Answer:
108 calories per cup
Step-by-step explanation:
Suppose that 10% of all bits transmitted through a digital communication channel are erroneously received and that whether any particular bit is erroneously received is independent of whether any other bit is erroneously received. Consider sending a very large number of messages, each consisting of 20 bits.
a. What proportion of these messages will have at most 2 erroneously received bits?
b. What proportion of these messages will have at least 5 erroneously received bits?
c. For what proportion of these messages will more than half the bits be erroneously received?
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.
PLS HELP ME!!! this is my third time posting this! FIND X!
Answer:
You are looking at a pair of parallel lines (a and b) and a transversal that crosses them both.
Now that you know what think back to when you learned the relationship between angles formed by a transversal and a set of parallel lines.
You can have same side exterior, same side interior, alternate interior and alternate exterior. Which set of these are these angles?
Remember same side interior and same side exterior angles are supplementary (they have a sum of 180 degrees). Alternate interior and alternate exterior angles are congruent. Knowing this how can an equation be written using the expressions in the image?
Step-by-step explanation:
Answer:
x = 3.4
Step-by-step explanation:
Since these two angles are opposite exterior angles, they are equivalent. that means that 5x - 2/3 = 3 1/3x + 5, from here you should simplify the terms so you have all of x on one side and all of the number on ther other, it should be 1 2/3x = 5 2/3, then all you have to do is divide both sides by 1 2/3 to get x which is 3.4 or 3 2/5
Please help please please
Answer:
4
Step-by-step explanation:
[tex] \frac{ {7}^{7} }{ {7}^{3} } = {7}^{7 - 3} = {7}^{4} [/tex]
please help! (URGENT)
Answer:
X = 5
Step-by-step explanation:
PLEASE HELP WHOEVER ANSWERS FIRST WILL GET BRAINLIEST!!
What is the equation for this linear function? Enter any answers to two decimal places
A quadratic function is described by the equation f(x) = (x - 3) ^ 2 Which statement about the graph of the function is true?
A The only zero of the function is 3 which is where the graph of the function intersects the x-axis
В. The only zero of the function is 3 which is where the graph of the function intersects the y-axis.
C.The only zero of the function is , which is where the graph of the function intersects the x-axis.
D.The only zero of the function is is where the graph of the function intersects the y-axis .
Answer: A) The only zero of the function is 3 which is where the graph of the function intersects the x-axis
Step-by-step explanation:
Remember, a quadratic function which has roots x = a, and x = b, can be written as:
p(x) = A*(x - a)*(x - b)
Where A is the leading coefficient. This is the factorized form of a quadratic.
We have the function:
f(x) = (x - 3)^2
Now, we could rewrite this as:
f(x) = (x - 3)*(x - 3) = 1*(x - 3)*(x - 3)
Then we wrote f(x) in its factorized form, from this, we can see that the roots of the function are x = 3, and x = 3 (we have the same root two times)
Then the only root of f(x) is x = 3.
Remember that a root (also called a zero) is the value of x where the function intersects the x-axis. then the correct option here is:
A) The only zero of the function is 3 which is where the graph of the function intersects the x-axis
The volume of a cube is 1.5 mº. Find the length of its edge to the nearest tenth of a meter.
Answer:
About 1.1 meters.
Step-by-step explanation:
Hope this helps! :D
Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. Let k>0 be the constant of proportionality. Assume the coffee has a temperature of 200 degrees Fahrenheit when freshly poured, and 11 minutes later has cooled to 190 degrees in a room at 62 degrees.
Required:
a. Write an initial value problem for the temperature T of the coffee, in Fahrenheit, at time t in minutes.
b. Solve the initial value problem in part (a).
Answer:
Tt = Ts + Ce^-kt
Tt = 62 + 138e^-0.0068t
Step-by-step explanation:
The initial value problem for the Newton cooling rate is :
Tt = Ts + Ce^-kt
Initial temperature,when freshly poured Ti = 200°F
Temperature after 11 minutes = 190°F
Temperature of room, Ts= 62°F
Using the relation :
Tt = Ts + Ce^-kt
Temperature after time, t
When freshly poured, t = 0
k = constant of proportionality
We can then solve for C and k as follows :
200 = 62 + Ce^-0k
200 = 62 + C
C = 200 - 62 = 138°F
Using the Temperature after 11 minutes ; we can find, k, proportionality constant:
Temperature, Tt after, t = 11 minutes = 190
Tt = Ts + Ce^-kt
190 = 62 + 138e^-11k
128 = 138e^-11k
128 / 138 = e^-11k
0.9275 = e^-11k
Take In of both sides :
−0.075223 = - 11k
k = −0.075223 / - 11
k = 0.0068
The model function becomes :
Ts = 62 ; C = 138
Tt = 62 + 138e^-0.0068t
Angle 1 is 135
Angle 2 is ?
Angle 3 is 135
Angle 3 is an exterior angle. What is the missing angle
A. 45
B. 80
C. 90
D. 180
Answer:
80
Step-by-step explanation:
di ko po alam kung tama ba
(sana po makatulong po)
the nth term of a sequence is 3n²÷2
find the second term of this sequence
find the fifth term
Picture is shown down below ( Math )
Answer:
a) quad 3
b) y-axis
c) quad 4
d) quad 2
e) quad 1
f) x-axis
bir çift ve bir tek rakam kullanarak yazılabilecek en küçük 2 basamaklı doğal sayı kaçtı
Equivalent fraction of 4/5
Answer:
12/15
Step-by-step explanation:
4*3=12
5*3=15
Answer: 8/10
Step-by-step explanation:
the sum of two numbers is 72 and their difference is 26. find two numbers?
9514 1404 393
Answer:
23, 49
Step-by-step explanation:
Let s represent the smaller of the two numbers. Then the larger is s+26, and the sum is ...
s + (s+26) = 72
2s = 72 -26
s = (72 -26)/2 = 23
Then the larger number is
s +26 = 49
The two numbers are 23 and 49.
_____
The reason we wrote the solution this way is to show you that the smaller number is half the difference between the given sum (72) and difference (26). This is the generic solution to a "sum and difference" problem. The smaller number is always half the difference of the give sum and difference. (Similarly, the larger is always half the sum of the given sum and difference.)
That is, the two numbers are always half the sum ± half the difference:
72/2 ± 26/2 = {36+13, 36-13} = {49, 23}
50 PTS
Please Make sure its easy to understand
Answer:
1) -95.
2) 15.
3) The conference center is on floor 5.
Step-by-step explanation:
1) Evaluating gives [tex]-52-30-13=-(52+30+13)=-(95)=-95.[/tex]
2) Substituting gives [tex]x+27=(-12)+27=15.[/tex]
3) After going 4 floors down, we are on level -4. After going 9 floors up to the desired room, we are on level -4+9=5. So the conference center is on floor 5.
Answer:
1. -95
2. 15
3. 5th Floor (-4 + 9)
Step-by-step explanation:
Find the length marked x in the diagram below
Answer:
x = 5.57
Step-by-step explanation:
= √8² + 7²
= √64 + 49
= √113
= 10.63
x = √12² - 10.63²
x = √144 - 112.99
x = √31.01
x = 5.568
x = 5.57
Determine if the two figures are congruent by using transformations
solve the following equation for x.
Answer:
9
Step-by-step explanation:
simplify both sides of the equation then isolate the variables. hope this helps
.
Simplify the expression below.
1/2x²+2+1/4x+8
plz help
Answer:
[tex] \frac{1}{2} {x}^{2} + 10 + \frac{1}{4} x[/tex]
Step-by-step explanation:
[tex] \frac{1}{2} {x}^{2} + 2 + \frac{1}{4} x + 8[/tex]
[tex]2 + 8 = 10[/tex]
[tex] \frac{1}{2} {x}^{2} + 10 + \frac{1}{4} x[/tex]
If 64= a, then a is equal to
Where are the answers?
Which strategy uses place value to correctly solve for 321 x 4?
Answer:
300x4 =1200
20x4 = 80
1x4 =8
1288
Step-by-step explanation:
Break apart 321 = 300+20+ 1
This is the hundreds, tens, and ones
Then multiply each by 4
Add all together to get answer
Suppose X∼N(6.5,1.5), and x=3.5. Find and interpret the z-score of the standardized normal random variable. Provide your answer below:
Answer: x= 3.5 is -2. The mean is 6.5.
z score to the left is 2
Step-by-step explanation:
X is a normally distributed random variable with μ=6.5 (mean) and σ=1.5 (standard deviation). To calculate the z-score,
z=x−μσ=3.5−6.51.5=−31.5=−2
This means that x=3.5 is two standard deviations (2σ) below or to the left of the mean. This makes sense because the standard deviation is 1.5. So, two standard deviations would be (2)(1.5)=3, which is the distance between the mean (μ=6.5) and the value of x (3.5).
Using the normal distribution, it is found that x = 3.5 has a z-score of -2, which means that it is 2 standard deviations below the mean.
--------------------------------
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is from the mean, above or below.
X∼N(6.5,1.5), which means that [tex]\mu = 6.5, \sigma = 1.5[/tex].The measure is [tex]X = 3.5[/tex]The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.5 - 6.5}{1.5}[/tex]
[tex]Z = -2[/tex]
The measure x = 3.5 has a z-score of -2, which means that it is 2 standard deviations below the mean.
A similar problem is given at https://brainly.com/question/13383035
what is the symbol of an inverse function
Answer:
f(-1
Step-by-step explanation:
The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse".
resolver las siguientes multiplicaciones de fraciones
Answer:
Which one?
Step-by-step explanation:
Select the correct answer from each drop-down menu.
Describe the relationship between the area of a circle and its circumference.
The -blank-
is -blank-
times the -blank-
times the circunference.
Answer:
hey im not completely sure but i think its the RADIUS is 1/3 times the AREA time the circumference
Step-by-step explanation:
When three times a number is subtracted from 36, the result is 4 plus the number. What is the number?
Answer:
x = 8
The number is 8
Step-by-step explanation:
36 – (3x) = 4 + x
36 – (3 • 8) = 4 + 8
36 – 24 = 12
12 = 12
x = 8
I hope this helps.
Find the slope and y-intercept of y – 3x = 2
Answer:
slope is 3/1 y=2
Step-by-step explanation:
pleaseee anwser quick!!! 10 points!
Answer:
I think quadratic
Step-by-step explanation:
Select the correct answer.
A figure in the second quadrant is reflected over the y-axis. In which quadrant will the reflected figure appear?
Answer:
It would land on the first quadrant.
Step-by-step explanation:
Bashir deposits money into a savings account every year. In his first year of saving money, he deposited $1,500.
Each year after that, he deposited $2,250. Write an explicit expression to represent the total amount of money, in
dollars, Bashir has deposited into his account, where n represents the number of years he has been contributing
money to the account.
For n ≥ 1, the explicit expression is
Will mark BRAINLYIST
Answer:
1500 + 2250 =
Step-by-step explanation:
Answer:
aₙ = 2250n - 750Step-by-step explanation:
This is an arithmetic progression with:
The first term a₁ = 1500Common difference d = 2250Required expression is:
aₙ = a₁ + (n - 1)daₙ = 1500 + (n - 1)2250 = 1500 + 2250n - 2250 = 2250n - 750