A special type of door lock has a panel with five buttons labeled with the digits 1 through 5. This lock is opened by a sequence of three actions. Each action consists of either pressing one of the buttons or pressing a pair of them simultaneously.

Answers

Answer 1

There are several ways the door can be locked, these ways illustrate combination.

There are 3375 possible combinations

From the question, we have:

[tex]\mathbf{n = 5}[/tex] --- the number of digits

[tex]\mathbf{r = 3}[/tex] ---- the number of actions

Each of the three actions can either be:

Pressing one buttonPressing a pair of buttons

The number of ways of pressing a button is:

[tex]\mathbf{n_1 = ^5C_1}[/tex]

Apply combination formula

[tex]\mathbf{n_1 = \frac{5!}{(5-1)!1!}}[/tex]

[tex]\mathbf{n_1 = \frac{5!}{4!1!}}[/tex]

[tex]\mathbf{n_1 = \frac{5 \times 4!}{4! \times 1}}[/tex]

[tex]\mathbf{n_1 = 5}[/tex]

The number of ways of pressing a pair is:

[tex]\mathbf{n_2 = ^5C_2}[/tex]

Apply combination formula

[tex]\mathbf{n_2 = \frac{5!}{(5-2)!2!}}[/tex]

[tex]\mathbf{n_2 = \frac{5!}{3!2!}}[/tex]

[tex]\mathbf{n_2 = \frac{5 \times 4 \times 3!}{3! \times 2 \times 1}}[/tex]

[tex]\mathbf{n_2 = 10}[/tex]

So, the number of ways of performing one action is:

[tex]\mathbf{n =n_1 + n_2}[/tex]

[tex]\mathbf{n =5 + 10}[/tex]

[tex]\mathbf{n =15}[/tex]

For the three actions, the number of ways is:

[tex]\mathbf{Action = n^3}[/tex]

[tex]\mathbf{Action = 15^3}[/tex]

[tex]\mathbf{Action = 3375}[/tex]

Hence, there are 3375 possible combinations

Read more about permutation and combination at:

https://brainly.com/question/4546043


Related Questions

A walking path across a park is represented by the equation y=-2x-7. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-2,-3). Identify the equation that represents the new path.

A. y = 1/2 x - 2

B. y = 2x +1

C. y = -2x-7

D. y = -1/2 x- 4

Answers

Answer:

d

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Find the measure of each angle indicated 12,13,14

Answers

Answer:

Step-by-step explanation:

12. 15 (3x5x1)

13.  8  (4x2x1)

14. 18 (6x3x1)

PLEASE HELP IM BEGGGINGGG

Answers

Answer:

the answer is (a) a//b

Step-by-step explanation:

perpendicular means that two lines that do not cross over each other.

Can anyone help asap please

Answers

Step-by-step explanation:

a=32(alternate angles are equal)

b=a=32

c=17(all sides of rhombus are equal in length)

d=17(all sides of rhombus are equal in length)

e=90

f=90(diagonals intersect at right angles)

I am a 4 digit number.My hundred's digit is 4 less than my thousands digit.My unit's digit is 7 less than my ten's digit.My ten's digit is 3 more than my hundred's digit.My thousand's digit is the largest single digit number.what number am i?​

Answers

Answer:

9581

Step-by-step explanation:

subtract (3x^3-2x+5)-(-4x^3+3x-6)

Answers

Answer:

7x^3-5x+11

Step-by-step explanation:

(3x^3-2x+5)-(-4x^3+3x-6)

Distribute

3x^3-2x+5+4x^3-3x+6

Simplify

7x^3-5x+11

3x³-2x+5-(-4x³+3x-6)3x³-2x+5+4x³-3x+63x³+4x³-2x-3x+5+67x³-5x+11

Find m Give explanation please

Answers

Answer:

m < FGN = 88°

Step-by-step explanation:

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles (also known as remote interior angles).

Given the exterior angle, m <FGN = (7x + 18)°, and the two remote interior angles, m < E = 38° and m < F = (6x - 10)°:

The following equality statement can be established according to the exterior angle theorem:

m < E  + m < F  = m <FGN

38 + 6x - 10 = 7x + 18

Combine like terms:

28 + 6x = 7x + 18

Subtract 6x from both sides:

28 + 6x - 6x = 7x - 6x + 18

28 = x + 18

Subtract 18 from both sides:

28 - 18 = x + 18 - 18

10 = x

Next, substitute the value of x = 10 into the equality statement to determine whether it is the correct value of x, and to find the measures of < FGE and < F.

m < E  + m < F  = m <FGN

38° + (6x - 10)° = (7x + 18)°

38 + 6(10) - 10 = 7(10) + 18

38 + 60 - 10 = 70 + 18

88 = 88 (True statement).

Therefore, m < FGN = 88°

Find the missing side of each triangle. Leave your answer in simplest radical form.
(Please show ur work)

Answers

>> Answer

___________

[tex] \: [/tex]

[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]

Step by step :

x² = 12² + 10²

x² = 144 + 100

x² = 244

x = 2[tex]\bold{\sqrt{61}}[/tex]cm

May I please receive help?
Please

Answers

Answer:

<R=56 degrees; <Q=62 degrees; <S=62 degrees

Step-by-step explanation:

5x+12=4x+22 (This is because the two angles are congruent to each other.)

x+12=22

x=10

Now, plug it in.

5(10)+12=50+12=62 degrees

62(2)=124 degrees (This is because the two angles are congruent and equal)

180-124=56 degrees

Ig1000+log342 - 1 -123​

Answers

Answer:

log(342) - 121

Step-by-step explanation:

-121 + log(342) is a transcendental number

-115.165189262937394847783249972808918485...

Suppose y varies directly as x, and y=14 when x=4. What is the value of y when x=9

Answers

Given :-

y varies directly as x, and y=14 when x=4.

To Find :-

the value of y when x=9 .

Solution :-

According to Question ,

y = kx ( k is constant )

When y = 14 and x = 4 ,

14 = k(4)k = 14/4k = 7/2

When x = 9 ,

y = 7/2*9 y = 63/2y = 31.5

the sum of a number and 11

Answers

Hello!

The sum of a number and 11:

Let's say that the number is x. So the expression "the sum of a number and x" looks like this:

x+11

Hope this helps you!

~Just an emotional teen who listens to her favourite songs

[tex]SilentNature[/tex]

Hey there!

Guide:

• The word “sum” means “add” or “addition”

• The word “difference” means “subtract” or “subtraction”

• The word “product” means “multiply” or “multiplication”

• The word “quotient” means “divide” or “division”

NOW THAT WE HAVE ALL OF THAT INFORMATION, WE CAN SOLVE FOR YOUR EQUATION

“The SUM of a number and 11”

Well since the “number” is unknown we can label it as “a” so we can know what we’re ADDing to 11…

So, your equation should be: a + 11

Answer: a + 11

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

hello can anyone help with this?

The distance between Heysham and the Isle of Man is 80 km.
A hovercraft travels at 50 km per hour.
How long does the journey take?

Answers

50/1 =80/x
50x=80
Divide both sides of the equal sign by 50 to get variable by itself
x= 1.6
Your answer is 1.6 of an hour for the journey

Answer:

1 hour 36 minutes

Step-by-step explanation:

Amount of time the journey takes = 80km ÷ 50km/h

                                                        = 1.6h

                                                        = 1h 36mins


What is 0.000000000325 in scientific notation?

Answers

Answer:

3.25*10^-10(is.3.25E−10)

3.25x10^-9

The coefficient must be between  1 and 10The negative exponent means the number is small

Hope it helps!

~Just a joyful teen

[tex]GraceRosalia :)[/tex]

The car travels with constant acceleration reaching a speed of v m/s after 6 seconds. The car then travels at a constant speed of v m/s for a further 2 seconds. The car travels a total distance of 150 metres. Work out the value of v

Answers

v=30m/s velocity is 30 ms-1

Directions:Classify the following polynomials by degree and number of terms.

ANYONE PLEASE HELP ME WITH MY QUESTIONS 2 AND 3 I REALLY NEED THE ANSWER RIGHT NOW BECAUSE I HAVE TO PASS THIS LATER I HOPE Y’ALL CAN HELP ME:(
I’LL MARK BRAINLIEST FOR THOSE WHO CAN ANSWER IT CORRECTLY!

Answers

Answer:

Question 2: The degree is 3 and the terms are 2, Binomial

Question 3: The degree is 2 and the terms are 3, Polynomial

Step-by-step explanation:

Solve. Show work

Y = -1/2 (-2) + 2

Answers

Answer:

[tex]→y = \frac{ - 1}{2} ( - 2) + 2[/tex]

[tex]→y = 1 + 2[/tex]

[tex]→y = 3[/tex]

Answer:

[tex]y=3[/tex]

Step-by-step explanation:

First distribute:

[tex]y=-\frac{1}{2} (-2)+2[/tex]

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

Add:

[tex]y=3[/tex]

Hope this helps! :)

Order each set of numbers from least to greatest.
1: -4,-7, 3, 16,-18
2: -12, 20, 24, -39, -24
3: 9,-57,-64, -32, 0
4: -3,-13, -24,-1,-8

Answers

Answer:

1. -18,-7,-4,3,16

2. -39,-24,-12,20,24

3. -64,-57,-32,0,9

4. -24,-14,-8,-3,-1

Step-by-step explanation:

Negative numbers are always least.

Find an equation in point-slope form for the line having the slope m= - 4 and containing the point (4,5).
The equation in point-slope form is
(Use integers or fractions for any numbers in the equation.)

Answers

Answer:   y - 5 =  - 4 (x - 4)

Step-by-step explanation:

The point-slope form of a line is (y - y₁) = m(x - x₁)

Since we know the slope (m) is -4

And the point  ( x₁, y₁ ) is (4, 5)

Then we can just plug these into the equation above:

                               ⇒  y - 5 =  - 4 (x - 4)

I often use Desmos to check my answer. As seen below, the equation does pass through the point (4, 5).                                      

32.28 in
expanded form​

Answers

Step-by-step explanation:

expanded form is adding each place value together with zeros replacing all other spots

32.28

30.00 + 2.00 + 00.20 + 00.08

each month for 6 months laras bank account balance decreased by $84. Witch quantity describes the total change in laras bank account balance

Answers

Answer:

Step-by-step explanation:

0

Look at the image and determine a answer please.

Answers

Answer:

Dividing

Step-by-step explanation:

z = -72

Find the slope of each line.

Answers

Answer:

Slope: - 5/2

Step-by-step explanation:

RIGHT


ACUTE


OBTUSE


EQUIANGULAR

Answers

Step-by-step explanation:

option B is correct answer ( Acute angle triangle)

hope this helps you.

Answer:

Acute triangle

Step-by-step explanation:

Acute triangle have less than 90 degrees

The perimeter of this rectangle si __________ units

Answers

The answer for this question is 14

L + B (x2) = 7+2 (x2)

9 x 2 = 18 (si units can be cm, m..?)

Please help! See algebra question..

Answers

Answer:

n=-10

Step-by-step explanation:

n+3=-7

n=-7-3

n=-10

this helps thank you

branlist please

Answer:

n = -10

Step-by-step explanation:

solving a one step equation with a missing variable

step 1: subtract 3 from both sides of the equation then simplify

ex: n + 3 - 3 = -7 - 3   (n = -10)

step 2: take your answer of n which is -10 and add plug it in into your original equation n + 3 = -7 and solve to check your answer

ex: n + 3 = -7   (-10 + 3 = -7)

add

-10 + 3 = -7

-7 = -7   (if both sides of the equation are the same numbers like -7 = -7 then your answer is true making n = -10 your answer) i would love to get brain if this is correct and helps <(^w^)>

Hello I really need help 30 points

Answers

Answer:

C

Step-by-step explanation:

The vertical line test determines that more than 1 point falls on the vertical line making the graph NOT a function

(re-asking this question) please help asap! ill give brainliest.
write 571/7 as a mixed number

(the numerator is 7, while 571 is the denominator)

Answers

Answer:

Using a calculator, if you typed in 517 divided by 7, you'd get 73.8571. You could also express 517/7 as a mixed fraction: 73 6/7.

Step-by-step explanation:

so 73 6/7 is your answer

Answer:

81 4/7

Step-by-step explanation:

Does this help?

3. Due to leakage, 30% of the water was lost from a water tank. If
only 340 liters of water is left in the tank now, find the total
capacity of the water tank?
HELPP

Answers

Answer:

1133.3 liters of water after leakage.

Step-by-step explanation:

x*.30=340

x=340/.30

x=1133.33

The total capacity of the water tank is 1133.33 liters of water after leakage.

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.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We have given Due to leakage, 30% of the water was lost from a water tank. If only 340 liters of water is left in the tank now, then we need to find the total capacity of the water tank.

x*.30 = 340

x = 340/.30

x = 1133.33

Hence, the total capacity of the water tank is 1133.33

Learn more about the unitary method;

https://brainly.com/question/23423168

#SPJ2

Here’s another one.. so sorry if this confused you..

(Also I got this question wrong..)

Answers

Answer:

hmmm did you try 14?

It’s prob 13,


I dunno.. I keep thinking since it has the eighth meaning 8. Do 20-8=13
Other Questions
2. Identify the like terms in the expression -6 - 3x2 + 3x - 4x + 9x2. Can you help me with this? Im stuck OriginaDNA: CGGACACTGCTCTCCCAAGAGTATCAGTCCTCTTTAGAAGACCTGAATTCATTTCTTCTTmRNA:AAS:Mutation 1DNA: CGGACACTGCTCTCCCAAGAGTATCAGTCCTCTTTAGAAGACCTGTAACTCATTTCTTCTmRNA :AAS:Mutation 2DNA: CGGACACTGCTCTCCCAAGAGTATCAGTCCTCTTTAGAAGACCTGAGTTCATTTCTTCTTmRNA:AAS:Mutation 3DNA: CGGACACTGCTCTCCCAAGAGTATCAGTCCTCTTTAGAAGACCTGAATTCATTTTTTCTTmRNA:AAS: PLSSS HELP MEEE ASAPA!!Which pair of elements has reactivity that is similar to Fluorine, F? What is the value of b?bB+42B-20 upper respiratory tract infections after giving birth nucleic acids are assembled in the _____ direction. The half-life of Carbon-14 is 5730 years. Suppose a fossil is found with 50% of Carbon-14 as compared to a living sample. How old is the fossil?A) 5730 yearsB) 57 yearsC) 5728 yearsD) 572 years what was the forbidden fruit in the garden of eden Which statement correctly compares the function shown on this graph withthe function y = 4x + 2?87651543 21 2 3 45A. The function shown on the graph has a greater rate of change, buta lower starting point.B. The function shown on the graph has a greater rate of change anda higher starting point.C. The function shown on the graph has a smaller rate of change, buta higher starting point. What's the first thing you should do if you find yourself involved in a conflict? Profit and loss. Help plz What is the first term of the quotient of the following division problem?(x^3-1) (x+2)-0.51x^2x^4 A car of mass 850 kg rests on a slope at 25 to the horizontal. Calculate the magnitude of the component of the cars weight which acts parallel to the slope what is the significance of sending the third messenger with the two previous messengers? I dont know what to do What is the theme of the story in (My grandmother's hair by Cynthia Rylant?) The acceleration due to gravity on Earth is 9.8 m/s? What is the weight of a 75 kg person on Earth?O 9.8 NO 75 NO 85 NO 735 N Polk had two aims in the war. One was to acquireCalifornia. What was the second?to capture Mexico Cityto seize the New Mexico territoryoto annex TexasDONE I will give Brainliest to the first person