Answer:
-4
Step-by-step explanation:
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.
POSSIBL
Mariko needs to solve the equation below for D. Which correctly describes the step he should take?
M=
= p
Subtract V from both sides.
Divide both sides by V.
Multiply both sides by V.
O Divide both sides by D.
1
2
which step should I take
Answer:
Divide both sides by V
Step-by-step explanation:
The equation is not well written.
Mariko needs to solve the equation below for D. Here is the equation:
M = DV
For Mariko to get D, he needs to make D the subject of the formula by dividing both sides of the equation by the coefficient of D i.e V as shown;
Divide both sides by V
M/V = DV/V
V at the denominator will cancel out the V at the numerator to have:
M/V = D
Rearrange
D = M/V
Therefore, the statement which correctly describes the step he should take is:
Divide both sides by V. Option B is correct.
X - 6 < -4 please help
Answer:
x<2
Step-by-step explanation:
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
Solve for x: 1 over 3 (2x − 8) = 4.
2
6
10
Answer:
the answer is x= 10
Step-by-step explanation:
Help with math. please
Answer:
B. 1 9/10 (19/10)
Step-by-step explanation:
3 4/5 is equal to 19/5
We would need to divide 19/5 by 2
Make 2 a fraction. 2/1
Flip the number: 1/2
Multiply 19/5 by 1/2
19/10
Simplify.
1 9/10
Hope I helped :)
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Question 1
Sione just landed a great job as an engineer where he will make $55,000 a year. The
company he will work for guarantees a 3% pay increase each year so it's employees
salaries keep up with inflation. At the end of the 1* year Slone will have made $55,000
dollars.
1. What is the recursive function that will represent this situation?
a. m(t) = m(t - 1) + 0.03, m(1) = 55000
b. m(t) = m(t-1). 0.03, m(1) - 55000
c. m(t) = m(t-1) + 1.03, m(1) - 55000
d. m(t) = m(t-1). 1.03, m(1) = 55000
Answer:
Option (d)
Step-by-step explanation:
If the current salary of Sione is represented by the function m(t - 1),
Next year his salary m(t) gets hike of 3%.
So, the next year salary of Sione will be represented by,
m(t) = m(t - 1) + 3% of m(t - 1)
= m(t - 1) + 0.03 × m(t - 1)
= m(t - 1)(1 + 0.03)
= 1.03m(t - 1)
Since, at the end of year 1 his salary was $55000,
Recursive function will be,
m(t) = 1.03m(t - 1) = 55000
Therefore, Option (d) will be the answer.
How does light travel so you can see in the dark
Answer:
Step-by-step explanation:
Light travels as a wave. But unlike sound waves or water waves, it does not need any matter or material to carry its energy along. This means that light can travel through a vacuum—a completely airless space. ... It speeds through the vacuum of space at 186,400 miles (300,000 km) per second.
The engineers designing the All Aboard Railroad between Boca Raton and Jupiter decide to create parallel tracks through this portion of the railway. To illustrate their plans to the county commission, they use a coordinate plane. The southbound track will have an equation of 2x + 5y = 15. What is the equation of the parallel northbound track that runs through the point (4, – 2)?
Answer:
there are no signs between the x and y and constant
it could be
2x+5y=15
2x+5y=-15
-2x+5y=15
2x-5y=15
for ax+by=c, the equation of a line paralell to that is
ax+by=d where a=a, b=b, and c and d are constants
(for this answer, I'm going to use 2x+5y=15)
given 2x+5y=15, the equation of a line paralell to that is 2x+5y=d
to find d, subsitute the point (4,-2), basically put 4 in for x and -2 for y to get the constant
2x+5y=d
2(4)+5(-2)=d
8-10=d
-2=d
the eqaution is 2x+5y=-2 (Only if the original equation is 2x+5y=-15
pls mark me brainlest
Answer:
2x+ 5y= -2
Step-by-step explanation:
On a spelling test, Lucy got 4 out of 5 correct. If Lucy got
20 questions correct, then how many quesitons did she
miss?
Answer:
4
Step-by-step explanation:
Answer:
She missed 4 questions
Step-by-step explanation:
4/5=8/10=16/20
please help fast and expalin.
Answer: 10,000
Step-by-step explanation:Hope this helps!
Find |x| when x = – 15.
HELP ME PLEASEE
Answer: 15
Step-by-step explanation: | | means the absolute value the absolute value of -15 is 15 because it is 15 units away from 0.
Triangle ABC is translated 5 units to the right and 4 units up to create triangle A'B'C'.
What is the measure of B?
The measure of the angle B is 74 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Triangle ABC is translated 5 units to the right and 4 units up to create triangle A'B'C'.
If triangle ABC is translated 2 units up and 2 units right, that means that all the vertices of the triangle are translated by the same units 2 up and 2 right.
The angle sum property of a triangle;
80 + 26 + B = 180
B = 180 - 106
B = 74
Therefore, the size and shape of the triangle wouldn't change.
The triangle A'B'C' will still have the same size and shape, and all the sides will have the same length.
Hence, the measure of the angle B is 74 degrees.
Learn more about the triangles;
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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
A rectangle has length 8x 104 mm and width 4 x 104 mm. The rectangle's length is how many times
its width?
The rectangle's length is times its width.
(Type a whole number.)
Answer:
Step-by-step explanation:
It would be 2.
8/4=2
10^(4-4)=10^0 or 1
2*1=2
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.
help me answer please
Answer:
x=21
Step-by-step explanation:
supplementary angles add up to 180°
7x-3+2x-6=180
collect like terms
9x-9=180
add 9 to both sides
9x=189
divide both sides by 9
x=21
0.75 (6+d)=12 step by steP
Answer:
Step-by-step explanation:
step 1: 0.75 x 6 = 4.5
step 2: 0.75 x d = 0.75d
step 3: 4.5 + 0.75d = 5.25d
It's correct answer
Slove 4(5x-2)= 2(9x+3)
Answer:
x=7
Step-by-step explanation:
divide both sides by two. distribute on the left side. minus 9x on both sides. add 4 on both sides, and you get 7.
Answer:
x = 7
Step-by-step explanation:
Firstly, use the distributive property to distribute the 4 and the 2 respectively.
[tex]4(5x-2) = 2(9x+3)[/tex]
[tex]20x-8=18x+6[/tex]
Then, isolate the variable. Start by subtracting 18x from both sides.
[tex]2x - 8 = 6[/tex]
Add 8 to both sides.
[tex]2x = 14[/tex]
Divide both sides by 2.
[tex]x=7[/tex]
What is (7.8 x 10) • (1.0 x 10)
780 is the answer. Hope this helps :)
1Write an equation in slope intercept form for a line that contains the
points (-3.2) and (6, 1).
Answer:
y=-[tex]\frac{1}{9}[/tex]x+[tex]\frac{5}{3}[/tex]
Step-by-step explanation:
6 : 4 is equivalent to
Answer:
12 : 8, 18 : 12, 24 : 16, 30 : 20
Step-by-step explanation:
These are the four after 6:4. I didn't know which you needed.
Answer:
3:2
Step-by-step explanation:
If you want to simplify 6:4, it also makes an equivalent equation. To simplify this, we divide by the greatest number that both numbers can be evenly divided by. 6 and 4 can both be divided by 2, which is the biggest number we can divide both numbers by.
6/2=3
4/2=2
The ratio is now simplified/equivalent to 3:2.
I hope this helps...have an amazing day c:
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
Which statement is modeled by 2p + 5 < 11
Group of answer choices
The sum of 5 and 2 times p is at least 11
5 added to the product of 2 and p is less than 11
2 times p plus 1 is at most 11
the product of 2 and p added to 5 is 11
what 3+6+9
answer 4 pointss
ayo the answer is 18.
Answer:
3+6+9
9+9= 18
Therefore 3+6+9=18
Helppppp please !!!!!
Answer:
The answer is A) 1/8^2
Step-by-step explanation:
Both of the equations simplified equal 1/64.
The sum of 3 consecutive even integers is 48. Find all three inters
Answer: 15 16 17
Step-by-step explanation: Add them together and you should get 48
HURRY, PLEASE HELP!!!
Answer:
Equilateral, Isosceles, and Scalene triangles all have at least one pair of equal angles.
The angles must have the same degree and most of the time come when connected by or adjoined by 2 equal side lengths.
guys hurry i have a starter
idk what the answer
Answer:
The letter E
HOPE THIS HELPS YOU Do mark as brainliest