days ,how much overtime per day must 60 men can work to finish an road 2 km in 32 days , 12 hours being a day's work ?​

Answers

Answer:

Solution with step by step explanation is the image attached below

Use the SLOPE FORMULA to find the slope of the line that passes through the given points.
(1.3) and (4-7)

Answers

Answer:

[tex]m=\frac{4}{5}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Point (1, -3)

Point (-4, -7)

Step 2: Find slope m

Substitute:                    [tex]m=\frac{-7+3}{-4-1}[/tex]Add/Subtract:               [tex]m=\frac{-4}{-5}[/tex]Simplify:                        [tex]m=\frac{4}{5}[/tex]

During a period of 112 minutes, a music station played 40 minutes of commercials. What
is the ratio of music they played to commercials they played?

Answers

Answer:

9:5

Step-by-step explanation:

112 - 40 = 72. 112 represents the total time, but you are comparing music to commercials, so you have to subtract the commercial time from the total time.Find the GCF of 72 and 40, which is 8. Divide 72 and 40. The simplified ratio is 9:5.

The recently released iPhone XS Max comes in three different storage sizes: 64GB, 256GB, and 512GB. The price of the 64GB phone is $1,099. If prices were proportional to the phone's storage size, how much would the 256GB phone and the 512GB phone cost
Any help please

Answers

Answer:

iPhone XS Max: $1,249/256GB,

$1,449/512GB

Step-by-step explanation:

Got it !!!

Which equation has infinitely many solutions?

Answers

The answer is b the second one

PLEASE HELP ME SIMPLIFY THIS PLEASE SHOW WORK TO! THANK YOU 5.3x - 9 + 7.6x

Answers

Answer:

12.9x - 9

your welcome

-3 -2e -7 = 10
e =

Solve for e

Answers

Answer:e=-10

Step-by-step explanation:

-2e-7=13

-2e=20

e=-10

What is the image of 2,-1 after a reflection over the y axis

Answers

There are no images included, but it would be -2,-1.

i need help!
Check all that are solutions to −0.25 ≤ 0.5sin(2x) and over 0° ≤ x ≤360°

Answers

Answer:

A C E

Step-by-step explanation:

Please answer this thanks

Answers

Answer:

c

Step-by-step explanation:

Apply the distributive property to the expression to write an equivalent expression.


5x + 35


Complete the statements.


Find the GCF of

.

Now, factor out the GCF by dividing each term in the expression by

.

5x divided by the GCF is

, and 35 divided by the GCF is

.


The equivalent expression is

.




SOMEONE PLS HELP I'M. DYING PLS

Answers

5 • 30 = 150 5•5= 25 so 175x 175x / 5x = 35

Answer:

I don't get it everyone is telling the wrong answers am here to tell you guys and girls the right answer. The answer is :   D     A    B    B   C   your welcome                                                                  

What is 5 to the 3 power simplifyed

Answers

Answer: 125

Step-by-step explanation:

5^3=5*5*5=125

Answer:

125

Step-by-step explanation:

5^3 = 5 times 5 times 5

5 times 5 = 25

25 times 5 = 125

HELP PLEASE HELP ILL GIVE U 15 points and BRAINLIEST to the correct answer (DONT guess please)

Consider the function.
f (x)= -80 +4
What is the value of f (-1/4)?
A. 0
B.2
C. 3
D. 6

Answers

It should be C. 3.
Yes

Answer: the answer is b

Step-by-step explanation:

Just trust me

4) What are all the subsets of (3, 5, 7)?

Answers

ANSWER: 1 is a subset of 3,5,7

Answer:

X=(0,3) (3,0) Y=(0,5)(5,0) Z=(7,0) (0,7)

Step-by-step explanation:

suppose ,3=x ,5=y and 7=z

0 is the common number

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.

Which statement about the diagram is true

Answers

Answer:

AB have the length of 9

Step-by-step explanation:

5 is to short 14 is too long in between would be 9

Someone please help thanks

Answers

Answer:

P=8T/V

Step-by-step explanation:

V=8T/P

PV=8T

P=8T/V

Please help...20 points! And explain

Answers

Perpendicular = opposite sign and reciprocal
The slope of perpendicular line would be -2
Equation y= -2x

Reduce the fraction and find the domain.
[tex]\frac{a(x-2y)}{b(2y-x)}[/tex]

Thanks!

Answers

Answer:

-a/b

Step-by-step explanation:

a(x - 2y)/b(2y - x) =            ⇒ consider x - 2y = - (2y - x)-a(2y - x)/b(2y - x) =-a/b

what is 40/17 rounded to the nearrst hundreth as a decimal ​

Answers

Answer:

★ 40 over 17 is roughly 2.35294, which can be rounded to the nearest hundredth as 2.35

Step-by-step explanation:

Hope you have a great day :)

40 over 17 should be correct and can I get marked brainless

Write -2(pi)/9 in degrees.

Answers

Answer:

-40 DEGREES

Step-by-step explanation:

What is the rate of change for the line that goes through the points (8,14) and (11, 19.25)​

Answers

Answer:

1.75

Step-by-step explanation:

The rate of change for the line that goes through the points (8,14) and (11, 19.25)​ is known as the slope expressed as;

slope m = y2-y1/x2-x1

Substitute the coordinate pairs into the formula;

m = 19.25-14/11-8

m = 5.25/3

m = 1.75

Hence the rate of change for the line is 1.75.

I need some help with these, I would appreciate it.

Answers

The first one I think is B

A researcher studying koi fish collected data on three variables, A, B, and C. The following residual plots show the residual for a model for predicting each variable from the age of the fish.

A conclusion that a linear model between the variable and age is appropriate is supported by which plot or plots?
1.)A Only
2.)B Only
3.)C Only
4.)A and C only
5.)B and C only

Answers

Answer: A Only

Step-by-step explanation:

To determine that a linear model is appropriate, the residual plot should be randomly dispersed.

Answer:

1

Step-by-step explanation:

Is 13 a solution to the compound inequality d>5 and x<10

Answers

Answer:

Step-by-step explanation:

13>5 is correct but 13 < 10 is not correct

so 13 is not a solution

What is the value of [(3/5)^0]^-12

Answers

Answer:

The value is 1

Step-by-step explanation:

3/5 = 0.6

0.6^0 = 1

1^-12 = 1

need help.. The midpoint of GH is M(-6,-3). One endpoint is H (-4,4) Find the coordinates of endpoint G.

Answers

Answer:

The coordinates of G are: (-8, -10)

Step-by-step explanation:

Mid point formula:

[tex]x = \dfrac{x_1+x_2}{2}\\y = \dfrac{y_1+y_2}{2}[/tex]

Where,

[tex](x,y)[/tex] are the coordinates of the mid point of the points [tex](x_1,y_1)[/tex]  and [tex](x_2,y_2)[/tex].

As per question statement, we are given that:

[tex]x_2=-4\\y_2=4[/tex]

and

[tex]x=-6\\y=-3[/tex]

To find:

[tex]x_1 = ?\\y_1 = ?[/tex]

Solution:

Let us use the mid point formula:

[tex]-6 = \dfrac{x_1-4}{2}\\\Rightarrow -12=x_1-4\\\Rightarrow x_1=-12+4\\\Rightarrow \bold{x_1=-8}[/tex]

[tex]-3 = \dfrac{y_1+4}{2}\\\Rightarrow -6=y_1+4\\\Rightarrow y_1=-6-4\\\Rightarrow \bold{y_1=-10}[/tex]

The coordinates of G are: (-8, -10)

For which value of Theta is tan Theta equal to sin Theta?
A. pi
B. pi/2
C. pi/4
D. pi/6​

Answers

Answer:

a. pi

Step-by-step explanation:

An african elephant in rhe wils will eat for as long as 16 hours each day. For how many hours does an elephant eat in one year? There are 365 days in one year.

Answers

Answer:

5840

Step-by-step explanation:

16 x 365 is 5840

Answer:

5,840

Step-by-step explanation:

16x365=?

16x365=5,840

HELP!! Determine whether the pair of lines are parallel, perpendicular, or neither. 8x=3y+2 -16x+6y=2.

Answers

Answer:

24x - 9y=0

Step-by-step explanation:

8x=3y+2-16x+6y=2

8x=9y+2-16x=2

8x+16-9y=2-2

24x-9y=0

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