if n is an integer for which the greatest common factor of n and 18 is 6 and the least common multiple of n and 9 is 126, what is the value of n?'

Answer:

There are 8! (8 factorial) ways for 8 people to be seated in an 8-passenger van. This is because there are 8 choices for the first person to sit, 7 choices for the second person, 6 choices for the third person, and so on, until there is only 1 choice for the last person. Therefore, the total number of ways for the 8 people to be seated is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 8!, which is equal to 40,320.

Answer:

Step-by-step explanation:

Answer:

X =  1

X = -4/5

Hope this helps!

The weighing of the balance scale required to find a lighter counterfeit coin among four coins, is twice.

In just two balance scale weighs, it is feasible to identify which of four coins is the lighter fake coin. Here is one approach:

Then, weigh the two groups against one another after splitting the four coins into two groups of two coins each. The lighter counterfeit currency must belong to the group that is lighter than the other if there are two groups. If the two groups of coins weigh the same, then one of the two remaining coins must be the lighter counterfeit coin.

Weigh the two coins from the lighter group (or the two still present, if the first step was unsuccessful) against one another.

To learn more about balance scale: https://brainly.com/question/20454395

#SPJ4

The value of (3/8+3/4)(1/3+1/6) in its most basic form of fraction is 5/8.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

Here,

(3/8+3/4)−(1/3+1/6)

=3/8+3/4

=(3+6)/8

=9/8

=1/3+1/6

=(2+1)/6

=3/6

=1/2

=9/8-1/2

=(9-4)/8

=5/8

The value of (3/8+3/4)−(1/3+1/6) is 5/8 in the simplest form of fraction.

To know more about fraction,

https://brainly.com/question/24638688

#SPJ4

Answer: 8

Step-by-step explanation: Utilizing the POWER of order of operations we will multiply the 2 and 3 together first to get 6 and then add the 2 to get 8. Hope this helped :)

Answer: 8

Step-by-step explanation:

Parenthesis (Please)

Exponent (Excuse)

Multiplication (My)

Division (Dear)

Addition (Aunt)

Subtraction (Sally)

2x3= 6

6+2=8

There are 144 ways to place 4 pairs of shoes per shelf in the store.

What is a permutation?

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged. Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged. With permutations, the order of the arrangement matters.

This question can be solved using basic logic . One can also solve this by using permutations.
Since 12 different models arrive and 4 pairs of shoes should be placed per shelf , the answer can be sort by

4!×3! = [ 4×3×2×1] × [3×2×1] = 24×6 = 144.

( Because 4 pairs of shoes can be interchanged among themselves , therefore 4! , and 12/4=3 , so the 12 pair of shoes can be organised amongst 3 shelves , and hence 3!)
Therefore , none of the options is correct. The correct answer is 144 ways.
To know more about permutations , go to https://brainly.com/question/1216161

#SPJ4

Therefore , the mean time until the one-hundredth call is 4.35 ,the mean time between call numbers 50 and 80 is 1.30 and s the probability that three or more calls occur withing 15 seconds is 0.754

The Poisson distribution, used in probability theory and statistics, is a discrete probability distribution that expresses the likelihood that a specific number of events will take place within a predetermined window of time or space, provided that they do so at a known constant mean rate and regardless of the interval since the last event.

Here,

Thus, calls occur according to a poisson process with λ=23 calls per minute

a)X is the time until the one-hundredth call , X has Erlang distribution with rate of 23 and r =100

E(X)=r/ λ = 100/23 =4.35

b)The expected time between call numbers 50 and 80 is the same as the expected time until the 30th call this is Erlang distribution with rate of 23 and r =30

E(X)=r/ λ =30/23=1.30

c)P(N≥3)  λ=23, x=1/4  ,λx=5

1-P(N≤2) = 1- ∑  [tex]\frac{e^{-5}-5^{k}}{k!}[/tex](from k=0 to 2 )=0.754

Therefore , the mean time until the one-hundredth call is 4.35 ,the mean time between call numbers 50 and 80 is 1.30 and s the probability that three or more calls occur withing 15 seconds is 0.754

To know more about poisson distribution , visit

https://brainly.com/question/7283210

#SPJ4

The equation (A) x² - 4x + 3√2 = 0 has no real roots.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

(A) x² - 4x + 3√2 = 0

b² - 4ac = (-4)² - 4(1)(3√2)

= 16 - 12√2

= 16 - 12(1.414)

= 16 - 16.968

= -0.968 < 0

There are no true roots to the equation.

(B) x² + 4x - 3√2 = 0

b² - 4ac = (4)² - 4(1)(-3√2)

= 16 + 12√2 > 0

There are 2 different real roots in the equation.

(C) x² - 4x - 3√2 = 0

b² - 4ac = (-4)² - 4(1)(-3√2)

= 16 + 12√2 > 0

There are 2 different real roots in the equation.

(D) 3x² + 4√3x + 4 = 0

b² - 4ac = (4√3)² - 4(3)(4)

= 48 - 48

= 0

The equation contains two equal roots.

Therefore, the equation (A) x² - 4x + 3√2 = 0 has no real roots.

Know more about equations here:

https://brainly.com/question/28937794

#SPJ4

Answer:

Step-by-step explanation:

x^2 - 3x + 2x - 6

x^2 - x - 6

The remainder will be 33, 9, 7, and 14 for options a, b, c, and d respectively.

The Remainder is the extra part of a number that restricts the number to be divided completely.

a)

(19² mod 41) mod 9

Let us determine 361 mod 41

a=361 = 328+33= 8*41+33 =8d+33

The remainder is the constant in the final expression: 361 mod 41=33

33 mod 9 = 6 (since a=33= 27+6=3*9+6=3d+6)

b)

(32³ mod 13)² mod 11

Let us determine 32 mod 13

a=32=26+6=2*13+6+2d+6

The remainder is the constant in the final expression: 32 mod 13=6

[tex](6^{3} mod13)^{2} mod 11\\(216mod13)^{2} mod 11[/tex]

Let us determine 216 mod 13

a= 216= 208+8=16*13+8 = 16d+8

The remainder is the constant in the final expression: 216 mod 13=8

[tex]8^{2} mod 11\\64 mod 11[/tex] = 9 (since, 64= 55+9= 11*5+6= 11d+6)

c)

(7³ mod 23)² mod 31

[tex](343mod23)^{2} mod 31\\[/tex]

Let us determine 343 mod 23

a=343=322+21=14*23+21=14d+21

The remainder is the constant in the final expression: 343 mod 23= 21

[tex]21^{2} mod 31 = 441 mod 31=7[/tex] (since a = 441=434+7=14*31+7=14d+7)

d)

(21² mod 15)³ mod 22

[tex](441mod15)^{3} mod 22[/tex]

Let us determine 441 mod 15

a=441 = 435+6= 29*15+6= 29d+6

The remainder is the constant in the final expression: 441 mod 15= 6

[tex]6^{2} mod 22=36mod22= 14[/tex] (since a = 36= 22+14= 1*22+14= d+14)

To know more about remainders visit: brainly.com/question/23148931

#SPJ4

Answer:

The lowest common denominator is 8

Step-by-step explanation:

To find the lowest common denominator, we look at the multiples

Multiples of 4: 4,8,12,16,20

Multiples of 8: 8,16,24

The 1st common multiple is 8

The lowest common denominator is 8

Answer: 96

Step-by-step explanation:

The easy way to do this is to start backward. The last step she did before she got 10.5 as her answer was dividing her answer by 2.

So we can just multiply 10.5 by 2 to reverse the last step.

After doing that we get 21. The step Lara did before dividing by 2 was subtracting 11.

So we can just add 11 to 21 to reverse this step.

After doing that we get 32. The step Lara did before subtracting 11 was dividing by 3.

So we can just multiply 32 by 3 to reverse this step.

After doing that we get 96. So the number that Lara started with is 96.

Answer: 11,500 grams

Step-by-step explanation: 920/8=115 115*100= 11,500

Answer:

62.625

Step-by-step explanation:

First, we divide 33.4 by 4 to see what ONE gallon weighs.
33.4/4=8.35

8.35*7=58.45+(8.35*(1/2))= 62.625

Therefore, your answer is 62.625

I hope you understand my explanation. I pride myself on making my answers, short, descriptive, yet easy to read.

please give brainliest! Thanks! Hope this helped.

Answer:

62.625 lb

Step-by-step explanation:

Define the variable:

Set up a ratio of weight to number of gallons:

[tex]\implies x:7.5=33.4 :4[/tex]

Solve for x:

[tex]\implies \dfrac{x}{7.5 }=\dfrac{33.4}{4}[/tex]

Cross multiply:

[tex]\implies 4x=33.4 \cdot 7.5[/tex]

[tex]\implies 4x=250.5[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4x}{4}=\dfrac{250.5}{4}[/tex]

[tex]\implies x=62.625[/tex]

Therefore, the weight of 7.5 gallons of water is 62.625 lb.

There are 3 dimes and 12 nickels

Two or more expressions with an Equal sign is called as Equation.

Given,

let x = the number of dimes

then  4x = the number of nickels =y

0.05(4x) = the value of the nickels

0.10x = the value of the dimes

Since the total value of the coins is $0.90 we can write the equation:

0.05(4x) + 0.1x = 0.90

0.2x + 0.1x = 0.90

0.3x = 0.90

Divide both sides by 0.3

x = 3

Hence, there are 3 dimes and 12 nickels

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The value of area under the normal curve at a z-score of 0.33 with respect to the mean is 0.63 (2 dp).

It is a value that describes the deviation of a value from the standard deviation. Z-score is the number of standard deviations a given data point lies above or below mean.

To find the area under the normal curve at a specific value of z we look into the normal distribution table.

At 0.33 we can see that the value is 0.6293. This value is given from the center, which is the mean of the data.

To learn more about z-score visit the link below:

https://brainly.com/question/15016913

#SBJ4

The energy in an 871 KJ cup of yogurt will last for 18.71 minutes .

In the question ,

it is given that ,

efficiency is = 20% = 0.20 .

the rate of work is 155W ,

we know that Efficiency = [tex]\frac{E_{obtain} }{E_{consumed} }[/tex]

substituting the values ,  

we get ,

[tex]E_{consumed}[/tex] = 155/0.20

= 775 J/sec .

This means that for work of 155W it require to consume energy at the rate of 775 J/sec .

we know that the formula for time , energy and rate  is

Time  = Energy/Rate

time = 871000/775

= 1123 seconds

= 18.71 minutes

Therefore , The energy in the yogurt will last for 18.71 minutes .

Learn more about Efficiency here

https://brainly.com/question/13082009

#SPJ4

Any value x not explicitly associated with a positive probability is taken as P(X=x) = 0. The function pX(x)= P(X=x) for any x in the range of X is given as a probability. It is often called the probability mass function of a discrete random variable X.

Binomial Distribution:

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each with its own It has a Boolean result: success (for probability p) or failure (for probability q = 1-p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, d. H. n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.

The binomial distribution is commonly used to model the number of successes in a sample of size n drawn from a population of size N with replacement. If sampling is performed without replacement, the resulting distribution is hypergeometric rather than binomial because the plots are not independent. However, for N much larger than n, the binomial distribution remains a good approximation and is widely used.

In the binomial distribution, the trials to be investigated must have the same probability of success. For example, if you toss a coin, the probability of flipping the coin is 1/2. 0.5 for each trial because there are only two possibilities.

Binomial Random Variable:

This is a special kind of discrete random variable. A binomial random variable counts the number of times a particular event occurs over a fixed number of trials or trials.

Learn more about Random Variable:

https://brainly.com/question/29350065

#SPJ4

The number of bracelets and the number of necklaces will be 10 and 5, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

A gem dealer had a proper measure of gold to make wristbands and pieces of jewelry. The amount of gold in every armband is 5 grams and the amount of gold in every accessory is 16 grams. A goldsmith utilized 130 grams.

Let 'x' be the number of Bracelets and 'y' be the number of Necklaces. Then the equation is given as,

5x + 16y = 130

The term 16y in the equation should be a multiple of 5 to get the whole value.

If the value of y is 5. Then the number of bracelets is given as,

5x + 16(5) = 130

5x + 80 = 130

5x = 50

x = 10

The number of bracelets and the number of necklaces will be 10 and 5, respectively.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2

Answer:

49

Step-by-step explanation:

10 weeks = 70 days

0.7 : 1 = x : 70

x = 0.7 * 70

x = 49

The chance of a difference this large (or larger) happening by chance would be 6.03%

In this question, we have been given a die is rolled 1,000 times. the total number of spots is 3,711 instead of the expected 3,500

We need to find the chance of a difference this large (or larger) happening by chance.

The total number of spots is 3,711 instead of the expected 3,500.

So, the difference is:

3711 - 3500 = 211

So, the chance of a difference:

211/3500

= 0.0603

= 6.03%

Therefore, the chance of a difference this large happening by chance = 6.03%

Learn more about chance here:

https://brainly.com/question/23247150

#SPJ4

The necessarily simplified answer to the provided experiment is given as x = 1 ± √2.

A mathematical expression is simplified when it is replaced with a simpler, usually shorter, equivalent expression.

So, for the given phrase (x + 1)2 - 4(x + 1) + 2 = 0, find the simple answer as follows:
The expression is:  (x + 1)² – 4(x + 1) + 2 = 0

Replace x + 1 = u in the preceding equation:

u² - 4u + 2 = 0

u² - 4u +4 - 4 + 2 = 0

(u - 2)² = 2

u - 2 = ±√2

replace with u = x + 1:

x + 1 - 2 = ±√2

x - 1 = ±√2

x = 1 ± √2

Therefore, the necessarily simplified answer to the provided experiment is given as x = 1 ± √2.

Know more about simplification here:

https://brainly.com/question/723406

#SPJ4

Correct question:
Solve (x + 1)2 – 4(x + 1) + 2 = 0 using substitution. u = Select the solution(s) of the original equation.

There were 682 children's and 332 adults were admitted when the entrance charge to an park is $4 for adults and $1.50 for children.

Given that,

The entrance charge to an amusement park is $4 for adults and $1.50 for children. 351 persons visited the park on one particular day, and 1014 dollars in entrance fees were collected.

We have to find how many people and kids were allowed inside.

We know that,

We get equations as,

1.5x+4y=351 ----->equation(1)

The other equation is

x+y=1014 ----->equation(2)

Take the equation(2)

x+y=1014

y=1014-x

Substitute y=1014-x in equation(1)

1.5x+4y=351

1.5x+4(1014-x)=351

1.5x+2056-4x=351

1.5x-4x=351-2056

-2.5x=-1705

2.5x=1705

x=1705/2.5

x=682

Substitute x=682 in equation(2)

y=1014-x

y=1014-682

y=332

Therefore, There were 682 children's and 332 adults were admitted when the entrance charge to an amusement park is $4 for adults and $1.50 for children.

To learn more about adults visit: https://brainly.com/question/28898057

#SPJ4

The two points that represent Justine‘s function for the yards left to hike in terms of the hours she spent hiking are; (0, 320) and (4, 0)

From the table in the attached file, we see that;

Justine started when Michael was 320 yards from the top.

This coordinate is expressed as (0,320)

where;

0 represents the time Justine started

320 represents the number of yards left.

Now, it is clear that every minute, Justine covers 80 yards.

Thus;

After 1 minute, Justine will have:

(320 - 80) yards left

After 2 minutes, Justine will have:

(320 - 80 - 80) yards left

After 3 minutes, Justine will have:

(320 - 80 - 80 - 80) yards left

After n minutes, Justine will have;

(320 - 80n) yards left

Thus, the possible coordinates are:

(0, 320), (1, 240), (2, 160), (3, 80), (4, 0)

Read more about true coordinates at; https://brainly.com/question/16094976

#SPJ1

The valid converse of the statement is, Yes. If x + 4 is even, then x is even. If x is even, then x + 4 is even.

A conditional statement's opposite is produced when the hypothesis and conclusion are switched around. The converse statement is known as p⇒ q in geometry. In logic and mathematics, the reverse of a categorical or implicational statement is the outcome of reversing its two constituent statements, and it is denoted by the symbol q⇒ p. The opposite of the implication P ⇒ Q is Q P. The inverse of the categorical assertion All S are P is that All P are S.

Given,

If x is even, then x + 4 is even.

The valid converse of the statement is,

Yes. If x + 4 is even, then x is even.

To learn more about converse, visit:

https://brainly.com/question/28446960

#SPJ1

The evaluation of the composite figures, distances and coordinates in the question indicates;

24. The volume of the figure is about c) 1440 cm³

25) The distance of the airport from the plane is about c) 41,043.6 feet

26) The coordinates of the vertex U are c) (-5, -7)

A composite figure is a figure that is composed of two regular figures.

24. The figure is a composite figure comprising of a cylinder and a cone.

Volume of the cylinder = π × 5² × 15 = 375·π

Volume of the cone = (1/3) × π × 5² × (25 - 15) = (83 1/3)·π

The volume of the figure is therefore; 375·π + (18 1/3)·π ≈ 1440

25) The height of the plane = 12,000 ft

The angle of elevation to the airplane = 17°

Let r represent the direct distance of the airport from the plane, we get;

sin(17°) = 12000/r

x = 12000/(sin(17°) ≈ 41,043.6

The direct distance from the plane to the airport which is the hypotenuse side of the right triangle in the figure is about; d) 41,036.6 feet

26) The coordinates of the vertices of the triangle are; R(-6, -3), S(3, 3), and T(4, -1)

The type of quadrilateral represented by quadrilateral RSTU = A parallelogram

The slope of the side ST = (-1 - 3)/(4 - 3) = -4

Equation of the side RU is therefore;

y - (-3) = (-4) × (x - (-6)) = -4·x - 24

y = -4·x - 24 - 3 = -4·x - 27

y = -4·x - 27

The slope of the side RS = (3 - (-3))/(3 - (-6)) = 2/3

Equation of the side TU = y - (-1) = (2/3)·(x - 4) = (2/3)·x - (8/3)

y = (2/3)·x - (8/3) - 1 = (2/3)·x - (11/3)

y = 0.2·x - 1.8

The x-coordinate of the point U can be therefore obtained from the equation;

-4·x - 27 = (2/3)·x - (11/3)

x = -5

y = -4×(-5) - 27 = -7

Learn more about writing algebraic equations here:

https://brainly.com/question/14512742

#SPJ1

The  missing side length in the given right triangle is d) 23.6cm if the other two sides lengths are 14cm and 19cm respectively. So, correct option is d.

We know very well that if a triangle is a right angled it means that  Pythagorean Theorem is applicable on it.

Pythagorean Theorem states that if a triangle is right angled then the sum of square of two sides which are originating from that angle which is 90 degree is equal to square of third side.

In other words,a²+b²=c² where a and b are two sides originating from 90 degree angle and c is the third side which is opposite of the 90 degree angle.

Now, we have a=14 and b=19cm,we need to find value of c.

So, putting the values, we get

=>14² + 19² =c²

=>c²=361+196

=>c² = 557

=>c=√557

=>c=23.6cm

Hence, missing side length is d)23.6cm

To know more about  Pythagorean Theorem, visit here:

https://brainly.com/question/14930619

#SPJ4

(Complete question) is:

what is the missing side length in this right triangle if the other two sides length are 14cm and 19cm respectively ? round the answer to the nearest tenth.5.7 cm5.7 cm12.8 cm12.8 cm23.6 cm

Another name for  equilateral quadrilateral is rhombus since equilateral means that all of its sides are equal in length.

Another name for an equiangular quadrilateral, is a rectangle.

Another name for a regular quadrilateral is a  square, one in which all sides are congruent and all angles are congruent.

Due to the equality of its sides, an equilateral triangle is also known as a regular polygon or regular triangle.

Equiangular simply implies "equal angles." 2. A triangle with acute angles is one in which each of the three internal angles is smaller than 90 degrees.

A quadrilateral is a rhombus if each of its diagonals bisects the vertex angles through which it travels.

∴Another name for  equilateral quadrilateral is rhombus since equilateral means that all of its sides are equal in length.

Another name for an equiangular quadrilateral, is a rectangle.

Another name for a regular quadrilateral is a  square, one in which all sides are congruent and all angles are congruent.

To learn more about equilaterals visit:

https://brainly.com/question/9872652

#SPJ4

Answer:

The two equations that can be used are 7.50a + 4.50s = 3150, and

 a + s = 500.

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

a + s = 3,150  NO

7.5a + 4.5s = 3,150 YES

a + s = 500    YES

7.5s + 4.5a = 500  NO

Step-by-step explanation:

We know that a + s = 500.

Total sales would be the product of the number of adult and student tickets times their repsective prices:

Total Sales ($) = $7.50a + $4.50s = $3150

Leaving off the units for the next steps, we have two equations and we can rearrange one of them to substitute into the other.  

1)   Rearrange the first equation to isolate a:  a = 500-s

Now use this definition of a in the second equation:

7.50a + 4.50s = 3150

7.50(500-s) + 4.50s = 3150

3750 - 7.5s + 4.50s = 3150

 -3s = -600

    s = 200  student tickets were sold

Use a+s=500 to find a:  

a+200 = 500

     a=300   300 adult tickets were sold.

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

The two equations we used to find this answer were:

7.50a + 4.50s = 3150, and

 a + s = 500

The answer is false because the answer will be 0.04863%

To find the periodic interest rate we have to know about the following terms:-

Interest Rate (R)

It is the nominal interest rate or "stated rate" in percent. r = R/100

Compounding Periods (m)

It is the number of times compounding will occur during a period.

Periodic Interest Rate (P)

This is the rate per compounding period, such as per month when your period is year and compounding is 12 times per year.

R ={  (1 + i/m) to the power m/n - 1 }

Where,

i = nominal annual rate

n = number of payments per year i.e., 12 for monthly payment, 1 for yearly payment and so on.

m = number of compounding periods per year

The period interest rate per payment is integral to the calculation of annuity instruments including loans and investments.

So, R = 0.04863%

To know more about the Periodic interset rate

https://brainly.com/question/24353477

#SPJ4