PLEASE HELP ASAP
I NEED HELP WITH THIS MATH

PLEASE HELP ASAP I NEED HELP WITH THIS MATH

Answers

Answer 1

Step-by-step explanation:

remember :

when multiplying terms with the same base, we add the exponents.

when dividing terms with the same base, we subtract the exponent of the denominator from the exponent of the numerator.

when putting exponent on exponent, we multiply the exponents.

a negative exponent means 1/...

e.g. 6^-4 = 1/6⁴

1/6^-4 = 1 / 1/6⁴ = 6⁴

so,

1.

(3^-4 × 3²)/3 = 3^-2 × 3^-1 = 3^-3 = 1/3³ = 1/27 =

= 0.037037037...

2.

(4²)^-1 × 4² = 4^-2 × 4² = 4⁰ = 1

3.

(2^-4 / 2^-2)^-1 = (2^-4 × 2²)^-1 = (2^-2)^-1 = 2² = 4

4.

(3^-3)² / (3²)^-1 = 3^-6 / 3^-2 = 3^-6 × 3² = 3^-4 =

= 1/3⁴ = 1/81 = 0.012345679...


Related Questions

Complete the equation of the line through (−10,3) and (-8,-8)

Answers

Answer:

\(\boxed{y = -5,5x - 52}\)

Step-by-step explanation:

Equation of a straight line: y = kx + b

Points: (-10,3) and (-8,-8)

Сompose the system of equations:

\(\displaystyle \left \{ {{3=-10k + b} \atop {-8=-8k + b}} \right\) \(\displaystyle \left \{ {{b= 3 + 10k} \atop {b=8k - 8}} \right \Longrightarrow 3 + 10k = 8k - 8\)

\(3 + 10k = 8k - 8\)

\(2k = -11|:2\)

\(k = -5,5\)

\(b = 3 + 10k = 3 + 10 \cdot ( -5,5) = 3 - 55 = -52\)

\(y = -5,5x - 52\)

The length of a rectangular poster is 9 more inches than half its width. The area of the
poster is 20 square inches. Solve for the dimensions (length and width) of the poster.

Answers

The.dimensions (length and width) of the poster include 10 inches and 2 inches.

How to calculate the dimensions?

Let the width be represented by w.

The length based on the information given will be: (w/2) + 9 = 0.5w + 9

The area is 20 inches²

It should be noted that length × width = area.

This will be:

= (0.5w + 9) × w = 20

0.5w² + 9w = 20

0.5w² + 9w - 20 = 0

Multiply through by 2

w² + 18w - 40 = 0

w² + 20w - 2w - 40 = 0

w(w + 20) - 2(w + 20)

(w - 2) = 0

w = 0 + 2

Width = 2 inches

Length = 0.5w + 9

= 0.5(2) + 9

= 1 + 9

= 10 inches.

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y=3x-1 y=-2x+4 what is the sum of x and y in the solution to the system​

Answers

Answer:

y=1,2 y=2

Step-by-step explanation:

Please need help, will give brainlist

Please need help, will give brainlist

Answers

C and E are correct! I hope this helps!

One factor of the polynomial 3x3 + 20x2 - 21x + 88 is (x + 8). what is the other factor of the polynomial? (note: use long division.)
oa (3x2 - 4x+11)
b. (3x - 4x)
c. (3x2 +11)
d. (3x2 + 4x - 11)

Answers

The other factor of the polynomial is a. 3x2-4x+11

Given polynomial is 3x3 + 20x2 - 21x + 88 and the factor is (x+8)

We need to find another factor using long division method

So,

We will divide the polynomial by the factor to find the another factor

Therefore,

\(\sqrt[x+8]{3x^3+20x^2-21x+88}\)

Now calculating

First multiplying \(3x^2\) with (x+8) so , \(3x^2\) will be in the quotient

We get \(3x^3+24x^2\)

simplifying the calculation for \(3x^3+20x^2\) and \(3x^3+24x^2\)

We get the remainder is \(-4x^2-21x+88\)

Second we will multiply -4x with (x+8) Where -4x will be in the quotient

We get \(-4x^2-32x\) and then we will simplify the equation

We get 11x +88 as a remainder

The quotient we get is \(3x^2-4x\)

Third we will multiply +11 with (x+8) Where +11 will be in the quotient

we get 11x+88

Simplifying the equation we get the remainder 0

So the quotient we get is  (3x2 - 4x+11)

Hence the another factor of the polynomial is  (3x2 - 4x+11)

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Mr. Bradley is building a storage closet. He has four boards that are 9 feet long. He needs to cut boards into 18 inches long. What is the greatest number of 18-inch pieces that Mr. Bradley can cut from the four wooden boards? (1-foot = 12 inches)

PLEASE HELP. And dont answer if you dont know please it just a waste of time. This is a test

Answers

Answer:

The answer would be 6

Marking brainless (how ever u spell this)!

Marking brainless (how ever u spell this)!

Answers

Answer:

brainliest*

Step-by-step explanation:

c

What is y??? Pls help meeee I don’t understand how to do it

What is y??? Pls help meeee I dont understand how to do it

Answers

Answer:

what do you want the slope? The y cordinate is where the points are on the y axis.

Step-by-step explanation:

the slope needs to be included

Cubic Coating : Frozen specimens are stored in a cubic metal box that is x inches on each side. The box is
surrounded by a 2 inch thick layer of foam insulation.
(i) Find a polynomial function V x( ) that gives the total volume in cubic inches for the box and insulation.
(ii) Find the total volume if x is 10 inches.
(iii) Use the remainder theorem to find the total volume when x is 10 inches.

Answers

The attached answer is not mine, but is by a fellow Brainly user - isha00333

Keep in mind this is only for the first question.

These answers are by Brainly user aman1234e9 :

(ii) To find the total volume when x is 10 inches, we substitute x = 10 into the polynomial function:

V(10) = 8(10)^3 + 48(10)^2 + 96(10) + 64

V(10) = 8,864 cubic inches

Therefore, the total volume when x is 10 inches is 8,864 cubic inches.

(iii) To use the remainder theorem to find the total volume when x is 10 inches, we divide the polynomial function V(x) by (x-10) and evaluate the remainder.

We can use long division or synthetic division to perform the division, but using synthetic division, we have:

10 | 8 48 96 64

80 1280 2240

8 128 1376 2304

The remainder is 2304, so the total volume when x is 10 inches is 2304 cubic inches.

Cubic Coating : Frozen specimens are stored in a cubic metal box that is x inches on each side. The box

what is the answer to this? :(5x^4)^3

Answers

Answer:

it is 25 or 35

Step-by-step explanation:

can someone tell the answer of 22 number​

can someone tell the answer of 22 number

Answers

The answer is p4q3
The reason being is when you multiply exponents with each other they end up adding with each other
can someone tell the answer of 22 number

Answer:

♕ \( \large{ \tt{ E\: X \: P \: L \: A \: N \: A\: T \: I \: O \: N}} : \)

♨ \( \underline{ \large{ \tt{G \: I \: V \: E \: N}}} : \)

Length ( l ) = ( pq )² cm & breadth ( b ) = ( p²q ) cm

✎ \( \underline{ \large{ \tt{T\: O \: \: F \: I \: N \: D}}} : \)

Area of the rectangle

☄ \( \underline{ \large{ \tt{S\: O \: L \: U \: T \: I \: O \: N}}} : \)

\( \boxed{ \text{Area \: Of \: Rectangle = l \: × \: b}}\)

Plug the values and then simplify !

\( \large{ \bf{↬( {pq)}^{2} \times {p}^{2}q }}\)

\( \large{ \bf{↬ {p}^{2} {q}^{2} \times {p}^{2} q}}\)

\( \large{ \bf{ ↬{p}^{2 + 2} {q}^{2 + 1}}} \)

\( \boxed{\large{ ↬\bf{ {p}^{4} {q}^{3}}}} \)

\( \boxed{ \boxed {\tt{⟿ \: Our \: Final \: Answer : \boxed{ \underline{ \tt{ {p}^{4} {q}^{3} \: cm²}}}}}} \)

۵ \( \underline{ \large{ \tt{REMEMBER}}} : \) To multiply two terms with same base , their indices are added and the same base is taken.

✢ \( \underline{ \large{ \tt{STUDY \: TIP}} }: \)

Write notes in your own words - don't just copy from your textbook. ✔

♪ Hope I helped!.

ツ Have a wonderful day / evening ! ♡

# StayInAndExplore ! ☂

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

the ratio of freshmen to sophomores was 12 to 16. if there were 3220 in all, how many were sophomores?

Answers

The number of sophomores after reducing ratio 1840.

What is ratio?

 A ratio in math displays how many times one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit. In a similar way, the ratio of oranges to all other fruits is 8:14, while the ratio of lemons to oranges is 6:8.

Here the ratio is,

=> freshmen: sophomore = 12: 16

Here there total is 3220.

Total ratio = 12+16 = 28 ,

Then ,

28 = 3220

16 = x

After inter multiplication ,

=> x = \(\frac{3220*16}{28}\)

=> x = 1840.

Hence the number of sophomores is 1840.

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Yup there's more pls help

Yup there's more pls help
Yup there's more pls help

Answers

top half:
D (x-2, y+3) E (x-3, y(+\-) 0) F (x+1, y-2)
P (x+1, y+2) Q (x+3, y+4) R (x+5, y+2)

Steve claims that the points (-4,8) (8,8) and (-4,3) form a right triangle. Use the distance formula and the Pythagorean theorem to determine if Steve is correct. Show your work and explain your reasoning.




(question 7)

Answers

Yes, the points are the vertices of a right triangle and we will prove that by using the Pythagorean theorem.

Are these the vertices of a right triangle?

Remember that the distance between two points (a, b) and (c, d) is:

distance = √( (a - c)² + (b - d)²)

The distance between (-4, 8) and (8, 8) is:

d₁ = √( (-4 - 8)² + (8- 8)²) = 12

The distance between (8, 8) and (-4, 3) is:

d₂ = √( (8 + 4)² + (8- 3)²) = 13

The distance between (-4, 8) and (-4, 3) is:

d₃ = = √( (-4 + 4)² + (8 - 3)²) = 5

if the Pythagorean theorem is true, then the sum of the squares of the two shorter sides must be equal to the square of the larger side, then we must have that:

5² + 12² = 13²

Solving that we get:

25 + 144 = 169

169 = 169

This is true, so yes, the vertices are the vertices of a right triangle.

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PLEASE HELPP!! i’ve been struggling with this problem for the past 30 min.. lessons about polynomials.

PLEASE HELPP!! ive been struggling with this problem for the past 30 min.. lessons about polynomials.

Answers

Answer:

39.77 -> 39 or 40, depending on rounding

Step-by-step explanation:

Since 2002-1992 is 10. T would equal 10. At that point, it would be a gesture of plugging in 10 whereever you see a "t" and solve for both

Let X
=
A
.
¯¯¯¯¯¯
B
C
. Evaluate X for
(a) A
=
1
,
B
=
0
,
C
=
1
, (b) A = B = C = 1 and ( c) A = B = C = 0.

Answers

The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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The volume of a gas at 19 pounds per square inch pressure is 3 liters. If the gas is compressed into a 750-milliliter container, what will be the pressure of the gas?

Answers

Answer:

76psi

Step-by-step explanation:

P1 x V1 = P2 x V2

P1=19psi

P2=

V1=3L

V2=750ml (0.75 L)

19x3=0.75

=76

Four less than the product of 3 and a number is 8. Use the variable c for the unknown number

Answers

Let's solve the given problem, where we have to use the variable c for the unknown number. "Four less than the product of 3 and a number is 8".

The given statement can be expressed in a mathematical equation as follows:3c - 4 = 8Adding 4 on both sides, we get:3c = 8 + 43c = 12Dividing both sides by 3, we get:c = 4Hence, the value of the unknown number is 4.

We have used the variable c to represent the unknown number. It is given that "Four less than the product of 3 and a number is 8", which can be written as:3c - 4 = 8Solving this equation, we get the value of c as 4. Thus, the unknown number is 4.Therefore, the required answer is: The value of the unknown number is 4.

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Use the quadratic formula to find the solutions to the equation y = 5x² - 9x + 3.
What are the zeros of the equation?

Use the quadratic formula to find the solutions to the equation y = 5x - 9x + 3.What are the zeros of

Answers

On solving the provided question, we can say that the quadratic equation is  y = 5x² - 9x + 3 this quadratic equation can not factorized further

What is quadratic equation?

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation is

y = 5x² - 9x + 3

this quadratic equation can not factorized further

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How do you find the length of a rectangle with coordinates?

Answers

To find the length of a rectangle with given coordinates, you need to use the distance formula. The distance formula is a mathematical formula that is used to find the distance between two points in a plane.

The distance formula is given by -

d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points, and d is the distance between the points.

To find the length of a rectangle, you will need to use the distance formula to find the distance between two points that are on opposite sides of the rectangle. For example, you can use the distance formula to find the length of the rectangle by finding the distance between the points \((x_1, y_1)\)and \((x_2, y_2)\), where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of two points on opposite sides of the rectangle.

For example, consider a rectangle with the following coordinates:

(1, 1); (1, 5); (5, 5); and (5, 1)

To find the length of this rectangle, you can use the distance formula to find the distance between the points (1, 1) and (1, 5). The distance formula is:

d =\(\sqrt{(x2 - x1)^2 + (y2 - y1)^2}\)

= \(\sqrt{(1 - 1)^2 + (5 - 1)^2}\)

=\(\sqrt{0 + 16}\)

= \(\sqrt{16}\)

= 4

Therefore, the length of the rectangle is 4 units.

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Simplify the expression.
5.1m2.3m
Question content area bottom
Part 1
5.1m2.3m

enter your response here
​(Simplify your answer. Use integers or decimals for any numbers in the​ expression.)

Answers

The simplification of the expression is determined as 11.73 m².

What is simplification of the expression?

To simplify a mathematical expression is to represent it in the least complicated form possible.

In general the simplest form is one that has used the fundamental properties of numbers, exponents, algebraic rules, etc. to remove any duplication or redundancy from the expression.

The given expression is as follows;

(5.1 m)(2.3 m)

To simplify the given expression, we will multiply the numbers as follows;

5.1 m x 2.3 m = 11.73 m²

Thus, the simplification of the expression is determined as 11.73 m².

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The complete question is below:

Simplify the expression, 5.1m  x 2.3m.

(Simplify your answer. Use integers or decimals for any numbers in the​ expression.)

a frog is positioned at the origin of the coordinate plane. from the point (x, y), the frog can jump to any of the points (x 1, y), (x 2, y), (x, y 1), or (x, y 2). find the number of distinct sequences of jumps in which the frog begins at (0, 0) and ends at (4, 4).

Answers

The minimum number of jumps required for the frog to go from (0,0) to (4,4) and each distance is 5 units is 3.

Graph Theory, in discrete mathematics, is the study of the graph. A graph is determined as a mathematical structure that represents a particular function by connecting a set of points. It is used to create a  pairwise relationship between objects.

The graph is made up of vertices (nodes) that are connected by the edges (lines). The applications of the linear graph are used not only in Maths but also in other fields such as Computer Science, Physics and Chemistry, Linguistics, Biology, etc. In real-life also the best example of graph structure is GPS, where you can track the path or know the direction of the road.

We have, the initial position of frog =(0,0)

The endpoint of the jump of frog is (4,4)

The minimum number of jumps required for the frog to go from (0,0) to (4,4) and each distance is 5 units is 3

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Vincent deposit $165 at the end of each quarter at an annual
interest rate of 6% compounded quarterly. After how many years will
he has $9,000?

Answers

It will take approximately 3.96 years (or approximately 3 years and 11 months) for Vincent's savings to reach $9,000.

To solve this problem, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where:

FV = Future Value

P = Payment (deposit amount)

r = Interest rate per compounding period

n = Number of compounding periods

In this case, Vincent deposits $165 at the end of each quarter, so P = $165. The annual interest rate is 6%, compounded quarterly, so the interest rate per compounding period, r, would be 6% divided by 4 (since there are 4 quarters in a year), which is 0.06/4 = 0.015.

We want to find the number of years, n, it will take for Vincent's savings to reach $9,000. Let's substitute the given values into the formula and solve for n:

9,000 = 165 * [(1 + 0.015)^n - 1] / 0.015

To solve this equation, we can use algebraic techniques or a financial calculator. Solving the equation, we find that n is approximately 15.83.

Since n represents the number of quarters, we need to convert it to years by dividing it by 4 (since there are 4 quarters in a year):

n (in years) = 15.83 / 4 ≈ 3.96

Therefore, it will take approximately 3.96 years (or approximately 3 years and 11 months) for Vincent's savings to reach $9,000.

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Consider a sample with data values of 55, 56, 70, 61, 53, 57, 50, 73, 52, 69, and $2. Compute the mean, median, and mode.
If required, round your answers to two decimal places.
Mean = ________
Median = _________
Mode = _________

Answers

The mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

Given data values are 55, 56, 70, 61, 53, 57, 50, 73, 52, 69, and 2. We need to calculate the mean, median, and mode of this sample.So, let's first arrange the data values in ascending order:2, 50, 52, 53, 55, 56, 57, 61, 69, 70, 73

Mean:The mean is the sum of all the data values divided by the total number of data values. So, we can use the following formula to calculate the mean:

Mean = (sum of all the data values) / (total number of data values)Sum of all the data values = 55 + 56 + 70 + 61 + 53 + 57 + 50 + 73 + 52 + 69 + 2 = 598Total number of data values = 11

Therefore,Mean = (sum of all the data values) / (total number of data values) = 598 / 11 = 54.36 (rounded to two decimal places)Therefore, the mean of the given data values is 54.36.

Median:The median is the middle value of a sorted data set. Since the data set has 11 data values, the median is the average of the 6th and 7th values (counting from smallest to largest).

Therefore, the median is :Median = (55 + 56) / 2 = 55.5Therefore, the median of the given data values is 55.5.

Mode:The mode is the data value that appears most frequently in the data set. In this case, there is no data value that appears more than once. So, there is no mode.

Therefore, the mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

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As the value of c increase toward infinity, what happens to the values of g(x) = 3x - 19

Answers

As x goes to infinity g(x) goes to infinity

A veterinary office pays PupFood $32. 75 for each bag of dog food. If the office spent $655, how many bags of food did they purchase? (Use only a number for your answer)

Answers

Answer:

20 Bags

Step-by-step explanation

The total costs would be given by the formula:

Total $ = (Bags of Food)*(Cost/bag)

We know total cost and price per bag:

$655 = (Bags of Food)*($32.75/bag)

Bags of Food = ($655/$32.75)

Bags of Food = 20 Bags

a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 411.0 gram setting. it is believed that the machine is underfilling the bags. a 35 bag sample had a mean of 406.0 grams. a level of significance of 0.05 will be used. state the hypotheses. assume the standard deviation is known to be 25.0.

Answers

Using a 35-bag sample with a mean of 406.0 grams, a known standard deviation of 25.0 grams, and a level of significance of 0.05, you can perform a one-tailed Z-test to determine whether to reject or fail to reject the null hypothesis.

To test if the potato chip manufacturer's bag filling machine is working correctly at the 411.0-gram setting, we will state the hypotheses using the given terms.

Null Hypothesis (H0): The machine fills bags correctly, with a mean weight of 411.0 grams (µ = 411.0 grams)
Alternative Hypothesis (H1): The machine is underfilling bags, with a mean weight less than 411.0 grams (µ < 411.0 grams)

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Passing through (-3,2) and (6,2) what is the slop intercept form of the equation of the line?

Answers

Answer:

The slope would be 0

Step-by-step explanation:

The y is the same, and it's not rising or running. The y will never change no matter what x is. Hope this helps!

At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0.07 and the probability that the flight will be delayed is 0.19. The probability that it
will not rain and the flight will leave on time is 0.75. What is the probability that it is
raining and the flight is delayed? Round your answer to the nearest thousandth.

Answers

Step-by-step explanation:

P(rain and flight delayed) = P(rain) x P(flight delayed) = 0.07 x 0.19

= 0.013 (nearest thousandth)

Answer: 0.01

Step-by-step explanation:

the person above did it wrong, this answer is for sure correct.

At LaGuardia Airport for a certain nightly flight, the probability that it will rain is0.07 and the probability

how many three-digit multiples of 3 can be written using numbers 1,3,5,9 if all digits are different?

Answers

Answer:   12

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

Explanation:

We have four values to pick from {1,3,5,9} and we want to form a three-digit number.

Kick one of those values out, let's say we kick out "9" at the end to get the subset {1,3,5}.

The sum of these remaining values is 1+3+5 = 9 which is a multiple of 3. Therefore three-digit numbers that have any order of 1,3,and 5 will be a multiple of 3.

Eg: 135/3 = 45 exactly.

There are 3*2*1 = 6 such numbers as shown at the very bottom of this solution post.

This is a permutation since the order matters.

Let A = 6 so we can use it later.

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

Go back to {1,3,5,9}

Now let's say we kicked "5" out this time.

We go from {1,3,5,9} to {1,3,9}

The digits sum to 1+3+9 = 13 which is not a multiple of 3

No matter how we arrange these digits, we won't get a multiple of 3.

Eg: 139/3 = 46.33 approximately

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

Let's go back to {1,3,5,9}. This time we'll kick out "3" from the group.

{1,3,5,9} shrinks to {1,5,9}

Add the values: 1+5+9 = 15 which is a multiple of 3.

Therefore, we get 6 more permutations (refer to the first section for similar steps). Let B = 6 so we can use it later.

Example: 159/3 = 53 exactly

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

Return back to {1,3,5,9} once more. We have one final value to kick out.

Let's remove the "1" to end up with {3,5,9}

Add the values: 3+5+9 = 17 which isn't a multiple of 3, so we ignore this sub-case. It's similar to the 2nd section shown above.

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

Each previous section had us remove exactly one value to have 3 digits leftover. This is a methodical way to guarantee we have looked through all possible cases.

The first case had us kick out 9 so that a permutation of {1,3,5} led to some multiple of 3. There were A = 6 cases for that section.

The third section had {1,5,9} which led to B = 6 more cases.

In total, there are A+B = 6+6 = 12 different three-digit numbers possible if we are only allowed to use {1,3,5,9} without repeats allowed. In other words, all three digits must be different.

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Check:

Here are the first 6 cases involving 1,3,5

number = 135number = 153number = 315number = 351number = 513number = 531

Here are the other 6 cases involving 1,5,9

number = 159number = 195number = 519number = 591number = 915number = 951
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