The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
What is Sample space?Sample space refers to the set of all possible outcomes or events that can occur in an experiment or random process. It is denoted by the symbol "S" and contains all the possible values, results, or states that can be observed or measured. In probability theory, the sample space is used to define the range of possible outcomes that can be observed or measured in a given experiment or event.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It quantifies the likelihood of an event happening based on the ratio of the number of favorable outcomes to the total number of possible outcomes. It is expressed as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
According to the given information:
When you roll a 12-sided dice, number of dots on the uppermost face is called as outcome. Now, whenever a dice is rolled we can get either 1, 2,3,4,5,6,7,8,9,10,11 or 12 dots on the uppermost face that is now outcome.
So experiment here is "Rolling a 12-faced dice" and list of possible outcomes is "{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}".
Sample space by its definition is list of all the possible outcomes of an experiment.
S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
To know more about sample space visit:
https://brainly.com/question/22087319
#SPJ1
Find the maximum value of = √ subject to the cost constraint K + 4L = 16.
Estimate the change in the optimal value of Q if the cost constraint is changes to K +
4L = 17
Answer:
This problem can be solved using the method of Lagrange multipliers. Let's define the Lagrangian function as: L(K, L, λ) = Q - λ(K + 4L - 16) Taking partial derivatives with respect to K, L, and λ, we get: dL/dK = 0 => 1 - λ = 0 => λ = 1 dL/dL = 0 => 1 - 4λ = 0 => λ = 1/4 dL/dλ = K + 4L - 16 = 0 Solving the last equation for K, we get: K = 16 - 4L Substituting this into the Lagrangian function, we get: L = Q - λ(16 - 4L + 4
A school bus has 22 rows of seats, and 4 students can be seated in each row. Students riding in the bus have filled 19 rows of seats, and 1/2 of the remaing seats. How many seats on the bus are empty?
Thus, remaining seats on the school bus that are empty is found as: 6 seats.
Explain about the fraction of number:The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts by which the whole has already been divided is shown by the denominator. It is positioned in the fraction's lower portion, just below fractional bar.How several sections of both the fraction are displayed or chosen is shown in the numerator. It is positioned well above fractional bar in the upper portion of the fraction.Given data:
Total rows of seats = 22Number of seats in each row = 4Filled rows = 191/2 of the remaining.Total seats in bus = Total rows of seats * Number of seats in each row
Total seats in bus = 22 * 4
Total seats in bus = 88
Filled seats = 19 * 4 = 76
Left seats = 88 - 76 = 12
Now, 1/2 of the 12 seats is filled = 6 seats.
remaining seats = 6
Thus, remaining seats on the school bus that are empty is found as: 6 seats.
Know more about the fraction of number
https://brainly.com/question/17220365
#SPJ1
Convert 3
2
3
years to months.
1 year = 12 months
Answer:
3878.65
Step-by-step explanation:
Answer: 3876
Step-by-step explanation:
If you are asking how many months are in 323 years, then the answer is 3,876 months
323(12)
8x÷4=100 What is the value of x in the equation?
Answer:
Solving 8x ÷ 4 = 100, we have:
2x = 100
x = 50
So the value of x is 50.
Answer:
x = 50
Step-by-step explanation:
To answer this question, we have to isolate the x. To do this, we have to get rid of any other numbers around it by doing the inverse of the operation.
1)
÷ 4 = ×4 to both sides8x ÷ 4 × 4 = 8x100 × 4 = 4008x = 4002)
8x = ÷ 8 to both sides8x ÷ 8 = x400 ÷ 8 = 50x = 50This means that x is 50!
To check our answer is correct we can substitute 50 to x in the question...
(8 × 50) ÷ 4 = 100It is correct!
Hope this helps, have a lovely day! :)
The temperature of one furnace is 1400°C and cools at a rate of 2.5°C per minute. The temperature of another furnace is 1200°C and is heated at a rate of 1.5°C per minute. Write an equation that models when the temperature of the two furnaces will be equal.
Answer:
1400 - 2.5t = 1200 + 1.5t
t = 50
Step-by-step explanation:
A trapezoid has an
area of 35 mm².
What is the height
of the trapezoid?
8 mm
6 mm
The height of the trapezoid is 7 mm.
A quadrilateral with one set of parallel opposite sides is referred to as a trapezium.
To find the height of a trapezoid when the area and the lengths of the parallel bases are given, we can use the formula:
h = 2A / ([tex]b_1 + b_2[/tex])
where
h is the height,
A is the area,
[tex]b_1[/tex] and [tex]b_2[/tex] are the lengths of the parallel bases.
As per given information in the question.
Using the given area of 35 mm² and the lengths of the parallel bases,
For [tex]b_1[/tex] = 8 mm and [tex]b_2[/tex] = 6 mm
we get:
h = 2 x 35 / (8 + 6) = 7 mm
For similar question on height of the trapezoid
https://brainly.com/question/31279008
#SPJ11
simplify -2(2x - 5) -4x
Answer: -8x +10
Step-by-step explanation:
-2(2x -5) -4x
1. simplify parthentheses
-4x +10 -4x
add like terms
-8x +10
Complete the square to solve the quadratic below. 1=2x^2+7x
the solutions to the quadratic equation 1 = 2x^2 + 7x are:
[tex]x= \frac{(-7+\sqrt{51} )}{4}[/tex] and [tex]x= \frac{(-7-\sqrt{51})}{4}[/tex]
ToToToToToToToToToToToToToToToToToToToToToToToToToToToToToToToTo solve this quadratic equation by completing the square, we need to rewrite the equation in the form of (x + p)^2 + q = 0, where p and q are constants. This will allow us to solve for x.
First, we can factor out the coefficient of the x^2 term, which is 2:
[tex]2x^2 + 7x - 1 = 0[/tex]
Next, we can isolate the x^2 and x terms on one side of the equation by subtracting 1 from both sides:
[tex]2x^2 + 7x = 1[/tex]
Now, we need to add and subtract a constant term inside the parentheses to create a perfect square trinomial. To determine this constant term, we take half of the coefficient of the x term (which is 7/2) and square it:
[tex](\frac{7}{2} )^{2} = \frac{49}{4}[/tex]
So we add and subtract 49/4 inside the parentheses:
[tex]2x^2 + 7x + \frac{49}{4} - \frac{49}{4} = 1[/tex]
We can simplify the left side by factoring the perfect square trinomial:
[tex]2(x + \frac{7}{4} )^2 - \frac{51}{8} = 0[/tex]
Now, we can solve for x by isolating the perfect square term and taking the square root of both sides:
[tex]2(x + \frac{7}{4} )^2 = \frac{51}{8}[/tex]
[tex](x + \frac{7}{4} )^2 = \frac{51}{16}[/tex]
[tex]x + \frac{7}{4}=±\sqrt{\frac{51}{16} }[/tex]
[tex]x = -\frac{7}{4} ± \sqrt{\frac{51}{16} } /2[/tex]
Simplifying this expression, we get:
[tex]x = (-7 ±\sqrt{51} )/4[/tex]
Therefore, the solutions to the quadratic equation 1 = 2x^2 + 7x are:
[tex]x = (-7 + \sqrt{51} )/4 and x = (-7 -\sqrt{51} )/4.[/tex]
To know more about quadratic equation go through:-
https://brainly.com/question/1214333
#SPJ1
Writing equations of lines
Which worksheet helps you figure out how much you can spend and invest?
Answer:
A monthly budget worksheet cause it shows your income and expenditure, so you are able to spend within your budget and it helps you know your disposable income
Explain how to simplify this expression: (7a + 9) + (4a - 7).
The simplified expression would be 11a + 2.
Simplifying an expressionIn order to simplify the given expression, we first need to combine like terms.
The terms can be combined by adding their coefficients:
(7a + 4a) = 11a(9 - 7) = 2Now we can substitute these combined terms back into the original expression:
(7a + 9) + (4a - 7) = 7a + 4a + 9 - 7
And then simplify further:
= 11a + 2
Therefore, the simplified form of the expression (7a + 9) + (4a - 7) is 11a + 2.
More on the simplification of expressions can be found here: https://brainly.com/question/11875858
#SPJ1
Please help with the question below
please write the answer in a decimal
Answer
15.71 cm
Explanation
Ling bought d donuts to share with coworkers. There were 6 donuts in each box. Write an expression that shows how many boxes of donuts Ling bought.
the expression would be used as follows:
Number of boxes of donuts (N) = 6 x Number of donuts (D)
Ling bought 108 boxes of donuts.
This expression is a mathematical equation that uses multiplication to calculate the number of boxes of donuts Ling bought.
What is mathematical equation?Equations are used to solve problems involving unknowns, such as how much a person owes for groceries or how many people are required to complete a certain task.
The expression that would show how many boxes of donuts Ling bought is:
Number of boxes of donuts (N) = 6 x Number of donuts (D)
In this expression, N represents the number of boxes of donuts Ling bought and D represents the number of donuts. This expression can be used to calculate the number of boxes of donuts Ling bought when the number of donuts is known.
For example, if Ling bought 18 donuts, the expression would be used as follows:
Number of boxes of donuts (N) = 6 x Number of donuts (D)
N = 6 x 18
N = 108
Therefore, Ling bought 108 boxes of donuts.
This expression is a mathematical equation that uses multiplication to calculate the number of boxes of donuts Ling bought. The expression can be used whenever the number of donuts is known and can be used to calculate the number of boxes of donuts Ling bought.
For more questions related to expression
brainly.com/question/1859113
#SPJ1
Let f(x) = IxI and g(x) = x^2
Find all values of x for which f(x) > g(x)
write your answer in interval notation
PLS HELP I WILL GIVE 50 POINTS
The interval in which the inequality is true is:
-1 < x < 1
For which values of x we have f(x) > g(x)?
Here we know that:
f(x) = |x|
g(x) = x²
Now, remember that in a product:
a*A
we have:
|a*A | > a if A > 1.
|a*A| < a if A < 1.
So, in a square like in g(x) = x²
if -1 < x < 1
Then the outcome will be smaller than the input, because we are multiplying by a numer smaller than 1.
Then:
f(x) > g(x)
|x| > x²
In the interval -1 < x < 1
Learn more about inequalities at:
https://brainly.com/question/24372553
#SPJ1
In a class of 20 children, 8 had one sister, 6 had 2 sisters. The mean number of children was 1. how many children had no sisters
There are no children in the class who have no sisters. This is because the mean number of children is 1, and some children have more than one sibling to Balance out those who have only one.
To solve this problem, we need to use some basic principles of statistics and probability. Let's start by identifying the key information provided in the problem. We know that there are 20 children in the class, and that some of them have sisters. Specifically, 8 children have one sister and 6 children have two sisters. We also know that the mean (average) number of children is 1, which means that on average, each child has one sibling.
To find out how many children had no sisters, we can use the following formula:
Total number of children - (number of children with one sister x 1) - (number of children with two sisters x 2) = number of children with no sisters
Using the values from the problem, we get:
20 - (8 x 1) - (6 x 2) = 0
This means that there are no children in the class who have no sisters. While this may seem counterintuitive, it's important to remember that the mean number of children is 1, which means that some children must have more than one sibling in order to balance out the others who have only one.
In summary, the answer to the question is that there are no children in the class who have no sisters. This is because the mean number of children is 1, and some children have more than one sibling to balance out those who have only one.
To Learn More About Balance
https://brainly.com/question/29372361
SPJ11
HELP PLSSSSSSSSSSSSSSSS
Answer:
H
Step-by-step explanation:
% of 11 year olds is 24
% of 12 year olds is 16
then ratio of
11 year olds : 12 year olds
= 24 : 16 ( divide both parts by 8 )
= 3 : 2
PLEASE ANSWER AND DONT PUT RANDOM SUTFF.
1. Which linear equation is being represented by the graph?
(A)y = -3/4x + 4
(B)y = 3/4x - 3
(C)y = 3/4x + 4
(D)y = -3/4x - 3
2. Which equation best represents the relationship between x and y in the graph?
(A)y = 3x - 2
(B)y = 2x + 3/2
(C)y = -1/2x + 3
(D)y = -2x + 3
Janct was driving home from work at a speed of 40 mph. Realizing she forgot her documents as she arrived home, she then drove back to work at a speed of 60 mph. What is her average speed for the entire trip?
A. 48 mph
B.49 mph
C. 50 mph
D. 52 mph
Answer: 50 mph
Step-by-step explanation:
- w/5 + 9 = 13 what w
Answer:
w = -20
"The beautiful thing about learning is that no one can take it away from you." :)
Are conditional probabilities always dependent?
Answer:
Two events are said to be independent if one event occurring does not affect the probability that the other event will occur. However, if one event occurring or not does, in fact, affect the probability that the other event will occur, the two events are said to be dependent.
If one event occurs or not, it does, in fact, affect the probability that the other event will occur, and then the two events are said to be dependent.
Jacob drove from Nicktown to Binghamton at
an average speed of 70 mph. If it took him 4
hours to get there, how far is Binghamton from
Nicktown?
A. 17.5 miles
B. 210 miles
C. 280 miles
D. 300 miles
Compare the following box plots below. Which of the following statements is NOT true?
Class B has a higher median
Class A has greater variability
Both A and B have students who are only children
Over half of the students in class A have two or more siblings
Comparing the box plots, the statements which are not true are Class A has greater variability and over half of the students in Class A have two or more siblings.
Based on the given box plots, we can make the following observations:
a) Class B has a higher median: True. We can see from the plot that the median line for Class B (represented by the orange line inside the box) is higher than the median line for Class A (represented by the blue line inside the box).
b) Class A has greater variability: False. We can see from the plot that the boxes for both classes have similar lengths, indicating similar variability. However, Class A has a few more outliers compared to Class B, which indicates some extreme values that are far from the median.
c) Both A and B have students who are only children: True. We can see from the plot that both classes have a box plot labelled "0" indicating that some students in each class are only children.
d) Over half of the students in class A have two or more siblings: False. We can see from the plot that the box labelled "2+" in Class A only covers about a third of the box, indicating that less than a third of the students have two or more siblings. Therefore, the statement is not true.
Therefore, the answer is b) Class A has greater variability and d) Over half of the students in Class A have two or more siblings.
To learn more about the median, refer:-
https://brainly.com/question/28060453
#SPJ1
Solve the systems by elimination.
10x + 10y = 40
5x + 3y = 8
Answer:
x = -2, y = 6
Step-by-step explanation:
First, find the opposite of 10 by multiplying 5x+3y=8 by -2 to eliminate 10x.
10x+10y=40
-2(5x+3y=8)
10x+10y=40
-10x-6y=-16 (Subtract 10y - 6y) (Subtract 40 - 16)
4y = 24 (Divide by 4 on both sides)
y = 6
Substitute 6 in the y value in any of the equations.
10x+10(6)=40 (Replaced 10y with 10(6) )
10x+60=40
-60 = -60 (Subtract 60 from both sides)
10x = -20 (Divide by 10 on both sides)
10 10
x = -2
3x + y = 3
x + y = 2
Solve the system of equations.
3x + y = 3
x + y = 2
Solve the system of equations.
A x = 12
, y = 3x = 1 2 , y = 3
B x = 32
, y = 12
x = 3 2 , y = 1 2
C x = 3, y = 12
x = 3, y = 1 2
D x = 12
, y = 32
x = 1 2 , y = 3 2
E x = 52
, y = -92
Answer: x = [tex]\frac{1}{2}[/tex] , y= [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given the following functions find and simplify (f-g)(1) f(x)=-x^2-x-3 g(x)=-1
To find (f-g)(1), we first need to find f(1) and g(1): f(1) = -(1)^2 - 1 - 3 = -5 g(1) = -1 Now we can substitute these values into (f-g)(x) = f(x) - g(x) and simplify: (f-g)(1) = f(1) - g(1) = (-5) - (-1) = -4 Therefore, (f-g)(1) = -4.
Write a matrix equation for the given systems of equations.
2x-6y-2z = 1
3y-2z=-5
2y + 2z = -3
Now, we can write the matrix equation as:
AX = B
| 2 -6 -2 | | x | | 1 |
| 0 3 -2 | | y | = | -5 |
| 0 2 2 | | z | | -3 |
How to solve the matricesTo write the given system of equations as a matrix equation, we will represent it in the form AX = B, where A is the matrix of coefficients, X is the column matrix of variables, and B is the column matrix of constants.
Given a system of equations:
2x - 6y - 2z = 13y - 2z = -52y + 2z = -3We can represent the matrices as follows:
A = | 2 -6 -2 |
| 0 3 -2 |
| 0 2 2 |
X = | x |
| y |
| z |
B = | 1 |
| -5 |
| -3 |
Now, we can write the matrix equation as:
AX = B
| 2 -6 -2 | | x | | 1 |
| 0 3 -2 | | y | = | -5 |
| 0 2 2 | | z | | -3 |
Read more about matrices here:
https://brainly.com/question/1279486
#SPJ1
Sneeze: According to a study done by Nick Wilson of Otago University Wellington, the probability a
randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on
a bench in a mall and observe 300 randomly selected individuals’ habits as they sneeze.
Task 1: What is and what is ?
Task 2: What are the mean and standard deviation?
Task 3: What are the conditions that must be met to use the normal approximation to the binomial
distribution? Are they met?
Thus, the mean and standard deviation for the randomly selected individuals is found as: mean = 80.1 and standard derivation = 7.66.
Explain about the standard deviation:The standard deviation is a measurement of how widely spaced out a set of data is from the mean. The bigger the dispersion or variability, the higher the standard deviation and the greater the magnitude of the value's divergence from its mean. It represents the absolute variability of a distribution.
Given data:
Number of population n = 300
probability p = 0.267
Mean is given as np:
np = 300*0.267
np = 80.1
standard derivation: √np(1 - p)
√np(1 - p) = √80.1(1 - 0.267)
√np(1 - p) = √58.7133
√np(1 - p) = 7.66
Thus, the mean and standard deviation for the randomly selected individuals is found as: mean = 80.1 and standard derivation = 7.66.
Know more about the standard deviation
https://brainly.com/question/475676
#SPJ1
Correct question:
According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe 300 randomly selected individuals’ habits as they sneeze.
What are the mean and standard deviation?
(3, -3) and (8, 12)
Step-by-step explanation:
what did you ask the question? ask it clearly please?? if you ask clearly the question. we also give answer
How do you solve this?
Below 10 in.*6 in.*14 in., the triangular prism's volume is 420 cubic inches.
The area of the base must be multiplied by the prism's height in order to determine the volume of a triangular prism.
The base of this triangular prism is a triangle with a base of 6 inches and a height of 10 inches, so its area is:
Area of base = (1/2) × base × height = (1/2) × 6 in × 10 in = 30 in²
The height of the triangular prism is given as 14 inches.
Hence, the triangular prism's volume is:
Volume = Area of base × height = 30 in² × 14 in = 420 cubic inches.
So, the volume of the triangular prism is 420 cubic inches.
To learn more about triangular prism, refer:-
https://brainly.com/question/22023329
#SPJ1
Tom and John are engaged in buying and selling certain products A and B. Tom BUYS 5 of product A but
SELLS twice as much of product B. John on the other hand SELLS three times what Tom BOUGHT of
product A and BUYS 13 of product B. At the end of the business day, John banks Ksh 110,000/- while
Tom banks Ksh 230,000.
Under the assumption that the sale prices for product A and B are the same for the two men, and the costs prices for the products A and B are also the same for the two men, obtain the following:
The price for product A which was determined as Ksh 42,727.27 and the price for product B as 44,363.63
Question: If there was a mark up of 25% on the cost price and a discount of 15% on the sale price, how
much would each of the partners have banked at the end of the business day?
Product A is priced at Ksh 55,000, while Product B is priced at Ksh 32,000.
How to calculate Product A and B?Assume that the selling price for both the two items A and B is "S" and the cost price for both is "C". Using this knowledge, we can create two equations that relate the costs and revenues of the two items, one for Tom and one for John:
Tom: 5C - 2(5S) = [tex]P_1[/tex]
John: 3(5C) - 13C = [tex]P_2[/tex]
where [tex]P_1[/tex] and [tex]P_2[/tex] represent Tom's and John's respective profits.
We are aware that John deposits Ksh. 110,000 while Tom deposits Ksh. 230,000 at the end of the business day. Thus, we can say:
[tex]P_1[/tex] = 230,000 - 5C
[tex]P_2[/tex] = 110,000 - 18C
These values are what we obtain when we enter them into the equations for Tom and John:
5C - 2(5S) = 230.000 - 5C
When we simplify these equations, we obtain:
10C - 10S = 230,000
2C = 110,000
Solving for C, we get:
C = 55,000
We may determine S by adding this value back into the original equation:
10(55,000) - 10S = 230,000
Simplifying this equation, we get:
S = 32,000
Therefore, the price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.
To know more about price, visit:
https://brainly.com/question/1153322
#SPJ1