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Related Questions
Suppose you have a 6-face unfair dice with numbers 1,2,3,4,5,6 on each of its faces. If the probability distribution of throwing a number up is as follows: 1 with probability 1/12 2 with probability 1/12 3 with probability 1/12 4 with probability 1/12 5 with probability 1/12 6 with probability 7/12 What are the mathematical expectation and variance of the dice based on the above probability distribution
Answers
Answer:
Expectation is equal to 4.75
Variance is equal to 3.02
Step-by-step explanation:
Consider the attached image.
Let [tex]x_i[/tex] denotes each of the outcome.
Expectation [tex]=E(X)[/tex] = ∑[tex]x_if(x_i)[/tex]
[tex]=1(\frac{1}{12}) +2(\frac{1}{12}) +3(\frac{1}{12}) +4(\frac{1}{12}) +5(\frac{1}{12}) +6(\frac{7}{12})[/tex]
[tex]=\frac{1}{12}+\frac{2}{12}+\frac{3}{12}+\frac{4}{12}+\frac{5}{12}+\frac{42}{12}\\\\=\frac{57}{12}\\\\=4.75[/tex]
[tex]E(X^2)=[/tex] ∑ [tex]x_i^2f(x_i)[/tex]
[tex]=1^2(\frac{1}{12}) +2^2(\frac{1}{12}) +3^2(\frac{1}{12}) +4^2(\frac{1}{12}) +5^2(\frac{1}{12}) +6^2(\frac{7}{12})[/tex]
[tex]=(\frac{1}{12}) +4(\frac{1}{12}) +9(\frac{1}{12}) +16(\frac{1}{12}) +25(\frac{1}{12}) +36(\frac{7}{12})\\\\=\frac{307}{12}[/tex]
Variance [tex]=E(X^2)-[E(X)]^2[/tex]
[tex]=(\frac{307}{12})-(\frac{57}{12})^2\\\\ =\frac{307}{12}-\frac{3249}{144}\\\\ =\frac{3684-3249}{144}\\\\ =\frac{435}{144}\\\\ =3.02[/tex]
translate the sentence into an equation
The sum of 6 times a number and 2 is equal to 3
Answers
Answer:
6x + 2 = 3
Step-by-step explanation:
x would represent the unknown number
The sum refers to addition
6 times a number would be 6x (you can use any variable, but for this example I'm using x)
When you put it all together, it is 6x + 2 = 3
The required equation is 6x + 2 = 3.
It is required to find the equation.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers
Given:
The sum of 6 times a number and 2 equals 3.
According to given question we have,
Let the number be x.
6 times a number would be
6x
The sum of 6 times a number and 2 equals 3.
6x + 2 = 3.
Therefore, the required equation is 6x + 2 = 3.
Learn more about equation here:
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The science teacher gives daily homework. For a random sample of days throughout the year, the median number of problems is 5 and the IQR is 2. The Spanish teacher also gives daily homework. For a random sample of days throughout the year, the median number of problems is 10 and the IQR is 1. If you estimate the median number of science homework problems to be 5 and the median number of Spanish problems to be 10, which is more likely to be accurate? Explain your reasoning.
Answers
Answer:
SCIENCE SEEMS MORE ACCURATE
Step-by-step explanation:
The interquartile range (IQR) = difference between the upper and lower quartile (Q3 - Q1)
The median can be estimated as :
(Q3 - IQR/2) or (Q1 + IQR/2).
FOR SCIENCE:
MEDIAN NUMBER = 5
IQR = 2
IQR = Q3 - Q1
Q3 = median + IQR/ 2 = 5 + 2/2 = 6
Q1 = median - IQR/2 = 5 - 2/2 = 4
FOR SPANISH:
MEDIAN = 10
IQR = 1
IQR = Q3 - Q1
Q3 = median + IQR/ 2 = 10 + 1/2 = 10.5
Q1 = median - IQR/2 = 10 - 1/2 = 9.5
Science has a lower median score and an interquartile range which is reasonable wider than Spanish with a larger median value (but a very narrow interquartile range).
Over 4 months, Ms. Berg wrote 4 equal checks totaling $250 to pay for her salon services. How many did she withdraw from her account to pay for her services?
Answers
Answer:
$62.50 because
Step-by-step explanation:
250÷4=62r2
62.50•4=250
Ms. Beg withdraw $62.5 from her account to pay for her services.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Ms. Berg wrote 4 equal checks totaling $250 to pay for her salon services.
to with
So, to withdraw from the account to pay for services each month
= 250/4
= 125/2
= 62.5
Hence, she withdraw $62.5 from her account to pay for her services.
Learn more about unitary Method here:
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Eight more than the quotient of thirty and a number is fourteen.
Answers
Answer:
The number is 5
Step-by-step explanation:
First, we turn words into an equation(using x as the unknown number). Then, we solve for x.
[tex]\frac{30}{x} +8=14\\\frac{30}{x}=6\\30=6x\\5=x[/tex]
The critical path for a project was found to be 37 days. The variances total 27. What is probability of completing in 43 days? Below is information that might be useful to answer the question. Answer to 2 decimal points
Answers
Answer:
0.1241.
Step-by-step explanation:
So, from the question we are given the following parameters or information or data which are going to help us in solving this particular question/problem. They are; [1]. The critical path for a project = 37 days, the variances total or variance of critical path or sum of variance on critical path]². = 27, the desired completion time/day = 43 days.
So, we will be making use of the formula given below;
The number of standard deviation = desired completion time/day - critical time or sum of critical path times ÷√[variance of critical path or sum of variance on critical path]².
The number of standard deviation = 43 - 37 ÷ √27 = 1.1547.
Thus, the probability of completing in 43 days = P(Z > 1.1547) = 0.1241.
1
Five friends went to the movies and each spent $5 on a ticket per movie and $2 on a bag of popcorn. They saw 2 movies. The movies also had a deal of pizza and a large bottle of soda for $12, which they split. How much did each friend pay for the movie trip and pizza?
Answers
Answer:
5+2 + 12/5 = $9.40
Step-by-step explanation:
Norbert’s Nursery is having a sale. Flats of flowers are priced as marked, including tax. Jake buys 2 flats of petunias at $5.25, 3 flats of daisies at $7.65, and 1 flat of begonias at $8.40. If he pays with a $50 bill, how much change should Jake receive?
Answers
Answer:
I am a student. Jake should receive 8.15 dollars in change. Please pick me brainliest! I am new to this website and I wanna help.
Step-by-step explanation:
Una partícula se mueve sobre el eje x de acuerdo con la ecuación del movimiento
s=f(t) donde s es la distancia dirigida al origen en pies a los t segundos.
a) La velocidad v(t) y la aceleración a(t) en el instante t.
b) El instante t en el que la velocidad es cero.
s= 6t-t²
s=t²-6t
s= t²-9t+24
Answers
Answer:
a)
s= 6t-t² --> v = 6 -2t --> a = -2
s=t²-6t --> v = 2t-6 --> a = 2
s= t²-9t+24 --> v = 2t -9 --> a = 2
b)
v = 6 -2t = 0 --> t = 3
v = 2t-6 = 0 --> t = 3
v = 2t -9 = 0 --> t = 9/2
Step-by-step explanation:
si s(t) es la distancia, la velocidad es la primera derivada v(t) = s'(t)
y la acceleracion es la segunda derivada : a(t)= v'(t) = s''(t)
s= 6t-t² --> v = 6 -2t --> a = -2
s=t²-6t --> v = 2t-6 --> a = 2
s= t²-9t+24 --> v = 2t -9 --> a = 2
Suppose that a regression line for some data transformed with logarithms predicts that when x equals 8, will equal 1.603. What does the regression line predict y will equal when x equals 8? Round your answer to the nearest whole number. A. 2 B. 40 C. 13 D. 28
Answers
Answer:40
Step-by-step explanation:
Answer:
B. 40
Step-by-step explanation:
aapeexxxxxab
. Solve for x. Show your work: 4(x+1)= -3x-10 :)
Answers
Answer:
x = - 2
Step-by-step explanation:
Distribute
4(x + 1) = -3x - 10
4x + 4 = -3x - 10
Subtract 4 from both sides of the equation
4x + 4 = -3x - 10
4x + 4 − 4 = −3x − 10 − 4
Simplify
Subtract the numbers
4x+4−4=−3x−10−4
4 = − 3 − 1 0 − 4
Subtract the numbers again
4 = − 3 − 14
Add 3x to both sides of the equation
4 = − 3 x − 1 4
4 + 3 = − 3 − 1 4 + 3
Simplify
Combine like terms
4 + 3 = -3x-14+3x
7x =−3x−14+3x
Divide both sides of the equation by the same term
7 = − 1 4
7 /7 = -14/7
Cancel terms that are in both the numerator and denominator
7x/7 = -14/7
x = -14/7
Divide the numbers
= − 1 4 /7
= − 2
A line passes through the point (-9,8) and has a slope of
-4/3
Write an equation in slope-intercept form for this line.
Answers
Answer:
y = -4/3x - 4
Step-by-step explanation:
Given
(x1,y1) = (-9,8)
slope, m = -4/3
Required
Determine the line equation
The equation is of the form
y - y1 = m(x - x1)
Substitute values for y1, x1 and m
y - 8 = -4/3(x - (-9))
y - 8 = -4/3(x + 9)
y - 8 = -4/3x - 12
y = -4/3x - 12 + 8
y = -4/3x - 4
Help please thanks :)
Answers
Answer:
the answer is part 3 : exactly 30 .....
The width of a rectangle
is 11 feet longer than the
length. The perimeter of the
rectangle is 70 feet. Find
the length and the width
Answers
Answer:
Hello! The answer to this problem is Length= 27 and Width= 8
Step-by-step explanation:
2(11+2x) +2x = 70
6x + 22 = 70
6x = 48
x = 8
Kai needs a car to get to work and school. He's decided on a used car with a cost of $12,000. According to his budget he can afford to pay up to $300 per month and car payments. Which loan offer is best for Kai?
Answers
Answer:
The answer is Offer 3 because it has the lowest total loan cost of the offers with a monthly payment in his budget
Answer: c, offer 3
Step-by-step explanation: just did the quiz
Yosef is trying to determine whether or not he drinks enough water each day today on average he drank 2/5 of a glass of water every hour for 10 hours, to determine how much water he had he set up the equation 2/5 x 10 =? What is the total amount of water yosef drak
Answers
Answer:
4 glasses
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Choose another name for plane s look at the picture for the full answer thank you for helping!
Answers
Answer:
c: plane ptm
Step-by-step explanation:
Four times the sum of f and g is identical to six times g
Answers
Answer:
4(f+g)=6g
Step-by-step explanation:
4(f+g)=6g
Which of the following is a true statement 68/5 - 22/5 = 9 1/5
Please somebody awnser
Answers
Answer:
The answer is D
Step-by-step explanation:
I took the test and got it right <3
Answer: The first question in the selection is correct!
Step-by-step explanation:
I NEED HELP REALLY REALLY FAST
Answers
Answer:
360
Step-by-step explanation:
360 because you multiply the height times the width and you get your answer hopefully this helps you
What is the percentage of change from 400 to 300?
Answers
Answer:
25%
Step-by-step explanation:
Answer:
25%
Step-by-step explanation:
400*.25=100
400-100=300
Hope this helps!!
If peter drove for 9 hours at an average speed of 63 miles per hour, how far did he drive?
Answers
Answer:
567 miles
Step-by-step explanation:
9 hours x 63 miles per hour = 567 miles total
Amy is having her birthday party at a roller skating rink. The rink charges a fee of $50 plus $8 per person. If Amy wants to spend at the most $170 for the party at the rink, how many people can she invite to her party? Write a let x statement, an inequality and solve.
Answers
Answer:
(170 - 50)/8 = X
Step-by-step explanation:
X = amount of people
(170 - 50)/8 = X
Inequality
X = Number of People
50+(8*X) [tex]\leq[/tex] 170
The x statement is x ≤ 15. An inference is a statement that expresses the relationship between two (or more) expressions using one of the five signs listed below.
What is meant by inequality?Inequality the state of not being equal, particularly in status, rights, and opportunities1 is central to social justice theories. However, it is prone to misunderstanding in public debate because it means different things to different people. Some distinctions, however, are universal. A solution to an inequality in x is a number that, when substituted for x, yields a true statement. So, for example, 4 is a solution, whereas 8 is not. An inequality's solution set is the set of all solutions.The expression 5x 4 > 2x + 3 resembles an equation, but the equals sign has been replaced by an arrowhead. It's an example of inequity.Therefore,
(170 - 50)/8 = X
X = Number of People Over 50 (170 - 50)/8 = X
Inequality (8 × X) ≤ 170
An inequality is a statement that expresses the relationship between two (or more) expressions using one of the five signs listed below.
To learn more about inequality, refer to:
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f(x) = 2x^3 g(x) = x-3
find f(2)
find g(4)
find (f+g) (x)
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[tex]f(x) = 2 {x}^{3} [/tex]
[tex]f(2) = 2 \times {2}^{3} = 2 \times 8 = 16 [/tex]
_________________________________
[tex]g(x) = x - 3[/tex]
[tex]g(4) = 4 - 3 = 1[/tex]
_________________________________
[tex](f + g)(x) = f(x) + g(x) [/tex]
[tex](f + g)(x) = 2 {x}^{3} + x - 3 [/tex]
_________________________________
Done...♥️♥️♥️♥️♥️
i have a test and only have an hour please hurry!
90 / 3* (9 +6)=?
Answers
Answer:
450
Step-by-step explanation:
9+6= 15
90/3= 30
30*15=450
Find the length of the segment...
NEED HELP FOR A TEST tomorrow
Answers
Answer:
The length of the segment is 5
I NEED HELP LIKE REALLY REALLY FAST
Answers
Answer:
56 inches I believe.
I'm not 100% sure.
The surface area is 50 square inches
g If a snowball melts so that its surface area decreases at a rate of 8 cm 2/min, find the rate at which the diameter decreases when the diameter is 9 cm.
Answers
Step-by-step explanation:
The snowball is spherical in nature
The total surface area of the ball = 4πr²
Or 4π(d/2)²
S = 4πd²/4
S = πd²
d is the diameter of the ball
The rate at which the area is decreasing is expressed as;
dS/dt = dS/dd • dd/dt
dd/dt is the rate at which the diameter is decreasing
dS/dd = 2πd
dS/dt = 2πd • dd/dt
dS/dt = 2π(9) • dd/dt
8 = 18π•dd/dt
dd/dt = 8/18π
dd/dt = 4/9(3.14)
dd/dt = 4/28.26
dd/dt = 0.1415cm/min
Hence the diameter is decreasing at the rate of 0.1415cm/min
BAKING A recipe for 1 apple pie calls for 6 cups of sliced apples. How
many cups of sliced apples are needed to make 4 apple pies?
Answers
Answer:
24 cups of sliced apples
Step-by-step explanation:
6 multiplied by 4=24
hope this helps
What is the slope-intercept form of 3x + 5y = -15?
Answers
3x+5y=1 in slope-intercept form is y=−35x+15 .