Damek has five number cards lying on the table. There are two number cards with digit 1, two number cards with digit 2 and one number card with 0. How many different three-digit numbers can Damek form? (Number cannot being with 0).

(P.S. Is there a way to find the answer without listing all the possibilities?)

Answers

Answer 1

Damek can form 14 three-digit numbers from the given situation. Hence, only 14 possibilities.

There are five number cards on the table.

2- digit 1 card

1- digit 0 card

2- digit 2 card

There is a possibility of putting 1 or 2 in the hundredth place.

If 1 is put in the hundredth place then there are 3 possibilities for tenth place 1,0,2

If 1 is put there then there is a possibility of 2 numbers 0,2 in ones place

If 2 is put then there is a possibility of 3 numbers 0,1,2 in ones place

If 0 is put then there is a possibility of 2 numbers 1,2 in ones place.

So, there are 7=(2+3+2) possibilities that the hundredth place is filled by 1.

Similarly, there will be 7 possibilities that the hundredth place is filled by 2.

Hence, there are 14 possibilities as required by the problem.

So, the possibilities of 3-digit numbers are (given the number cannot start with 0) 14.

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Related Questions

The area of a rectangle is 20 square meters. The length of the rectangle is (x-3) meters and the
width of the rectangle is (x - 2) meters. Find the length and the width of the rectangle.



With steps and explanation please.

Answers

Answer:

length = 4 cm

Width = 5 cm

Step-by-step explanation:

Area of rectangle:

      Area of rectangle = length * width

length = (x - 3) meters

Width = (x - 2) meter

Area = 20 square meters

  (x - 3)*(x - 2) = 20

Use FOIL method.

   x*x + (x)(-2) + (-3)*x + (-3)*(-2) = 20

                         x² -2x  - 3x + 6 =20

         Combine like terms

                        x² - 5x + 6  = 20

Now subtract 20 from both side

                     x² - 5x + 6 - 20 = 0

                           x² - 5x - 14  = 0

Factorize the equation and find the roots

         Sum = -5

   Product = -14

    Factors =  (-7) , 2

When we add (-7) + 2 = -5 and when we multiply (-7)*2 = -14

x² + 2x - 7x - 14 = 0

 x(x + 2) -7(x + 2) = 0

 (x + 2)(x - 7)  = 0

  x - 7 = 0    {Ignore (x + 2 = 0) as measurements wont't be in negative}

x = 7

length = x - 3

          = 7 - 3

   [tex]\sf \boxed{\bf length = 4 \ cm}[/tex]

width = x - 2

         = 7 - 2

    [tex]\sf \boxed{\bf width = 5 \ cm }[/tex]

find the range of the given function y= 8x +1, where x>2

Answers

Answer:

infinite or if where using whole numbers

y≥25

Hope This Helps!!!


What is the domain of the function shown in the
mapping?
Ox|x=-5, -3, 1, 2, 6}
O lyly=-9, -6, 0, 2, 4)
O {x|x=-9, -6, -5, -3, 0, 1, 2, 4, 6}
Oyly=-9, -6, -5, -3, 0, 1, 2, 4, 6}

Answers

Domain is the set of values for which the given function is defined. The correct option is A.

What is domain and range of a function?

Domain is the set of values for which the given function is defined, therefore the are values that the function can take.

Range is the set of all values which the given function can produce an output.

Domain of a function is the range of the inputs which the function can take, therefore, the domain of the function shown in the mapping is,

x|x= -5, -3, 1, 2, 6}

Hence, the correct option is A.

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Vincent and Aidan buy the same number of pens. Vincent buys packs of 6 pens, and Aidan buys boxes of 20 pens. What is the least number of pens each boy can have brought?

Answers

The least number of pens each boy can have brought is 60

How to determine the least number of pen?

We have:

Vincent = 6 packs

Aidan = 20 boxes

Factorize 6 and 20

6 = 1 * 2 * 3

20 = 1 * 2 * 2 * 5

Multiply all factors

LCM = 1 * 2 * 2 * 3 * 5

Evaluate the product

LCM = 60

Hence, the least number of pens each boy can have brought is 60

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The height in feet, h, of a model rocket t seconds after launch is given by the equation h (t) = 3 + 70 t minus 16 t squared. The average rate of change in h(t) between t = 1 second and t = 3 second is 6. What does the average rate of change tell you about the rocket?
The rocket is traveling six times as fast when t = 3 than it is when t = 1.
The rocket is at a greater height when t = 3 than it is when t = 1.
The rocket is 6 feet higher above the ground when t = 3 than it is when t = 1.
The rocket is traveling at a constant rate of 6 feet per second between t = 1 and t = 3.

Answers

The average rate of change in h(t) is 6.

What is Average Rate of change?

It is a measure of how much the function changed per unit, on average, over that interval.

h(t) = 3 + 70t - 16t²

Average rate of change

At t = 1 second

h(1) = 3 + 70(1) - 16(1)^2

h(1) = 57

At t = 3 second

h(3) = 3 + 70(3) - 16(3)^2

h(3) = 69

Average rate of change = Δh / Δt

=[h(3) - h(1)] / (3 - 1)

= (69 - 57) / 2

= 12 / 2

= 6.

Hence, the rate of change is 6.

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Jamaal is allowed to walk no farther than three blocks in either direction from his house. If his house is located on the 57th block of the town, which absolute value equation can be used to determine the farthest block to which Jamaal is allowed to walk?

|x – 57| = 0
|57 – 3| = x
|3 – 57| = x
|x – 57| = 3

Answers

Answer:

|x – 57| = 3

Step-by-step explanation:

let x be the farthest block to which Jamaal is allowed to walk.

the statement “Jamaal is allowed to walk

no farther than three blocks in either direction from his house.”

means

the distance between the 57th block and the farthest block = 3

means

|x – 57| = 3

Answer:

|x – 57| = 3

Step-by-step explanation:

let x be the farthest block to which Jamaal is allowed to walk.

the statement “Jamaal is allowed to walk

no farther than three blocks in either direction from his house.”

means

the distance between the 57th block and the farthest block = 3

means

|x – 57| = 3

Use the following information for problems 5-8.

f(2, 33) = 5.5, p < 0.01

1) how many groups were in this study?
a) 34
b)33
c) 3
d) 2

how many participants were in this study?
a) 36
b) 33
c) 3
d) 2

what is the f ratio?
a) 5.5
b) 2
c) 33
d) 0.01

Answers

The number of groups is 3, the number of participants is 36, and the f ratio is 5.5.

What are the null hypothesis and alternative hypothesis?

The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

f(2, 33) = 5.5, p < 0.01

From the above details, we can find the number of groups:

5) Number of groups = df for groups + 1

Number of groups  = 2+ 1 = 3

Option (c) is correct.

6) Number of participants =2 + 33 + 1 = 36

Option (a) is correct.

7) f ratio = 5.5

Option (a) is correct.

8) True; as the p-value is less than the 0.01 level.

Thus, the number of groups is 3, the number of participants is 36, and the f ratio is 5.5.

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Find the volume of this sphere.
Use 3 for pie.
V≈ [?]cm³
V = πr³
10 cm

Answers

Answer:

V ≈ 500 cm³

Step-by-step explanation:

Volume of a sphere: ⁴⁄₃πr³ (where r is the radius)

π (pi) ≈ 3r (radius) = diameter/2 ⇒ 10/2 = 5 cm

Substitute the given values into the formula:

⇒ V = ⁴⁄₃πr³

⇒ V ≈ (⁴⁄₃)(3)(5)³

⇒ V ≈ (⁴⁄₃)(3)(125)

⇒ V ≈ (⁴⁄₃)(375)

V ≈ 500 cm³

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Given: [tex]\textsf{Diameter = 10 cm, Volume = 4/3} * \pi*r^3[/tex]

Find:  [tex]\textsf{Determine the volume}[/tex]

Solution: First we need to determine the radius by dividing the diameter by 2 and after that we can plug in the information into the equation and simplify it until we get the volume.

Determine the radius

[tex]\textsf{Radius = Diameter / 2}[/tex][tex]\textsf{Radius = 10 cm / 2}[/tex][tex]\textsf{Radius = 5 cm}[/tex]

Plug in the values

[tex]\textsf{Volume = 4/3 } * \pi*r^3[/tex][tex]\textsf{Volume = 4/3 } * 3 * (5\ cm)^3[/tex]

Simplify the expression

[tex]\textsf{Volume = (4 * 3)/3} * (5\ cm)^3[/tex][tex]\textsf{Volume = 4} * (5\ cm)^3[/tex][tex]\textsf{Volume = 4} * 125\ cm^3[/tex][tex]\textsf{Volume = } 500\ cm^3[/tex]

After completing the steps we were able to determine that volume of the sphere that was provided is 500 cubed centimeters.

Solve for [x]. The polygons in each
2x-20
16
16
8

Answers

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 16 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

If two polygons are similar, their corresponding sides ratios will be equal to each other.

[tex]\qquad \tt \rightarrow \: \cfrac{8}{16} = \cfrac{2x - 20}{24} [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{1}{2} = \cfrac{2x - 20}{24} [/tex]

[tex]\qquad \tt \rightarrow \: 2x - 20 = \cfrac{24}{2} [/tex]

[tex]\qquad \tt \rightarrow \: 2x = 12 + 20[/tex]

[tex]\qquad \tt \rightarrow \: 2x = 32[/tex]

[tex]\qquad \tt \rightarrow \: x = 16[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

11 potters can make 143 pots in 8 days. How many potters will be required to make 169 pots in 4 days?​

Answers

26 potters will be required to make 169 pots in 4 days.

Given: 11 potters can make 143 pots in 8 days.

Step 1:

1 potter makes  143 pots in 8 × 11 days.

1 potter can make 1 pot in

(8 × 11)/143 days.

Step 2:

Let the number of potters required be x, then

x potters can make 1 pot in (8 × 11)/( 143 × x) days

x potters can make 169 pots in (8 × 11 × 169)/(143 × x ) days

Step 3:

The number of days given is 4. Hence equating the above equation to 4.

(8 × 11 × 169)/(143 × x ) = 4

Step 4:

Solve for x

14872/(143x) = 4

572x = 14872

x = 14872/572

x = 26

Thus, 26 potters will be required to make 169 pots in 4 days.

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Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!

Answers

Answer:

D

Step-by-step explanation:

definitely

Part 1 - Application Pick one of the two graphs below. Describe a situation which could be modeled by this polynomial graph. Be sure to label the x and y axis with what each will represent in your real life graph. Sample labels could include time, temperature, speed, distance and more. Be sure to add numbers to your axes as well and explain how you came up with your situation.

Answers

One good example of a situation that can be modeled by this Polynomial Graph is the price-time relationship between currency pairs being traded on the Foreign Exchange Market.

What is a Polynomial Graph?

A polynomial parameter graph is essentially a smooth continuous curve.

Although the forex graph attached has sharp undulations, when regressed and viewed via Polynomial Regression Indicators, they exhibit strong polynomial qualities that meet the requirements of the definition above.

It is to be noted that the Y-Axis is indicative of the price of the currency pairs (which could be any currency against another) and the X-Axis expresses time. See the attached graphs for a better picture.

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Each staple is made from 0.21 g of metal.
How many staples can be made from 1 kg of metal?

Answers

Answer:

4762

Step-by-step explanation:

0.21g x 10,000= 2100

0.21 x 5,000= 1050

0.21 x 4,000= 840

0.21 x 4700 =  987

0.21 x 4760 = 999.6

0.21 x 4762= 1000.02

( how much it's made from x the quantity = the grams or kg)

What is the value of x?

(See attached image for details.)

Enter your answer in the box.

x =

Answers

Answer:

x = 8°

y = 6°

Step-by-step explanation:

Hello!

All 3 sides of the triangle are equal, indicating that it is an equilateral triangle. The rules of this particular triangle say that all angles are equal to 60°.

We can solve for x by setting the equation 7x+4 to 60.

Solve for x7x + 4° = 60°7x° = 56°x = 8°

The value of x is 8°.

We can go ahead and solve for y by setting that equation to 60°.

Solve for y8y + 12° = 60°8y = 48°y = 6°

The value of y is 6°.

Clem's credit score is 733, while ingrid's credit score is 688. according to the
following table for a $150,000 mortgage, how much more would ingrid have
to pay per month than clem?
fico
interest monthly
score
rate
payment
720-850
5.59% $860
700-719
5.71% $872
675-699
6.25% $924
620-674
7.40% $1039
560-619
8.53% $1157
500-559
9.29% $1238

Answers

Ingrid would have to pay 64 per month more than clem.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given;

fico        interest monthly      score rate

720-850          5.59%             $860

700-719           5.71%              $872

675-699          6.25%             $924

620-674          7.40%              $1039

560-619           8.53%              $1157

500-559          9.29%               $1238

Clem's score is 733 which is 924 on the chart.

Ingrid's score is 688 which allows her to pay 860 per month.

924 - 860 =  64

Hence,

Ingrid would have to pay 64 per month more than clem.

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Find the range for the given domain: {-2, 0, and 1}and the function is y = 3x + 1.

Answers

Answer:

It's the first option: -5, 1 and 4

x=y²-1
2x - y = 4
Which of the following equations could be the result of using substitution to solve the system?
2y²-y-5=0
2y2-y-6=0
2y2-2y-5=0

Answers

Answer:

B) 2y² - y - 6 = 0

Given following:

x = y² - 1 ___equation 12x - y = 4 ___equation 2

Insert equation 1 into 2:

2(y² - 1) - y = 42y² - 2 - y = 42y² - y - 2 - 4 = 02y² - y - 6 = 0
x=y²-1

Put in second

2x-y=42(y²-1)-y=42y²-2-y=42y²-y-6=0

Here are three studies:

a: june asks eight of her friends if they plan on buying a school lunch that day.

b: sam selects a random sample of coins from his coin bank to see how many of them are older than 1982.

c: peyton randomly selects six eggs from a carton. she randomly assigns three of them to be boiled for 10 minutes and the other three are boiled for 15 minutes. after they have cooled she compares how easy they are to peel.

for which of these studies can we draw conclusions of cause and effect?

a
b
c
none of them

Answers

Answer:

The answer is C

Step-by-step explanation:

Just got it.

The length of a rectangle is 3 yd longer than its width. if the perimeter of the rectangle is 58 yd, find its length and width.

Answers

Answer:

Length = 16 yds

Width = 13 yds

Step-by-step explanation:

P = 2w + 2l

l = w + 3

58 = (2w + 2(w + 3))

58 = 4w + 6

52 = 4w

w = 13

L = w + 3

= 13 + 3

= 16

The length and width of the rectangle are 16,13yd.

The Length and Width of the rectangle can be found as:

Given:

The length of the rectangle is 3yds longer than the width which means length = w+3

and the perimeter is given by 58yd

Let W be the width and L be the length

We know that the perimeter of a rectangle is 2(L+w)

The perimeter of a rectangle is defined as the sum of all the sides of a rectangle

By simplifying we get

2(w+w+3)=58

2(2w+3)=58

2w=29-3

w=13

then the length of the rectangle will be w+3

                                                              13+3 = 16

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Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a square?

Shape ABCD is shown. Point A is at negative 3, 5. Point B is at 1, 7. Point C is at 3, 3. Point D is at negative 1, 1.

Answers

Options are not shown but…
A square has 4 equal length sides and a right angle

Or two equal length diagonals which are perpendicular

Or 4 right angled corners and two adjacent sides equal

Or perpendicular diagonals with the same midpoint

Using the last one…
Gradient of AC = (5 - 3)/(-3 - 3) = 2/-6 = -1/3
Gradient of BD = (7 - 1)/(1 - -1) = 6/2 = 3
-1/3 x 3 = -1 so AC and BD are perpendicular
Midpoint of AC = ((-3 + 3)/2 , (5 + 3)/2) = (0, 4)
Midpoint of BD = ((1 + -1)/2 , (7 + 1)/2) = (0, 4)
QED

Joe kept track of how much TV she watched each day for two weeks how many hours did she spend watching TV

Answers

The total hours joe spent watching TV each day for two weeks is 12 1/2 hours

Total hours spent watching TV

Total hours spent watching TV for two weeks = Number of hours × days

= (0 × 1) + (1/4 × 1) + (1/2 × 1) + (3/4 × 3) + (1 × 3) + (1 1/4 × 4) + (1 1/2 × 1)

= 0 + 1/4 + 1/2 + 9/4 + 3 + 5 + 3/2

= 8 + (1+2+9+6) / 4

= 8 + 18/4

= 8 + 4 2/4

= 8 + 4 1/2

= 12 1/2 hours

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Consider the following graph.

Which statement best describes Cheryl's commute?

A. Cheryl accelerated to 65 mph, made a stop for 5.5 minutes, and then decelerated to 45 mph.
B. Cheryl accelerated to 65 mph, drove at a constant speed for 5.5 minutes, and the decelerated to 45 mph.
C. Cheryl drove at a speed of 65 mph for 1 minute, drove at a constant speed for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes.
D. Cheryl drove at a speed of 65 mph for 1 minute, made a stop for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes

Answers

Cheryl drove at a speed of 65 mph for 1 minute, drove at a constant speed for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes.Option C is correct.

What is a graph?

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

Cheryl traveled at a steady pace for 5.5 minutes, then 45 mph for 2.5 minutes after traveling at 65 mph for a minute.

Statement C best describes Cheryl's commute.

Hence option C is correct.

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Help question is in the pic

Answers

Answer: D) -304

Step-by-Step Solution:

=> f(x) = 5x - 1
=> g(x) = 2x^2 + 1
=> Find value of (f * g)(-3)

First Substitute x as -3 in f(x) and g(x) :-

f(x) = 5x - 1
f(-3) = 5(-3) - 1
f(-3) = -15 - 1
=> f(-3) = -16

g(x) = 2x^2 + 1
g(-3) = 2(-3^2) + 1
g(-3) = 2(9) + 1
g(-3) = 18 + 1
=> g(-3) = 19

Now Multiply f(-3) with g(-3) :-

= f(-3) * g(-3)
= -16 * 19
=> -304

Therefore, (f * g)(-3) = -304


On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?

y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2

Answers

The correct answer is option B which is y > 3x + 2.

What is inequality?

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The given statement says that On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2)

The plot of the inequality is given in the graph attached with the answer the inequality will be y > 3x +2 which passes through the points (-3,-7 ) and ( 0, 2 ).

Therefore the correct answer is option B which is y > 3x + 2.

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The triangle inequality theorem states the sum of the lengths of any two sides of a triangle is _____ the length of the third side.

Answers

Answer:

see explanation

Step-by-step explanation:

the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

if the sides are a, b, c , then the following must be true

a + b > c

a + c < b

b + c > a

for the 3 sides to form a triangle

a. What type of triangle is Triangle ABC?
b. Give reasons for your answer

Answers

Since two of the angles are equal, hence the triangle ABC is isosceles triangle

What is a triangle?

A triangle is a  2D shape that has 3 sides and angles

From the given triangle

<CAB = 50 (alternate angle) and;

<ACB = 180 - (50 + 80)

<ACB = 180 -130

<ACB = 50 degrees

Since two of the angles are equal, hence the triangle ABC is isosceles triangle

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10. A In the adjoining Figure, ab is perpendicular to bc and ed is to cd while bc=cd . prove i) triangle abc is corresponding to triangle edc
ii)ab = cd

Answers

Part (i)

1) AB is perpendicular to BC, ED is perpendicular to CD, BC = CD (given)

2) Angles ABC and CDE are right angles (perpendicular lines form right angles)

3) Angles ABC and CDE are equal (all right angles are equal)

4) Angles ACB and DCE are equal (vertical angles are equal)

5) Triangles ABC and EDC are congruent (ASA)

Part (ii)

6) AB = DE (corresponding parts of congruent triangles are equal)

A school show had ticket sales of $1345 the first night and $935 the second night. 180 student tickets were sold and 110 adult tickets were sold on the first night. 100 student tickets were sold and 90 adult tickets were sold. find the price of a student ticket

Answers

Using a system of equations, it is found that the price of a student ticket is of $3.49.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables are given as follows:

Variable x: Price of a student ticket.Variable y: Price of an adult ticket.

Considering the revenues and the number of tickets sold, the equations are given as follows:

180x + 110y = 1345.100x + 90y = 935.

From the second equation:

90y = 935 - 100x

y = (935 - 100x)/90

y = 10.39 - 1.11x

Replacing in the first equation:

180x + 110y = 1345.

180x + 110(10.39 - 1.11x) = 1345

57.9x = 202.1.

x = 202.1/57.9

x = 3.49.

The price of a student ticket is of $3.49.

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Solve the equation 2x + 10 = 30.

Answers

Answer:

X=10

Step-by-step explanation:

1. Subtract 10 from both sides

2. Simplify

3. Divide both sides by the same factor

4. Simplify

ask any question if u don’t understand 33737373

Write the word phrases into an algebraic expression : 4 less than 5 times a number "p"

Answers

Answer: 5p - 4

5 times ‘p’ = 5p
4 less than ‘p’ = p - 4

Therefore,
=> 5p - 4
Other Questions
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