A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 5-lb batches. Let X 5 the number of batches ordered by a randomly chosen customer, and suppose that X has pmf. Compute E(X) and V(X). Then compute the expected number of pounds left after the next customer’s order is shipped and the variance of the number of pounds left.
Answers
Complete Question:
A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 5-lb batches. Let X = the number of batches ordered by a randomly chosen customer, and suppose that X has the pmf shown in the table below. Compute E(X) and V(X).
Then compute the expected number of pounds left after the next customer’s order is shipped and the variance of the number of pounds left.
NOTE: The pmf is shown in the file attached
Answer:
Expected number of batches, E(X) = 2.0 batches
Variance of batches, V(X) = 0.8 batches²
Expected number of pounds left, E(Y) = 90 lb
Variance of pounds left, V(Y) = 20 lb²
Step-by-step explanation:
The company has 100 batches and it sells to customers in 5 lb batches. The number of pounds left after each customer is filled will be modeled by the mathematical formula: Y = 100 - 5X
The expected value of X, E(X) can be calculated using the formula:
[tex]E(X) = \sum x p(x)[/tex]
E(X) = (1*0.3) + (2*0.5) + (3*0.1) + (4*0.1)
E(X) = 0.3 + 1 + 0.3 + 0.4
E(X) = 2.0
Expected number of batches, E(X) = 2.0 batches
The variance of X, V(X) can be calculated using the formula:
[tex]V(X) = E(X^2) - [E(X)]^2\\ E(X^2) = \sum x^2 p(x)\\ E(X^2) = (1^2 *0.3) + (2^2 * 0.5) + (3^2 * 0.1) + (4^2 * 0.1)\\ E(X^2) = 0.3 + 2 + 0.9 + 1.6\\ E(X^2) = 4.8\\V(X) = 4.8 - 2^2\\V(X) = 0.8[/tex]
Variance of batches, V(X) = 0.8 batches²
Y = 100 - 5X
E(Y) = E(100 - 5X)
E(Y) = 100 - 5E(X)
E(Y) = 100 - 5(2)
E(Y) = 90 lb
Expected number of pounds left, E(Y) = 90 lb
Variance of the number of pounds left:
V(Y) = V(100 - 5X)
V(Y) = V(100) + V(-5X)
V(100) = 0
V(Y) = (-5)² V(X)
V(Y) = 25 * 0.8
V(Y) = 20
Variance of pounds left, V(Y) = 20 lb²
The question is incomplete. Here is the complete question.
A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 5-lb batches. Let X 5 the number of batches ordered by a randomly chosen customer, and suppose that X has the following pmf.
x 1 2 3 4
P(x) 0.3 0.5 0.1 0.1
Compute E(X) and V(X). Then compute the expected number of pounds left after the next customer’s order is shipped and the variance of the number of pounds left.
Answer: E(X) = 2
V(X) = 0.8
Expected number of pounds left = 90
Variance of the number of pounds left = 20
Step-by-step explanation: Since this is a probability distribution, to determine E(X), which is a measure of central tendency:
E(X) = ∑[x*P(x)]
E(X) = 1*0.3+2*0.5+3*0.1+4*0.1
E(X) = 2
V(X) is the variance for this type of distribution and is calculated as:
V(X) = ∑{[x - E(x)]²*P(x)} = (1-2)²*0.3+(2-2)²*0.5+(3-2)²*0.1+(4-2)²*0.1
V(X) = 0.8
The number of pounds left after the next costumer's order is shipped is given by the equation: Y = 100 - 5X
The expected number is equal to E(Y), which is this case is:
E(Y) = E(100 - 5X)
One property of E(X) is that if a and b are constants:
E(aX+b) = aE(X) + b
Taking that a = - 5 and b = 100:
E(100 - 5X) = (-5).2 + 100
E(Y) = 90
The variance of the number of pounds left is given by:
V(Y) = V(100 - 5X)
For variance, the property is: if a and b are constants:
V(aX+b) = a²V(X)
V(100 - 5X) = (-5)²*0.8
V(Y) = 20
Related Questions
Find the value of x for which r || S.
A) 44
B) 10
C) Can't be determined.
D) 14
Answers
Answer:
x=44
Step-by-step explanation:
For the two lines to be parallel, the two angles have to add to 180 degrees
45+3x+3 =180
Combine like terms
3x+48 = 180
Subtract 48 from each side
3x+48-48=180-48
3x=132
Divide each side by 3
3x/3 = 132/3
x =44
Carl wants to put up a glow-in-the-dark sticker display on his bedroom ceiling. He needs a gallon of black paint which costs $12. The stickers cost $18 per package and he wants to buy 2 packages. Which of the following is a good estimation of how much change Carl will get back if he gives the cashier $60?
Answers
Answer:3a ?
Step-by-step explanation:
Answer:
✈️?
Step-by-step explanation:
All corresponding sides are proportional (same ratio) in similar figures. True or False
Answers
Answer:
True
Step-by-step explanation:
The corresponding sides are proportional if they have the same ratio. The statement is true.
Answer:
true
Step-by-step explanation:
Lauren's birthday is in January. Determine the approximate probability that her brother, Adam, also has a birthday in January.
A) 1/2
b) 1/6
c) 1/12
d) 1/144
Please helpp!!
Answers
A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following. 1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute. 2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses. Which statement is correct? Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses. Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes. Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute. Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house.
Answers
Answer:
Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
Step-by-step explanation:
Let's rule out the options given one by one.
Option 1: Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses.
This is not true, because 1.2 is a rate, it just means that the carrier can finish 1 house in a minute, and also have time to get started delivering to the second house. The total number of houses has to be a whole number, but the rate doesn't.
Option 2: Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes.
This option is also incorrect. Delivering mail for 7.5 minutes just means 7 minutes and 30 seconds, which is definitely possible.
Option 3: Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
This option is correct. 1.2 is the rate of which the carrier delivers mail.
Option 4: Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house.
This option is also incorrect. Although it is possible to deliver mail for 7.5 minutes, it is not the unit rate, it is the total amount of time it would take.
Answer:
Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
Step-by-step explanation:
Please answer correctly ASAP !!!!!!!! Will mark brainliest !!!!!!!!!
Answers
Answer:
(x-2) (x+2)
I'll explain in comments if you need
There are 15 students going on a field trip. If 3/5 of them pack there lunches, how many students pack their lunches?
Answers
Answer:
9 pack their lunches
Step-by-step explanation:
Take the number of students and multiply by the fraction that pack their lunches
15 *3/5 =
15/5 * 3
3*3
9
Solve for x. Round your answer to the nearest thousandth. a. 8.691 c. 6.474 b. 6.252 d. 12.956
Answers
Answer:
The answer is B 6.252
Step-by-step explanation:
Given: y // z Prove: measure of angle 5 plus measure of angle 2 plus measure of angle 6 equals 180 degrees
Answers
Step-by-step explanation:
Given: y // z Prove: measure of angle 5 plus measure of angle 2 plus measure of angle 6 equals 180 degrees
Jennifer can do 8 math problems in 20 minutes. How long would it take her to complete a 10 question test at the same rate?
Answers
Answer:
25 minutes
Step-by-step explanation: 20 divided by 8 equals 2.5 so she take 2 and a half minutes per question. 2.5 plus 2.5 equals 5 so just add five minutes on her original time. 25 minutes
Answer:
25 minutes
Step-by-step explanation:
→You can set this problem up as a proportion, like so:
[tex]\frac{8}{10} =\frac{20}{x}[/tex]
→Cross multiply:
[tex]\frac{8x}{200}[/tex]
→Divide 200 by 8:
x = 25
49 - 3 + 9 times 8 divided by 2
Answers
Answer:
82
Step-by-step explanation:
49 - 3 + 9 times 8 divided by 2
Answer:
82
Step-by-step explanation:
49 -3 + 9*8/2
PEMDAS
Multiply and divide from left to right
49 -3 + 72/2
49 -3 + 36
Add and subtract from left to right
46 +36
82
Based on the side lengths given (a, b, and o, which triangles are right triangles?
Answers
Answer:
2 & 3
Step-by-step explanation:
Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex].
If the values given in each option satisfy the theorem, the sides will make a right triangle.
For Option One:[tex]4^2+6^2=8^2\\=> 4^2=16\\=> 6^2=36\\=>8^2 =64\\16+36=64\\\boxed{52\neq 64}[/tex]
The sides would not make a right triangle.
For Option Two:[tex]6^2+8^2=10^2\\=> 6^2 = 36\\=> 8^2=64\\=> 10^2=100\\36+64=100\\\boxed{100=100}[/tex]
The sides would make a right triangle.
For Option Three:[tex]5^2+6^2=\sqrt{61}^2\\ => 5^2=25\\=>6^2=36\\=>\sqrt{61}^2=61\\ 25+36=61\\\boxed {61=61}[/tex]
The sides would make a right triangle.
For Option Four:[tex]6^2+9^2=12^2\\=> 6^2=36\\=>9^2=81\\=>12^2=144\\36+81=144\\\boxed{117\neq 144}[/tex]
The sides would not make a right triangle.
The correct answer should be options two and three.
Find the volume of this prism.
pls ;(
Answers
Answer:
Go to google and write how to find a volume of a prism
Step-by-step explanation:
By the way what i am going to say is a small tip you can use
Go to google write ( quizlet) and you can write the name of your book the volume and the chapter rand the lesson believe me you will find what you want
If you didn't find the answers you can talk with me so i can give other programs because i have want to help you
increase as a percent:
The price of a car increased from $32 000 to $36 000.
Answers
Answer:
12.5% increase
Step-by-step explanation:
Take the new price minus the original
36000-32000 = 4000
Divide by the original
4000/32000 = .125
Multiply by 100%
.125*100%
12.5% increase
Answer:
12.5%
Step-by-step explanation:
There is an 1/8 increase and 1/8 as a percent is 12/5%
please help! find the area is the parallelogram.
Answers
Answer:
24cm^2
Step-by-step explanation:
3cm times 8cm = 24cm^2
Answer:
A=b*h
Step-by-step explanation:
base=5
height=3
5*3=15
15 is the answer
Emily has a bag of 20 fruit flavoured sweets 7 of the sweets are strawberry flavoured 11 are lime flavour and two are lemon flavour Emily takes a random sweet from the bag write down the probability that emily took the orange flavour
Answers
ANSWER: 0
IT IS BECAUSE THERE IS NO ORANGE FLAVOURED SWEET.
= 0/20 = 0
Create a trinomial where the GCF of the trinomial is 5m^3
Answers
Answer:
5m^5 + 15m⁴ + 35m³
Step-by-step explanation:
GCF means greatest common factor.
The Greatest common factor of two monomials for example, is the product of the common prime factors of both monomials.
We are to develop a trinomial which would have 5m³ as its greatest common factor.
To Create a trinomial where the GCF of the trinomial is 5m³, we would find a trinomial that can't be factored and multiply it by 5m³.
A trinomial is a polynomial which has three terms (monomials) connected by addition or subtraction.
Let's consider the trinomial m² + 3m + 7
This trinomial cannot be factored because there are no common factors between them. The constants to be considered are 3 and 7.
3 is a prime number and therefore can only be factored to 1 and 3.
7 is a prime number and therefore can only be factored to 1 and 7.
Since there are no common factors other than 1, the constants cannot be factored.
By multiplying 5m³ with the trinomial m² + 3m + 7
We would have:
5m³ (m² + 3m + 7) = 5m^5 + 15m⁴ + 35m³
From the above, the trinomial where the GCF of the trinomial is 5m³ = 5m^5 + 15m⁴ + 35m³
PLEASE HELP me solve algebraically. J) 4(1-2j) = 7(2j + 10) K) 4/3h=12 L) n/5= 2 + n/3 M) d/4 - 2/3 = 2 N= 7= -2 (-3 - x)
Answers
Answer:
J ) j = - 3,
K ) h = 9,
M ) d = - 24,
N ) x = 1 / 2
Step-by-step explanation:
J )
[tex]4(1-2j) = 7(2j + 10),\\4-8j=14j+70,\\-8j=14j+66,\\\\-22j=66,\\j = - 3,\\\\Solution, j = - 3[/tex]
I applied the distributive property, resulting in the second step. Afterwards I subtracted 4 from either side of the equation, received - 22j = 66 after combining like terms, and divided - 22 on either side to get j = -3.
K )
[tex]4 / 3h = 12,\\4h = 36,\\h = 36 / 4 = 9\\\\Solution, h = 9[/tex]
Multiplying each end of the equation by 3 resulted in the simplified expression 4h = 36. Dividing either side by 4, I got h = 9.
M )
[tex]d / 4 - d / 3 = 2,\\3d - 4d = 24,\\- d = 24,\\\\Solution, d = - 24[/tex]
Taking the LCM of 4 and 3, I got 12, multiplying either side by 12 / 12. Combining like terms and dividing - 1 on either side of the equation - d = 24, I received d = - 24.
N )
[tex]7 = - 2 * ( - 3 - x ),\\- 3 - x = - 7 / 2,\\- x = - 1 / 2,\\\\Solution, x = 1 / 2[/tex]
After dividing the first equation by - 2 on each end, I received a simplified equation that, by adding 3 on it's part, got x to be = 1 / 2
The graphs below have the same shape. What is the equation of the red
graph?
Answers
Answer:
Step-by-step explanation:
Answer:
The answer is A.
Step-by-step explanation:
Realize that the red graph is simply the blue graph shifted downwards. Hence, we simply need to subtract the units shifted from the original equation.
We see that the red graph shifted downwards by 3 units. Thus, we simply need to subtract three from the original equation.
Thus we have:
[tex](4-x^2)-3[/tex]
Which gives:
[tex]1-x^2[/tex]
Here, 1 is also the y-intercept, verifying our answer.
A swimming pool is being drained at a constant rate of 800 gallons per hour. After 5 hours of draining, 11,000 gallons of water remain in the pool.
Answers
Answer:
Step-by-step explanation:
In 5th hour remainder is 11,000 gal
Therefore at 4th hour 11,800 gal
At 3rd hour 12,600 gal
At 2nd hour 13,400 gal
at 1st hour 14,200 gal
Part B
At the beginning there is 15,000 gal
Before the draining began, the pool contained 14,200 gallons of water.
The water is being drained at a rate of 800 gallons per hour.
The function f(t) = 14,200 - (800t - 800)
Find the polynomial f(x) of degree 3 has the following zeros
9, 0, -7
Answers
Answer:
x³ - 2x² - 63x
Step-by-step explanation:
Zeroes = 9 , 0 , -7
Factors = (x - 9) x (x + 7)
Polynomial = x (x - 9)(x + 7)
Polynomial = x (x² -2x - 63)
= x³ - 2x² - 63x
a man travels 600km apart by train and partly by car.it takes 8 hours 40 min if he travels 320km by train and rest by car. it would take 30min more if he travels 200km by train and rest by car . find the speed of the train and by separately.
Answers
Answer: speed of train = 94.53 km/h
Speed of car = 59.98 km/h
Step-by-step explanation:
Let x = speed of the train
Let y = speed of the car
The total distance travelled by the man is 600 km. It takes 8 hours 40 min if he travels 320km by train and rest by car. This means that the distance travelled by car is 600 - 320 = 280km
60 minutes = 1 hour
The total time of travel = 8 + (40/60) = 8.67 hours
Total time = total distance/total speed
8.67 = 320/x + 280/y
320/x = 8.67 - 280/y
320/x = (8.67y - 280)/y
Cross multiplying, it becomes
320y = x(8.67y - 280)
y = x(8.67y - 280)/320- - - - - - - - - - -1
it would take 30min more if he travels 200km by train and rest by car. The total time would be 8.67 + 0.5 = 9.17 hours
Distance covered by the car is 600 - 200 = 400 km
Therefore,
9.17 = 200/x + 400/y
200/x = 9.17 - 400/y
200/x = (9.17y - 400)/y
Cross multiplying, it becomes
200y = x(9.17y - 400)
y = x(9.17y - 400)/200 - - - - - - - 2
Equating equation 1 to equation 2, it becomes
x(8.67y - 280)/320 = x(9.17y - 400)/200
Dividing both sides by x, it becomes
(8.67y - 280)/320 = (9.17y - 400)/200
Cross multiplying, it becomes
200(8.67y - 280) = 320(9.17y - 400)
1734y - 56000 = 2934.4y - 128000
2934.4y - 1734y = - 56000 + 128000
1200.4y = 72000
y = 72000/1200.4
y = 59.98 km/h
Substituting y = 59.98 into equation 1, it becomes
59.98 = x(8.67 × 52.98 - 280)/320
52.98 × 320 = x(459.3366 - 280)
16953.36 = 179.3366x
x = 16953.36/179.3366
x = 94.53 km/h
If there are 16 ounces in a pound. How many pounds are in 24 ounces?
Answers
Answer: 1.5 pounds
Step-by-step explanation: 16 oz(one pound) + 8oz(half a pound)= 24oz
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!
Answers
Answer:
The answer is A.
Step-by-step explanation:
As you multiply first equation by -5, you will get the coefficient of x is -5. So when both equations add up, you will eliminate x variable as -5 + 5 = 0, leaving y variable for the solutions.
Answer:
A.
Step-by-step explanation:
If we multiply the first equation by -5 we'll get -5x.
Then on adding the x terms are eliminated.
[tex] \sqrt[4]16 - 6 \sqrt[3]343 + 18 \sqrt[5]243 - \sqrt{196} [/tex]
Answers
Answer:
Step-by-step explanation:
= 2- 6*7 + 18*3 - 14
=2-42+54-14
=2 + 12- 14
= 14-14
=0
Answer:
the ans is 0
Step-by-step explanation:
=2- 6*7 + 18*3 - 14
=2-42+54-14
=2 + 12- 14
= 14-14
=0
C is the midpoint of AD. B is the midpoint of AC. BC = 14. What is
the length of BD?
Answers
Answer:
Length of segment BD = 42 units
Step-by-step explanation:
Since C is the midpoint of AB,
Then segment AC = segment CD
Since B is the midpoint of BC,
Then the length of segment AB = Length of segment BC = 14 units
Length of AC = 2 × (14)
= 28 units
Length of AC = length of CD = 28 units
Length of segment BD = Length of BC + length of CD
= 14 + 28
= 42 units
Therefore, length of segment BD is 42 units.
Find the percent change if 70 is changed by 12
Answers
Answer:
[tex]82.8571428571[/tex] %
Solution:
[tex]70*x/100=12[/tex]
[tex]x/100=12/70[/tex]
[tex]70x=1200[/tex]
[tex]x=1200/70[/tex]
[tex]x=17.1428571429[/tex]
[tex]100-17.1428571429=82.8571428571[/tex]
Please help me answer.
Answers
Answer:
Slope-intercept: y=3/4x+1
Sorry idk how to do general form
Step-by-step explanation:
Slope-intercept form is y=mx+b, m being the slope, b being the y-intercept.
The slope of this graph is 3/4, and the y-intercept is 1.
Answer:
Slope-intercept form: [tex]y=\frac{3}{4}x+1[/tex]
General form: [tex]-3/4x+y-1[/tex]
Step-by-step explanation:
Firstly, to get the slope intercept form, we need to find the slope and the y-intercept. To find the slope, we can use the slope formula and calculate the "rise over run" for these two points. The coordinate of the first point is (0, 1) , and the coordinate of the second point is (4, 4). If x1 = 0, x2 = 4, y1 = 1, and y2 = 4, we can plug those values into the slope formula that I mentioned earlier, which is [tex]\frac{y_{2}-y_{1}}{x_{2}-{x_{1}}}[/tex]. So, after we plug in those values we get in the two points, we can see that [tex]\frac{4-1}{4-0}[/tex], so the slope is [tex]\frac{3}{4}[/tex]. The x moves right 4 times and the y goes up 3 times. Finally, the y-intercept value is 1 because when x = 0, y is 1, and the point we used for the slope formula (0, 1) proves that. For the slope-intercept form, [tex]mx+b[/tex], where m is the slope and b is the y-intercept, m is [tex]\frac{3}{4}[/tex] and b is 1. So, our final answer for the slope-intercept form is [tex]y=\frac{3}{4}x+1[/tex]. Now we can find the general form. To do this, we must get one side of the equation to equal 0. Using our slope-intercept equation, [tex]y=\frac{3}{4}x+1[/tex], we can subtract y from both sides to get 0 on the left, like this: [tex]0=\frac{3}{4}x+1-y[/tex]. Then, we can rearrange the variables to general form: [tex]0=\frac{3}{4}x-y+1\\[/tex]. That is our general form answer. To recap, to find the slope, find the coordinates of the two points, and then plug in those points into the slope formula to find the steepness of the line. Then, add the y intercept that we can see on the graph. For general form, subtract y from both sides and rearrange the equation. Hope this helps!
The graph of which function passes through the point (0,2/pi)?
y=cos-1(x)
y=csc-1(x)
y=sec-1(x)
y=sin-1(x)
thanks!
Answers
Answer:
[tex]y=sin^{-1}x[/tex]
Step-by-step explanation:
Given: A point is [tex](0,2\pi)[/tex]
To find: function whose graph passes through the given point
Solution:
A trigonometry explains the relationship between the sides and the angles of the triangle.
The inverse trigonometric functions [tex]sin^{-1}x\,,\,cos^{-1}x\,,\,tan^{-1}x[/tex] help to find the value of an unknown angle of a right triangle when length of two sides are given.
Consider [tex]\sin y=x[/tex]
Put [tex]y=2\pi[/tex]
[tex]sin 2\pi=0[/tex]
So, point [tex](0,2\pi)[/tex] satisfies the function [tex]y=sin^{-1}x[/tex]
Therefore, graph of function [tex]y=sin^{-1}x[/tex] passes through [tex](0,2\pi)[/tex]
Answer:it’s A y=cos^1(x)
Step-by-step explanation:
Edge 2020
Prachi, the office manager at a private practice, identified several quantitative relationships surrounding a patient's visit and wait time and modeled them with the following functions:
Answers
Answer: W(P(t))
Step-by-step explanation: look at the letter infront of the ()
The waiting time for a patient is given by the expression w(p(t)).
What is a quantitative relationships?The relationship between objects (or objects' components) in terms of their relative number, size, or degree. ratio. two quantities' respective magnitudes (usually expressed as a quotient).A statement function is referred to by utilizing its name as an operand in an expression together with any parameters it has. Voici how execution is carried out: Actual arguments are assessed if they are expressions. There are comparable fake arguments and real arguments.A resume's summary statement can assist in guiding the reader from your present training and experience to the kind of job you are looking for. Your summary statement should be three to five lines long and should highlight your qualifications for the position you're applying for as well as the industry.To learn more about quantitative relationships refer to:
https://brainly.com/question/25316214
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