Answer:
[tex]P(X=0)=(9C0)(0.55)^9 (1-0.55)^{9-0}=0.000757[/tex]
[tex]P(X=1)=(9C1)(0.55)^9 (1-0.55)^{9-1}=0.0083[/tex]
[tex]P(X=2)=(9C2)(0.55)^9 (1-0.55)^{9-2}=0.0407[/tex]
[tex]P(X=3)=(9C3)(0.55)^9 (1-0.55)^{9-3}=0.1160[/tex]
And adding we got:
[tex] P(X < 4) = 0.000757 +0.0083+0.0407 +0.1160= 0.2626[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of correct answers", on this case we now that:
[tex]X \sim Binom(n=9, p=0.55)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X < 4) =P(X=0) +P(X=1) +P(X=2) +P(X=3) [/tex]
And we can find the individual probabilities:
[tex]P(X=0)=(9C0)(0.55)^9 (1-0.55)^{9-0}=0.000757[/tex]
[tex]P(X=1)=(9C1)(0.55)^9 (1-0.55)^{9-1}=0.0083[/tex]
[tex]P(X=2)=(9C2)(0.55)^9 (1-0.55)^{9-2}=0.0407[/tex]
[tex]P(X=3)=(9C3)(0.55)^9 (1-0.55)^{9-3}=0.1160[/tex]
And adding we got:
[tex] P(X < 4) = 0.000757 +0.0083+0.0407 +0.1160= 0.2626[/tex]
The following simple linear regression analyzes the relationship between the number of classes students are taking (the independent variable, labeled in the following output as X[,2]) and the number of books they have in their backpack (the response) at randomly chosen times. Assume all relevant assumptions are met. Which of the following are correct interpretations of the slope?
a. Each additional class a student takes is associated with about a 58.7% increase in the number of books in their backpack on average.
b. Each additional class a student takes is associated with about an additional 0.587 books in their backpack on average.
c. Taking an additional class causes students to carry 0.587 extra books with them on average.
d. The population average number of books in a studentâs backpack is 0.587.
Answer:
The answer is B.
Step-by-step explanation:
Why do we say that the answer is B?
For each additional class there is a significant increase that represents a minimum value over a total of books, that is, 100% that will always remain, therefore the increase will be an additional average over the other "books" that are already in backpack.
What is the value of X?
Answer:
x = 41 ft
Step-by-step explanation:
35(35+23) = 29(29+x)
2030 = 29(29+x)
70 = 29 + x
x = 41 ft
What is the average rate of change for this function for the interval from x= 1
to x = 3?
Answer:
The average rate of change is 12x=12.0x.
Description:
Function: x= 1x = 3 convert to short form: x 1x 3
Interval: x= 1 , x 3
Steps:
Input: Find the average rate of change of f(x)=3x2 on the interval [x,3x].
We have that a=x, b=3x, f(x)=3x2
Thus, f(b)−f(a)b−a=3((3x))2−(3(x)2)3x−(x)=12x.
Answer: the average rate of change is 12x=12.0x.
Please mark brainliest
Hope this helps.
Answer:
3
Step-by-step explanation:
A P E X
What are the names for the sides of a triangle?
Answer:
there are none
Step-by-step explanation:
a triangle its is own shape and does not have any name for each side.
Which of the following sequences is arithmetic? A 3, 9, 15, 21, 27, . . . B 3, 9, 17, 27, 39, . . . C 3, 9, 27, 81, 243, . . .
Answer:
A) 3, 9, 15, 21, 27, . . .
Step-by-step explanation:
EDGE 2020
Answer:
The second answer is 6.
Step-by-step explanation:
D=6
Find and of the function = − −( − ).
Answer:
Thats not possible
Step-by-step explanation:
There is no:
numbersvariablesonly negative signsYou have also been asked to set up the basket ball court what is the circumference of the circle
Answer: circumference of the circle is 11.31 meters
C=\pi d\\C=\pi (2r)\\C=2\pi r
Where radius (r) is half of diameter (d)
Since radius of the circle shown in 1.8m, we plug it in the formula and get:
C=2\pi r\\C=2\pi (1.8)\\C=11.31
So C = 11.31 meters
At a local college, 138 of the male students are smokers and are non-smokers. Of the female students, are smokers and are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers?
Answer:
The probability that both the male and female student are non-smokers is 0.72.
Step-by-step explanation:
The complete question is:
At a local college,178 of the male students are smokers and 712 are non-smokers. Of the female students,80 are smokers and 720 are nonsmokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers?
Solution:
Let, X denote the number of non-smoker male students and Y denote the number of non-smoker female students.
It is provided that:
X' = 178
X = 712
Tx = 890
Y' = 80
Y = 720
Ty = 800
Compute the probability of selecting a non-smoker male student as follows:
[tex]P (\text{Non-smoker Male student})=\frac{712}{890}=0.80[/tex]
Compute the probability of selecting a non-smoker female student as follows:
[tex]P (\text{Non-smoker Female student})=\frac{720}{800}=0.90[/tex]
Compute the probability that both the male and female student are non-smokers as follows:[tex]P(\text{Non-smoker Male and Female})=P(\text{Non-smoker Male})\times P(\text{Non-smoker Female})[/tex]The event of any female student being a non-smoker is independent of the male students.
[tex]P(\text{Non-smoker Male and Female})=0.80\times 0.90[/tex]
[tex]=0.72[/tex]
Thus, the probability that both the male and female student are non-smokers is 0.72.
After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 0.5 6/ (t+4)3 feet per year, where t is the time (in years)
(a) Find the number of feet that the tree will grow in the second year.
(b) Find the number of feet the tree will grow in the third year.
(c) The total number of feet grown during the second year is_____________ ft.
Answer:
a) 0.5367feetb) 0.5223feetc) 0.7292feetStep-by-step explanation:
Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).
The amount of growth can be gotten by integrating the given rate equation as shown;
[tex]\int\limits {0.5 + \frac{6}{(t+4)^{3} } } \, dt \\= \int\limits {0.5} \, dt + \int\limits\frac{6}{(t+4)^{3} } } \, dx } \, \\= 0.5t +\int\limits {6u^{-3} } \, du \ where \ u = t+4 \ and\ du = dt\\= 0.5t + 6*\frac{u^{-2} }{-2} + C\\= 0.5t-3u^{-2} +C\\= 0.5t-3(t+4)^{-2} + C[/tex]
a) The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from t =1 to t = 2
[tex]\int\limits^2_1 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_1\\= [0.5(2)-3(2+4)^{-2}] - [0.5(1)-3(1+4)^{-2}]\\= [1-3(6)^{-2}] - [0.5-3(5)^{-2}]\\ = [1-\frac{1}{12}] - [0.5-\frac{3}{25} ]\\= \frac{11}{12}-\frac{1}{2}+\frac{3}{25}\\ = 0.9167 - 0.5 + 0.12\\= 0.5367feet[/tex]
b) The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from t =2 to t = 3
[tex]\int\limits^3_2 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^3_2\\= [0.5(3)-3(3+4)^{-2}] - [0.5(2)-3(2+4)^{-2}]\\= [1.5-3(7)^{-2}] - [1-3(6)^{-2}]\\ = [1.5-\frac{3}{49}] - [1-\frac{1}{12} ]\\ = 1.439 - 0.9167\\= 0.5223feet[/tex]
c) The total number of feet grown during the second year can be gotten by substituting the value of limit from t = 0 to t = 2 into the equation as shown
[tex]\int\limits^2_0 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_0\\= [0.5(2)-3(2+4)^{-2}] - [0.5(0)-3(0+4)^{-2}]\\= [1-3(6)^{-2}] - [0-3(4)^{-2}]\\ = [1-\frac{1}{12}] - [-\frac{3}{16} ]\\= \frac{11}{12}+\frac{3}{16}\\ = 0.9167 - 0.1875\\= 0.7292feet[/tex]
The math SAT is scaled so that the mean score is 500 and the standard deviation is 100. Assuming scores are normally distributed, find the probability that a randomly selected student scores
Answer:
a. P(X>695)=0.026
b. P(X<485)=0.44
Step-by-step explanation:
The question is incomplete:
a. higher than 695 on the test.
b. at most 485 on the test.
We have a normal distribution with mean 500 and standard deviation of 100 for the test scores. We will use the z-scores to calculate the probabilties with the standard normal distribution table.
a. We want to calculate the probability that a randomly selected student scores higher than 695.
We calculate the z-score and then we calculate the probability:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{695-500}{100}=\dfrac{195}{100}=1.95\\\\\\P(X>695)=P(z>1.95)=0.026[/tex]
a. We want to calculate the probability that a randomly selected student scores at most 485.
We calculate the z-score and then we calculate the probability:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{485-500}{100}=\dfrac{-15}{100}=-0.15\\\\\\P(X<485)=P(z<-0.15)=0.44[/tex]
find the value of the expression :1/216^-2/3 + 1/256^-3/4 + 1/243^-1/5
Answer:
103
Step-by-step explanation:
A number to the power of a negative exponent, means 1 divided by that same number to the power of the positive exponent.
1/(216^(-2/3)) + 1/(256^(-3/4)) + 1/(243^(-1/5))
Break it apart into three pieces.
1/(216^(-2/3))
216^(2/3) = 36
1/(256^(-3/4))
256^(3/4) = 64
1/(243^(-1/5))
243^(1/5) = 3
So...
1/(216^(-2/3)) = 36
1/(256^(-3/4)) = 64
1/(243^(-1/5)) = 3
Add the numbers gives:
36 + 64 + 3 = 103
The system of equations above has solution (x,y).
What is the value of x ?
Answer: [tex]\frac{21}{4}[/tex]
Step-by-step explanation:
Multiply each side by 2 to get rid of the fraction on the right side. That basically gets rid of the 1/2 and the 2.
Youre now stuck with 2x + y = 21. They gave us y which is 2x. 2x + 2x = 4x
You now have 4x = 21
Divide each side by 4 to get x = 21/4
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0.18 and the probability that the flight will be delayed is 0.14. The probability that it
will not rain and the flight will leave on time is 0.74. What is the probability that the
flight would leave on time when it is not raining? Round your answer to the thousand
Answer:
0.902 = 90.2% probability that the flight would leave on time when it is not raining
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Not raining
Event B: Flight leaving on time.
The probability that it will rain is 0.18.
This means that there is a 1 - 0.18 = 0.82 probability of not raining. So [tex]P(A) = 0.82[/tex]
The probability that it will not rain and the flight will leave on time is 0.74.
This means that [tex]P(A \cap B) = 0.74[/tex]
What is the probability that the flight would leave on time when it is not raining?
[tex]P(B|A) = \frac{0.74}{0.82} = 0.902[/tex]
0.902 = 90.2% probability that the flight would leave on time when it is not raining
A family of five rents a kayak and splits the total time, k, equally. Each family member spent less than 25 minutes kayaking. Which values can be used to complete the math sentence below so that it accurately represents the situation?
Answer:
k ÷ 5 < 25
Step-by-step explanation:
Edg.
Answer:
k ÷ 5 < 25
Step-by-step explanation:
write (2n^2)^3 without exponents
Answer:
8n x n x n x n x n x n x n
Step-by-step explanation:
(2n^2)^3 = 8n^ 6
Now just write "n" 6 times and there you go
The given expression without exponents can be written as 8×n×n×n×n×n×n.
The given expression is (2n²)³.
We need to write the given expression without exponents.
What is an exponent?The exponent of a number shows how many times the number is multiplied by itself. For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times.
Now, the given expression can be simplified as follows:
(2n²)³=2³×(n²)³
=2×2×2×[tex]n^{6}[/tex] (∵[tex](a^{m}) ^{n}=a^{m\times n}[/tex])
=8×n×n×n×n×n×n
Therefore, the given expression without exponents can be written as 8×n×n×n×n×n×n.
To learn more about exponents visit:
https://brainly.com/question/219134.
#SPJ2
Question 14
For the following system of equations, determine how many solutions there are.
6x + y = -1 and -6x - 4y = 4
Answer:
The system of equations has a one unique solution
Step-by-step explanation:
To quickly determine the number of solutions of a linear system of equations, we need to express each of the equations in slope-intercept form, so we can compare their slopes, and decide:
1) if they intersect at a unique point (when the slopes are different) thus giving a one solution, or
2) if the slopes have the exact same value giving parallel lines (with no intersections, and the y-intercept is different so there is no solution), or
3) if there is an infinite number of solutions (both lines are exactly the same, that is same slope and same y-intercept)
So we write them in slope -intercept form:
First equation:
[tex]6x+y=-1\\y=-6x-1[/tex]
second equation:
[tex]-6x-4y=4\\-6x=4y+4\\-6x-4=4y\\y=-\frac{3}{2} x-1[/tex]
So we see that their slopes are different (for the first one slope = -6, and for the second one slope= -3/2) and then the lines must intercept in a one unique point. Therefore the system of equations has a one unique solution.
Estimate and then solve the equation. X - 17 4/5=-13 1/5
Answer: 5 (estimate)
Step-by-step explanation:
x - 17 4/5 = -13 1/5
Estimate: x - 18 = -13
x - 18 + 18 = -13 + 18
x = 5
actual answer without estimating using exact numbers is 4 3/5 (so estimate is reasonable)
Ms. Barclay orders birthday cupcakes for the month of June from an online vendor. Each cupcake costs $1.25 and there is a one-time delivery fee of $3.25. The total cost of the order is $14.50. How many cupcakes did Ms. Barclay order?
Answer:
Ms. Barclay ordered 9 cupcakes.
Step-by-step explanation:
$1.25x9=11.25
11.25+3.25=$14.50
Evaluate each expression. 16 5/4 x 16 1/4 / (16 1/2)/2=
Answer: the answer is 4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
4 on edgunity 2020
Elena has a bottle that has a capacity of 34 quarts. What is the maximum amount of liquid that can be stored in this bottle?
A clothing store determines that in order to sell x shirts, the price per shirt should be p(x)=100−x dollars. Getting x shirts from the supplier costs the store C(x)=1,600+20x dollars. If the store’s revenue from selling x shirts is R(x)=x⋅p(x), for what value of x will the store’s cost and revenue be equal?
Answer:
x= -40
Step-by-step explanation:
Cost
C(x)=1,600+20x
P(x)=100-x
Revenue=x*p(x)
=x*(100-x)
=100x-x^2
Cost=Revenue
1600+20x=100x-x^2
1600+20x-100x+x^2=0
1600-80x+x^2=0
Solve using quadratic formula
Formula where
a = 1, b = 80, and c = 1600
x=−b±√b2−4ac/2a
x=−80±√80^2−4(1)(1600) / 2(1)
x=−80±√6400−6400 / 2
x=−80±√0 / 2
The discriminant b^2−4ac=0
so, there is one real root.
x= −80/2
x= -40
Chen spent 7 hours at school on Friday he spent 30 minutes at lunch 50 minutes at a school assembly and the rest in class how much time did Chen spend in class
Answer:
5 hours and 40 minutes would be class
Step-by-step explanation:
We know that the total time is 7 hours, which in minutes would be:
7 * 60 = 420
420 minutes would be class, now, we subtract the other times that are not to be in class and it would be:
420 - 30 - 50 = 340
So we could say that in class it takes 340 minutes, and if we spend hours it would be:
340/60 = 5.67 hours or also 5 hours and 40 minutes would be class.
Balu and Pumba shared 2/3 of a cake. Balu got to eat three times as much cake as Pumba. What fraction of the whole cake did Balu eat?
Pleas answer help and answer correctly.
Answer:
In fraction, Balu ate 1/2 of the whole cake
Step-by-step explanation:
Balu and Pumba shared 2/3 of a cake.
Balu eats three times as much cake as Pumba.
So let's take the 2/3 they shared as a whole.
Let's Balu share be x
And pumbs share be y
X = 3y
But x + 3y = 2/3
Since x = 3y
Y = x/3
x + x/3 = 2/3
4x/3 = 2/3
X = (2*3)/(4*3)
X = 2/4
X = 1/2
Balu ate half of the whole cake
In fraction, Balu ate 1/2 of the whole cake
Can anyone help???????
Answer:
80
Step-by-step explanation:
For every additional 10 hrs, you get 200 more dollars.
A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is this distance?
Answer:
150
Step-by-step explanation:
If you draw a diagram, this will be a rectangle and the line across cuts it into a right triangle, with a base of 120 and a height of 90. The need to know the length of the hypotenuse of the triangle, so we can use the pythagorean theorem.
90^2 + 120^2 = c^2
c=150
a cereal box is an example of a
Answer: recantagle
Step-by-step explanation:
A college job placement center has requests from five students for employment interviews. Three of these students are math majors, and the other two students are statistics majors. Unfortunately, the interviewer has time to talk to only two of the students. These two will be randomly selected from among the five. What is the sample space for the chance experiment of selecting two students at random
Answer:
Step-by-step explanation:
The following is the information provided
number of students is 5
The number of math major = 3
The number of statistic major = 2
Label math students as A, B, C
And statistic students as D, E
The total number of ways to select two students from 5 students is 10
The sample space is S = {AB,AC,BC,AD,AE,BD,BE,CD,CE,DE}
Yes , in the sample space the events are equally alike
What is the probability that both selected students are statistics majors
The selected students of statistic major are DE
the probability that both selected students are statistics majors is [tex]\frac{1}{10}[/tex]
= 1/10
What is the probability that both students are math majors
The selected students of statistic major are AC,AB,BC
the probability that both selected students are math majors is [tex]\frac{3}{10}[/tex]
= 3/10
What is the probability that at least one of the students selected is a statistics major
Number of ways to select at least one of the students selected is a statistic major is {AD,AE,BD,BE,CD,CE,DE}
the probability that at least one of the students selected is a statistics major is [tex]\frac{7}{10}[/tex]
7/10
What is the probability that the selected students have different majors
Number of ways to select students with different major is {AD,AE,BD,BE,CD,CE,}
the probability that the selected students have different majors is [tex]\frac{6}{10}[/tex]
6/10
On a recent trip, Lamar's distance varied directly with the number of hours he drove. He traveled 288 miles in 6 hours. Which equation shows Lamar's distance, d, based on the number of hours, h, he drove?
(A) d = 6h
(B) d = 50h
(C) d = 48h
(D) d = 288h
Answer:
d = 48 h
Step-by-step explanation:
Lamar's distance traveled is directly proportional to the number of hours be drove.
So distance (d) ∝ hours (h)
Lamar traveled 288 miles in 6 hours
Since d ∝ h
then d = kh [ where k is the proportionality constant ]
if 288 = k × 6
k = =288/48
Therefore, equation will be d = 48 h will be the equation
A marketing analyst randomly surveyed 150 adults from a certain city and asked which type of tooth paste they were currently using - Extra Whitening or Regular. 96 said they were currently using Extra Whitening while the rest said they were using Regular. The analyst wants to determine if this is evidence that more than half of the adults in this city are using Extra Whitening. Suppose a p-value from the correct hypothesis test was 0.0003. Which of the following is a correct interpretation of this p-value?
A. HA: p_extra White > p_Regular.
B. HA: p > 0.5, where p = the proportion of all adults in this city using Extra Whitening.
C. HA: p = 0.64, where p = the proportion of all adults in this city using Extra Whitening.
D. HA: p=0.5, where p = the proportion of all adults in this city using Extra Whitening.
3. The difference between two numbers is 5
Answer:
The difference of two numbers is 5 and the difference of their reciprocals is 1/10. find the no.s
Step-by-step explanation:
⇒ x(x-5) = 50
⇒ x2 - 5x - 50 = 0
⇒ x2 - 10x + 5x - 50 = 0
⇒ x (x - 10) + 5 (x - 10) = 0
⇒ (x+5) (x-10) = 0
⇒ (x+5) (x-10) = 0
⇒ x = -5 or 10
⇒ x = 10 (x = -5 , rejected)