Suppose we want to.choose 2 letters without replacement from the 3 letters A,B and C how many ways can this be done if the order of choice is taken into consideration. How many ways can this be done if the order of the choices is not taken into consideration?
Answers
The number of ways to choose the letters is given as follows:
Order matters: 6 ways.Order does not matter: 3 ways.What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
\(P_{(n,x)} = \frac{n!}{(n-x)!}\)
Hence, if the order matters, the number of ways is given as follows:
P(3,2) = 3!/(3 - 2)! = 6.
The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
Hence, if the order does not matter, the number of ways is given as follows:
C(3,2) = 3!/(2! x 1!) = 3.
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Related Questions
A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel.
The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that
changes a 1 to a 0 with probability 0.1 and changes a 0 to a 1 with probability 0.2. Show your work below.
a. What is the probability a 1 is received?
b. If a 1 is received, what is the probability a 0 was sent?
Answers
Answer:
A: the probability that a 1 is received is 0.56.
B: the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).
Step-by-step explanation:
To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.
a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.
Let's denote:
P(1 sent) = 0.6 (probability a 1 is sent)
P(0→1) = 0.2 (probability a 0 is flipped to 1)
P(1 received) = ?
P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)
= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)
= 0.6 * (1 - 0.2) + 0.4 * 0.2
= 0.6 * 0.8 + 0.4 * 0.2
= 0.48 + 0.08
= 0.56
Therefore, the probability that a 1 is received is 0.56.
b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.
Let's denote:
P(0 sent) = ?
P(1 received) = 0.56
We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).
Using Bayes' theorem:
P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)
P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08
P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56
Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):
P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56
Simplifying:
P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56
= 0.08 * (1 - P(0 sent)) * (1 / 0.56)
= 0.08 * (1 - P(0 sent)) * (25/14)
= (2/25) * (1 - P(0 sent))
Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).
A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?
30 POINTS HELPPPPP PLS Simplify the following. Do not Evaluate
30^7
Answers
29% of a university's freshman class are majoring in Economics. If 870 students in the freshman class are Economics majors, how many students are in the freshman class?
Answers
Answer:
x=3000
Step-by-step explanation:
870=29/100x
x=3000
If the line represented by y=-1/4 x -2 is dilated by a scale factor of 4 centered at the origin, which statement about the image is true?
Answers
Answer:
a.
Step-by-step explanation:
Dilation does not change the direction (slope) of any lines. The slope of the image line is the same as the original when the line is subject to dilation. The y-intercept point (0, -2) will be multiplied by the dilation factor, so will become 4(0, -2) = (0, -8). The dilated line will have equation ...
y = -1/4x -8 . . . . . matches choice A
AB and AD are tangent to circle C. Find the length of AB, if AB = 8x and AD = x + 9. Round your answer to 2 decimal places.
Answers
When a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency. This means that triangle ABD is a right triangle with AB as the hypotenuse.
We can use the Pythagorean theorem to find the length of AB:
AB^2 = AD^2 + BD^2
Since AD = x + 9 and BD = 8x - (x + 9) = 8x - x - 9 = 7x - 9, we can substitute these values into the equation:
(8x)^2 = (x + 9)^2 + (7x - 9)^2
64x^2 = x^2 + 18x + 81 + 49x^2 - 126x + 81
64x^2 = 50x^2 - 108x + 162
14x^2 + 108x - 162 = 0
Dividing the equation by 2, we get:
7x^2 + 54x - 81 = 0
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
a = 7, b = 54, c = -81
x = (-54 ± √(54^2 - 4 * 7 * -81)) / (2 * 7)
x = (-54 ± √(2916 + 2268)) / 14
x = (-54 ± √5184) / 14
x = (-54 ± 72) / 14
Now we solve for x:
Case 1: x = (-54 + 72) / 14 = 18 / 14 = 9 / 7
Case 2: x = (-54 - 72) / 14 = -126 / 14 = -9
Since the length of a segment cannot be negative, we discard the second case and focus on the positive solution.
Therefore, x = 9/7.
Substituting this value back into AB = 8x:
AB = 8 * (9/7) = 72/7 ≈ 10.29
Rounding to 2 decimal places, the length of AB is approximately 10.29 units.
Answer:
To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:
8x = x + 9
Solving for x, we get:
x = 1.5
Therefore, AB = 8x = 8(1.5) = 12.
To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:
AB^2 + BD^2 = AD^2
Substituting the values, we get:
12^2 + BD^2 = (1.5 + 9)^2
Simplifying, we get:
BD^2 = 56.25
Taking the square root of both sides, we get:
BD = 7.5
Hence, the length of AB is 12 and the length of BD is 7.5.
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If f(x)
=
OA.
A.
2+1, what is the value of f-¹ (3)?
22
B. 19
OB.
C.
O D.
13
OE. 11
Answers
The value of the inverse function f-¹ (3) is (e) 11
Calculating the value of the inverse functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x - 8
To calculate the inverse value at f-¹ (3)
We set the value to 3
using the above as a guide, we have the following:
x - 8 = 3
Evaluate the like terms
x = 11
Hence, the value of the inverse function is (e) 11
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Complete question
if f(x) = x - 8, what is the value of f-¹ (3)?
Factor completely 2x² - 18x + 36.
O 2(x − 6)(x − 3)
O 2(x − 6)(x + 3)
O2(x − 3)(x + 6)
O2(x + 3)(x + 6)
Answers
Answer: 2(x − 6)(x − 3) is the answer
Step-by-step explanation:
Please answer fast I need the Answer
Answers
Answer:
just do it urself
Step-by-step explanation:
The 10th term of an AP is -27 and the 5th term is -12, what is the 18th term?
Also find the sum of its 25 terms.
Answers
Answer:10th term: -27
5th term: - 12
d= -27+12/5
= -3
a+(n-1)d=-12
a+(5–1)d=-12
a+4d= -12
a=-12–4d
a=-12-(4×-3)
a=-12+12=0
18 term=a + (18–1)d
=0+(17×-3)
51
a+9d=-27......(1)
a+4d=-12.....(2)
make a the subject of equation 2 and put into equation 1
-12+4d+9d=-27
-12+13d=-27
d=-15\13
put d into equation 1
a+9(-15/13)=-27
a=16.6
a+17d=x
17+16.6(-15/13)
x=-2 is the 18th term
25÷2(16.6+15.6(-15/13)
=-208.4
Does this table represent a function? Why or why not?
O
X
2
3
3
4
5
y
1
4
3
2
5
A. Yes, because there are different y-values.
B. Yes, because every x-value corresponds to exactly one y-value.
C.
No, because the y-values are positive.
D. No, because one x-value corresponds to two different y-values.
SUBMIT
Answers
The given table does not represent a function. The correct answer is D. No, because one x-value corresponds to two different y-values.
To determine if the table represents a function, we need to check if every x-value corresponds to exactly one y-value. Let's analyze the given table:
x | y
-------
O | 1
X | 4
2 | 3
3 | 2
3 | 5
4 |
5 |
From the table, we can see that the x-values are not unique. Both the values 3 and 4 appear twice in the x-column, but they have different corresponding y-values.
This violates the definition of a function, which states that each input (x-value) should have only one output (y-value).
Therefore, the given table does not represent a function.
The correct answer is D. No, because one x-value corresponds to two different y-values.
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Part 1: 12% annual interest on 132000 for 8 days
Part 2: 12% annual interest on 106,750 for 20 days.
If it helps, it's a 5 year note. Assuming 365 days in a year.
Answers
The interest for Part 1 is approximately $385.10.
The interest for Part 2 is approximately $709.31.
To calculate the interest for Part 1 and Part 2The formula is as follows:
Interest is calculated as follows: Principal * Rate * Time
Where
Principal represents the starting sumThe interest rate is rateTime measures length in years.Part 1:
$132,000 is the principal.
(Decimal) Rate = 12% = 0.12
Time = 8 days/365 days.
How much interest is there in Part 1?
Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10
Therefore, the interest for Part 1 is approximately $385.10.
Part 2:
$106,750 as the principal
(Decimal) Rate = 12% = 0.12
Time = 20 days / 365 days.
How much interest will there be in Part 2
Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31
Therefore, the interest for Part 2 is approximately $709.31.
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HELP PLS ASAPPPPPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: C; 5.32
Step-by-step explanation: If you are short $5.32, then that is represented as -5.32. The opposite of -5.32 is +5.32 or just 5.32. I hoped this helped!
HElp plssssssssssssssssssssss
Answers
Answer:
7-16=-9
.
...................
1/2x - 3 =7
helppp please.
Answers
Answer:
x = 20
Step-by-step explanation:
Original Equation:
1/2x - 3 = 7
(1/2x can be written as 0.5x)
0.5x - 3 = 7
Add 3 to both sides.
0.5x = 10
Divide both sides by 0.5
x = 20
Hope this helped :)
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PLEASE HELP DUE IN 3 minutes
Answers
Answer:
Answer is B
Step-by-step explanation:
A fair coin is tossed 10 times. Find the probability of satisfying the condition that that the coin does not land on tails twice in a row
Answers
The probability of tossing 10 tails in a row is \(\frac{1}{1024}\)
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that,
When a fair coin is tossed 10 times, the sample size (n) is:
n = \(2^{10}\)
This is so because a fair coin has 2 sides.
So, we have:
n = 1024
There is only one occurrence of having 10 tails in a row in the 1024 possible outcomes.
So, the probability is:
P = \(\frac{1}{1024}\)
Therefore,
The probability of tossing 10 tails in a row is \(\frac{1}{1024}\)
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Savannah drove 716 miles on Monday. She drove another 572 miles one Tuesday. About how many more miles did she
drive on Monday than Tuesday?
400
300
200
100
Answers
the answer is 144 not sure what you're supposed to do with that. 144 rounded would just be 100.
716 - 572 = 144
Is the simplified form of 2^3x2^6 rational
Answers
Answer: it is not rational.
Step-by-step explanation: 2 to the power of 3 is 8. 2 to the power of 6 is 64. 64x8 is 512. 512 is not a perfect square therefore it is a irrational number.
6x + 3y = 3 3x - y = 4
Answers
Answer:
x = 1
y = -1
Step-by-step explanation:
Given equations:6x + 3y = 3 -------------(1)
3x - y = 4 ----------------(2)
Multiply Eq. (2) by 2
2(3x - y) = 4 × 2
6x - 2y = 8 -------------(3)
Subtract Eq. (3) from Eq. (1)
6x + 3y - (6x - 2y) = 3 - 8
6x + 3y - 6x + 2y = -5
3y + 2y = -5
5y = -5
Divide 5 to both sides
y = -5/5
y = -1Put y = -1 in Eq. (1)
6x + 3(-1) = 3
6x - 3 = 3
Add 3 to both sides
6x = 3 + 3
6x = 6
Divide 6 to both sides
x = 1\(\rule[225]{225}{2}\)
help me please
graph the image of each shape using the translation given
Answers
Answer:(0,4)
Step-by-step explanation:
WILL GIVE BRAINLIST IF CORRECT!!
The diameter of a red blood cell is about 0.0008 cm. The diameter of a whooping cough virus is about 2.5 x 10-5 cm. What is the approximate ratio of the diameter of the red blood cell to the diameter of the whooping cough virus? LOOK AT PICTURE
A.) 3.2 × 10^1
B.) 3.1 × 10^-3
C.) 3.1 x 10^-2
D.) 3.2 × 10^2
Answers
Answer:
b
Step-by-step explanation:
as 2.5 × 10-^5 is 250000 and b is 3100 and if you do 10-5 + 10-3 it is 10-8 which will give u 0.0008cm I think if my calculations r correct
Answer:
a
Step-by-step explanation:
just did it and got right
If you are solving the equation by factoring, which of the following equations would you use the zero product property on?
(x - 5)(x - 10) = 0
(x - 5)(x + 4) = 0
(x + 5)(x + 10) = 0
Answers
Answer:
You would use the zero product property on (x - 5)(x - 10) = 0 and (x - 5)(x + 4) = 0 because they are both in factored form and set equal to 0.
Step-by-step explanation:
Select the phrase from the drop-down menu that
best completes the sentence.
Several values of a quadratic function are given
in the table.
X -5
y
-7
-2 -1 2
8 9
6
8 9
0 -40 -72 -91
There is a maximum between the two input values
>
Finish
Answers
Answer:
"of -1 and 2."
Step-by-step explanation:
The quadratic function has a maximum value between the two input values of -1 and 2, with a maximum output of 9.
What is 19c9 in statistics
Answers
The value of C( 19, 9) using the property of Combination is 92,378.
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
We know the Formula for combination
C( n, r) = n!/ r! (n- r)!
We have to find C( 19, 9) where n= 19 and r= 9
C( 19, 9)
= 19! / 9! (19-9)!
= 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10! / 9! 10!
= 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 / 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2
= 19 x 17 x 13 x 11 x 2 x 2 x 2 / 6 x 5
= 92,378
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Question:
Given the demand equation p=190/q+10 where 10<0<85, for what value of q is | n | a maximum? For what value is it minimum?
Answers
The maximum and minimum value of η at q = 10 and q = 85 respectively.
The demand equation is p = 190/ (q + 10) where 10 < 0 < 85.
η is the elasticity of demand.
Then, the elasticity of demand is given as:
η = ( dq/ dp) × ( p / q )
Now, we have p = 190/ (q + 10)
Therefore,
p ( q + 10 ) = 190
pq + 10p = 190
q = ( 190 - 10p ) / p
Now,
dq / dp = ( d/dp ) ( ( 190 - 10p ) / p )
dq / dp = ( -190/ p² )
Substituting these values in the elasticity demand,
η = ( dq/ dp) × ( p / q )
η = ( -190/ p² ) × ( p / q )
η = ( -190/ pq )
η = ( -190/ [190 / (q + 10 ) ]q )
η = [ - ( q + 10 ) / q ]
| η | = | - ( q + 10 ) / q |
η = ( q + 10 ) / q = 1 + 10/q
The critical point is when | η' | = 0.
η' = ( d / dq ) ( 1 + 10/q )
η' = - 10/ q²
- 10/ q² = 0
Hence, - 10/ q² is not defined.
Therefore, the function is not defined at q = 0.
Therefore, q = 0 is not a solution.
We have 10 ≤ q ≤ 85
The value of functions at the endpoint,
At q = 10,
η = ( 1 + 10/q )
η = ( 1 + 10/10 )
η = 1 + 1 = 2
At q = 85,
η = ( 1 + 10/q )
η = ( 1 + 10/85 )
η = 1.11764
Therefore, the absolute value of the elasticity of demand is maximum at q = 10.
The absolute value of the elasticity of demand is minimum at q = 85.
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what as 9 squared? i need this
Answers
The numbers of customers that visited a store each hour for several hours after the store opened at 8 am are shown in the table. Hours after 8 am 1 3 4 6 9 Number of Customers 2 15 18 13 0 Which statement best describes the data?
Answers
The statement which best describes the data given is C) The data can be modeled by a quadratic function.
Given a data,
The numbers of customers that visited a store each hour for several hours after the store opened at 8 am are shown in the table.
It is clear that the number of customers increases to 18 for the first 4 hours and then decreases to 0 after 9 hours.
So this data cannot be modeled by a linear function or an exponential function.
Also since the number of customers arriving is not constant, this cannot be expressed as constant function.
So it is quadratic function.
Hence the correct option is c.
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A house is infested with mice and to combat this the householder acquired four cats cyd, Greg, Ken, and Rom, The householder observes that only half of the creatures caught are mice. A fifth are voles and the rest are birds. 20% of the catches are made by Cyd, 45% by Greg, 10% by Ken and 25% by rom. a) What is the probability of a randomly selected catch being a mouse caught by Cyd? b) Bird not caught by Cyd? c) Greg's catches are equally likely to be a mouse, a bird or a vole. What is the probability of a randomly selected d) The probability of a randomly selected catch being a mouse caught by Ken is 0.05 . What is the probablity that a catch being a mouse caught by Greg? e) Given that the probability of a randomly selected catch is a mouse caught by Rom is 0.2 verify that the catch made by Ken is a mouse? probability of a randomly selected catch being a mouse is 0.5 . f) What is the probability that a catch which is a mouse was made by Cyd?
Answers
Note that the probabilities are given below.
What are the probabilities?
a) the probability of a randomly selected catch being a mouse caught by Cyd
p(Catching a mount) x p(Cyd made the catch)
= 0.5x .2
= 0.1
b) the probability of a bird not caught by Cyd is 0.5 x 0.8 = 0.4.
Thus
P(that a catch is a bird) x p(the Cyd didn't make the catch)
= 0.3 x 0.8
=0.24
c) The probability of a randomly selected catch being caught by Greg is 0.45
To calculate, we say
(0.5 x0.45) + (0.3 x 0.45) + (0.2 x .45)
= 0.45.
d)
P (mouse caught by Greg) = (0.45 x 0.5) / 1
= 0.225.
e) P(catch is a mouse caught by Ken and catch is a mouse)
= P(catch is a mouse | catch is made by Ken) x P(catch is made by Ken)
= 0.05 x 0.1
= 0.005
f)
P (catch made by Cyd | catch is a mouse)
= 0.1 x 0.2 / 0.5
= 0.04
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Lisa mixed 1 part of apple juice and 2 parts of vanilla yogurt to make a smoothie. How many parts of apple juice did Lisa mix with each part of vanilla yogurt?
one over three
two over five
one over two
two over one
Answers
Answer:
1/3
Step-by-step explanation:
There are 1+2=3 total and since there is 1 apple juice it is 1/3
Answer:
1/3
Step-by-step explanation:
Choose the best selection for the
quadrilateral with vertices at the
following points:
(-3,0), (-3,-3), (0,-3), (0,0)
Hint: Start by graphing the points.
Distance Formula: d = √(x2-x₁)² + (Y2 − ₁)²
A. Trapezoid
C. Rectangle
B. Rhombus
D. Square
Answers
Answer:
D. Square
Step-by-step explanation:
You want the best name for the quadrilateral with vertices (-3, 0), (-3, -3), (0, -3), and (0, 0).
GraphA graph of the points is shown in the attachment. We notice the vertices are aligned with the grid, so the corner angles are all right angles.
The differences of x-coordinates and y-coordinates are both 3, so the side lengths of this rectangle are all 3 units.
The figure is all of a rectangle, rhombus, and square.
The most specific name for the figure is Square.
__
Additional comment
A trapezoid has one pair of parallel sides. This figure has two pairs of parallel sides, so is not a trapezoid.
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