Answers
Answer:
Step-by-step explanation:
a) (3,5)
b) 3 units
c) 10 units
Hope that helps!
Related Questions
Suppose that an appliance is constructed in such a way that it requires that n independent electronic components are all functioning. Assume that the lifespan of each of these, Tj, is an exponential random variable with parameter λj.
a. Let X be the random variable giving the lifespan of the appliance. Find the CDF and PDF for X.
b. Find the expected value of X.
c. Now find the median lifespan of the appliance (that is, the time t at which half of the appliances are likely to have broken and half to be working ).
Answers
Answer:
Step-by-step explanation:
[tex]T_j \sim exp ( \lambda j) \ \ \ j = 1 (1) n \\ \\ f_{Tj}(tj) = \lambda j e^{-\lambda j tj } , tj>0 \\ \\ P\Big[ Tj> x\Big] = \int \limits ^{\infty}_{x} \lambda j e^{-\lambda j tj}\ dtj \\ \\ = e^{-\lambda j x}, x > 0 \\ \\ \\ \\ a) F_x (x) \\ \\ = P[X \le x ] \\ \\ = 1 - P[X> x] \\ \\ = 1 - \pi \limits ^{n}_{j =1} \Big\{ P[T_j > x ] \Big \}[/tex]
[tex]\text{This is because the appliance has the capacity to work for more than (x) }[/tex][tex]\text{hours if and only if all the "n" components work more than (x) hours.}[/tex]
[tex]\text{Then:}[/tex]
[tex]= 1 - e \ \pi^{n}_{j=1} \ e^{-\lambda j x} \\ \\ = 1 - e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}[/tex]
∴
[tex]CDF = 1 - e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ x>0[/tex]
[tex]PDF =\Big( \sum \limits ^{n}_{j =1} \lambda j\Big) e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ x>0[/tex]
[tex]f_x(x) = \Big( \sum \limits ^{n}_{j =1} \lambda j\Big) e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ x>0[/tex]
(b)
[tex]E(x) = \int \limits ^{\infty}_{o }x f_x (x) \ dx \\ \\ = \int \limits ^{\infty}_{o }x \ \Big( \sum \limits ^{n}_{j =1} \lambda j\Big) e^{- (\sum \limits ^{n}_{j=1} \lambda j)x}\ , \ dx[/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j=1} \lambda j} \ \ \int \limits ^{\infty}_{o} \Big [(\sum \limits ^n_{j=1} \lambda j )x \Big] e ^{-\Big ( \sum \limits ^{n}_{j=1} \lambda j \Big)x} \ \ d \Big( x \sum \limits ^n_{j=1} \lambda j \Big)[/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j= 1} \lambda j} \int \llimits ^{\infty}_{o} t e^{-t} \ dt[/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j= 1} \lambda j} \int \llimits ^{\infty}_{o} t e^{-t} \ dt \ \ \ \ \text{\Big[By transformation }t =( \sum \limits ^n_{j=1} \lambda j )x \Big][/tex]
[tex]= \dfrac{1}{\sum \limits ^n_{j= 1} \lambda j}[/tex]
(c)
[tex]Let \ \ l_y_{\dfrac{1}{2}} \text{ be the median}[/tex]
∴
[tex]F(l_y_{\dfrac{1}{2}}) = \dfrac{1}{2} \\ \\ 1 - e ^{-\Big (\sum \limits ^{n}_{j=1} \lambda j \Big)} {l_y}_{\frac{1}{2}} = \dfrac{1}{2} \\ \\ \dfrac{1}{2} = e^{-\Big (\sum \limits ^{n}_{j=1} \lambda j \Big) } {l_y}_{\frac{1}{2}} \\ \\ - In 2 = {-\Big (\sum \limits ^{n}_{j=1} \lambda j \Big)} {l_y}_{\frac{1}{2}} \\ \\ \\ \\ \mathbf{ {l_y}_{\frac{1}{2}} = \dfrac{ In \ 2}{\sum \limits ^{n}_{j=1} \lambda j }}[/tex]
The height of a thrown ball is a quadratic function of the time it has been in the air. The graph of the quadratic function is the parabolic path of the ball.The vertex of the graph is (1, 20) and the path of the ball includes the point (0,4). What is an expression that defines this function? Write the quadratic function in vertex form.
Answers
Answer:
f(x) = a(x - 1) + 20
Step-by-step explanation:
Vertex form is written in this format: f(x) = a(x - h) + k. The vertex point is written in the form (h,k). To write the vertex in the equation, fill in the digits where they belong.
Hope it helps!
The ball's parabolic route is represented by the quadratic function's graph. The quadratic function is x²-2x+4=0.
Given that,
A thrown ball's height is a quadratic function of the amount of time it has been in the air. The ball's parabolic route is represented by the quadratic function's graph. The ball's route includes the location (1, 20), which is the graph's vertex (0,4).
We have to find what does the expression for this function look like? In vertex form, write the quadratic function.
What is the vertex form of a parabola?Use y= a(x-h)² + k as the vertex form of a parabola.
(The parabola opens upward if "a" is positive and downward if "a" is negative.) Additionally, the vertex of the (h,k) is a parabola.
The vertex of the parabola (h,k) is (1,20)
The a value is 4 and y as 0.
y=a(x-h)²+k
0=4(x-1)²+20
0=4(x²-2x+1)+20
0=4x²-8x-4+20
0=4x²-8x+16
4x²-8x+16=0
x²-2x+4=0
Therefore, the quadratic function is x²-2x+4=0.
To learn more about quadratic visit: https://brainly.com/question/22364785
#SPJ2
Plz help quick I will give brainly points
Answers
Can somebody help me plsssss
Answers
5,0 is not a solution to the system of linear inequalities.
In a pre-election poll, 58% of a large random sample of voters responded as planning to vote for the school enhancement millage. A 95% confidence interval was computed for the proportion of all such voters who plan to vote for the school enhancement millage. Review each of the following statements regarding the meaning of the 95% confidence level. Determine if it is a correct (true) meaning or incorrect (false).
Answers
Answer: Hello the statement related to your question is missing attached below is the statement
answer : The statement is false
Step-by-step explanation:
The statement is false
This is because a confidence interval gives a range of values for an unknown parameter.
A 95% confidence interval is calculated and it gives a lower and upper limit in which the 58% of the voters can fall into i.e. The 58% of voters can fall within the upper and lower limit of the 95% confidence interval and not exactly 95% . Hence the statement is false.
Complete the table following the linear function rule. I don’t know what to do at all.
Answers
Answer:
-2, 1, 4
Step-by-step explanation:
What's all equivalent to 7/8
Answers
Answer:
0.875?
Step-by-step explanation:
I just did 7 divided by 8
Answer:
14/16
49/56
Step-by-step explanation:
I looked it up for you!!!
Exercise 8.3.4: Selecting coders for 3 different projects. About (a) A manager must select three coders from her group to write three different software projects. There are 7 junior and 3 senior coders in her group. The first project can be written by any of the coders. The second project must be written by a senior person and the third project must be written by a junior person. How many ways are there for her to assign the three coders to the projects if no person can be assigned to more than one project
Answers
Answer:
168 ways
Step-by-step explanation:
Given
[tex]Junior = 7[/tex]
[tex]Senior = 3[/tex]
Required
Number of ways 3 project can be assigned
Starting with the second project.
This can be assigned to only senior coders
So:
[tex]n_1 = 3[/tex]
Then, the third project.
This can be assigned to only junior coders
So:
[tex]n_2 = 7[/tex]
At this point, we are left with 2 senior coders and 6 junior coders
Since the first can be assigned to anybody.
[tex]n_3 =2+ 6[/tex]
[tex]n_3 =8[/tex]
The number of selection is then calculated as:
[tex]n = n_1 * n_2 * n_3[/tex]
[tex]n = 3 * 7 * 8[/tex]
[tex]n = 168[/tex]
Mike needs to buy a water tank. The tank must fit inside a storage box that is shaped like a cube with the side lengths of 30 feet. Water tanks are available in cylinders, cones, square pyramids, and spheres. Mike wants to buy the tank that has the largest capacity. What shape tank should Mike buy?
Answers
Answer:
sphere
Step-by-step explanation:
sphere has a larger volume
On a map, the distance of two inches is equal to ten miles. How many
miles does 4 inches represent on the map?
10
20
30
40
Answers
identify each coefficient for 3m. this question is on my homework what Is the answer?
Answers
Answer: 3
Step-by-step explanation: The number in front of your variable is called your coefficient so we say that 3 is the coeficient.
Make sure to understand that a variable
is just a letter that represents any number.
Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Answers
Answer:
d≈21.99
Step-by-step explanation:
HELP PLEASE I NEED HALP
Answers
Answer:
16
Step-by-step explanation:
8x2
Ali's dog weighs 8 times as much as her cat together the two pets weigh 54 lb how much does Ali's dog weigh
Answers
Answer:
48
Step-by-step explanation:
Cat = x
Dog = 8x
x + 8x = 54
9x = 54
x = 6, Dog = 8 * 6 = 48
Solve for x In the equation.
Answers
Answer:
x = 16
Step-by-step explanation:
[tex] \frac{2x - 5}{x + 8} = \frac{22.5}{20} [/tex]
Cross multiply
[tex] (2x - 5)*20 = (x + 8)*22.5 [/tex]
[tex] 40x - 100 = 22.5x + 180 [/tex]
Collect like terms
40x - 22.5x = 100 + 180
17.5x = 280
Divide both sides by 17.5
x = 280/17.5
x = 16
Trisha and Beth are going to play a couple video games. Trisha has her favorite and beth has adifferent favorite. if 2 games are chosen at random out of the total games, what is the chance that both of their favorites are chosen?
Answers
Answer:
2/12 or 1/6
Step-by-step explanation:
12 games total
they have 2 games that are there favorite
PLEASE HELP ME ITS URGENT ❗❗❗❗❗❗❗❗❗❗❗
Answers
Answer: W is your answer :)
Step-by-step explanation:
A line that includes the point (7,0) has a slope of 1. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
Step-by-step explanation:
i think that the equations might be y = x - 7
Whoever responds first will get marked Best!
Elizabeth's family pool is 25 feet long, 15 feet wide and 10 feet deep. The pool has to be filled. What is the volume of water they should put in the pool?
Part A Explain the steps you would take to find the volume of the pool.
Part B. What is the volume of the water in the pool?
a. 3750 ft
B.50 ft
c. 3375 ft
d. 3755 ft
Answers
Answer:
Part A:
I would multiply the length, width, and depth of the pool to find the volume of it. That would be how much water can fit inside. 25 ft x 15 ft x 10 ft = 3750 ft
Part B:
a. 3750 ft
A shape is made of 9 right triangles of equal size and three identical rectangles. Each rectangle measures 7 mm wide and 3 mm high. What is the total area, in square mm of the shape?
Answers
Answer:
21
Step-by-step explanation:
ill mark brainlist plss help
Answers
Answer:
Hey mate.....
Step-by-step explanation:
This is ur answer....
○ 28 cm2Hope it helps!
Mark me brainliest pls....
Follow me! ;)
Wayne charges the following for repairing washing machines:
£28 call-out charge + £16 for each half-hour he spends on the repair
If a repair costs £76, how long did it take?
Answers
48/16= 3
1hr and a half
A manufacturer of cream filled donuts collected data from its automatic filling process. The amount of cream inserted into the donuts is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 donuts. The correct value of t to construct a 90% confidence interval for the true mean amount of cream filling is _______.
Answers
Answer:
The appropriate solution is "1.7109". A further explanation is provided below.
Step-by-step explanation:
The given values are:
Sample size,
n = 25
Degree of freedom,
[tex]df=n-1[/tex]
[tex]=25-1[/tex]
[tex]=24[/tex]
At 90% confidence level,
[tex]\alpha=1-90 \ percent[/tex]
[tex]=1-0.9[/tex]
[tex]=0.1[/tex]
and,
[tex]\frac{\alpha}{2}=\frac{0.1}{2}[/tex]
[tex]=0.05[/tex]
Now,
The correct values of t will be:
= [tex]t_{\frac{\alpha}{2}, df }[/tex]
= [tex]t_{0.05,24}[/tex]
= [tex]1.7109[/tex]
please help me with this :)))
Answers
Answer:
C, 33 1/3%
Step-by-step explanation:
Because there are only two even number that follow this rule: 2<x≥6, and since there are only 6 possible outcomes, the probabilty is 2/6, which is 1/3. In a percent form, this is 100%*2/3, or 33 1/3%.
slove for q: q/10 = 4
Answers
Answer:
4
Step-by-step explanation:
Answer:
1/10 = 4
Step-by-step explanation:
if 25,m+1,35 are arithmetic sequence then find the value of m
Answers
Answer:
m = 29
Step-by-step explanation:
You are counting by fives.
25, 30, 35
m + 1 = 30
m + 1 - 1 = 30 - 1
m = 29
25, (29 + 1), 35
25, 30, 35
The value of m is equal to 29
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.
We are counting by fives.
m + 1 = 30
Now subtract 1 on both sides;
m + 1 - 1 = 30 - 1
m = 29
Thus substituting the value to find other terms;
25, (29 + 1), 35
The sequence is
25, 30, 35
Learn more about arithmetic sequence here:
https://brainly.com/question/3702506
#SPJ2
The Total cost to rent 5 chairs and 3 tables is $31 dollars. What is the cost to rent each chair and each table? No links please
Answers
Answer:
b
Step-by-step explanation:
180 students in a 10th grade class high school take a survey about which video game consoles they own. 80 students answer that one of the consuls is a PlayStation 90 answer that one of the consules is an Xbox out of these there are 30 who are both systems > continue reading on picture pls help very important
Answers
Answer:
Ur answer is in attachment
Step-by-step explanation:
please mark me as brainliest
The probability that a student has both box and a console is 1/6 and the P(B/A) = 0.378
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here, the number of students with both video games is 30 thus
The probability that a student has both box and a console is 30/180=1/6
And the conditional probability P(B/A) is = 1/6/0.44
= 0.378
Hence, The probability that a student has both box and a console is 1/6, and the P(B/A) = 0.378
Learn more about probability here:
https://brainly.com/question/30034780
#SPj2
Carl has visited 49 of the 50 states.
What percent of the states has he visited?
Need help quick
Answers
Answer:
98%
Step-by-step explanation:
helppppppppppppppppppppp
Answers
Answer:
26 square feet
Step-by-step explanation:
I dont know if this is right