Using the lognormal and the binomial distributions, it is found that:
The 90th percentile of this distribution is of 136 dB.There is a 0.9147 = 91.47% probability that received power for one of these radio signals is less than 150 decibels.There is a 0.0065 = 0.65% probability that for 6 of these signals, the received power is less than 150 decibels.In a lognormal 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{\ln{X} - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of [tex]\mu = 3.5[/tex].The standard deviation is of [tex]\sigma = \sqrt{1.22}[/tex]Question 1:
The 90th percentile is X when Z has a p-value of 0.9, hence X when Z = 1.28.
[tex]Z = \frac{\ln{X} - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{\ln{X} - 3.5}{\sqrt{1.22}}[/tex]
[tex]\ln{X} - 3.5 = 1.28\sqrt{1.22}[/tex]
[tex]\ln{X} = 1.28\sqrt{1.22} + 3.5[/tex]
[tex]e^{\ln{X}} = e^{1.28\sqrt{1.22} + 3.5}[/tex]
[tex]X = 136[/tex]
The 90th percentile of this distribution is of 136 dB.
Question 2:
The probability is the p-value of Z when X = 150, hence:
[tex]Z = \frac{\ln{X} - \mu}{\sigma}[/tex]
[tex]Z = \frac{\ln{150} - 3.5}{\sqrt{1.22}}[/tex]
[tex]Z = 1.37[/tex]
[tex]Z = 1.37[/tex] has a p-value of 0.9147.
There is a 0.9147 = 91.47% probability that received power for one of these radio signals is less than 150 decibels.
Question 3:
10 signals, hence, the binomial distribution is used.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.For this problem, we have that [tex]p = 0.9147, n = 10[/tex], and we want to find P(X = 6), then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{10,6}.(0.9147)^{6}.(0.0853)^{4} = 0.0065[/tex]
There is a 0.0065 = 0.65% probability that for 6 of these signals, the received power is less than 150 decibels.
You can learn more about the binomial distribution at https://brainly.com/question/24863377
Simplify the following expression.
(42x + 59y) + (-14x + 35y)
A.
28x + 94y
B.
56x + 94y
C.
56x + 24y
D.
28x + 24y
Answer:
A. 28x + 94y
Step-by-step explanation:
First, line up the like terms as if you were adding vertically, and combine them.
(42x + 59y)
+ (-14x + 35y)
(28x + 94y)
Hope this helps :)
What is the solution of the system of equations?
your desmos graph is really weird as the point is between 4 and 8 but with the one y=-x+5 we can see that the y intercept is 5 and the x value is 0
so the point is 0,5
A car is traveling down a highway at a constant speed, described by the equation d=65t , where d represents the distance, in miles, that the car travels at this speed in t hours.
Complete the statement about the meaning of 65 in this situation.
The car travels_________ miles in ________ hour.
Step-by-step explanation:
10 1
20 miles car travel 65t hb
Which of the following is equivalent to the expression 2/5 divided by 4 ?
A
5/2×4
B
2/5
C
2/5×1/4
D
2/5÷1/4
Answer:
C) 2/5×1/4
Step-by-step explanation:
Dividing by a number is the same by multiplying by the reciprocal of the number.
For Example:
1/2 divided by 3 would be the same as 1/2 x 1/3
So for this problem we are given that 2/5 is divided by 4 which would be the same as 2/5 multiplied by the reciprocal of 4 which is 1/4 and thus the answer is option C which is 2/5×1/4
Paul was thinking of a number. Paul adds 1.2 to the number the doubles the result to get an answer of 68.3. Form an equation with x from the information
Answer:
(x+1.2)2=68.3
Step-by-step explanation:
(x+1.2)2=68.3
In the figure below, BD and AC are diameters of circle P.
What is the arc measure of minor arc DC in degrees?
Answer: 19
Step-by-step explanation:
2 lines crossing create 2 pairs of equal angles. The opposite angles are the same. Same goes in a circle.
9514 1404 393
Answer:
arc DC = 19°
Step-by-step explanation:
The acute central angles are vertical angles, so have the same measure. Vertical angles with the same measure intercept arcs with the same measure. The measure of the arc is the measure of the central angle it subtends.
Arc AB = Arc DC = 19°
The graph of f(x) = x² is transformed to create the graph of g(x) = f(x + 6). Which
statement is true?
A The graph of g(x) reflects the graph of f(x) across the x-axis.
B The graph of g(x) reflects the graph of f(x) across the y-axis.
CThe vertex of the graph of g(x) is 6 units to the left of the vertex of the graph of f(x).
DThe y-intercept of the graph of g(x) is 6 units above the y-intercept of the graph of f(x).
Answer:
Given a function \displaystyle f\left(x\right)f(x), a new function \displaystyle g\left(x\right)=-f\left(x\right)g(x)=−f(x) is a vertical reflection of the function \displaystyle f\left(x\right)f(x), sometimes called a reflection about (or over, or through) the x-axis.
Given a function \displaystyle f\left(x\right)f(x), a new function \displaystyle g\left(x\right)=f\left(-x\right)g(x)=f(−x) is a horizontal reflection of the function \displaystyle f\left(x\right)f(x), sometimes called a reflection about the y-axis.
Step-by-step explanation:
a coin is flipped 3 times and lands on heads each time. What is the probability of it landing on tails on the fourth flip?
Answer:
1/4
Step-by-step explanation:
since the dice would be rolled 4 times, and the dice rolled heads 3 times, the probability of the coin land8ng of tail on the 4th flip is 1/4
The probability of it landing on tails on the fourth flip will be 1/4.
What is probability?
Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
Given that a coin is flipped 3 times and lands on heads each time. The probability of getting head on the fourth flip will be:-
Probability = Number of favorable outcomes / Number of sample
Number of favorable outcomes = tails = 1
Number of samples = 4
Probability = 1 / 4
Therefore, the probability of it landing on tails on the fourth flip will be 1/4.
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3) The recipe calls for 6 cups of flour for every 2 1/3 cups of sugar. How many cups of flour
are needed per cup of sugar?
Answer:
Im pretty sure its 3 cups
Step-by-step explanation:
What is a variable in the expression below?
12+2.6z-2
A) z
B) 2.6
C) -2
A variable is a letter in the equation that can be replaced by a number.
In the equation shown the variable is the letter z.
Answer: A) z
hhhhhhhhhhhhhhhhhhhhhheeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeellllllllllllllllllllllllllllllllllllpppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
E
Step-by-step explanation:
Like and give 5 star rating
A man flies a kite 354 feet in the air when he runs out of string, what is the angle of elevation if he had 200 yards of string to begin with
Answer:
Step-by-step explanation:
Assuming the string is straight (it will not be so due to gravity and wind load)
θ arcsin(354 / (200(3)) = 36°
Unit #2 - Lesson #13 Exit Ticket: A tour company for large groups charges a one time fee of $200 plus an
additional $25 per person who goes on the tour. They must make at least $1,650 to make the tour profitable. Let
n be the number of people going on the tour. Write and solve an inequality in terms of n that represents all numbers
of people who can go on the tour to make it profitable.
Answer:
200+25n>1650
Step-by-step explanation:
200 is the one time fee
25n for $25 per person
> because they must make more than 1650 to be profitable
I want to know what the letter a is , and how to do it.1/3 + a 5/4
STEP
1
:
5
Simplify —
4
Equation at the end of step
1
:
1 5
(— + a) - — = 0
3 4
STEP
2
:
1
Simplify —
3
Equation at the end of step
2
:
1 5
(— + a) - — = 0
3 4
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 3 as the denominator :
a a • 3
a = — = —————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
1 + a • 3 3a + 1
————————— = ——————
3 3
Equation at the end of step
3
:
(3a + 1) 5
———————— - — = 0
3 4
STEP
4
:
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 4
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
3 1 0 1
2 0 2 2
Product of all
Prime Factors 3 4 12
Least Common Multiple:
12
Calculating Multipliers :
4.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 4
Right_M = L.C.M / R_Deno = 3
Making Equivalent Fractions :
4.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. (3a+1) • 4
—————————————————— = ——————————
L.C.M 12
R. Mult. • R. Num. 5 • 3
—————————————————— = —————
L.C.M 12
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
(3a+1) • 4 - (5 • 3) 12a - 11
———————————————————— = ————————
12 12
Equation at the end of step
4
:
12a - 11
———————— = 0
12
STEP
5
:
When a fraction equals zero :
5.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
12a-11
—————— • 12 = 0 • 12
12
Now, on the left hand side, the 12 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
12a-11 = 0
Solving a Single Variable Equation:
5.2 Solve : 12a-11 = 0
Add 11 to both sides of the equation :
12a = 11
Divide both sides of the equation by 12:
a = 11/12 = 0.917
a = 11/12 = 0.917
Answer:
11/12
Step-by-step explanation:
You want to subtract 5/4 minus 1/3 but you cant so you have to find the greatest denominator first which would be 12 because 3x4=12.
Since you multiplied 4x 3 to get 12 then you will multiply the 5 by 3 and the 1 by 4 to get this -> 5/4= 15/12 1/3= 4/12
Then subtract 15/12- 4/12= 11/12
a=11/12
solve pls brainliest
Answer:
-3
Step-by-step explanation:
using pemdas, we first divide -18 by 6 to get -3. next, we subtract -3 from -6: -6-(-3)=-6+3=-3
Answer: -3
Step-by-step explanation:
For this, you want to use PEDMAS
This is Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction. The first step would be to divide -18/6. This will come out to -3
Hey everyone! Need this question ASAP. Can anybody help me? (Look at photo)
Two relationships are described below: Relationship A: It took 2 people 12 hours to build a deck. It would have taken 3 people 4 hours to build the same deck. Relationship B: Jack earned $24 after 3 hours of work. Then, he earned $40 after 5 hours of work. Which statement is true about these relationships?
Answer:
im pretty sure its b but if its not then i apologise
simplify 4y(4y-4)-4(-4y+5+4y2)
Can someone answer this for me
Answer:
s=4
Step-by-step explanation:
area of square is side*side
so that means s*s=16
so s = 4
You exchange 50 AED, and receive 12 Euro. How many Euros would you receive for 1 AED? Please explain step by step on how you solved the problem. (Using equations like multiplication, devision, adding, subtracting.)
Answer:
Step-by-step explanation:
if 50 AED= 12 Euro
for 1 AED ? Euro
50AED/1AED= 12Euro/x
cross multiplication:
50*x=12*1
50*x=12
x=12/50
x=0.24 Euro
so for 1AED you will get 0.26 Euro
It takes Shawn 4 more hours to stain a deck than Michelle. Together it takes them 4.8 hours to complete the work. How long would it take Shawn to stain the deck by himself?
Answer:
4.4 hours
Step-by-step explanation:
It would take Shawn 4.4 hours, as this would give a time of .4 hours to Michelle, totaling 4.8 hours
What is the output, or dependent variable or
quantity?
Х
f(x)
у
DONE
Answer:
x is the input, or independent variable and f(x) is the output, or dependent variable or quantity. f(2) represents the output (y-value) when x = 2. The value of f(2) is 2.
Step-by-step explanation:
If the values of a variable depends on the other variable, then it called dependent variable.
If the value of a variable does not depend on the other, then it is called independent variable.
If a function is f(x)=x, then x is an independent variable and f(x) is a dependent variable.
The given function is
Here, x is the input, or independent variable and f(x) is the output, or dependent variable or quantity.
The notation f(a) represents the output (y-value) when x = a. So, f(2) represents the output (y-value) when x = 2.
Substitute x=2 in the given function.
The value of f(2) is 2.
Answer:
f(x)
Step-by-step explanation:
PLEASE HELP ⁉️ POR FAVOR SOMEONE IM DESPERATE tHIS IS DUE IN THE mORiNG!
Answer:
Just in case you want me to answer all the questions, I will
Step-by-step explanation:
Question 1): answer is 25
Question 2): answer is 24
Question 3): answer is 100%
24/25 = 96/100
Box Question 1): 21/25 = 84/100
Box Question 2): 15/20 = 75/100
Box Question 3): 47/50 = 94/100
Box Question 4): 28/30 = 93.3/100
Box Question 5): 19/45 = 42.2/100
Box Question 6): 3/4 = 75/100
If a digit is underlined, put a line ONLY over the underlined digit, it is repeating
I'm not completely sure if this is correct, but I really think it is..
I hope this helps!
Solve.
w−(−1/6)=1.08
Enter your answer as a fraction in simplest form in the box.
Answer:
137/150
Step-by-step explanation:
We can solve for w by adding -1/6 to both sides of the equation.
w -(-1/6) = 1.08
w = 1.08 +(-1/6) = 108/100 -1/6
w = 54/50 =1/6 = 162/150 -25/150
w = 137/150
Match the event with the most appropriate probability word: The roll of a normal fair dice will show a 7.
A. Certainly
B. Likely
C. Evens
D. Unlikely
E. Impossible
F. Other
Answer this, plz.
Answer:
Option 3
Evens
. . . . . .. . ..
2. Twenty machines can embroider 1000 sweaters in 5 days.
a. In how many days can 10 machines embroider the same 2000 sweaters?
b. How many machines would needed to embroider 5000 sweaters in 10 days?
Answer:
a) 20 days
b) 50 machines
determine the slope and y intercept and write the equation in slope intercept form
Answer: slope is 2 and the y-intercept is 1 intercept form is y=2x+1
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the blue
graph?
A) g(x) = (x-4)^2
B) g(x) = (x+4)^2
C) g(x) = x^2 + 4
D) g(x) = x^2 - 4
The graphs of f(x) and g(x) are related by transforming one of the two graphs.
The equation of the blue graph is [tex]\mathbf{g(x) =(x - 4)^2}[/tex]
From the graphs, we have:
[tex]\mathbf{f(x) =x^2}[/tex]
f(x) is transformed to the right by 4 units.
The rule of this transformation is:
[tex]\mathbf{g(x) \to f(x - 4)}[/tex]
So, we start by calculating f(x - 4)
Given that:
[tex]\mathbf{f(x) =x^2}[/tex]
Substitute x - 4 for x in f(x)
[tex]\mathbf{f(x - 4) =(x - 4)^2}[/tex]
Also, recall that:
[tex]\mathbf{g(x) \to f(x - 4)}[/tex]
So, we have:
[tex]\mathbf{g(x) =(x - 4)^2}[/tex]
Hence, the equation of g(x) is [tex]\mathbf{g(x) =(x - 4)^2}[/tex]
Read more about transformation at:
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A class of 22 students has taken an exam, and the mean of their scores is 76.5. One student takes the
exam late, and scores 92. After including the new score, what is the mean score for all 23 exams? Round
to the nearest hundredth.
i'll mark brainliest, thanks in advance!
Answer:
SSS
Step-by-step explanation:
are 2 isosceles right triangles congruent, have both sides and angles equal, so the answers are all valid, the simplest is SSS, 2 sides are the same and marked on the drawing, the third is the same accordingly
I need help with this problem no where on Brainly
Answer:
blue graph
Step-by-step explanation:
that graph looks similar to e^x
so f(-x) will be similar to e^-x
so it will be a reflection over y axis
see the picture below