Answer:
a) 0.677
b) 0.0431
c) 0
Step-by-step explanation:
For each bit, there are only two possible outcomes. Either it is correctly received, or it is erroneously received. Whether any particular bit is erroneously received is independent of whether any other bit is erroneously received. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
10% of all bits transmitted through a digital communication channel are erroneously
This means that [tex]p = 0.1[/tex]
Messages of 20 bits:
This means that [tex]n = 20[/tex]
a. What proportion of these messages will have at most 2 erroneously received bits?
This is [tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.1)^{0}.(0.9)^{20} = 0.1216[/tex]
[tex]P(X = 1) = C_{20,1}.(0.1)^{1}.(0.9)^{19} = 0.2702[/tex]
[tex]P(X = 2) = C_{20,2}.(0.1)^{2}.(0.9)^{18} = 0.2852[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1216 + 0.2702 + 0.2852 = 0.677[/tex]
b. What proportion of these messages will have at least 5 erroneously received bits?
This is
[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]
In which
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.1)^{0}.(0.9)^{20} = 0.1216[/tex]
[tex]P(X = 1) = C_{20,1}.(0.1)^{1}.(0.9)^{19} = 0.2702[/tex]
[tex]P(X = 2) = C_{20,2}.(0.1)^{2}.(0.9)^{18} = 0.2852[/tex]
[tex]P(X = 3) = C_{20,3}.(0.1)^{3}.(0.9)^{17} = 0.1901[/tex]
[tex]P(X = 4) = C_{20,4}.(0.1)^{4}.(0.9)^{16} = 0.0898[/tex]
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.1216 + 0.2702 + 0.2852 + 0.1901 + 0.0898 = 0.9569[/tex]
Then
[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.9569 = 0.0431[/tex]
c. For what proportion of these messages will more than half the bits be erroneously received?
This is [tex]P(X \geq 11)[/tex]
[tex]P(X = 11) = C_{20,11}.(0.1)^{11}.(0.9)^{9} \approx 0[/tex]
If 11 is approximately 0, the rest(11, 12, 13,...) will also be approximately 0. So this proportion is 0.
how do I graph y=(x-2)-4
4√6 X 2√2
4√3
16√3
32√3
8√12
Answer:
Step-by-step explanation:
4√6 X 2√2 4√3 16√3 32√3 8√12
Answer: 16√3
Step-by-step explanation:
Determine the solution to the system of equations {4x+15y=40
-8x-5y=20}
And write your solution as an ordered pair.
Step-by-step explanation:
4x+15y= 40-5y= 20
= 4x+15y+5y= 40-20
4x+20y= 20
1 pt
1. If your job pays you $ 60,000 annually. What is your monthly salary to the nearest cent?
Since you need the monthly salary, and you are given the annual salary, use the formula
Monthly Salary = Annual Salary/12 since there are 12 months in a year ( 1 point)
O $5,000
$2,500
O $8.70
on
O None are Correct
Answer:
Hi, since their are 12 months in the year, you divide 60,000 (the annual salary), by the amount of months in the year to find the monthly salary. The answer is 5,000.
please help i reaaly need help
Answer:
6/65
Step-by-step explanation:
using the proper calculator, and through solving.
Help! Will give brainliest!
Answer:
6 or 5
Step-by-step explanation:
what is the surface area of this shape?
Answer:
135.42 yd²
Step-by-step explanation:
Surface area of triangular prism = 2(BA) + PH
Where,
Triangular base area (BA) = ½bh = ½*4*3 = 6 yd²
Perimeter of triangular base (P) = 4 + 3.61 + 3.61 = 11.22 yd
Height of prism (H) = 11 yd
Surface area = 2(6) + 11.22 × 11
= 12 + 123.42
Surface area = 135.42 yd²
"35 degrees above 0 positive or negative
Answer:
Positive
Please mark me brainliest!!!!!!
Positive!
Anything above 0 is positive.
Bye!! <3
-Lexi
100 people went to a picnic. 32 people got sick with food poisoning. The Public HealthDepartment narrowed it down to either the chicken salad or the cream pie. They determined that80 people ate chicken salad, 75 people ate cream pie, 33 people ate chicken salad cream pie anddid not get sick, 5 ate neither food and did not get sick, 40% of the people who ate chicken saladgot sick, and 36% of the people who are cream pie got sick. Was it the chicken salad or thecream pie
Answer:
It was the chicken salad.
Step-by-step explanation:
If you multiply each amount of people that ate one or the other and how many got sick, you get:
Chicken salad: 32
Cream pie: 27
And 32 people got sick so it must be the chicken salad.
Find the volume.
18 cm
12 cm
9 cm
Answer:
1944....
Step-by-step explanation:
f(x)= 2/x-2 find (fof) (i)
Answer:
Step-by-step explanation:
cant see pic
for every 5 green apples there are 2 red apples what is the raito
Answer:
5:2
Step-by-step explanation:
If you know the area of a circle, how can you find is radius
Answer:
πr^2=area
r=√area/π
r=√7×area/22...../
a doll maker puts a small bag of 5 hair ribbons inside each box with a doll how many bags of 5 hair ribbons can be made from 45 hair ribbons
Answer:
divide 45 by 5
you get 9
the answer is 9
Answer:
45 / 5 = 9
Step-by-step explanation:
this.is your answer it's quite simple if u need more help lmk
Solve for a.
12 =-2a + 6
Answer:
a=-3
Step-by-step explanation:
First, subtract 6 from both sides
6=-2a
divide -2 from both sides
-3=a
What is the value of the expression 13.5- 6.48
13.5-6.48=7.02
Step-by-step explanation:
You just pine them up and subtract. So the decimal points would be one under another. The 6 would be under the 3. Lastly the 4 would be under the 5 and the 8 would be beside the 4. Then you just subtract...or use a calculator
What is the value of x?
Enter your answer in the box.
Answer:
136
Step-by-step explanation:
68 * 2 = 136
One gallon is approximately 3.79 liters. Write a direct variation equation that relates 2 gallons to y liters.
370
Answer:
2 gallons x 3.79 = 7.58 liters
Step-by-step explanation:
1 gallon = 3.79 liters
so
2 gallons x 3.79 liters = 7.58 liters
2 x 3.79 = y liters
Whats 200x3 I tried to answer it but it difficult and I knew you guys could help me?
Answer:
600
Step-by-step explanation:
200x3=600
Answer:
its 1200
Step-by-step explanation:
what is 452÷6 in long division
Answer: 75.333333...
Step-by-step explanation: Might want to round that number to the nearest tenths. This number is a repeating digit.
Here we will show you step-by-step with detailed explanation how to calculate 452 divided by 6 using long division.
Before you continue, note that in the problem 452 divided by 6, the numbers are defined as follows:
452 = dividend
6 = divisor
Step 1:
Start by setting it up with the divisor 6 on the left side and the dividend 452 on the right side like this:
6 ⟌ 4 5 2
Step 2:
The divisor (6) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:
0
6 ⟌ 4 5 2
Step 3:
Multiply the divisor by the result in the previous step (6 x 0 = 0) and write that answer below the dividend.
0
6 ⟌ 4 5 2
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.
0
6 ⟌ 4 5 2
- 0
4
Step 5:
Move down the 2nd digit of the dividend (5) like this:
0
6 ⟌ 4 5 2
- 0
4 5
Step 6:
The divisor (6) goes into the bottom number (45), 7 time(s). Therefore, put 7 on top:
0 7
6 ⟌ 4 5 2
- 0
4 5
Step 7:
Multiply the divisor by the result in the previous step (6 x 7 = 42) and write that answer at the bottom:
0 7
6 ⟌ 4 5 2
- 0
4 5
4 2
Step 8:
Subtract the result in the previous step from the number written above it. (45 - 42 = 3) and write the answer at the bottom.
0 7
6 ⟌ 4 5 2
- 0
4 5
- 4 2
3
Step 9:
Move down the last digit of the dividend (2) like this:
0 7
6 ⟌ 4 5 2
- 0
4 5
- 4 2
3 2
Step 10:
The divisor (6) goes into the bottom number (32), 5 time(s). Therefore put 5 on top:
0 7 5
6 ⟌ 4 5 2
- 0
4 5
- 4 2
3 2
Step 11:
Multiply the divisor by the result in the previous step (6 x 5 = 30) and write the answer at the bottom:
0 7 5
6 ⟌ 4 5 2
- 0
4 5
- 4 2
3 2
3 0
Step 12:
Subtract the result in the previous step from the number written above it. (32 - 30 = 2) and write the answer at the bottom.
0 7 5
6 ⟌ 4 5 2
- 0
4 5
- 4 2
3 2
- 3 0
2
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 452 divided by 6 calculated using Long Division is:
75
2 Remainder
Mark as brainlist
Gap sells jeans that cost $21.00 and sell for $29.95. the percent of markup based on cost is
Answer:
is this actually a question?
Step-by-step explanation:
Need help! What are the coordinates of point P?
Answer:
the first circle.
Step-by-step explanation:
please mark brainliest of answers correct. have a nice day!
Answer:
A) -4,3
Step-by-step explanation:
For his long distance phone service, Ryan pays a $6 monthly fee plus 8 cents per minute. Last month, Ryan's long distance
bill was $18.64. For how many minutes was Ryan billed?
Answer:
15.8 I think
Step-by-step explanation:
18.64 - 6 = 12.64
0.8 times 15.8 is 12.64 so I think 15.8
Sally bought 10 pencils for
$1.50, how much is it per pencil? Don't forget $ in
the front.
Answer:
$0.15 per pencil
Step-by-step explanation:
1. Divide
1.50 divided by 10 = 0.15
2.Answer
$0.15 per pencil
Please help, I will give brainliest.
Answer:
I believe it is c but don't quote me on it
What are the values of b and c?
Answer:
c = 40 degrees ; b = 100 degrees
Step-by-step explanation:
Since this is a isosceles triangle, sides WV and WU are the same length.
c = 40 degrees
There are 180 degrees in a triangle.
180 - 40 - 40 = 100
b = 100 degrees
I hope this helps!
"Seven eights of a number is 63" equation and solve
Answer:
x = 72
Step-by-step explanation:
7/8 * x = 63
x = 63 / (7/8)
x = 72
The length of a rectangle is three times its width, if the area of the rectangle is 108cm2, find its perimeter
Answer:
The perimeter of rectangle is 48 cm.
Step-by-step explanation:
First, you have to form an expression for the length and the width. Let x be the width :
width = x cm
length = 3 × x = 3x cm
Then, you have to apply area of rectangle formula, A = length × width to find the value of x.Let area equals to 108 :
A = length × width
108 = 3x × x
3x² = 108
x² = 108 ÷ 3
x² = 36
x = √36
x = 6 cm
Lastly, you have to find perimeter :
length = 3 × 6 = 18 cm
width = 6 cm
Perimeter = 2(length + width)
P = 2(18 + 6)
P = 2(24)
P = 48 cm
Answer:
48cm
Step-by-step explanation:
how Do you graph an
absolute valve function
Answer:
To graph the absolute value, you need to know where the vertex is, so the numbers will be going down, then turn and start going back up, or going up and then turn and start going down, the middle point will be the vertex and should be the center point of the table.
Lisa makes $78.37 per day. If she works 8 12
hours, how much does she make in 1 hour?
