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

The table shows the weekly profits of a fruit
vendor. What is the mean profit for these weeks?
Week
1
2
3
4
Profit -$125 -$86
$54
- $35
The mean profit is $

Answers

Answer:

-48

Step-by-step explanation:=-48

The mean profit of the fruits will be $75.

What is mean?

Mean is defined as the ratio of the sum of the number of data sets to the total number of data. The mean is just like an average it is calculated by taking the ratio of the sum of all the numbers to the total count of the numbers.

Given that the weekly profit of the fruits is $125, $86, $54, and $35. The mean will be calculated as:-

Mean = ( 125 + 86 + 54 + 35 ) / 4

Mean = 300 / 4

Mean = $75

Therefore, the mean profit of the fruits will be $75.

To know more about mean follow

https://brainly.com/question/968894

#SPJ5

20+20 omg.please help :( ​

Answers

Answer:

40

Step-by-step explanation:

I need help with this! 20 points pls dont take advantage.

the average adult drinks 1095 cups of coffee annually, About how many cups does the average adult drink per week? 1 year=52 weeks

15
91
21
3​

Answers

Answer:

the answer is 21

Step-by-step explanation:

If they drink 1,095 cups per year, and there are 52 weeks in a year, you would divide 52 from 1,095(1,095/52) to get your answer which is 21.05769231. If you round it to the nearest whole number, than it is 21. I hope this helps have a great day.

Solve five and three sixths minus two and one third.

(GIVING EXTRA POINTS ON THIS ONE! IM ALSO GIVING BRAINLIEST!) (Btw three and two ninths is incorrect :) )

A) Two and three eighteenths

B) two and two ninths

C) three and two ninths

D) three and three eighteenths

(Here is an image if needed) :

Answers

Answer:

3 3/18

Step-by-step explanation:

I did this on paper, but im typing on computer, sorry I cant send a photo

Answer:

D is the answer 3 3/18 i am sure it is correct

Which of the following equations represent linear functions?

y=x2−3x

4x+y=5

y=|2x+1|

y=−5

Answers

Answer:

its y=-5x

Step-by-step explanation:

Why?

linear functions have only the slope, they dont include the y-intercept

4n-(7-6n)


Helppp plz

Answers

4n - (7-6n)
4n -7 +6n (multiply minus to 7-6n)
10n -7 is the answer

equivalent fraction of 6/126

Answers

Answer:

1/21

Step-by-step explanation:

Answer:

1/21

Step-by-step explanation:

6/126 = 1/21 because 6 divided by 6 equals 1 and 126 divided by 6 equals 21.

(c) What is the value of p if 4x² + 20x + p is a
perfect square​

Answers

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

[tex]( {a + b})^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]

_________________________________

[tex]4 {x}^{2} + 20x + p = [/tex]

[tex]( {2x})^{2} + 2(2x)(5) + p = [/tex]

Thus ;

[tex]p = {5}^{2} [/tex]

So

[tex]p = 25[/tex]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Determine the check digit for the UPCs that have these initial 11 digits. a) 73232184434 b) 63623991346 c) 04587320720 d) 93764323341

Answers

Answer:

The check digits

a) x₁₂ ≡ 5( mod 10 )

b) x₁₂ ≡ 2( mod 10 )

c)  x₁₂ ≡ 0( mod 10 )

d)  x₁₂ ≡ 3( mod 10 )

Step-by-step explanation:

Given the data in the question;

We know that the formula for determining the UPCs check is;

3x₁ + x₂ + 3x₃ + x₄ + 3x₅ + x₆ + 3x₇ + x₈ + 3x₉ + x₁₀ + 3x₁₁ + x₁₂ ≡ 0( mod 10 )

now we will substitute the given values to determine the value of the last bit

a)

73232184434

we substitute into the formula

3×7 + 3 + 3×2 + 3 + 3×2 + 1 + 3×8 + 4 + 3×4 + 3 + 3×4 + x₁₂ ≡ 0( mod 10 )

                                                                                          x₁₂ ≡ 5( mod 10 )

b)

63623991346

we substitute into the formula

3×6 + 3 + 3×6 + 2 + 3×3 + 9 + 3×9 + 1 + 3×3 + 4 + 3×6 + x₁₂ ≡ 0( mod 10 )

                                                                                           x₁₂ ≡ 2( mod 10 )

c)

04587320720

we substitute into the formula

3×0 + 4 + 3×5 + 8 + 3×7 + 3 + 3×2 + 0 + 3×7 + 2 + 3×0 + x₁₂ ≡ 0( mod 10 )

                                                                                           x₁₂  ≡ 0( mod 10 )

d)

93764323341

we substitute into the formula

3×9 + 3 + 3×7 + 6 + 3×4 + 3 + 3×2 + 3 + 3×3 + 4 + 3×1 + x₁₂ ≡ 0( mod 10 )

                                                                                         x₁₂ ≡ 3( mod 10 )

A statement of an employee's biweekly earnings is given below.




Earnings


Deductions




Week Ended


Regular


FED. SOC. MED STATE


WITH. WITH. CARE. WITH.


NET PAY


8/18


$_____


$72.00 $35.05 $15.54 $14.40


$793.01



What is the employee's gross pay?


A.

$900.50


B.

$1000


C.

$930


D.

$975.10

Answers

Answer:

kjj ,mStep-by-step explanation:

Which lines from Natalie Merchant's song "Wonder" most likely inspired R. J. Palacio to give August's mother's great determination in the novel Wonder? O Doctors have come from distant cities just to see me O stand over my bed disbelieving what they're seeing with love, with patience and with faith she'll make her way I'm over your heads how I confound you and astound you​

Answers

Answer:

C)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The guy above me is correct

Question 2 (1 point)
For problem 2 - 26, what is the slope of line C?
A
B
2-26.
D
+
E
8
10
2
a
m = 2
Ob
m = -2/3
c
m = 0

Answers

Answer:

Option e: 2/3 is the correct answer.

Step-by-step explanation:

The slope of a line is given by:

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

Two-points on line are needed to calculate slope of a line. In the attached diagram, two points are highlighted which are located on line C.

The two points are:

(x1,y1) = (9,4)

(x2,y2) = (3,0)

Putting the values in the formula

[tex]m = \frac{0-4}{3-9}\\=\frac{-4}{-6}\\=\frac{2}{3}[/tex]

The slope of line C is: 2/3

Hence,

Option e: 2/3 is the correct answer.

Find the slope of the line on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.

Answers

Answer:

m= 1

Step-by-step explanation:

find to ordered pair on the graph and [tex]y^{1} - y^{2} \\ x^{1} - x^{2}[/tex]

Each week, Mrs.Mack buys exactly 3 5/8 pounds of cheese for her mac-and-cheese recipe. She chooses from these kinds of cheese. Mrs.Mack buys as many packages as she needs— up to three packages of any kind. What packages of cheese (and how many of each kind) does Mrs.Mack buy? 7/8pounds of american cheese. 0.5 pounds of cheddar cheese. 0.2 pounds of swiss cheese. HELP PLEASE

Answers

9514 1404 393

Answer:

3 packages of American (7/8 lb)2 packages of cheddar (1/2 lb)

Step-by-step explanation:

The amount of cheese Mrs Mack needs is an odd number of eighths of a pound. So, she must buy an odd number of the 7/8 pound packages.

If she were to buy any 1/5 pound packages, she would have to buy a multiple of 5 of them so as to have an integral number of eighths. The only suitable multiple is 0.

If Mrs Mack buys 1 of the 7/8 pound packages, she cannot make up the difference with half-pound packages. She must buy 3 of the 7/8 pound packages, for a total of 2 5/8 pounds of American cheese. The remaining pound can be bought as 2 of the 1/2 pound packages.

To buy 3 5/8 pounds, Mrs Mack must purchase ...

  3 packages of American cheese (7/8 lb each)

  2 packages of Cheddar cheese (1/2 lb each)

What is the value of X in this Diagram

I will give a brainlist for the correct answer

Answers

Answer: 31°

Step-by-step explanation:

180° - 149° = 31°

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. The probability that the average pregnancy length for nine randomly chosen women exceeds 268 days is about a) 0.35 b) 0.40 c) 0.65 d) 0.27

Answers

Answer:

The probability is    [tex]P( \= X > 268 ) =0.35376[/tex]

Step-by-step explanation:

From the question we are told that

   The mean is  [tex]\mu = 266[/tex]

    The standard deviation is  [tex]\sigma = 16[/tex]

Generally the standard error of mean is mathematically represented as

        [tex]\sigma_{\= x} = \frac{\sigma}{\sqrt{n} }[/tex]

=>     [tex]\sigma_{\= x} = \frac{16}{\sqrt{9} }[/tex]

=>     [tex]\sigma_{\= x} = 5.33[/tex]

Generally the probability that the average pregnancy length for nine randomly chosen women exceeds 268 days is mathematically represented as

        [tex]P( \= X > 268 ) = P (\frac{ \= x - \mu }{ \sigma_{\= x}} > \frac{268 - 266}{5.33 } )[/tex]

[tex]\frac{\= X -\mu}{\sigma_{\= x} }  =  Z (The  \ standardized \  value\  of  \ \=  X )[/tex]  

          [tex]P( \= X > 268 ) = P (Z > 0.3752 )[/tex]

From the z table  the area under the normal curve to the right  corresponding to  0.3752  is

P (Z  >  0.3752)   =    0.35376

So  

       [tex]P( \= X > 268 ) =0.35376[/tex]

Simplify 6(x + 2)- x(x - 1)

Answers

-x^2+7x+12


Let’s use distributive property
6(x+2)-x(x-1)

6x+12

Now the other part of the expression
-x(x-1)
-x^2+x

Put both parts of the expression together

6x+12 -x^2+x

-x^2+7x+12

Hope this helps

The length of the rectangle is 3ft less than twice the width,and the area of the rectangle is 27ft^2,find the diameter

Answers

Answer:

The dimensions of rectangle are:

width = w = 4.5 ftlength = l = 6 ft

Step-by-step explanation:

Let 'l' be the length and 'w' be the width of the rectangle

The length 'l' of the rectangle is 3ft less than twice the width 'w'.

so

[tex]l=2w-3[/tex]

Also, the area of the rectangle is 27ft^2.

[tex]A=27\:ft^2[/tex]

As the area of the rectangle has the formula:

[tex]\:A\:=\:l\times w[/tex]

so

[tex]27=\:l\times w[/tex]

so the equation becomes

[tex]27=\left(2w-3\right)\times \:w[/tex]

[tex]27=2w^2-3w[/tex]

[tex]2w^2-3w-27=0[/tex]

[tex]\left(w+3\right)\left(2w-9\right)=0[/tex]

if   [tex]ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]

[tex]w+3=0\quad \mathrm{or}\quad \:2w-9=0[/tex]

[tex]w=-3,\:w=\frac{9}{2}[/tex]

as the width can not be negative, so

[tex]w=\frac{9}{2}=4.5[/tex] ft

As

[tex]l=2w-3[/tex]

[tex]l=2\left(4.5\right)-3[/tex]

[tex]l=9-3[/tex]

[tex]l=6[/tex]

So the dimensions of rectangle are:

width = w = 4.5 ftlength = l = 6 ft

what is the equation of aline that passes through the point (4,-8) and has a slope of -1/2?

Answers

Answer:

The equation of the line will be:

[tex]y=-\frac{1}{2}x-6[/tex]

Step-by-step explanation:

Given

slope = m = -1/2point (4, -8)

Point slope form:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

substituting the values m = -1/2 and the point (4,-8)

[tex]y-\left(-8\right)=\frac{-1}{2}\left(x-4\right)[/tex]

[tex]y+8=\frac{-1}{2}\left(x-4\right)[/tex]

subtract 8 from both sides

[tex]y+8-8=\frac{-1}{2}\left(x-4\right)-8[/tex]

[tex]y=-\frac{1}{2}x-6[/tex]

Therefore, the equation of the line will be:

[tex]y=-\frac{1}{2}x-6[/tex]

Evaluate the expression 9x for x= 2.
9x = when x = 2.
(Simplify your answer.)

Answers

Plug in 2 for x so 9x when x=2 is 9(2) nine times two is
18

Pls answer professionally or with the right answer I’m beg you

Answers

1) y=106 x=106 2) z=68 y=112 x=112

Answer:

Step-by-step explanation:

Hello friend!!!

here's ur answer

1) <y = 180 - 74 = 106° ( linear pair )

<x = <y ( alternate angles )

therefore, <x = <y = 106°

2) <x = 68° ( corresponding angles )

<y = 180 - 68 = 112° ( linear pair )

<z = 112° ( vertically opposite angles )

Hope this helps

plz mark as brainliest!!!!!

Given: △ABC, m∠A=60°
m∠C=45°, AB = 9
Find: Perimeter of △ABC
Area of △ABC
ABC is scalene

Answers

Answer:

Perimeter = 32.3

Area = 95.24

Step-by-step explanation:

Given:

△ABC, m∠A=60°

m∠C=45°, AB = 9

To find:

Perimeter of △ABC

Area of △ABC

Solution:

Using angle sum property in a triangle:

m∠A + m∠B + m∠C = 180°

m∠B = 180° - 45° - 60° = 75°

As per Sine Rule:

[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]

Where  

[tex]a[/tex] is the side opposite to [tex]\angle A[/tex]

[tex]b[/tex] is the side opposite to [tex]\angle B[/tex]

[tex]c[/tex] is the side opposite to [tex]\angle C[/tex]

[tex]\dfrac{BC}{sin60^\circ} = \dfrac{AC}{sin 75^\circ} = \dfrac{AB}{sin 45^\circ} \\\Rightarrow \dfrac{BC}{\frac{\sqrt3}{2}} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow BC = 12.73\times 0.87 \\\Rightarrow BC = 11.08[/tex]

[tex]\Rightarrow \dfrac{AC}{0.96} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow AC = 12.73\times 0.96 \\\Rightarrow AC = 12.22[/tex]

Perimeter of △ABC = AB + BC + AC = 9 + 11.08 + 12.22 = 32.3

Area of a triangle is given as:

[tex]\dfrac{1}2\times ab sin(angle\ between\ a\ and\ b)[/tex]

[tex]\Rightarrow \dfrac{1}{2}\times AB\times AC\times sinA\\\Rightarrow 9\times 12.22\times sin 60\\\Rightarrow \bold{95.24}[/tex]

BRAINLIEST FOR CORRECT ANSWER!
At a sale, dresses were sold for $24 each. This price was 12% of a dress's original price. How much did a dress originally cost?

Answers

Answer:

$200

Step-by-step explanation:

To find the original price, divide the price by 0.12:

24/0.12

= 200

So, the dress originally cost $200

Answer:

$200.

Step-by-step explanation:

To find the original price, divide the discounted price by 0.12.

$24 ÷ 0.12% = $200

The dress originally cost $200.

7. Jenny is saving to buy a laptop worth $960. Her parents promise to match every $3 saved
by her with $5 of their own.
a. How much will Jenny contribute?
b. How much will Jenny's parents have to pay?

Answers

First off, if you divide $960/$8, you will get 120 “sets” of payment. Multiply this value by the amount of money Jenny is responsible for paying and the amount her parents are responsible for paying to find their total contributions.

a. Jenny will have to pay $600

b. Jenny’s parents will contribute $360 to her new laptop.

Please help this one is also due tomorrow

Answers

The correct answer is 0.73737373 or answer C. An irrational number is a number that cannot be expressed as a fraction for any integers and. . Irrational numbers have decimal expansions that neither terminate nor become periodic


Cathy's food usually costs $212.90 a week. One week, it cost $198.98. How
much less money did she spend that week?

Answers

Answer:

$13.92

Step-by-step explanation:

$212.90-198.98

Solve for h: h + 4.18 = 19.74​

Answers

H= 15.56. Because 19.74 - 4.18 will equal 15.56

I don’t understand this at all pls help I will mark brainliest

Answers

Answer:

D

Step-by-step explanation:

-2/3 is -.666

-3/5 is -.60

1/2 is .5

and 5/8 is a little more than half since 4/8 is half. so -2/3, -3/5, 1/2, 5/8, or D

A surgical procedure requires choosing among four alternative methodologies. The first can result in five possible outcomes, the second can result in two possible outcomes, and the remaining methodologies can each result in four possible outcomes. What is the total number of outcomes possible?

Answers

Answer:

15 possible outcomes

Step-by-step explanation:

Since each one of these methodologies are not related to one another and they do not need to be chosen in any order or consecutively then the possible outcomes would only need to be added all together to calculate the total possible outcomes. Since each outcome is independent. Therefore,

m1 = 5 outcomes

m2 = 2 outcomes

m3 = 4 outcomes

m4 = 4 outcomes

5 + 2 + 4 + 4 = 15

we can see that there are a total of 15 possible outcomes

Mrs. Chin paid a 20 percent tip on the bill for lunch.

Percents
Total
20%
20%
20%
20%
20%
100%
$2.75
$2.75
$2.75
$2.75
$2.75


If the tip amount was $2.75, what was the bill for lunch before the tip was added to it?
$5.50
$13.75
$16.50
$55.00

Answers

Answer:

The bill before the tip was $13.75 if you add a 20% tip of $2.75 the total bill including the tip would be $16.50

The bill before the tip is $13.75

Answer:

Answer is B  hope it helps

Step-by-step explanation:

Other Questions
Three times a number is at most negative six.3x5-6O 3x2-6O 3x-6 Four friend do yard work for their neighbors over the weekend earning $15, &20, and $40, respectively. They decide to split their earnings equally among themselves. In total how much will the friend who earned $40 give to the others? The project ........ on time . a) was not completed b) was not completing by them c) not completed d) not complete by the How did Hamilton's supporters get his debt plan approvedThey promised not to raise taxes on states that had little debtThey increased spport for American manufacturingThey made a deal to put the new national capital in the south could anybody do these On the moon, the acceleration due to gravity is one-sixth that of earth. That is gmoon = gearth /6 = (9.8 m/s2 )/6 = 1.63 m/s2 . What effect, if any, would this have on the period of a pendulum of length L? How would the period of this pendulum differ from an equivalent one on earth? What is the slope on this graph Question 1 (1 point)What is an advantage of the wireless option for peripheral? what is the slope of this graph? Tell me your favorite number and explain why it is your favorite number in minimum 2 sentences. Four more than twice a number is half the number six times. Find the number. ILL MARK U BRAINLIEST!!!!! how does the speaker support his idea that his soul has grown deep like the rivers I need help please Which set of statements explains how to plot a point at the location(-33.-2)Start at the origin. Move 3 units right because the x-coordinate is - 33.-3-3is between 3 and 4. Move 2 units dowA because the y-coordinate is -2.Start at the origin. Move 3 units down because the x-coordinate is 3.1.-3 is between -3 and -4. Move 2 unitsleft because the y-coordinate is -2.O Start at the origin. Move 3 units down because the x-coordinate is -3-3.7.-32 is between -3 and -4. Move 2 unitsright because the y-coordinate is -2.Start at the origin. Move 3 units left because the x-coordinate is -3-35-3 is between -3 and -4. Move 2 unitsdown because the y-coordinate is -2. III. Your uncle is telling you to do things that you are already doing. Answer him using thepresent progressive and double object pronouns, following the example. Write only onesentence for each thing he says. Make sure you have at least two examples of each form:attaching the pronouns to the present progressive, and placing the pronouns before the verb.Watch out for accent marks! (16 points; 4 points each)Example: Treme el peridico. Ya te lo estoy trayendo or Ya estoy trayndotelo.8. Lvanos los platos.9. Preprame un caf.10. Ordename la vaca.11. Dinos la verdad. Please help me !!!! ASAP hellpppppp please I will give brainliest If All Dreams Come To A End What Will Happen To My DreamGirl? Which ordered pair is a solution of the equation?5x2y=18