The lifetime in months of a transistor in a certain application is random with probability density function:
f(x) = {0.4e^-0.4x, x>0 0, x<0
a. Compute the mean lifetime.
b. Compute the standard deviation of the lifetimes.
c. Compute the cumulative distribution function of the lifetime.
d. Compute the probability that the lifetime will be less than 6 months.
e. Compute the 60^th percentile of the lifetime.
Answer:
Explained below.
Step-by-step explanation:
The probability density function of lifetime in months of a transistor in a certain application is:
[tex]f(x)=0.4\cdot e^{-0.4x};x>0[/tex]
The probability density function suggests that the random variable X follows a exponential function with parameter λ = 0.4.
(a)
Compute the mean lifetime as follows:
[tex]\mu=\frac{1}{\lambda}=\frac{1}{0.40}=2.5[/tex]
Thus, the mean lifetime is 2.5 months.
(b)
Compute the standard deviation of the lifetimes as follows:
[tex]\sigma=\sqrt{\frac{1}{\lambda^{2}}}=\sqrt{\frac{1}{0.40^{2}}}=2.5[/tex]
Thus, the standard deviation of the lifetimes is 2.5 months.
(c)
The cumulative distribution function of the lifetime is:
[tex]CDF=1-e^{-0.40x}[/tex]
(d)
Compute the probability that the lifetime will be less than 6 months as follows:
[tex]P(X<6)=\int\limits^{6}_{0} {0.40\cdot e^{-0.40x}} \, dx[/tex]
[tex]=0.40\times [\frac{e^{-0.40x}}{-0.40}]^{6}_{0}\\\\=-1\times [e^{-0.40\times6}-e^{-0.40\times0}]\\\\=-0.090718+1\\\\=0.909282\\\\\approx 0.9093[/tex]
Thus, the probability that the lifetime will be less than 6 months is 0.9093.
(e)
Compute the 60th percentile of the lifetime as follows:
[tex]P(X<x)=0.60\\\\\int\limits^{x}_{0} {0.40\cdot e^{-0.40x}} \, dx=0.60\\\\0.40\times [\frac{e^{-0.40x}}{-0.40}]^{x}_{0}=0.60\\\\-1\times [e^{-0.40\times x}-e^{-0.40\times0}]=0.60\\\\1-e^{-0.40x}=0.60\\\\e^{-0.40x}=0.40\\\\-0.40x=\ln(0.40)\\\\-0.40x=-0.916291\\\\x=2.2907275\\\\x\approx 2.3[/tex]
Thus, the 60th percentile of the lifetime is 2.3 months.
I have ti find the two solutions to this equation. This problem deals with imaginary numbers i
[tex] {3x}^{2} - x + 4 = 0[/tex]
Answer:
[tex] x = \dfrac{1}{6} + \dfrac{i\sqrt{47}}{6} [/tex] or [tex] x = \dfrac{1}{6} - \dfrac{i\sqrt{47}}{6} [/tex]
Step-by-step explanation:
Use the quadratic formula.
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4(3)(4)}}{2(3)} [/tex]
[tex] x = \dfrac{1 \pm \sqrt{1 - 48}}{6} [/tex]
[tex] x = \dfrac{1 \pm \sqrt{-47}}{6} [/tex]
[tex] x = \dfrac{1}{6} \pm \dfrac{i\sqrt{47}}{6} [/tex]
[tex] x = \dfrac{1}{6} + \dfrac{i\sqrt{47}}{6} [/tex] or [tex] x = \dfrac{1}{6} - \dfrac{i\sqrt{47}}{6} [/tex]
solve each system by substitution. 5) y=-2
4x - 3y = 18
Answer:
x = 3
y = − 2
Step-by-step explanation:
Tommy is purchasing items from an online store. The store charges $6 shipping and handling for each package. Write an expression to represent the total shipping costs. How much will Tommy pay in shipping and handling for 2 packages? (use x as the variable) When entering your answers use only numbers a lower case x and No spaces The equation that represents this scenario is The shipping and handling for 2 packages would be dollars. (only put the number please)
Answer:
The expression to represent the total shipping costs for x package is 6x.
Tommy will pay $ 12 in shipping and handling for 2 packages.
Step-by-step explanation:
Given that the shipping and handling charge for 1 package = $ 6
So, by using the elementary method, the shipping and handling charge for x package is $ 6x.
Hence, the required expression to represent the total shipping costs for x package is 6x.
For 2 package, x=2
So, the shipping and handling charge for 2 package
=6x2
=12.
So, Tommy will pay $ 12 in shipping and handling for 2 packages.
What’s two times to.
Answer:
4
Step-by-step explanation:
Basic times tables
Answer:
4
Step-by-step explanation:
2+2
=
4
I hope this helps!
guys hurry i have a starter
idk what the answer
Answer:
The letter E
HOPE THIS HELPS YOU Do mark as brainliestThe value in dollars, f(x), of a certain car after x years is represented by the equation f(x) = 25,000(0.86)^x. To the nearest dollar, how much more is the car worth after 2 years than after 3 years?
a. $18,490
b. $34, 391.40
c. $15,901.40
d. $2,588.60
Answer:
588.6
Step-by-step explanation:
Multiply
0
by
0.86
x
.
f
(
x
)
,
x
y
e
a
r
s
,
f
(
x
)
=
25
,
0
,
2
y
e
a
r
s
,
3
y
e
a
r
s
,
a
,
18
,
490
,
b
,
34
,
391.4
,
c
,
15
,
901.4
,
d
,
2
,
588.6
what are the solutions of the equation below
(x-2)(x+9)=0
Answer: {2, -9}
Step-by-step explanation: Think of these two binomials, x -2 and x + 9,
as two numbers that are multiplying together to equal zero.
In order for two numbers to multiply together to equal zero,
either one number or the other number must equal zero.
So for two binomials to multiply together to equal zero,
either one binomial or the other binomial must equal zero.
So we can split this problem up into two parts.
If (x - 2)(x + 9) = 0, then either x - 2 = 0 or x + 9 = 0.
On the left, add 2 to both sides and we have x = 2.
On the right, subtract 9 from both sides and we have x = -9.
For our final answer we use set notation.
So our answer is {2, -9}.
Answer:
2 and -9
Step-by-step explanation:
x-2=0
x=2
x+9=0
x=-9
The average number of seeds in a package of cucumber seed is 95. The numb
of seeds in the package can vary by eight. What are the maximum and
minimum number of seeds that could be in a package?
Select the correct equation and solutions that match this situation.
Answer:
103 at most and 87 at least
Step-by-step explanation:
95-8=87 seeds
95+8=103 seeds
Answer with step-by-step explanation:
Max: 25 + 3 = 28
Min: 25 - 3 = 22
Hope this helped!
State whether the data described below are discrete or? continuous, and explain why. The volumes left parenthesis in cubic feet right parenthesis of different rooms Choose the correct answer below. A. The data are discrete because the data can take on any value in an interval. B. The data are discrete because the data can only take on specific values. C. The data are continuous because the data can take on any value in an interval. D. The data are continuous because the data can only take on specific values.
Answer:
The correct answer is:
The data are continuous because the data can take on any value in an interval. (C)
Step-by-step explanation:
Discrete data are data that can take on certain limited values. There is a limit to what values can be assigned to such data. For example, the number of children in a school will just be whole numbers, either 20 or 50 or 55 or 108, etc, you cannot have 100.5 children. This makes it limited to the values it can take on, hence it is discrete
Continuous data, on the other hand, are data that can take on any value within a scale. The possibility of assigning a value is unlimited. for example height. The height can be 3m, 3.8m, 4.57m, etc, there's no limit to the possibility that a height can take. Other examples are; temperature, weight, acceleration, volume etc. In this example the volume of a room in cubic feet can be 30ft³, 50.6ft³, etc. The possibilities are endless, hence it is a continuous data.
What is the equation of the line that passes through the point (5,0) and has a slope
of -1
Answer:
y = -x + 5
Step-by-step explanation:
X, Y, and B is given using fomula y = m(x) + b
Subsitute those variables.
0 = -(5) + b
Solve for m.
0 = -5 + b
+5 +5
b = 5.
Then plug in the b and take out the x and y.
y = -x + 5
Answer:
y = -x + 5
Step-by-step explanation:
What is the greater 205/1000 or 0.205
Answer:
It is equal none of them is greater than the other
Step-by-step explanation:
Answer:
They are the same.
Step-by-step explanation:
205/1000 is .205
The median of a set of consecutive odd integers is 138. If the greatest integer in the set is 145, what is the least integer in the set?
Answer:
131
Step-by-step explanation:
Given that:
Median of a consecutive odd integers = 138
Greatest integer In dataset = 145
Least integer in dataset =
Since the integers are consecutive ;
Number of integers to greatest integer value : Greatest integer - median value = 145 - 138 = 7
Hence, 7 integers before the median value should give us the least integer value ;
138 - 7 = 131
CHECK:
131,132,133,134,135,136,137,138,139,140,141,142,143,144,145
Median = (n+1)/2 th term
Median = (15+1)/2 = 8th term = 138
Highest = 145
Least = 131
Answer:
131
Explanation:
It was in a Mathcounts competition
9 divided by 2,488 ??????
Answer: 0.0036173633440514 = [tex]\frac{9}{2,488}[/tex]
Answer:
00.0036173633
Step-by-step explanation:
use calculator
Please help and hurry please
Which could be the first step in solving the equation represented by the model below?
3 x tiles and 4 negative 1 tiles = 2 x tiles and 5 positive 1 tiles
Add 4 positive unit tiles to each side.
Remove 4 unit tiles from each side.
Add 6 positive unit tiles to each side.
Remove 6 unit tiles from each side.
Answer:
the answer is a
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation:
What is (7.8 x 10) • (1.0 x 10)
780 is the answer. Hope this helps :)
Cooper is a salesperson who sells computers at an electronics store. He makes a base pay amount of $60 per day regardless of sales and he earns a commission of 1.5% of the dollar amount of all sales that he makes. Write an equation for P,P, in terms of x,x, representing Cooper's total pay on a day on which he sells xx dollars worth of computers.
Answer:
P= 0.015x+60
Step-by-step explanation:
thats the right answer
If Cooper is a salesperson who sells computers at an electronics store. He makes a base pay amount of $60 per day regardless of sales and he earns a commission of 1.5% of the dollar amount of all sales that he makes. Then P = 0.015x + 60 is total pay.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Cooper's base pay is $60 per day
He gets $60 even for not selling computers,
meaning P= 60 when x=0, which is the y-intercept.
Now if Cooper makes a commission of 1.5% for all sales,
His earning will be increased by 1.5%.
The percentage value should be changed to decimal value. By Dividing 1.5 by 100
1.5/100=0.015
The amount of money earned in a given day increases $0.015 for each $1 of sales made.
Here x, representing Cooper's total pay on a day on which he sells x dollars of worth computers.
P = 0.015x + 60
Hence P = 0.015x + 60 is the total pay of cooper .
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
A cookie recipe called for 3 3.5 cups of sugar for every 246
cups
of
flour. If you made a batch of cookies using 4 cup of flour, how many
cups
of sugar would you need?
O 54/35 cups of sugar for 4 cups of flour
O 1 19/35 cups of sugar for 4 cups of flour
O 6 6/35 cups of sugar for 4 cups of flour
O 5 2/5 cups of sugar for 4 cups of flour
Answer:
D=5 2/5 cups of sugar for 4 cups of flour
Step-by-step explanation:
I cross multiplied and man was that a lot of fractions
what is the difference between the mean and the median of the set ( 3 ,8 ,10 ,15)
Answer:
You can think of the mean being acually mean because you have to do more work. When solving for the mean you add all the answers together then divide by the amount of numbers you have. For example, you have the numers (1, 2, 3) add them together (1+2+3) to get 6 then divide by 3 (6/3) to get a mean of two. The median is also fairly easy to remember. You line your numbers up least to greatest, left to right. and mark one off of each side at a time. If you have a even amount of numbers and reach the center, you add the two centers together then divide by to to get the median. If you have an odd amount of numbers, there should be one in the exact center left over.
Step-by-step explanation:
Mean) 3+8+10+15=36, 36/4=9 ANSWER=9
Median) 8+10=18, 18/2=9 ANSWER=9
In the case, the mean and median are the same and depending on context you could choose either method. It also helps that there is no outlyer. If there were on I would recomend finding the median.
Michael earns $8 an hour to baby sit the Jackson family. How many hours does he have to 1 point
baby sit to earn $56?
Answer:
7 hours
Step-by-step explanation:
56/8=7
The value of y varies directly with x. When y=30, x=0.75. What is the value of y when x=5.25?
Answer:
210
Step-by-step explanation:
According to this question, y varies directly with x. Mathematically, This means that:
y =kx
Where k is the constant variable
If y=30 and x=0.75, then k will be;
k = y/x
k = 30/0.75
k = 40
Since k = 40,
y = 40x
Therefore, when x=5.25, the value of y will be:
y = 40x
y = 40 × 5.25
y = 210.
Stephen collected data from a travel website. The data included a hotel's distance from Times Square in
Manhattan and the cost of a room for one weekend night in August. A table containing these data appears below.
0
1
1
3
4
7.
19
Distance From
Times Square
(city blocks) (x)
Cost of a Room
(dollars) (y)
293 263
244
224
185
170
219
153
136
111
Stephen calculated the linear regression equation to be y = -7.8x + 246.3. Using this equation, find the cost of a
room 5 city blocks away from Time Square.
1) $195
2) $207
3) $238
4) $285
What’s the answer?
Answer:
$207
Step-by-step explanation:
Given the following :
Data:
X : Distance From Times Square (city blocks)
Y: Cost of a Room (dollars) (y)
The linear regression model generated for the data :
y = -7.8x + 246.3
y = predicted variable ; - 7. 8 = slope of model ; x = predictor variable ; 246.3 = intercept
Using the model:
The cost of a Room 5 block away :
x = 5
y = -7.8(5) + 246.3
y = - 39 + 246.3
y = $207.3
Juan And his little brother had a pizza divided into eight slices of equal size juan ate 5 slices and his little brother ate the rest what fractional part did each person eat? juan ate 5 of 8 slices or his brother ate of 8 slices pieces or?
Answer:
Juan ate 5/8 his little brother ate 3/8
Step-by-step explanation:
Answer:
juan = 5/8
brother = 3/8
I need help guys.
Solve for x
y = x-v/b
Answer: I hope this is what you are looking for
Step-by-step explanation:
so the answer is
x=y +v/b
if MrBeast has 2,000 subscribers, and on the next 2 weeks he has now 44,000 subs. what was his subs during those two weeks?
Answer:
He got 42,000 subs in the 2 weeks.
Step-by-step explanation:
ANSWER:
42,000
SOLUTION:
44,000
- 2,000
42,000
I WILL MAKE YOU BRAINLESS PLEASE EXPLAIN HOW YOU GOT THE ANSWER
The closing price of a share of stock in company XYZ is $25.69 on Thursday. If the change from the closing price on Wednesday is -$0.75, find the closing price on Wednesday. $26.44 $24.94 $25.75 $25.06
The closing price on Thursday was $25.69 and on Wednesday, it went down by 0.75. and it went down again by 0.75 which brought it to $25.69.
That would mean the closing price on Wednesday was $26.44 (25.69 + 0.75)
what 3+6+9
answer 4 pointss
ayo the answer is 18.
Answer:
3+6+9
9+9= 18
Therefore 3+6+9=18
(6 - 4) × 9
sjjdcnjcbdc
Answer:
18
Step-by-step explanation:
(2) x 9
18
That's it
Byeeeee
1 belive it is 117 if that is not right 203
Answer:
what??
Step-by-step explanation:
Lemonade was on sale last week ;it cost $12 for every 4 packs of lemonade.How much do 2 packs of lemonade cost
Answer:
$6
Step-by-step explanation:
Each pack is $3
So therefore if you multiply 2($3) it is $6 for two packs