The moment generating function of the random variable X is given by m(t) = e^(t^2+3t) for all t ∈ R.
(a) Differentiating m(t) with respect to t will give us the moments of X. The first derivative of m(t) is:
m'(t) = (2t+3)e^(t^2+3t)
we set t = 0 in m'(t):
m'(0) = (2(0)+3)e^(0^2+3(0)) = 3
Therefore, E[X] = 3.
we differentiate m'(t):
m''(t) = (2+2t)(2t+3)e^(t^2+3t)
Setting t = 0 in m''(t):
m''(0) = (2+2(0))(2(0)+3)e^(0^2+3(0)) = 6
Therefore, E[X^2] = 6.
(b) The mean and variance of X can be calculated based on the moments we obtained.
The mean of X is given by E[X] = 3.
The variance of X can be calculated using the formula:
Var(X) = E[X^2] - (E[X])^2
Substituting the values we found:
Var(X) = 6 - 3^2 = 6 - 9 = -3
Since the variance cannot be negative, it suggests that there might be an error or inconsistency in the given moment generating function. It is important to note that variance should always be a non-negative value.
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HeLp I yEaH i HaVe AsKeD fOr LiKe 20 AnsWeRs BuT i NeEd ThEm AnSwErEd Or I fAiL AhAhA but please help even if you just answer one question
Answer:D
Step-by-step explanation:
What is the slope of the line that
passes through these two points?
(-3, 1)
(3, 3)
slope =
Answer: M=1/3
Step-by-step explanation: We know how to find the slope by using the formula: y2-y1/x2-x1
Then we get 3-1/3--3=2/6=
1/3
9) A carton contains 2 litres of tropical juice. The juice consists of 25% mango juice, 30% pineapple juice, and the rest is guava juice. Find how many millilitres of each juice went into the carton of tropical juice.
The carton of tropical juice contains 500 ml of mango juice, 600 ml of pineapple juice, and 900 ml of guava juice.
To find the amount of each juice that went into the carton of tropical juice, we'll calculate the quantities based on the given percentages.
Let's denote the volume of mango juice as M (in milliliters), the volume of pineapple juice as P, and the volume of guava juice as G. Since the total volume of the carton is 2 liters, we have 2000 milliliters as the total volume.
According to the given information, mango juice accounts for 25% of the total volume, pineapple juice accounts for 30%, and the remaining volume is guava juice.
We can express these relationships as equations:
M + P + G = 2000 (Equation 1)
M = 0.25 * 2000 (Equation 2)
P = 0.30 * 2000 (Equation 3)
G = 2000 - (M + P) (Equation 4)
From Equation 2, we have M = 0.25 * 2000 = 500 ml.
From Equation 3, we have P = 0.30 * 2000 = 600 ml.
Substituting these values into Equation 4, we get:
G = 2000 - (500 + 600) = 900 ml.
Therefore, the quantities of each juice that went into the carton of tropical juice are as follows:
Mango juice: 500 ml
Pineapple juice: 600 ml
Guava juice: 900 ml
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Chloe has a bag of marbles with 5 blue marbles, 1 white marbles, and 3 red marbles.
Find the following probabilities of Chloe drawing the given marbles from the bag if the first marble(s) is(are) returned to the bag after they are drawn.
a) A Blue, then a red =
b) A red, then a white =
c) A Blue, then a Blue, then a Blue =
a) The probability of Chloe drawing a blue marble, then a red marble, with replacement is (5/9) * (3/9) = 15/81 ≈ 0.185.
b) The probability of Chloe drawing a red marble, then a white marble, with replacement is (3/9) * (1/9) = 3/81 ≈ 0.037.
c) The probability of Chloe drawing three blue marbles in a row, with replacement, is (5/9) * (5/9) * (5/9) = 125/729 ≈ 0.172.
For each probability, we multiply the probabilities of drawing each marble consecutively, taking into account that the marble is returned to the bag after each draw. The denominator is 9 because there are a total of 9 marbles in the bag. The numerators reflect the number of marbles of each color in the bag.
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Use the figure to find the measures of the numbered angles. PLZZZ HELPPPP
angle 1 = 90°
angle 2 = 90°
angle 3 = 90°
angle 4 = 90°
angle 5 = 90°
angle 6 = 90°
angle 7 = 90°
Answer:
All of them are 90 degrees.
Step-by-step explanation:
Convert: 24 yards = _____ feet
72 feet
48 feet
76 feet
8 feet
Answer:
24 yards = 72 feet
Step-by-step explanation:
3 feet per yard
24 x 3 = 72
Factor the expression: x^2 +10x+9
Answer:
(x+1)(x+9)
Step-by-step explanation:
Hope this helps!
help me asap plss school is done in 4 mins plsssss help me asap
Answer:
3(y +8) (d+e) /4
Step-by-step explanation:
I gotta get to class too soon so my explanation here is just to get this sent. hopefully it does. I tried my best. could be wrong
Use a known Maclaurin series to obtain a Maclaurin series for the given function. f(x) = xe^7x [infinity]
f(x) = ∑
n=0
Find the associated radius of convergence, R. R =
Using the known Maclaurin series expansion for e^x: e^x = 1 + x + (x^2 / 2!) + (x^3 / 3!) + ...
We can obtain the Maclaurin series for the function f(x) = xe^(7x) by multiplying the Maclaurin series for e^x by x:
f(x) = x(1 + 7x + (7x)^2 / 2! + (7x)^3 / 3! + ...)
Simplifying further:
f(x) = x + 7x^2 + (49x^3 / 2!) + (343x^4 / 3!) + ...
Therefore, the Maclaurin series expansion for f(x) is:
f(x) = x + 7x^2 + (49x^3 / 2!) + (343x^4 / 3!) + ...
The associated radius of convergence, R, can be determined by applying the ratio test. In this case, we have an infinite power series with terms involving powers of x. The ratio test states that if the limit of |a_(n+1) / a_n| as n approaches infinity is L, then the radius of convergence is R = 1 / L.
In our case, applying the ratio test yields a limit of 0 as n approaches infinity. Therefore, the radius of convergence R is infinite, indicating that the Maclaurin series for f(x) converges for all values of x.
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Find the number of subsets in the set (x l x is a day of the week)
a. 124
b. 256
c. 127
d. 128
Solve the linear congruence 2x + 6 = 4(mod 8).
The solution to the linear congruence 2x + 6 ≡ 4 (mod 8) is x ≡ 3 (mod 8).To solve the linear congruence 2x + 6 ≡ 4 (mod 8), we need to find the values of x that satisfy the congruence equation.
First, let's simplify the equation:
2x + 6 ≡ 4 (mod 8)
Subtracting 6 from both sides:
2x ≡ 4 - 6 (mod 8)
2x ≡ -2 (mod 8)
Next, we can simplify -2 (mod 8) by adding 8 to it:
-2 ≡ 6 (mod 8)
Now the congruence equation becomes:
2x ≡ 6 (mod 8)
To solve for x, we need to find the multiplicative inverse of 2 modulo 8. The multiplicative inverse of 2 is 4, as 2 * 4 ≡ 1 (mod 8).
Multiplying both sides of the congruence equation by 4:
4 * 2x ≡ 4 * 6 (mod 8)
8x ≡ 24 (mod 8)
Simplifying the equation:
8x ≡ 24 (mod 8)
x ≡ 3 (mod 8)
Therefore, the solution to the linear congruence 2x + 6 ≡ 4 (mod 8) is x ≡ 3 (mod 8).
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Can someone help me with this. Will Mark brainliest.
Answer:
1. True
2. True
3. True
Donna made $357 for 17 hours of work. At the same rate, how many hours would she have to work to make $189?
Answer:
9 hours.
Step-by-step explanation:
$357 / 17 = $21. ($21 per hour.)
$189/$21 = 9. BOOM
A paint color is made using 4 drops of red and 5 drops of blue for each 5 gallons of paint. How many gallons of paint are being colored when 45 drops of color are used?
A veterinarian says you should feed a 5-year-old beagle
2/3 cup of dog food twice a day. According to the veterinarian, how much food should the beagle eat in a 30 days?
Answer:
40 cups of food
Step-by-step explanation:
First, you would multiply 2/3 by 2, which gives you 4/3. That means the beagle will eat 1 and 1/3 of a cup a day. If you multiply that by 30, you get 40.
An author of a book gets 3% of the price of each book sold. He received $24,380. How many copies of the book were sold, if each book was sold for $32.00?
Please Explain
divide the number by 32 then divide what you get by 3 and last times 100 equals 25,395.83333333 round it if you want to to 25,395.8
Solve the following system of equations using addiction
Answer:
3x+y=13
+2x-y=12
SOlve it like what you would normally do
3x+2x=5x
y+(-y)=0
13+12=25
Basically
5x+0=25
Bring down all appropiate signs
Now solve that
5x=25
x=5
Now to find “y”
Plug in The “x”
3*5=15
15+y=13 now solve that and you’d get -2
If you plug it into the other one, it would be the same thing
2*5=10
10-y=12
-y=2
y= -2
x=5
y= -2
please tell me where to drag the numbers! thank you!
Answer:
1. 7
2. 3
3. 2 and 2
Step-by-step explanation:
first is 7
second is 3
third is 2 and 2
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Have a great day, be safe and healthy
Thank u
XD
Consider the following. x=3cos(θ),y=4sin(θ),−π/2≤θ≤π/2 (a) Eliminate the parameter to find a Cartesian equation of the curve.
The Cartesian equation of the curve is 4x² + 3y² = 36.
We can eliminate the parameter θ by using the trigonometric identity cos²(θ) + sin²(θ) = 1, which gives us:
x²/9 + y²/16 = cos²(θ) + sin²(θ) = 1
Multiplying both sides by 16 to get rid of the fraction, we have:
16(x²/9 + y²/16) = 16
4x² + 3y² = 36
Therefore, the Cartesian equation of the curve is 4x² + 3y² = 36.
The Cartesian equation 4x² + 3y² = 36 represents an ellipse centered at the origin with semi-axes lengths of 2√3 and 2√2. The standard form for the equation of an ellipse centered at the origin is:
(x²/a²) + (y²/b²) = 1
where a and b are the semi-axes lengths of the ellipse. To convert the given equation to this standard form, we need to divide both sides by 36:
(4x²/36) + (3y²/36) = 1
Simplifying:
x²/9 + y²/12 = 1
Comparing with the standard form, we have:
a² = 9 and b² = 12
Therefore, the semi-axes lengths are √9 = 3 and √12 ≈ 3.464.
So, the equation 4x² + 3y² = 36 represents an ellipse centered at the origin with semi-axes lengths of 3 and approximately 3.464.
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The average low temperature in Tobermorey in October is 5 C. In February it is 23 C lower. What is the average low temperature in Tobermorey in February?
please show your answer
(It’s a math question about negative numbers and positive numbers on the number line)
Answer:
-18 C
Step-by-step explanation:
we have to do this operation
5 - 23
we can proceed like this
if we do 5-5 we reach the 0
23 - 5 = 18
now we have to do 18 steps to the left of the zero, that it means reach -18, that is the answer of the question
1. 232 is 8 times the sum of Mark's and his sister's ages. His sister is 21. Find Mark's age.
2. George went to the store for a sale on designer socks. Each pair was $3 off. She bought 6 pairs for $31.20. How much was the original price of the socks?
Answer:
a. 8 years
b. $49.20
Step-by-step explanation:
The computation is shown below:
a. The mark age is
Given that
232 is 8 times of the sum of mark and his sister ages
And, his sister is 21
So,
Let us assume the mark age be x
now
8(x + 21) = 232
x + 21 = 29
x = 29 -21
x = 8
b. The original price of the socks is
As each pair get $3 off
And she bought 6 pairs for $31.20
= $31.20 + 6 × $3
= $31.20 + 18
= $49.20
Questions are in the image above.
Answer:
hope this helps
you will find all answer in the photo i sent
please help 6th grade math
Answer:
B
Step-by-step explanation:
PLEASE GRAPH THE ANSWER AND HAVE A PICTURE ATTACHED. I WILL REALLY APPRECIATE IT :)
-Also no links please...
Answer:
The first is (-1, 1) and the second is (2, -2)
Step-by-step explanation:
Which of the following is true?
A-9< -2
B-7 < -7
C-1 = -1
D-8 >-3
that's the correct answer!
1 point
Ravi is shooting arrows at a target. The experimental probability that one
will hit a bull's eye is 12. If Ravi shoots 20 arrows, how many times can he
expect to hit a bull's eye?
O 10
O 20
Answer:
20
Step-by-step explanation:
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!
Answer:
Option A
Step-by-step explanation:
You're welcome.
May someone please help me with this :)
Answer: It would be option D :)
Step-by-step explanation: the formula for volume in a cylinder is π r squared times height. You plug those in and that’s your answer!
Convert: 76 ounces = _____ pounds _____ ounces
Answer:
4 pounds 12 ounces
Step-by-step explanation:
there are 16 ounces in 1 pound so 76/16 = 4.75 and .75 is equal to 12 ounces.
76 ounces is equal to 4 pounds and 12 ounces.
To convert 76 ounces to pounds and ounces, we need to consider that 1 pound is equal to 16 ounces.
Here's how to proceed:
Divide the total number of ounces by 16 to find the number of pounds:
76 ounces ÷ 16 ounces/pound = 4.75 pounds
Since 4 pounds = 4 x 16 pounce/ pound
= 64 ounces ,we subtract this amount from the total of 76 ounces to determine the remaining ounces:
= 76 ounces - 64 ounces
= 12 ounces
Therefore, 76 ounces is equal to 4 pounds and 12 ounces.
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Soon Yee was putting together her notebook after the first day of
school. She bought a pack of 200 sheets of loose-leaf notebook
paper and some dividers. She wanted to put the same amount of
paper in each of the four sections for her core subjects: math,
history, English and science. She figured that herſtwaelective
courses (art and music) each only needed half bf the amount of
paper that a core subject needed. How many sheets of paper did
she put into the art section of her notebook?
Answer: Since her art and music sections each only had half the number of sheets of paper as a core subject, together the two sections had the same amount of paper as a core subject. Therefore, it is almost like her notebook had five core subjects, rather than four core subjects and two electives. If she divided the 200 sheets equally among the five core subjects, there would be 200 ÷ 5 = 40 sheets in each section. Now we can see that art would actually have half of this amount, or 20 sheets of paper.