The mean, variance, and standard deviation for the probability distribution given are A. Mean = 5.5; B. Variance = 13.875; C. Standard Deviation = 3.722.
The mean, variance and standard deviation of the probability distribution can be calculated using the formula. The mean is calculated by summing up the product of all the values and their respective probabilities and then dividing it by the total probability. In this case, the mean is calculated as:
(1*0.587 + 3*0.115 + 9*0.21 + 12*0.088)/(0.587 + 0.115 + 0.21 + 0.088) = 5.5.
The variance is calculated by summing up the product of the squares of the values and their respective probabilities and then dividing it by the total probability. In this case, the variance is calculated as:
(1^2*0.587 + 3^2*0.115 + 9^2*0.21 + 12^2*0.088)/(0.587 + 0.115 + 0.21 + 0.088) = 13.875.
The standard deviation is the square root of the variance and it is calculated as √13.875 = 3.722.
Learn more about Standard Deviation here:
https://brainly.com/question/475676
#SPJ4
Greg has 14 as many songs on his computer as Mark. Raj has 6 fewer than 60% of the songs that Mark has. Mark has 720 songs on his computer.
Using percentage and equations, Greg has 734 songs, Raj has 426 songs and Mark has 720 songs
What is PercentagePercentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent symbol, "%". For example, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. Percentages have no dimension, which it's why they are dimensionless number. for example 60% of a number, then it means 60 per cent of its whole.
In this problem, we can write an equations and solve to determine the number of songs Greg has on his computer.
Let;
x = number of songs Greg hasy = Number of songs Raj hasSince Mark has 720 songs in his computer;
x = 14 + 720
x = 734
Greg has 734 songs
We can calculate the number of songs Raj has by;
y = 60%(720) - 6
y = [(0.6) * 720] - 6
y = 426
Learn more on percentage here;
https://brainly.com/question/843074
#SPJ1
Russel is doing an experiment for a science fair project. He fills a beaker with water three times. He puts 16.5 mililiters of water in each test tube. How many full test tubes can Russel fill with water? 1. Describe one way to estimate the solution to this problem. 2. Russel calculates correctly and says the answer to the problem is 36.36 test tubes. Is Russel's answer reasonable? Explain
The number of full test tubes Russel fill with water must be discrete number and not rational. 36 test tubes is the answer.
How to Know Cylinder Volume ?Volume of a cylinder can be known either by the use of formula (V = πr²h) or by measuring with the volume of a known liquid.
Given that Russel is doing an experiment for a science fair project. He fills a beaker with water three times. He puts 16.5 milliliters of water in each test tube. How many full test tubes can Russel fill with water?
1. Describe one way to estimate the solution to this problem.
By dividing the amount of milliliters of water in the baker by 16.5 ml
2. Russel calculates correctly and says the answer to the problem is 36.36 test tubes. Is Russel's answer reasonable?
No! The reason is based on the fact that the answer must be a whole number and not a decimal number since the question centered on number of full test tubes filled with water.
Therefore, the correct answer should be 36 test tubes.
Learn more about Volume here: https://brainly.com/question/1972490
#SPJ1
Can someone please explain how to do inequalities in math.
please add an example too.
SHOW YOUR WORK 256 divided by 6400
Factor the expression completely.
x^4-15x^2+54
Answer:
x^2(x^2 - 15) + 9(x-6)(x+1)
Step-by-step explanation:
To factor the expression x^4 - 15x^2 + 54 completely, we need to find the common factors in each term. In this case, we can see that the terms x^4 and -15x^2 share a common factor of x^2. To factor this out, we can use the difference of squares factorization:
x^4 - 15x^2 + 54 = x^4 - 15x^2 + (9x^2 - 9x^2) + 54
= x^2(x^2 - 15) + 9(x^2 - 6)
= x^2(x^2 - 15) + 9(x-6)(x+1)
Since x^2-15 can't be factored further. The expression is fully factored.
We can check this by multiplying it back and it should be the same as original expression.
6 x/11 ➕1
What does x equal
X is 55 after rearranging the equation given
Angle AOB is a central angle with a measure of 110 degrees.
What is the measure of its arc AB?
The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
Given that,
In the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
We have to find the measure of the ACB arc.
We know that,
Suppose that AB is the minor arc that is m(arc AB) = 110°
We know that measure of the major arc is 360°- measure of minor arc.
m(arc ACB)= 360- m(arc AB)
m(arc ACB)= 360-110
m(arc ACB)= 250°
Therefore, The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
To learn more about arc visit: https://brainly.com/question/24199694
#SPJ1
5. Measure the length of each leg and the hypotenuse of this triangle: a.f = units ag units fg = units
To find the length of the side opposite the angle, multiply the hypotenuse by sin(). Alternatively, to obtain the side next to the angle, multiply the hypotenuse by cos()
What is Hypotenuse triangle?The term "hypotenuse" refers to a right-angled triangle's longest side as compared to the base and perpendicular lengths. The right angle, the largest angle of the three angles in a right triangle, is opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other triangles. When we study the right-angled theorem, Pythagoras Theorem, or Pythagorean Theorem, this is better understood.
Hypotenuse TheoramPythagoras theorem defines the hypotenuse theorem. This theorem states that the square of a right-angled triangle's hypotenuse side is equal to the sum of its base and perpendicular squares, so that;
Hypotenuse2 = Base2 + Perpendicular2
The square root of the sum of the base and perpendicular squares of a right-angled triangle provides the formula to get the hypotenuse. The hypotenuse formula is represented as follows:
Hypotenuse = √[Base2 + Perpendicular2]
Length of the hypotenuse:Hypotenuse length: In the scenario where the square root is not a perfect square, we take an approximation of the root here in order for the solution to appear.Additionally, the squares of the base and the height should always be added to establish the value, however this does not provide a perfect square.Due to the imperfect square-root number, we must therefore approximation the solution.To know more about Hypotenuse Triangle refer to:
https://brainly.com/question/2217700
#SPJ1
How do you write log in e form?
Log to exponential form is very useful to easily perform complicated numeric calculations. The logarithmic form
loga N=x
can be easily transformed into the exponential form as:
ax=N
Normally, large astronomical and scientific calculations are written in exponential form, and here we can use the log to exponential form of transformation.
Logarithms are occasionally transformed using antilog tables to normal form, rather than transforming into exponential form.
Log to exponential form required specific formulas of logarithms and exponents. Logarithms help in easily transforming the multiplication and division across numbers into addition and subtraction.
And exponentials help in working across numbers with different bases and different powers.
To know more about Log form:
https://brainly.com/question/857062
#SPJ4
Rewrite 14x4y3 − 42x3y4 using a common factor.
The expression 14x⁴y³ - 42x³y⁴ is rewritten to 14x³y³(x - y)
What is an algebraic expression?
An algebraic expression can be described as a mathematical expression that is made up of terms, coefficients, variables, factors and constants.
They are also made up of some arithmetic operations, such as;
SubtractionMultiplicationDivisionBracketParenthesesAddition, etcFrom the information given, we have the algebraic expression;
14x⁴y³ - 42x³y⁴
Now, factor the common numbers, we have;
14(x⁴y³ - 3x³y⁴)
Factor the common variables, we get;
14x³y³(x - y)
Hence, the expression is 14x³y³(x - y)
Learn more about algebraic expressions here:
https://brainly.com/question/4344214
#SPJ1
y=-5 8x+5y=-17 substitution
[tex]8x+5y=-17[/tex] when y is -5
Substitute for y with given value:
[tex]8x+5(-5)=-17[/tex]
[tex]8x-25=-17[/tex]
Add 25 to both sides:
[tex]8x-25+25=-17+25[/tex]
[tex]8x=8[/tex]
Divide both sides by 8:
[tex]\dfrac{8x}{8} =\dfrac{8}{8}[/tex]
[tex]\fbox{x = 1}[/tex]
What is the 3 triangular number?
A triangular number succession is the representation of numbers as just an ordered set of equilateral triangles. The order of these numbers is 1, 3, and 6.
What exactly is meant by triangular numbers?A triangular number is one that may be written as the sum of a initial n positive integers.
A good example of a triangular number is 6, which may be written as 1+2+3 when the first three positive integers are added together.Triangular numbers make up a sequence if one considers the sum of the first positive integer as the initial element, the sum of the first two positive integers as the second element, and so on.If a number equals that sum of such initial n positive integers, then n denotes the position of that particular triangular number with in the series.Triangular numbers can be used to create equilateral triangles.The first 3 triangular numbers are therefore 1, 3, and 6.
To know more about the triangular numbers, here
brainly.com/question/13968949
#SPJ4
when journalizing an accounts payable account what account is credited
a. it depends on the transaction
b. accounts payable
c. cash
d. accounts receivable
Answer:
cash
Step-by-step explanation:
debit - account payable
credit - cash
how to get the Y intercept when you don't have a 0 X coordinate?
Answer: You plug in y as 0 into your equation.
Step-by-step explanation:
Do the above thing OK.
If 2x − 1 ≤ f(x) ≤ x2 − 2x + 3 for x ≥ 0, find lim x→2 f(x).
The limit as x approaches 2 or lim x→2 is 4.
When calculating a limit, the goal is to find the value of the function as x approaches the given value. In this case, the given value is 2. As x approaches 2, the values of the function will approach 4, which is the upper bound of the given inequality. This means that the limit as x approaches 2 is 4.
To prove this, we can look at the inequality and find the values of the function at x = 1 and x = 3. For x = 1, the function value is -1, which is less than 4. For x = 3, the function value is 7, which is greater than 4. This means that the function values are increasing as x gets closer to 2, so the limit as x approaches 2 is 4.
Learn more about Limits here:
https://brainly.com/question/27129946
#SPJ4
2/3 of the students in a class passed their math test. If 16 of students passed the test, how many students are in the class
Answer:
24 students are in the class
Step-by-step explanation:
Let x represent the total number of students in the class. We have the equation:
(2/3)x = 16
x = 24 students
So, there are 24 students in the class.
Answer:
24 students
Step-by-step explanation:
16/2=8
8*3=24
What are the 3 possible solutions for any quadratic?
There are three basic methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square.
quadratic equations
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax^2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
factoring
factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
Learn more about quadratic equations here :-
https://brainly.com/question/30098550
#SPJ4
1. What is the unit of measurement for speed using the metric system?
Answer:
meter per second(m/s)
Answer:
Hey there! The metric system has a unit called meters per second for measuring speed. It's abbreviated as m/s and it's used to measure how far something travels in a certain amount of time. For example, if something goes 50 meters in 10 seconds, its speed would be 50 m/s / 10 s = 5 m/s. There are other units for measuring speed too, like kilometers per hour (km/h) and centimeters per second (cm/s). It just depends on what you're measuring and how precise you need to be.
________________________________________________________
How do things like distance and time affect the speed of an object?Well, speed is all about how far something goes in a certain amount of time. So if you increase the distance traveled or decrease the time it takes to travel that distance, the speed will increase. On the other hand, if you decrease the distance traveled or increase the time it takes to travel that distance, the speed will decrease.
Why is it important to measure and calculate speed in certain situations?There are all sorts of situations where knowing the speed of something is important. For example, if you're driving a car, it's important to know how fast you're going so you can stay safe and follow the speed limits. In sports, measuring speed can help coaches and players improve their performance. And in science, measuring the speed of light or other phenomena can help us better understand the world around us. So as you can see, speed is a pretty important concept!
2x³ +x² -25x +12 factorised
The correct solutions for "x" after factorizing the cubic equation are:
x1 = -4
x2 = 0.5
x3 = 3
Cubic Equation:
A cubic polynomial in mathematics is a polynomial whose highest degree is three. A cubic equation is one that contains a cubic polynomial.
Either one real root or three real roots are present in every cubic equation. The cubic equation is written as ax^3+bx^2+cx+d=0.
Therefore, standard form of the cubic equation is: ax^3 + bx^2 + cx + d = 0
Given: 2x³ +x² -25x +12
On comparing with the standard form of the cubic equation, we get;
a=2
b=1
c=-25
d=12
After factorizing the cubic equation, we have three roots.
x1 = -4
x2 = 0.5
x3 = 3
To learn more about "cubic equation" here:
brainly.com/question/7764519
IS this statement true. When two conjugates are multiplied, the product is a
difference of two squares
Therefore the product of two conjugates is a difference of two squares.
What are conjugates?When two binomials have the same terms but different arithmetic operators in the center of these related words, they are said to be conjugate. For instance, the conjugate of p + q is p - q.
Define binomial numbers.An integer known as a binomial number is produced by evaluating a homogeneous polynomial with two terms, also known as a binomial.
This statement is true.
The conjugates of a complex number are two complex numbers that differ only in their signs. They are of the form a + bi and a - bi.
When two conjugates are multiplied, the product is (a + bi)(a - bi) = a^2 + (bi)^2 = a^2 - b^2 + (2abi) = (a^2 - b^2) + (2ab)i.
which is in the form (a^2 - b^2) + (2ab)i = (a^2 - b^2) + (2ab)i = (a+b)(a-b)
So the product of two conjugates is a difference of two squares.
To know more about integers visit: https://brainly.com/question/15276410
#SPJ4
19. The Beaufort Scale measures the intensity of tornadoes. For a tornado
3
with Beaufort number B, the formula v = 1. 9B2 may be used to
estimate the tornado's wind speed in miles per hour. Estimate the wind
speed of a tornado with Beaufort number 9.
The the wind speed of a tornado with Beaufort number 9 is 51.3 miles per hour.
What is speed?
Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in meters per second (m/s) in this example because the distance is measured in meters (m) and the time is measured in seconds (s).
Given:
The Beaufort Scale measures the intensity of tornadoes. For a tornado
with Beaufort number B, the formula [tex]v = 1.9B^\frac{3}{2}[/tex] may be used to
estimate the tornado's wind speed in miles per hour.
We have to estimate the wind speed of a tornado with Beaufort number 9.
Plug B = 9 in the formula [tex]v = 1.9B^\frac{3}{2}[/tex]
⇒
[tex]v = 1.9(9)^\frac{3}{2} \\v = 1.9(27)\\v = 51.3[/tex]
Hence, the the wind speed of a tornado with Beaufort number 9 is
51.3 miles per hour.
To know more about speed, click on the link
https://brainly.com/question/26862717
#SPJ4
The rectangular floor of a classroom is 26 feet in length and 36 feet in width. A scale drawing of the floor has a length of 13 inches. What is the perimeter, in inches, of the floor in the scale drawing?
HURRYYY I NEED HELP AGAIN!
Answer: 62 inches
Step-by-step explanation:
26÷13 =2
so 2 is the scale factor
so 36÷2= 18
18+18+13+13=62
I HOPE THAT HELPED
What kinds of problems are not solved by algorithms?
Answer:
Undecidable Problems
Step-by-step explanation:
A university just acquired more land which is shown by the triangle in the diagram. What is the area of the land that the university just aquired?
Therefore , the solution of the given problem of area comes out to be the land acquired by university is of 3 miles square area.
Define area.The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.
Area = length x breadth.
Here,
Given : A triangle land which has
height = 2miles
and base = 1.5+ 1.5 = 3 miles
Thus,
To find the area of triangle :
=> Area = 1/2*b*h
=>Area = 3*2/2
=> Area = 3 miles square
Therefore , the solution of the given problem of area comes out to be the land acquired by university is of 3 miles square area.
To know more about area, visit
brainly.com/question/27683633
#SPJ1
Write a system of equations to describe the situation below, solve usi
the blanks.
Parent volunteers at Salem High School are processing yearbook orde
an option to get the basic yearbook or a deluxe option, which includes
protective cover. In Mrs. Wu's class, 21 basic yearbooks and 6 deluxe
ordered, for a total of $2,025. The students in Mr. Boyer's class ordere
and 18 deluxe yearbooks, for a total of $2,763. How much does each
The basic yearbook costs $
and the deluxe yearbook costs $
Submit
Answer: $52.57 for each basic yearbook and $153.5 for each deluxe yearbook
Step-by-step explanation:
First, do Mr. Boyer's class to find out how much each deluxe yearbook is:
2,763 ÷ 18 = $153.5
Then do, Mrs. Wu's class: First, multiply 153.5 by the 6 deluxe yearbooks ordered;
153.5 x 6 = 921
After, subtract 921 from 2,025:
2,025 - 921 = 1104
The remaining $1104 is the total cost of the 21 basic yearbooks ordered. Divide the total cost by the number of yearbooks ordered to find the unit price:
1104 ÷ 21 = 52.5714285714
Round to the nearest hundredth: $52.57
Please give brainliest
How do you solve a 3 by 3 system of equations using matrices?
The solutions can be read off of the diagonal entries in the reduced matrix.
To solve a 3 x 3 system of equations using matrices, first we need to create the augmented matrix for the system of equations. The augmented matrix contains the coefficients of the variables and the constants for each equation on each row. Then we can use row operations to reduce the augmented matrix to reduced row-echelon form. This can be done by adding or subtracting rows to each other, multiplying or dividing a row by a non-zero number, and swapping two rows. After reducing the matrix to row-echelon form, we can back-substitute the solutions to the system of equations. The solutions can be read off of the diagonal entries in the reduced matrix. For example, if the matrix is reduced to the form [a b c d e f g h i] then the solution to the system of equations is x = d/a, y = e/b, and z = f/c.
Learn more about matrix here:
https://brainly.com/question/11367104
#SPJ4
What is the interval of zero?
If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If the confidence interval for a correlation or regression includes zero, that means that if you run the experiment again there is a good chance of finding no correlation in the data.
In both of these cases, you will also find a high p-value when you run the statistical test, meaning that the results could have occurred under the null hypothesis of no relationship between variables or no difference between groups.
To learn more about null hypothesis:
https://brainly.com/question/28920252
#SPJ4
Is halting undecidable?
Therefore , the solution of the given problem of tractable problem comes out be it is the most frequently encountered problem that has been discovered to be insoluble.
What is a tractable problem?a process that completes a manageable task in a polynomial amount of time. The polynomial upper bound is used. If an issue cannot be resolved in a polynomial amount of time, it is referred to as being intractable. The bound's minimum is exponential.
Here,
There is no programme that can resolve the halting difficulty for sufficiently general computer programs,
making it the most frequently encountered problem that has been discovered to be insoluble.
The type of computer software we're discussing must be made clear.
Therefore , the solution of the given problem of tractable problem comes out be it is the most frequently encountered problem that has been discovered to be insoluble.
To know more about tractable problem , visit
brainly.com/question/30142700
#SPJ4
Will give you brainlist
What are the two equations to set up to solve the equation?
|3x-2|=19
3x-2=
~QUESTION 2~
3|x+2|-7=14
x=_______
_____
~QUESTION 3~
-2|2x+3|+14(greater than and equal to symbol) -16
= < with line * < with line
The two equation to set up to solve the equation |3x - 2| = 19 are
3x - 2 = 193x - 2 = -19Question 2
x = 5 OR -9
Question 3
x ≥ 6 OR x ≥ -9
What is absolute value?Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.
A number can never have a negative absolute value.
How to write the absolute value equationThe equation is written in the form below
|3x - 2| = 19
removing the absolute value sign
3x - 2 = ± 19
the two equations are
3x - 2 = 19
3x - 2 = -19
Question 2
solving for x
3|x + 2| - 7 = 14
3|x + 2| = 14 + 7
3|x + 2| = 21
divide through by 3
|x + 2| = 7
removing the absolute value sign
x + 2 = ±7
solving for x for positive value
x + 2 = 7
x = 5
solving for the negative sign
x + 2 = -7
x = -9
Question 3
-2|2x+3| + 14 ≥ -16
-2|2x+3| ≥ -30
dividing through by -2
|2x+3| ≥ 15
2x+3 ≥ ±15
solving for the positive sign
2x+3 ≥ 15
x ≥ 6
solving for the negative sign
2x+3 ≤ -15
x ≥ -9
Learn more absolute values here:
https://brainly.com/question/29532815
#SPJ1
Solve the system. 3x+y = 10 y = 6x+1 Enter your answer by filling in the blanks. The solution is (/,/)
The estimated solution of the system 3x + y = 10 and y = 6x + 1 is (1, 7)
What is an equation?An equation is used to show the relationship between numbers and variables.
The standard form of a linear equation graph is:
y = mx + b
Where m is the slope of the line and b is the y intercept.
Given the linear equation:
3x + y = 10
y = -3x + 10 (1)
y = 6x + 1 (2)
Subtracting equation 2 from 1 to solve using elimination method gives:
0 = -9x + 9
9x = 9
x = 1
put x = 1 in eqn 2:
y = 6(1) + 1
y = 7
The solution is (1, 7)
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1