How many three digit numbers can be made from the digits 1,\ldots,9 if repetitions of digits are not allowed?

Answers

Answer 1
9 values for each digit, order matters: 123 is different than 321, and no repetion

9*8*7 = 504

Look at a simpler example, with 1, 2, 3:

123
132
213
231
312
321

6 numbers

3*2*1 = 6
Answer 2

There are 84 three digit numbers can be made from the digits 1, ..., 9

What is Combination?

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

The numbers are,

⇒ 1, 2, ..., 9

Now,

All the three digit numbers can be made from the digits 1, ..., 9 are;

⇒ [tex]^{9} C_{3}[/tex]

⇒ 9! / 3! 6!

⇒ 9 × 8 × 7 / 6

⇒ 84

Thus, There are 84 three digit numbers can be made from the digits

1, ..., 9.

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Related Questions

Segment DE is midsegment of triangle ABC. What is the length of segment DE?
A) 5
B) 10
C) 15
D) 20

Answers

(X+5)2=X+15
2X+10=X+15
X=5
A) 5 :)

Answer:

B) 10

Step-by-step explanation:

If DE is midsegment of the triangle, we know that AC measures twice as DE.

In the problem we have that AC = x + 15 and DE = x + 5

Writing this as an equation we have:

[tex]x + 15 = 2(x+5)\\x+15=2x +10\\15-10=2x-x\\5=x[/tex]

Therefore x = 5 and the length of segment DE is:

x + 5 = 5 + 5 = 10

Therefore the correct answer is B) 10

Which number is greatest?

a. 3.4 × 10-2

b. 4.3 × 10-3

c. 5.2 × 10-4

d. 6.1 × 10-4

Answers

a) =27.2
b) = 30.1
c) =31.2
d) =36.6

answer = D

Answer:

the answer is d 6.1x 10-4

Step-by-step explanation:

In a right triangle angle C measures 40 degrees. The hypotenuse of the triangle is 10in long. What is the approximate length of the side adjacent to angle C?

Answers

https://us-static.z-dn.net/files/dc0/3fhttps://us-static.z-dn.net/files/dc0/3f8c9cbb3558907fd513c03e3db25ee1.jpg

Find 2 consecutive positive even integers such that the product of the 1st and 2nd is 2 less than 5 times the 3rd. Use an algebraic solution.

Answers

Assume the smaller one is x, then the other ones will be x+2 and x+4

x(x+2) + 2 = 5(x+4)

x^2 + 2x - 5x - 18 = 0

-> x^2 - 3x - 18 = 0

-> (x-6)(x+3) = 0

-> x = 6 or -3, since x must be positive, then x = 6

So the numbers are: 6, 8, 10

The square root of 12 is between A.) 3 and 4 B.) 4 and 5 C.) 5 and 6 D.) 6 and 7

Answers

-Hai There!


-Your answer to this question is letter A.


-Correct me if I'm wrong. (:







√12 is between √9 and √16

√9 = 3 and √16 = 4, so
 
√12 is between 3 and 4



is this correct? if not please let me know how to solve it

Answers

That is correct.
You have applied the distributive law.
it is correct. you used the distributive property.

In EFG, mE = 30, mF = 60, and mG = 90. Which of the following statements about EFG are true?

Answers

[tex]FG=cos60^o * EF = \frac{1}{2} * EF \\ \\ EG = cos30^o * EF = \frac{ \sqrt{3} }{2} * EF \ \ \ \text{[B is true]} \\ \\EG=tan60^o*FG= \sqrt{3}*FG \ \ \ \text{[C is true]} \\ \\ EF= \frac{FG}{cos60^o}= \frac{FG}{ \frac{ 1 }{2} } = 2*FG \ \ \ \text{[F is true]}[/tex]

Statements B, C, and F are all true based on the given angle measures in triangle EFG.

Let's reevaluate the statements with the given angle measures in triangle EFG:

m∠E = 30°

m∠F = 60°

m∠G = 90°

A. FG = √3/2 EF

FG = (EF * √3) / 2

This statement is true. FG is indeed equal to √3/2 EF.

B. EG = √3/2 EF

EG = (EF * √3) / 2

This statement is true. EG is equal to √3/2 EF.

C. EG = -√3 FG

EG = -√3 * FG

This statement is true. EG is equal to -√3 FG.

D. EF = -√3 FG

EF = -√3 * FG

This statement is true. EF is equal to -√3 FG.

E. EG = 2 FG

EG = 2 * FG

This statement is true. EG is equal to 2 FG.

F. EF = 2 FG

EF = 2 * FG

This statement is true. EF is equal to 2 FG.

Statements B, C, and F are all true based on the given angle measures in triangle EFG.

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The size of a bicycle is determined by the diameter of the wheel. You want a 24-in bicycle for Christmas. What is the circumference of one of the wheels? A 75.4 in B 75.3 in C 37.7 in D 37.6 in

Answers

Answer:

The circumference of one of the wheels is:  

                     Option: A    75.4 in.

Step-by-step explanation:

The 24-in bicycle means that the diameter of the wheel of the bicycle isL 24 in.

We know that the wheel of the bicycle is in the shape of a circle.

This means that the diameter of circle is: 24 in.

Hence, the radius(r) of circle is: 12 in.

( since we know that the radius(r) of the circle is half the diameter(d) of the circle)

Now, we are asked to find the circumference of the circle.

The circumference(C) of the circle is given by:

C=2πr

i.e.

C=2×3.14×12

i.e.

C=75.36 in.

which to the nearest tenth is: C=75.4 in.

Which of the expressions are equivalent to the one below? Check all that apply. (10 + 8) • 2

Answers

this is an exercise in distributive property and commutative property

distributive
a(b+c)=ab+ac
in this case
2(10+8)=(2*10)+(2*8)
so it is B

also commutative
a+b=b+a
(10+8)(2)=(8+10)(2)


So B and D are the correct answers
(10+8) =18
18×2=36

B and D are equivalent to (10+8) · 2


Hope this helps : )

The perimeter of a triangle is 86 inches. The largest side is four inches less than twice the smallest side. The third side is 10 inches longer than the smallest side. What is the length of each side?

Answers

Hello,
Assume x the smallest side.
y the third side
z the largest side
z=2x-4
y=10+x
x+y+z=86
==>x+(10+x)+(2x-4)=86
==>4x=86-10+4
==>x=20, y=30 and z=36

Someone please answer this for me

Answers

Each gallon costs $1.25
$15/$1.25 each= 12 gallons
Final answer: C
15/1.25 =C.12 that would be the answer

A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that angle ADC is a right angle and that angle BDC is 32° greater than mangle ADB. Solve an equation to find angle BDC and angle ADB.

Answers

Answer:

m∠ADB = 29° and m∠BDC = 61°

Step-by-step explanation:

It is given that m∠ADC = 90°

Since m∠ADB + m∠BDC = 90° [∠ADB and ∠BDC are complimentary]

Since ∠BDC = ∠ADB + 32°

So, m∠ADB + m∠ADB + 32° = 90°

2(m∠ADB) + 32° = 90°

2(m∠ADB) = 90 - 32

2(m∠ADB) = 58°

m∠ADB = 29°

Since m∠ADB + m∠BDC = 90°

So, m∠BDC + 29° = 90°

m∠BDC = 90 - 29

             = 61°

Therefore, m∠ADB = 29° and m∠BDC = 61°

m∠ADB = 29° and m∠BDC = 61°

Solving this will just be based on some basic angle theorems in a triangle.

We are given; m∠ADB = 29° and m∠BDC = 61°  We are told that m∠ADC is a right angle. This means that; m∠ADC = 90°

Now, since m∠ADC = 90°, it means that;

m∠ADB + m∠BDC = 90° (because m∠ADB and m∠BDC are complimentary angles due to the fact that angle at point D is 90°)

We are also told that;

m∠BDC is 32° greater than angle m∠ADB

This means that we can write as;

m∠BDC = m∠ADB + 32°

From earlier, we saw that;

m∠ADB + m∠BDC = 90°

Thus, putting m∠ADB + 32° for m∠BDC, we will have;

m∠ADB + m∠ADB + 32° = 90°

2(m∠ADB) + 32° = 90°

     Subtract 32° from both sides to get;

2(m∠ADB) = 90° - 32°

2(m∠ADB) = 58°

m∠ADB = 58°/2

m∠ADB = 29°

Puttting 29° for m∠ADB into; m∠ADB + m∠BDC = 90° gives us;

29° + m∠BDC= 90°

       Subtract 29° from both sides to get;

m∠BDC = 90° - 29°

m∠BDC = 61°

In conclusion, m∠ADB = 29° and m∠BDC = 61°

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2x^3+2x^2-19x+20=0 find the roots of the polynomial equation

Answers

the answer is   x=-4, (3±i)/2

Answer:

[tex]\frac{3+i}{2} , \frac{3-i}{2} , -4[/tex]

Step-by-step explanation:

I need to know how to find angle "H"

Answers

check the picture below.  Recall your SOH CAH TOA.

12 POINTS PLZ HELP ONLY HAVE 3 MINUTES LEFT

Which statement about histograms is true?

Data is organized in categories.

Data appears as bars that are all about the same height.

Data is organized in equal intervals.

Data appears as bars that do not touch.

Answers

Answer:

c

Step-by-step explanation:

The correct statement about Histogram is Data is organized in equal intervals.

What is Histogram?

A histogram is a graphical representation of discrete or continuous data. The area of a bar in a histogram is equal to the frequency. The y -axis is plotted by frequency density (which is proportional to the frequency) and the x -axis is plotted with the range of values divided into intervals.

Given:

Equal in breadth and corresponding to equal class intervals are the bars. However, they can occasionally be displayed as a wider variety within their groups, such as in size classes.

The width and data being achieved, for instance, forces a true event of varying class sizes in education upon the base of the graph.

and, for the purpose of displaying evenly spaced-out numerical data. The bars should be in close proximity to one another but not overlap. You can view the frequency distribution of the data or the number of pieces of data contained in each interval using these intervals.

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Sarah decides to take her six-year-old son to the circus the price for the child ticket is $4.75 dollars Less in the price for the adult ticket if we represent the price for the child ticket using the variable X how would you write the algebraic expression for the adult ticket price

Answers

Since the child ticket is y-4.75 (saying y is the adult ticket), we need to solve for y in y-4.75=x. Adding 4.75 to both sides, we get y=x+4.75

The volume of a sphere with radius r is 4 3 πr 3 . what is the volume of a sphere with radius 5

Answers

Final answer:

To find the volume of a sphere with a radius of 5, plug the value into the formula V = (4/3)πr³. The result is approximately 523.6 cm³.

Explanation:

The question asks for the volume of a sphere with a given radius. The formula to calculate the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius of the sphere.

To find the volume of a sphere with radius 5, we substitute r with 5 in the formula:

V = (4/3)π(5)³

V = (4/3)π(125)

V = (4/3)π(125) = 500/3π cm³

The volume of a sphere with radius 5 is therefore 500/3π cubic centimeters, which is approximately 523.6 cm³ when rounded to one decimal place.

. In the algebraic expression mc034-1.jpg 7, 17, and –10 are _____ terms. operations. coefficients. variables.

Answers

Answer:

Coefficient

Step-by-step explanation:

The correct option is A.

In the algebraic expression 7a+17b-10c, 7, 17 , and −10 are coefficients.

A. Coefficients. The numbers 7, 17, and -10 are coefficients in the expression 7a + 17b - 10c because they are the constants that multiply the variables a, b, and c respectively.

B. Incorrect. Operations are mathematical actions like addition, subtraction, multiplication, or division, not the constants themselves.

C. Incorrect. Variables, denoted by a, b, and c, are letters or symbols representing unknown or changing quantities, not the constants.

D. Incorrect. Terms are the individual parts of an expression separated by addition or subtraction, consisting of a coefficient and possibly a variable or variables multiplied together. The numbers 7, 17, and -10 are coefficients within the terms of the expression but are not terms themselves.

So, the correct option is A. Coefficients.

The complete question is here:

In the algebraic expression 7a+17b-10c, 7, 17 , and −10 are ______

A. coefficients.

B. operations.

C. variables.

D. terms.

Point C is the center of the circle. The measure of angle ACB is 12x – 7. Arc AB measures 10x + 7. Find the value of x.

Answers

check the picture below.

bear in mind that, arcs get their angle measurement from their central angle.  Thus, those two are equal.

Answer:

x=7

Step-by-step explanation:

Subtract 10x

from both sides of the equation.

12x−7−10x=7

Subtract 10x

from 12x

2x−7=7

Add 7

to both sides of the equation.

2x=7+7

Add 7 and 7

2x=14

Divide each term by 2 and simplify.

x=7

Triangle FGH is a right triangle. Angle G is a right angle, m∠F = 9x – 1, and m∠H = 3x + 7. What is m∠F?

Answers

interior angles of a triangle add up to 90 degrees

< F + < G + < H = 180
9x - 1 + 90 + 3x + 7 = 180
12x + 96 = 180
12x = 180 - 96
12x = 84
x = 84/12
x = 7

so < F = 9x - 1 = 9(7) - 1 = 63 - 1 = 62 <=====
< G = 90
< H = 3x + 7 = 3(7) + 7 = 21 + 7 = 28
added : 62 + 90 + 28 = 180
the angles of a triangle must add up to 180 degrees.

G = 90 (because it's a right angle)
F = 9x - 1
H = 3x + 7

90 + (9x - 1) + (3x + 7) = 180
(9x - 1) + (3x + 7) = 90
12x + 6 = 90
12x = 84
x = 7

now that we have x, we can find out the measure of angle F.

9(7) - 1
63 - 1
62

angle F is 62 degrees

WILL PICK BEST ANSWER IF ITS CORRECT TO ANSWER THESE FEW PROBLEMS
YOU MUST EXPLAIN WHY YOU KNOW

1)Which system of linear inequalities is represented by the graph?
(goes with pic 1)
y > 2/3x + 3 and y < -1/3x + 2
y > 2/3x + 3 and y < -1/3x + 2
y > 2/3x + 3 and y > -1/3x + 2
y > 2/3x + 3 and y >-1/3 x + 2

2)
Which system of linear inequalities is represented by the graph?
(goes with pic 2)
y > 2x – 1 and y < 2x + 2
y > 2x + 2 and y < 2x – 1
y < 2x + 2 and y > 2x – 1
y < 2x + 1 and y > 2x – 2

3)Which linear inequality is represented by the graph?
(goes with pic 3)
y > 2x + 2
y ≥ 1/2x + 1
y > 2x + 1
y ≥ 1/2x + 2

4)
What is the solution to the system of linear equations?
(goes with pic 4)
(–3, 0)
(–3, 3)
(0, 2)
(3, 1)

Answers

Part 1)

In this problem we have two lines

The equation of the fist line is

[tex]y=\frac{2}{3}x+3[/tex]

The solution is the shaded area above the dashed line

so

the inequality is

[tex]y>\frac{2}{3}x+3[/tex]

The equation of the second line is

[tex]y=-\frac{1}{3}x+2[/tex]

The solution is the shaded area below the full line

so

the inequality is

[tex]y\leq -\frac{1}{3}x+2[/tex]

therefore

the answer Part 1) is

[tex]y>\frac{2}{3}x+3[/tex] and [tex]y\leq -\frac{1}{3}x+2[/tex]

Part 2)

In this problem we have two lines

The equation of the fist line is

[tex]y=2x+2[/tex]

The solution is the shaded area above the full line

so

the inequality is

[tex]y\geq 2x+2[/tex]

The equation of the second line is

[tex]y=2x-1[/tex]

The solution is the shaded area below the full line

so

the inequality is

[tex]y\leq 2x-1[/tex]

therefore

the answer Part 2) is

[tex]y\geq 2x+2[/tex] and [tex]y\leq 2x-1[/tex]

Part 3)

In this problem we have only one line

The equation of the line is

[tex]y=2x+1[/tex]

The solution is the shaded area above the dashed line

so

the inequality is

[tex]y>2x+1[/tex]

therefore

the answer Part 3) is

[tex]y>2x+1[/tex]

Part 4)

we know that

the solution of the system of linear equations is the intersection both graphs

so

see the graph

the solution point is [tex](0,2)[/tex]

therefore

the answer part 4) is the option

[tex](0,2)[/tex]

PLEASE HELP!

Cynthia is constructing a circle inscribed in a triangle.She has partially completed the construction as shown below.What should her next step be in the construction (worth 50 points)

A. Connect vertex B to the arc markings to complete the angle bisector

B.use a straightedge to find the angle bisectors for angles A and B

C. Connect three arc markings together to form the triangle

D.use the arc markings to determine the radius to construct the circle

Please explain!

Answers

The correct next step that Cynthia should do is to:

D. use the arc markings to determine the radius to construct the circle

The arc markings are actually used as the baseline in determining the center and the radius of the circle. The arc markings are created with the use of a compass. All other choices are completely irrelevant because what we need is the arc and not the angles. The angles do not create the circle. Letter C is also wrong because what we are trying to form is the circle and not the triangle. The triangle is already created.

Quadrilateral LMNO is transformed according to the rule T(–2, 4). What are the coordinates of L’?  (3, –3) (3, 5) (9, –1) (9, 3)

Answers

A transformation specified with a rule T (x, y) means that the figure is undergoing a process of translation. Translation means that only the positions of the coordinates are changed with no other change on the angle, lengths or any other characteristic aside from the position alone.

So since the rule is T (-2, 4) then this means that the figure is moved 2 units left and 4 units up.

The initial coordinates of point L is:

point L = (5, 1)

The coordinates of L’ then is:

point L’ = L(5, 1) + T(-2, 4)

point L’ = (5 – 2, 1 + 4)

point L’ = (3, 5)

 

Answer:

(3, 5)

(3,5) is the answer.

Which of the following statements is true?
The number 2 /3 is an irrational number.
The number -4 is a whole number.
The number 9 is a rational number.
The number 5/8 is a natural number.

Answers

the number -4 is a whole number

A business’s assets are valued at $600,000, and the value depreciates 20% per year. Using the formula V(t) = V0(b)t, what is V0, what is (b), and what is the value of the assets after 5 (t) years? Show your work.
t = 5
V0 =
(b) =
Value after 5 years:

Answers

The formula is
V (t)=V0(b)^t
V (t) the value of the assets after 5 (t) years ?
V0 current value of assets 600000
B=1-0.20=0.8
T 5 years

So the value of assets after 5 years is
V (5)=600,000×0.8^(5)=196,608

Given f(x) = x + 2 and g(x) = x2 – 4, find the function (g/f)(x).

Answers

hello : 
(g/f)(x) = g(x) /f(x) = (x²-4)/(x+2)= (x-2)(x+2) /(x+2)
if : x ≠ -2  so : (g/f)(x) = = x-2

Annie found that 57 students in her school knew French and 23 of those students knew Spanish, as well. There were 11 students who did not know French but knew Spanish. There were 4 students who knew neither French nor Spanish. Which table best summarizes the data collected by Annie?

Knew Spanish Did not know Spanish Total
Knew French 57 34 91
Did not know French 11 4 15
Total 68 38 106

Knew Spanish Did not know Spanish Total
Knew French 12 34 46
Did not know French 11 4 15
Total 23 38 61

Knew Spanish Did not know Spanish Total
Knew French 23 34 57
Did not know French 11 4 15
Total 34 38 72

Knew Spanish Did not know Spanish Total
Knew French 23 34 57
Did not know French 4 11 15
Total 27 45 72

Answers

Answer:

Table C is the correct option.

Step-by-step explanation:

We are given,

Number of students which knew French = 57

Number of students which knew both French and Spanish  = 23

Number of students which knew Spanish but not French = 11

Number of students which knew neither French nor Spanish = 4

So, we get that,

Number of students not knowing French = 57 - 23 = 34

Hence, the table for the given situation is,

                              Knew Spanish    Did not know Spanish    Total

Knew French                  23                          34                         57

Did not know French      11                             4                           15

Total                               34                             38                        72

Thus, option C is correct.

option C is correct-

Four girls and three boys volunteer to represent their class at a school assembly.the teacher selects one name and then another from a bag containing the seven students names.what is the probability that both representatives will be girls

Answers

4/7*3/6
the answer is 2/7
A basket contains 13 pieces of fruit:5 apples,5 oranges,and three bananas.jonas takes a piece of fruit at random from the basket and then Beth takes a piece at random.what is the probability that Jonas will get an orange and Beth will get an apple ?

Sarah is y years old now. How could you represent her age 5 years ago?


y + 5
5 y
y - 5
y ÷ 5

Answers

you would have to subtract 5 from her age so the equation would by y-5

y-5..................................................


Meghan works at an ice cream shop and makes $8.25 per hour Lucas works at a landscaper and makes $6.50 per hour how much more does Meghan makes each hour ?

Answers

Find the difference of the two numbers.

8.25-6.5= 1.75

Final answer: $1.75
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