Suppose b is any integer. If b mod 12 = 7, what is 4b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 4b is divided by 12? Fill in the blanks to show that the same answer will be obtained no matter what integer is used for b at the start. Because b mod 12 = 7, there is an integer m such that b = 12m + . Multiply both sides of this equation by 4 and then simplify the right-hand side to find values of q and r such that 4b = 12q + r with 0 ≤ r < 12. The result is q = and r = . Now 0 ≤ r < 12, and q is an integer because ---Select--- . So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 4b is divided by 12 is . Need Help?

Answers

Answer 1

Answer:

4b mod 12 = 4

Step-by-step explanation:

Since b mod 12 = 7, it implies that there is an integer, m such that

b = 12m + 7.

We desire to find 4b mod 12

So, multiplying b by 4, we have

4b = 4(12m + 7)

4b = 4 × 12 m + 4 × 7

4b = 4 × 12 m + 28

4b = 4 × 12 m + 24 + 4

4b = 4 × 12 m + 12 × 2 + 4

Factorizing 12 out, we have

4b = 12(4m + 2) + 4

Since m is an integer 4m + 2 is an integer since the operation of adding and multiplication is closed for the set of integers.

comparing 4b = 12q + r with 4b = 12(4m + 2) + 4,

q = 4m + 2 and r = 4

So 4b mod 12 = 4, that is the remainder when 4b is divided by 12 is 4.

Answer 2

In this exercise we have to calculate the value of the unknown, so we have:

the value is 4

we know that the equation will be given as:

[tex]b = 12m + 7\\[/tex]

we need to multiply both sides by 4 to become another known equation, like this:

[tex]4b = 4(12m + 7)\\4b = 4 * 12 m + 4 * 7\\4b = 4 * 12 m + 28\\4b = 4 * 12 m + 24 + 4\\4b = 4 * 12 m + 12 * 2 + 4[/tex]

So factoring this equation we will find that:

[tex]4b = 12(4m + 2) + 4[/tex]

Thus, when making a comparison between the two equations, we have that:

[tex]4b = 12q + r \\4b = 12(4m + 2) + 4\\q = 4m + 2\\r = 4[/tex]

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Related Questions

A study is conducted to see how effective aspirin is in reducing temperature in children. A sample of 6 children suffering from influenza had their temperatures taken immediately before and 1 hour after administration of aspirin. The results are given below. We would like to conduct a paired differences t-test for this situation. The data follows:

Patient Temperature Before Temperature After Difference
1 103.7 102.6 1.1
2 103.7 102.7 1
3 100.7 98.8 1.9
4 102.7 103.5 -0.8
5 102.7 101.3 1.4
6 100.7 99.4 1.3
Mean 102.4 101.4 1
Std. Dev. 1.4 1.9 0.9

Required:
Calculate the appropriate test statistic of a matched pairs t-test for this data to see if taking aspirin will reduce a child's fever.

Answers

Answer:

Then t(s) is in the rejection region for H₀  we reject H₀  and conclude that the aspirin will reduce a child´s fever

Step-by-step explanation:

Tem.Before    Tem.After       diff.      

103.7                   102.6            1.1

103.7                   102.7             1

100.7                     98.8             1.9

102.7                    103.5            -0.8

100.7                      99.4             1.3

102.4                      101.41           (Mean)

1.4                             1.9              0.9       Std. Dev.

n =  6

df  =  6  -  1  =  5

CI we propose to be 95 %

Then  α  = 5 %  α = 0.05    

The test is a one-tail test ( we want to know if taking aspirin will reduce a child´s fever

Hypothesis test

Null Hypothesis                      H₀         μd  = 0

Alternative Hypothesis          Hₐ         μd > 0

(NOTE:)   μd (average) = Temp Before  -  Temp. after

Therefore if   μd >  0   means that there is a statistical difference between values before ( bigger ) and after  or that the aspirin will reduce a child´s fever

To find t(c)  from t-student table  df = 5  and α = 0.05

t(c)  =  2.015

To compute  t(s)

t(s)  =  μd/ sd/√n      t(s)  =  0.98/ 0.9/√6

t(s)  =  2.66

Comparing  t(s) and  t(c)

t(s) > t(c)    

Then t(s) is in the rejection region for H₀  we reject H₀  and conclude that the aspirin will reduce a child´s fever

Please help with question 2

Answers

Answer:

Step-by-step explanation:

7*(4) - 2(-3) - (-3)^2

28 +  6 - 9

34 - 9 = 25

HELP I NEED TO PASS!!!!!

A. g(x) = 2x-1
B. g(x) = 2x + 1
C. g(x) = 2x –1
D. g(x) = 2x+1

Answers

It’s b and d ? Both of those equations are the same if u haven’t noticed

An electrician leans an extension ladder against the outside wall of a house so that it

reaches an electric box 30 feet up. The ladder makes an angle of 68° with the ground.

Find the length of the ladder. Round your answer to the nearest hundredth of a foot if

necessary.

Answers

Answer: [tex]32.36\ ft[/tex]

Step-by-step explanation:

Given

Ladder is leaned and make an angle of [tex]68^{\circ}[/tex]

Electric box is 30 ft up the ground.

Suppose x is the length of ladder

From the figure, we can write

[tex]\Rightarrow \sin 68^{\circ}=\dfrac{30}{x}\\\\\Rightarrow x=\dfrac{30}{\sin 68^{\circ}}\\\\\Rightarrow x=32.36\ ft[/tex]

The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The length of the ladder is 32.356 feet.

What is Sine (Sinθ)?

The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,

[tex]\rm{Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The hypotenuse is the longest side of the triangle.

As it is given that the height of the electric box from the bottom is 30 feet, while the ladder makes an angle of 68° with the ground.

The length of the ladder can be found using the trigonometric functions, therefore, the length of the ladder can be written as,

[tex]\rm Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}\\\\\\Sine(\angle C) = \dfrac{AB}{\text{Length of the ladder}}\\\\\\{\text{Length of the ladder}}= \dfrac{AB}{Sine(\angle C) }\\\\\\{\text{Length of the ladder}}= \dfrac{30}{Sine(68^o) }\\\\\\{\text{Length of the ladder}}= 32.356\ feet[/tex]

Hence, the length of the ladder is 32.356 feet.

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Another name for NQ is? (Geometry)

Answers

Answer:

NQ : Summary

CodeNQOne-letter codeXMolecule name2-HYDROXYNAPHTHOQUINONESynonyms2-HYDROXY-1,4-NAPHTHOQUINONESystematic namesProgram Version Name ACDLabs 10.04 2-hydroxynaphthalene-1,4-dione OpenEye OEToolkits 1.5.0 2-hydroxynaphthalene-1,4-dione

If ∠P, ∠Q, and ∠R are given, as well as the value of p, then explain whether the Law of Sines or the Law of Cosines should be used to solve for q.

Law of Sines, two angles and an opposite side are known
Law of Sines, two sides and an opposite angle are known
Law of Cosines, two sides and the included angle are known
Law of Cosines, all sides are known

Answers

Answer:

Law of Sines, two angles and an opposite side are known

Step-by-step explanation:

Law of Sines, two angles and an opposite side are known

q/sinQ = p/sinP

q = p/sinP * sinQ

Stan knows that segment AB∥segment CD. He wants to use the definition of a parallelogram to prove that quadrilateral ABCD is a parallelogram. Which equation can he use?

Answers

Answer:

[tex]\frac{q - r}{m- n} = \frac{p - s}{m - n}[/tex]

Step-by-step explanation:

Given

See attachment for parallelogram

Required

Proof that ABCD is a parallelogram

We know that opposite sides are equal and parallel.

First, we calculate the slope of BC

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

So, we have:

[tex]m = \frac{q - r}{m- n}[/tex]

Next, the slope of AD using:

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

So, we have:

[tex]m = \frac{p - s}{m - n}[/tex]

For ABCD to be a parallelogram; then:

[tex]\frac{q - r}{m- n} = \frac{p - s}{m - n}[/tex]

NEED HELP ASAP!!! Giving brainliest!!!!!!!

Answers

C.(f-g)(x) = 4x^3 +5x²-7x-1

Step-by-step explanation:

Given information :

[tex]f(x) = 4 {x}^{3} + 5 {x}^{2} - 3x - 6 \\ g(x) = 4x - 5[/tex]

Find :

[tex](f - g)(x) = \\ (4 {x}^{3} + 5 {x}^{2} - 3x - 6) \\ - 4x -5[/tex]

Open bracket and Simplify

[tex]4 {x}^{3} + 5 {x}^{2} - 3x - 6 - 4x + 5 \\ 4 {x}^{3} + 5 {x}^{2} - 7x - 1[/tex]

The answer is c I agree with the answers above

Josh ate 7/8 pizza and Jerry ate 1/2 pizza. how much more did Josh eat then Jerry​

Answers

Step-by-step explanation:

6/5 this is the answer hopes this help

Factor completely, then place the factors in the proper location on the grid. 25a2 +9b2 + 30ab

Answers

Answer:

(5a+3b)(5a+3b) or SQ(5a+3b)

Step-by-step explanation:

Now you can plot by referring to the above factors


Select the correct answer.
What is this expression in simplified form?
5v2.9v6
OA. 45v3
OB. 90
O C. 90v3
OD. 45V2

Answers

Answer:

C. 90√3

Step-by-step explanation:

5√2 . 9√6 = 45√12 = 45×2√3

= 90√3

The simplified form is 90√3.

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Given expression is, 5√2×9√6

                               =5×9×√(2×6)

                               =45×√12

                               =45×2√3

                               =90√3

Hence, the simplified form is 90√3 .

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43
d. 34
Clear my choice
For the discrete series given as, X variable values - 32 with frequemcy 2,37 with frequency 5,
46 with frequency 3 and 48 with frequency 9, mode is
Select one:
O a. 9
O b. 48
O c. 37
O d. 5

Answers

Given:

The frequency distribution table is:

Values of variable X        Frequency

              32                                2    

              37                                5

              46                                3

              48                                9

To find:

The mode of the given data set.            

Solution:

We know that mode is the most frequent value of the data set.

In the given data set highest frequency is 9 that is corresponding to the value 48.

Therefore, the mode of the given data set is 48. Hence, the correct option is (b).

This are 3 different questions please help me

Answers

1. diginity
2.require
3.tuition

Please help me answer e, f and number 3. See the image below

Answers

Answer:

Prat two of e) 6/12 Both the numerator and denominator were multipled by three, the number of boxes we split each box into.

F) we can multiply both the numerator and denominator without changing the values, so 2a/2b or 10a/10b

Which of the following is the equation of a line in slope-intercept form for a
line with slope = and yintercept at (0, -1)?
O A. y - x-
1
B. y = 4x-1
O c. y= |x-1
O D. y=x+1

Answers

Answer:

y=1/4x - 1

Step-by-step explanation:

going off of the picture, I'd say this is your answer

12 Kendrick wants to build a slide for his son in the backyard. He buys a
slide that is 8 feet long. The height of the stairs is 5 feet. Find the
distance from the bottom of the stairs to the base of the slide.

Answers

5^2 + x^2=8^2
25+x^2=64
X=6.2

Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
To buy a car, you borrow $27,000 with a term of five years at an APR of 6%. What is your monthly payment? (Round your answer to the nearest cent.)
$
How much total interest is paid? (Round your answer to the nearest cent.)
$

Answers

Answer:

The correct answer is -

monthly payment = 521.99

total pain intrest = 4319.14

Step-by-step explanation:

Given:

a or the borrowed amount = 27000

r or the interest rate = 6%

n = 5 years or 60 months

Monthly payment = ?

total intreset = ?

Formula:

The formula for the monthly payment is -

[tex]\frac{a}{\frac{{[(1+r)^n]-1}}{[r(1+r)^n]}} = P[/tex]

or, [tex]\frac{ar}{[1-(1+r)^{-60}}[/tex] = P

Where, the amount of the loan = a

r = 0.005 (6% annual rate—expressed as 0.06—divided by 12 monthly payments per year)

n = 60 months

Solution:

Putting all the values in the either of the following formula will give monthly payments:

[tex]\frac{27000}{\frac{{[(1+0.005)^{60}]-1}}{[0.005(1+0.005)^{60}]}} = P[/tex] or  [tex]\frac{ar}{[1-(1+r)^{-60}}[/tex]

= 521.9856 or to the nearest cent 521.99.

The total intrest would be -

= (monthly payment*number of month) - amount borrowed

= 521.99*12-27000

= 31319.14-27000

= 4319.14

If you apply these changes to the linear parent function f(x)=x what is the equation of the new function vertically compressed by a factor of 3 reflect over the x axis

Answers

1x100 that is the answer

Answer:

Because this gravity of. The earth

what is the inverse of f(x)=2x-4

Answers

Step-by-step explanation:

Hey there!

The given function is; f(x) = 2x-4.

To find: f'(X)

Let f(X) be y, then;

y = 2x - 4

Interchanging"X" and "y" we get;

x = 2y - 4

or, X+4 = 2y

or, y = (X+4)/ 2

Therefore, f'(X) = (X+4)/2.

Hope it helps!

To the nearest degree, find the measure of angle A.

Answers

Cosine(angle) = adjacent leg/ hypotenuse

Cosine( angle ) = 18/20

Angle = arccos(18/20)

Angle = 26 degrees

Answer:

26°

Step-by-step explanation:

For a right triangle, we can use trigonometry equations :-

In this case we need to use cosine equation .

cos A = adjacent side / hypotenuse

cos A = 18 / 20

A = cos × 18/20

A = arccos × 18/20

A = 26°

i need help with this on my homework

Answers

ko  iê ế t???????????????    t

Difference Quotient. Correct answer is shown. It says multiply by conjugate but I don’t understand what that is and how they did it. TIA

Answers

9514 1404 393

Answer:

  3/(√(3(x+h)) +√(3x))

Step-by-step explanation:

The conjugate of a binomial is the same sum, but with the sign changed. That is (a +b) and (a -b) are a conjugate pair: each is the conjugate of the other.

The purpose of multiplying expressions involving roots or complex numbers by their conjugate is to take advantage of the relation ...

  (a +b)(a -b) = a² -b²

Here. you want to eliminate the h from under the radical, so squaring the radical containing h is useful for the purpose. Hence the conjugate gets involved.

"Multiply by the conjugate" means multiply both the numerator and the denominator by the conjugate. (Effectively, multiply by 1.)

__

  [tex]\displaystyle\frac{f(x+h)-f(x)}{h}=\frac{\sqrt{3(x+h)}-\sqrt{3x}}{h}\\\\=\frac{(\sqrt{3(x+h)}-\sqrt{3x})(\sqrt{3(x+h)}+\sqrt{3x})}{h(\sqrt{3(x+h)}+\sqrt{3x})}=\frac{3(x+h)-3x}{h(\sqrt{3(x+h)}+\sqrt{3x})}\\\\=\frac{3h}{h(\sqrt{3(x+h)}+\sqrt{3x})}=\boxed{\frac{3}{\sqrt{3(x+h)}+\sqrt{3x}}}[/tex]

_____

Additional comment

In the end, you will want the limit as h → 0, which will be 3/(2√(3x)). You will notice that h=0 no longer makes the denominator zero, so the limit is found by simple evaluation.

When the "binomial" is a complex number of the form a+bi, its conjugate is a-bi, regardless of the sign of b. That is, the conjugate of a complex number is found by negating its imaginary part. The sign of the real part is left alone.

Triangles A B C and A double-prime B double-prime C double-prime are shown. Triangle A double-prime B double-prime C double-prime is smaller and to the right of triangle A B C. Which transformations could have taken place to map △ABC to △A"B"C"? a reflection and a dilation a rotation and a dilation a translation and a dilation a reflection and a translation

Answers

C. a translation and a dilation

Step-by-step explanation:

the other person isn't wrong they just put it in the wrong order

Answer:c

Step-by-step explanation:took the test

What is the value of angle v?

Answers

Answer:

x = 5

Step-by-step explanation:

a) The third interior angle of this triangle is 180 - 20 x.  

The three interior angles must sum up to 180 degrees.

Therefore,  60 + 7x + 5 + 180 - 20x = 180, or

                       65  + 180 - 13x = 180, or

                               65 -  13x     = 0

Finally, 13x = 65, and so x = 5

9 Two people start writing reports on the same day. Both write 200-page reports. Writer A averages 8 pages a day, and writer B averages 5 pages per day. How much sooner will Writer A finish her report than will Writer B?

Answers

Answer:

15 days

+

Step-by-step explanation:

A

200 pages / (8 pages / day) =

= 200 pages days / 8 pages =

= 200 days / 8 = 25 days

B

200 pages / (5 pages / day) =

= 200 pages days / 5 pages =

= 200 days / 5 = 40 days

40-25 = 15 days

A will finish 15 days sooner than B.

A will finish her report 15 days sooner than B.

What is the ratio?

The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

Writer A averages 8 pages a day,

Number of pages per day written by writer A = 8 per day

Writer A will finish her report = Total pages / per day written by writer A

⇒ 200 pages / (8 pages / day)

⇒ 200 pages days / 8 pages

⇒ 200 days / 8

⇒ 25 days

Writer B averages 5 pages a day

Number of pages per day written by writer B = 5 per day

Writer B will finish her report = Total pages / per day written by writer A

⇒ 200 pages / (5 pages / day)

⇒  200 pages days / 5 pages

⇒  200 days / 5

⇒  40 days

Difference between both of time when they finished their report = 40-25 = 15 days

Hence, A will finish her report 15 days sooner than B.

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Qual é a frequência de cada gênero de leitura citados?​

Answers

Answer:

i velo you

Step-by-step explanation:

An assembly line consists of 21 tasks grouped into 5 workstations. The sum of the 21 task times is 85 minutes. The largest assigned cycle time is 20 minutes. What is the efficiency of this line

Answers

Answer:

The efficiency of this line is 0.85 = 85%.

Step-by-step explanation:

Efficiency:

The efficiency is given by the following formula:

[tex]E = \frac{T_t}{tn}[/tex]

In which [tex]T_t[/tex] is the total task time, [tex]t[/tex] is the largest assigned cycle time and n is the number of workstations.

5 workstations

This means that [tex]n = 5[/tex]

The sum of the 21 task times is 85 minutes.

This means that [tex]T_t = 85[/tex]

The largest assigned cycle time is 20 minutes.

This means that [tex]n = 20[/tex]

What is the efficiency of this line?

[tex]E = \frac{T_t}{tn} = \frac{85}{20*5} = \frac{85}{100} = 0.85[/tex]

The efficiency of this line is 0.85 = 85%.

Find the product of -9 and -3.

1. 0-3
2. 27
3. 0-27
4. 3

Answers

27 is the answer

gbu...

Answer:

- 9 × - 3 = 27

Step-by-step explanation:

when we multiply two negative numbers then the sign of the product convert to positive sign

I.e( - )×( - )= (+) product

create a frequency table and probability models to determine the probability the following outcome police officer kept recording of 75 drivers at a stop sign they observed 21 people who came to complete stop 46 who made a rolling stop and 8 that did not appear to a brake at all what is the probability that a randomly selected driver will come to complete stop

Answers

Answer:

0.28 = 28% probability that a randomly selected driver will come to complete stop

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

Recording of 75 drivers.

Of those, 21 came to a complete stop.

Then

21/75 = 0.28

0.28 = 28% probability that a randomly selected driver will come to complete stop

Factor t^2 - 5t + 6. Type your answer in the space provided. Do not type spaces in your answer. Use only lowercase letters and include all necessary parentheses, variables and operation signs. For example, if the answer is (x +1)(x+2), type (x+1)(x+2).

Answers

Answer:

(x-3) * (x-2

Step-by-step explanation:

Other Questions
In Sean's class there are 13 boys and 16 girls. Sean will randomly pull one of their names out of a hat to givea presentation to the class. Which of the following is the probability the student picked will be a girl?(1) 0.45(3) 0.62(2) 0.55(4) 0.81 Which point of view does the narrator use in the passage?Hilda, however, likes you. You are young and remind her of her sister, the professionalskater. "But I hate to skate," you say. And Hilda smiles, nodding. "Yup, that's exactlywhat my sister says sometimes and in the same way." "What way?" "Oh, I don't know,"says Hilda. "Your bangs parted on the side or something."From Lorrie Moore, Self-Help. Copyright 1985 by Lorrie Moorefirst personsecond personthird personSubmit what is a property of every mixture PLSSSS ANSWER!!!!!!!!! Read the excerpt from Sir Gawain and the Green Knight. [Arthur] said, "Knight, by heaven, your request is senseless. What you ask is such madness you deserve to have it granted. No knight I know is afraid of your great words. Give me your ax now, in the name of God, And I shall grant the boon that you have requested. He strides toward him and grasps him by the hand. Then proudly that other knight sets foot on the ground. Now Arthur has his ax, gripping the handle, And grimly swings it around, preparing to strike with it. The bold man stood towering before him . . . What chivalric value does Arthur display in the excerpt? religious devotion morality bravery physical strength All of the following are important clues for interpreting symbolism except for which one?synopsisrepeating patternssupporting detailsassociations from a ship at sea,the angle of elevation of the top and. bottom a vertical lighthouse standing on the edge of a vertical cliff are 31 abd 26, respectively. if the light house is 25.0m high,calculate the height of the cliff 2) What doessociety need to speedup the development process? The graph of an equation with a negative discriminant always has which characteristic? The 1935 Nuremberg laws impacted Jewish people by Which of the following refers to friction that acts on an object that is not moving? O A. Kinetic friction O B. Inertia O c. Contact force O D. Static friction HELP PLEASE!! Find the equation of a line that is parallel to y = 5x + 1 and passes through the point (3, -4).Give your answer in the form y = mx + b. Select the correct answer.Whichessay prompt indicates that you should write a narrative essay?O A.What did you learn the timeyou volunteered at a soup kitchen? B.If I had a million dollars .C.Global warming: Is it a myth or reality?D.Describe the health effects ofobesity. E.Why is carpooling good for the environment?Reset plssssssssssssssssssssss Find(g-f)(x) f(x)=1/x g(x)=x^2+2x-5 a. 1/x-x^2-2x+5b.1/x+x^2+2x-5c.x^2+2x-5-1/xd.1/x+x^2-5 Check whether (0, -2) is solution of the equation x - 2y = 4 or not. (2a^6-6a^3)^2 expand and combine like terms Which of the following accurately describes an interaction between two religions during the period of 600 BCE to 600 CE?A. Hindu traditions became central to ZoroastrianismB. Buddism provided the foundation for HinduismC. Christianity grew out of the Jewish faithD. Islam developed as an extension of Buddhism HIV and AIDS represent one of the most serious health issues facing the world today.True or false find the surface area of the composite figure