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]
Enter the value of b when the expression 9x + b is equivalent to
3(3x + 1).
BE
ker notes
Answer:
b = 3
Step-by-step explanation:
Isolate the variable, b. Note the equal sign, what you do to one side, you do to the other:
First, distribute 3 to all terms within the parenthesis:
3(3x + 1) =
3 * 3x = 9x
3 * 1 = 3
9x + b = 9x + 3
Isolate the variable, b. Subtract 9x from both sides:
9x (-9x) + b = 9x (-9x) + 3
b = 3
3 is your value for b.
~
What number is 40% of 720
Answer:
the answer should be 288
Answer:
288
Step-by-step explanation:
To solve this, you divide 40% by 100.
= (40% / 100) x 720
Then you multiply 0.4 by 720.
= 0.4 x 720
= 288
Find the area of the polygon shown
Answer:
18 feet
Step-by-step explanation:
(1*4)/2 = 2 (area of right triangle)
4*4=16 (area of square)
2+16=18
The tables below show the values of Y for different values of X
Answer:
Option D
Step-by-step explanation:
Rate of change of a linear function between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
Rate of change 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
From the given table,
Rate of change of the function between (-2, 6) and (-4, 9),
Rate of change 'm' = [tex]\frac{9-6}{-4-(-2)}[/tex]
m = [tex]\frac{3}{-2}[/tex]
Initial value = y-intercept
Let the equation of the line passing through a point (h, k) is,
y - k = m(x - h)
If a point (-2, 6) is lying on the graph of the function,
y - 6 = [tex]-\frac{3}{2}(x+2)[/tex]
y = [tex]-\frac{3}{2}x-3+6[/tex]
y = [tex]-\frac{3}{2}x+3[/tex]
Y-intercept of the function = 3
Therefore, initial value of the function = 3
Option D is the answer.
how many meters are equal to 5,253 centimeters? use how the placement of the decimal point changes when dividing by power of 10 to help you
Answer:
[tex]52.53\ \text{meters}[/tex]
Step-by-step explanation:
[tex]1\ \text{meter}=100\ \text{centimeter}[/tex]
[tex]1\ \text{centimeter}=\dfrac{1}{100}\ \text{meter}[/tex]
In the question the quantity that is required to be converted to meters is 5253 centimeters.
[tex]5253\ \text{cm}=5253\times \dfrac{1}{100}\\ =52.53\ \text{meters}[/tex]
So, the required measurement in meters is [tex]52.53\ \text{meters}[/tex].
Tyler has to savings accounts that his grandparents opened for him . One of the accounts Pay 8% annual interest Where as the other pay 10% annual interest. If you have $700 more invested at 10% then you invested at 8%, how much do you have invested in each account If the total amount of interest You earn in a year is $106?
Tyler invested $___at 8%, and $___at 10%
GIVING BRAINLIEST, A THANKS, 5 STAR RATING, AND A SHOUTOUT IN MY NEXT QUESTION. PLEASE PLEASE HELP. THANKEW!
How many different triangles with sides of measurements of 3, 4, and 5 are there? Please, please help. RSM. :D Thankew!
Step-by-step explanation:
x2 – 12x = 39
Please help me solve this! I need the answer ASAP
Answer:
x = 6 ± 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given
x² - 12x = 39
Using the method of completing the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(- 6)x + 36 = 39 + 36
(x - 6)² = 75 ( take the square root of both sides )
x - 6 = ± [tex]\sqrt{75}[/tex] = ± 5[tex]\sqrt{3}[/tex] ( add 6 to both sides )
x = 6 ± 5[tex]\sqrt{3}[/tex] ← solutions in exact form
Answer:
x = 6 ± 5* OR 6 - 5*
Step-by-step explanation:
In decimal form it would be either 14.66025403... or -2.66025403
Hope this helps!
Trucks in a delivery fleet travel a mean of 90 miles per day with a standard deviation of 36 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives less than 118 miles in a day. Round your answer to four decimal places.
Answer:
0.7823 = 78.23% probability that a truck drives less than 118 miles in a day.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Trucks in a delivery fleet travel a mean of 90 miles per day with a standard deviation of 36 miles per day.
This means that [tex]\mu = 90, \sigma = 36[/tex]
Find the probability that a truck drives less than 118 miles in a day.
This is the pvalue of Z when X = 118. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{118 - 90}{36}[/tex]
[tex]Z = 0.78[/tex]
[tex]Z = 0.78[/tex] has a pvalue of 0.7823
0.7823 = 78.23% probability that a truck drives less than 118 miles in a day.
A limo weighs 3 tons, 1,000 pounds. How many pounds does the limo weigh?
Note: 1 ton = 2,000 pounds
Answer:
2000 times 3 = 6000 + 1000 = 7000 pounds
Could someone help me with with 6-10??
Answer:
You need a protractor
Step-by-step explanation:
to measure the angles
Assume v is a vector in R^5. You wish to compute a vector w such that the th entry of w, denoted wi, is the sum of vi-1,vi, vi+1. For example wi is the sum of ,vo,v1 and v2. For elements at the endpoints of w, you will only account for two elements in your sum. For example wo, (assuming zero-based indexing) is the sum of vo and v1. Construct a matrix A such that Av=w.
Answer:
Use the drawing tools to form the correct answer on the graph.
Graph the line that represents this equation:
Step-by-step explanation:
Estimate 4/5x6/7
I WIL MARK BRAINLIEST IF ITS THE BEST ANSWER
Answer:
Simplify x6/7
4/5 x x6/7
Simplify 4/5
4/5 x x6/7
Finally the answer
4x6/35
how many miles is 2 hours
Answer:
if you go 70 miles in one hour you will go 140 miles in 2 hours
Step-by-step explanation:
Answer:
You need to be traveling at a certain speed to determine how many miles you travel in 2 hours. For example, if you go 70 miles in 1 hour, then you'll go 140 miles in 2 hours, as long as your speed is constantly 70 mph.
The height (in inches) of males in the United States is believed to be Normally distributed. The average height of a random sample of 50 American adult males is 69.72 inches and the standard deviation of the 50 heights is s = 4.23. The best pint estimate for the average height if males in the United States is_____inches. Give answer to the hundredths place.
Answer:
69.72 inches.
Step-by-step explanation:
The best point estimate for the average height if males in the United States is...
For large samples, as we have here, the best point estimate is the sample mean. In this question, the sample mean is of 69.72 inches, so the answer is 69.72 inches.
[tex] {x}^{2} - 9 \: {x }^{2} + x - 2[/tex]
how do i do this?
A circle has a diameter of 7 inches. Find the radius
Answer:
radius= 3.5 in
Step-by-step explanation:
Answer: 3.5
Step-by-step explanation:
The diameter is the length from one side of the circle to the other the radius is half that
pls help with math that’s attached
Answer:
TU = 28.5
Step-by-step explanation:
The triangles are congruent because of side-angle-side
TU = VU because corresponding sides of congruent triangles are congruent.
so:
3x + 9 = 7x - 17
simplify:
4x = 26
x = 6.5
TU = 3(6.5 + 9) = 19.5 + 9 = 28.5
Answer:
3x+9=7x-17
26 = 4x
x=6.5
TU:28.5
1. Find the degree measure and the length of arc AB:
120°
20 in.
Answer:
Degree measure of arc AB = 120°
Length of arc = 41.9 in.
Step-by-step explanation:
✔️Measure of Central angle is the same as Measure of the intercepted arc
Therefore,
Degree measure of arc AB = 120°
✔️Length of arc = [tex] \frac{\theta}{360} * 2 \pi r [/tex]
[tex] \theta = 120 [/tex]
r = 20 in.
Length of arc = [tex] \frac{120}{360} * 2 \pi * 20 [/tex]
= 41.887902
Length of arc = 41.9 in. (Nearest tenth)
Whoever responds first will get marked Best.
The amount of wallpaper needed to cover the wall is an example of which
A: area
B: volume
C:perimeter
D:length
Answer:
A area
Step-by-step explanation:
help me please ! !!!!!
Answer:
24Step-by-step explanation:
[tex]m < a = \frac{mde - mbc}{2} [/tex]
[tex] = \frac{119 - 71}{2} [/tex]
[tex] = \frac{48}{2} [/tex]
[tex]answer = 24[/tex]
hope it helps you
have a great day!!
In ΔKLM, l = 7 inches, k = 9.5 inches and ∠K=54°. Find all possible values of ∠L, to the nearest 10th of a degree.
Answer: 36.6
Step-by-step explanation: did on delta math
What are the vertices of AA'B'C'if AABC is dilated by a scale factor of 2? V ACO, 10) 10 00 6 B(8,6) 4 2 C(4,2) th 2 6 8 10 A. A' (0,5), B'(4,3), C' (2, 1) B. A' (0,10), B' (16,6), C' (8, 2) O C. A' (0,20), B'(8, 12), C'(4,4) D. A'(0,20), B (16,12). C'(8,4) < PREVIOUS Type here to search
Answer:
[tex]A' = (0,20)[/tex]
[tex]B' = (16,12)[/tex]
[tex]C' = (8,4)[/tex]
Step-by-step explanation:
Given
[tex]A = (0,10)[/tex]
[tex]B =(8,6)[/tex]
[tex]C=(4,2)[/tex]
[tex]k = 2[/tex] --- scale factor
Required
The coordinates of A'B'C'
This is calculated as thus:
[tex]A'B'C' = ABC * k[/tex]
So, we have:
[tex]A' = (0,10) * 2[/tex]
[tex]A' = (0,20)[/tex]
[tex]B' = (8,6) * 2[/tex]
[tex]B' = (16,12)[/tex]
[tex]C' = (4,2)*2[/tex]
[tex]C' = (8,4)[/tex]
the measures of the angles of a triangle are shown below. solve for x
Answer is in the file below
tinyurl.com/wpazsebu
Answer:
X = 3
Step-by-step explanation:
All you do is add the angles up and set them equal to 180.
HELPP ASAPPP
The rectangular prism shown is made up of cubes that measure 1/8 inch on each side. What is the volume, in cubic inches, of the rectangular prism?
Answer:
3/8
Step-by-step explanation:
3/4*1/2=3/8
3/8*1=3/8
*=multiply
Is 2(6 - 3x) + x equivalent to 2(3x) + x?
Answer:
No.
Step-by-step explanation:
2(6-3x)= 12-6x and 2(3x)+x= 7x
write the following mathematical expressions in simplest form 3.5 m + 2 (0.6 M - 5) + 4
Answer:hamburger
Hamburger
Step-by-step explanation:hamburger
Hamburger
solution to 3x+4=3x+4
The results can be shown in multiple forms;
4 = 4, All real numbers, Always true, Interval notation: (-∞,∞).
Move all terms containing [tex]x[/tex] to the left side of the equation.
[tex]Subtract\\3x+4-3x=4\\[/tex]
Combine the opposite terms in [tex]3x+4-3x[/tex]
[tex]Subtract\\3x from 3x.\\\\0+4=4\\\\Add\\0+4=4 \\4=4*[/tex]
Since [tex]4=4[/tex] the equation will always be true.
Which expression is equal to 97/33 ?
Answer:
2 31/33
Step-by-step explanation:
Answer:
=2.93939393
Step-by-step explanation:
97/33
=2.93939393
is the table linear or not
Answer:
No, the table is not linear.
Step-by-step explanation:
Between the x and y there has to be a constant rate. There is no constant rate.