The expected value of y is (D.) 35.5.
The expected value of a discrete random variable is found by multiplying each value of the variable by its corresponding probability and then summing these products. In this case, the probability distribution of y is given in the table.
To find the expected value of y, we need to calculate the sum of the products of each value of y and its corresponding probability.
y * probability = y * P(y)
The expected value of y is E(y) = 100.10 + 200.25 + 300.05 + 400.30 + 500.20 + 600.10
= 2 + 5 + 1.5 + 12 + 10 + 6 = 37.
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Your shifts productivity is slow because one person is not pulling his shares. the rest of the team is getting upset. what should you be most and least likely to do?
a rectangular field is to have 100 m2 in area. it was enclosed by fence. the north south sides costs $20/m, east-west sides cost $5/ m. what are the dimensions so that the cost is a minimum?
The dimensions of the rectangular field with a minimum cost are x = 50 m and y = 2 m.
Let x be the length of the north-south sides and y be the length of the east-west sides.
The area will be given by: A = xy
The cost will be given by: C = 20x + 5y
We have to find the dimensions (x and y) that minimize the cost C subject to the constraint that the area A is 100 m2.
Using the constraint, we have:
A = xy = 100
We can solve this equation for one of the variables in terms of the other, say x in terms of y.
We get: x = 100/y
Substituting this into the cost equation, we get:
C = 20(100/y) + 5y
Differentiating this equation with respect to y and equating it to 0, we get:
dC/dy = 20/y2 - 5 = 0
or, y2 = 4
or, y = ±2
We choose the positive value for y, so y = 2
Substituting this value of y in the equation for x, we get:
x = 100/2 = 50
Therefore, the dimensions of the rectangular field with a minimum cost are x = 50 m and y = 2 m.
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Give each trig ratio as a fraction in simplest form.
Answer:
[tex]df = \sqrt{ {29}^{2} - {20}^{2} } = 21 \\ \sin(d) = \frac{20}{29} \\ \cos(d) = \frac{21}{29} \\ \tan(d) = \frac{20}{21} \\ \sin(e) = \frac{21}{29} \\ \cos(e) = \frac{20}{29} \\ \tan(e) = \frac{21}{20} [/tex]
Answer:
Step-by-step explanation:
First, use the pythagorean theorem to complete the vales of each sides of the triangle. Then, use the respective trigonometric formulas and inverse the answer to compute the degree of every corners.
Solve the simultaneous equations by substitution 2 x − 3 y = 8
Answer:
To solve the simultaneous equations by substitution, we can first solve one equation for one of the variables, and then substitute that expression into the other equation. Here is one way to solve the given equation:
2x - 3y = 8
We can solve for x by adding 3y to both sides:
2x = 3y + 8
We can divide both sides by 2 to get x by itself:
x = (3y + 8)/2
Now we can substitute this expression for x into the other equation:
2((3y + 8)/2) - 3y = 8
Simplifying and solving for y:
3y + 8 - 3y = 8
8 = 8
So the solution for y is any value.
Now we can substitute the value of y into the equation x = (3y + 8)/2 and we'll get the value of x.
x = (3 * y + 8) / 2
For example if we substitute y = 2
x = (3 * 2 + 8) / 2 = 14/2 = 7
So the solution for the simultaneous equations is x = 7, y = 2
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What type of triangle is it if the lengths are 4 cm 5 cm and 6 cm?
A triangle with given lengths 4cm , 5cm , and 6cm is scalene and acute angled triangle.
As given in the question,
In the given triangle ,
Lengths of the sides of a triangle is given by :
4cm , 5cm , and 6cm.
All the sides are of different measure , it is a scalene triangle.
Apply cosine rule to find the measure of largest angle:
c = 6cm is the longest side opposite to largest angle.
c² = a² + b²- 2abcosα
⇒ 6² = 4² + 5² - 2(4)(5)cosα
⇒cosα = ( 16 + 25 - 36 ) / 40
⇒ cosα = 5/40
⇒ α = cos⁻¹( 1/8)
⇒ α = 82.8° < 90°
It is an acute angled triangle.
Therefore, for the given lengths of the triangle it is a scalene and acute angled triangle.
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the purpose of this lab is to find several types of samples given a population. your population is described below: population: the 24 students in a math 152 class. the following is the seating chart for the class. when choosing your sample only use the subject id not their name. describe how you found the sample fully including the technology you used and all steps you took.
To select a sample from the population of 24 math 152 students, I used stratified random sampling.
Stratified random sampling is when a population is divided into groups or strata, then a random sample is taken from each group. In this case, the population of 24 students was divided into two groups of 12. The first group was selected by randomly assigning each student a number from 1-12, then I used a random number generator to choose numbers from 1-12. The numbers that were chosen were the subjects for the first group. I repeated this process for the second group of 12, assigning each student a number from 13-24, then using the random number generator to choose the subjects for the second group. I repeated this process until I had a sample of 10 students. This process allowed me to create a sample that was representative of the entire population.
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Harley has 6 pints of lemonade. Rosie has 3 times as many pints of
lemonade as Harley.
a) How many pints of lemonade does Rosie have?
b) How many more pints of lemonade does Rosie have than Harley?
Give your answers as whole numbers or as fractions in their simplest form.
Answer: So in order to get a) you need to multiply 3 times 6 because Rosie has 3 times more pints than Harley so you would get 18. And to find b) you need to subtract the 6 from the 18 and you get 12. Rosie has 12 more pints than Harley.
Step-by-step explanation:
Is Ishmael or Ian correct?
Answer:
Ian is correct
Step-by-step explanation:
The range of a function is the set of all possible values that the function can take. In other words, it is the values of y lying between minimum and maximum
From the graph we can see that the minimum value of y = 0
Maximum value of y = 30
So the range is 0 ≤ y ≤ 30
So Ian is correct
(Note that y ≤ 30 can include negative values which is not possible in this case)
Given the points (3, -9) and (-9, 5) find the slope
Answer:0.5
Step-by-step explanation:
Hello I need some help with math
Answer:
y = 136
x=15
Step-by-step explanation:
to work this question out you must know the angles on a straight line add up to 180 degrees. By doing that we can find the top angle inside of the triangle.
180 - 104 = 76
to find x we need to know that angles in a triangle add up to 180 degrees.
180 = (3x-1) + 4x + 76
To solve for x, we can first simplify the equation.
180 = (3x-1) + 4x + 76
This can be re-arranged as:
(3x-1) + 4x = 104
and then combined as:
7x = 105
Finally, we can solve for x by dividing both sides by 7:
x = 105/7
x = 15
So the value of x that satisfies the equation is 15
to find y we need to know that angles on a line equal 180
180 = (3(15)-1) + y
180 = 44 + y
To find the value of y, we can subtract 44 from both sides
y = 180-44
y = 136
The triangle below has a total perimeter of 450 cm: picture of a triangle with sides 128 and 150. Third side unknown Write an equation and solve it to find the length of the longest side of the triangle. (1 point)
For the given perimeter and side length of the triangle , the equation and the measure of the longest side length of the triangle is given by :
Equation : x + 278 = 450 and side length = 172cm.
As given in the question,
The given measurements of the triangle are :
Perimeter of the triangle = 450cm
Measure of the two side length are :
Side length 1 = 128 cm
Side length 2 = 150 cm
let 'x' be the measure of the longest side length of the triangle we have,
Perimeter of the triangle = Side length 1 + Side length 2 + side length 3
⇒ 450 cm = 128 + 150 + x
⇒ 450 = 278 + x
Equation to represent the relation :
x + 278 = 450
Measure of the longest side of the triangle is :
⇒ x = 450 - 278
⇒ x = 172 cm
Therefore, the equation and the measure of the longest side length of the triangle with given perimeter and other side length is equal to
Equation : x + 278 = 450 and side length = 172cm.
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34 entre 250.6 con operacion
De acuerdo con la información del enunciado, el resultado de esta operación matemática (división) es 0,13
¿Cómo solucionar la división?Para solucionar la división, debemos realizar el siguiente procedimiento:Identificar las partes de la división (dividendo y divisor), en este caso como el divisor es más grande, debemos añadir un cero y una coma en el cociente para añadir un cero en el dividendo.Una vez hemos agregado un cero al dividendo, debemos identificar un número que al multiplicarlo con el divisor no de menor o igual al dividendo, en este caso sería 1, porque 250.6 * 1 = 250.6Entonces debemos hallar la diferencia entre 250.6 y 340, este procedimiento se hace con una resta y daría 89,4.Una vez hallamos este número, debemos identificar otro número para el cociente que multiplicado por 250,6 no de inferior o igual a 894, en este caso sería 3, 3 * 250,6 = 751.8En este paso debemos realizar otra resta para identificar la diferencia entre estos dos número. 894 - 751,8 = 142,2Esta división da como resultado un número decimal de varios valores por lo que podemos repetir este procedimiento tantas veces sea necesario dependiendo de la exactitud de nuestras necesidades.
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What single factor made the Hindu arabic number system superior
Invention of 0
What are the two purposes of numerals or digits
Show the cardinal value (how many)
And show the place value (10s, 100s, 1000s)
Natural numbers in a counting process
Does not include 0
1-2-3-4-5-6-7-8-9-10-11- infinity
Principle of closure
Addition- if you add any two natural numbers, the result will always be a natural number. Called closed under addition
Multiplication- if you multiply any two naturals, you get naturals. Called closed under addition
Subtraction- you cannot achieve closure when subtracting larger number from smaller number (i.e. 6-7)
Division - when you divide two natural numbers, it is possible to get a fraction. Not closed by division.
Integers
Positive and negative numbers, start at 0 and expand infinitely at both ends.
Closed under addition, multiplication, subtraction. NOT DIVISION
Rational numbers
Numbers that can be expressed as fractions, that is the quotient of two integers
Irrational numbers
Non terminating, repeating decimals
Three axioms of equality
Reflexive- law of identity. Any number reflects itself or is equal to itself (i.e. A=A)
Symmetric- any equality is reversible (i.e. A=B, then B=A)
Transitive property - possible to identity two numbers as being equal to a third quantity (a=b and b=c then a=c)
Commutative property
When adding, it doesn't matter the order
a+b=b+a
Order in which things are multiplied does not affect product (a*b=b*a)
Associative property
Law states that the order in which Addends are grouped, the sum will be unaffected. (a+b)+c = a + (b+c)
(A*b)*c = a(b*c)
Distributive property
Multiplication can be distributed over addition.
a(b+c)= (a*b) + (a*c)
Unity element
Number 1 is the identity element of multiplication. Any number multiplied by one equals itself
Zero element
Identity element for addition
Will destroy number, anything multiplied by 0 =0
Dividing by 0 is error.
0 /# = 0
The Hindu-Arabic numeral system is superior to other numeral systems because of its invention of the number 0. This allows for the representation of the concept of nothingness or absence, which allows for the development of more advanced mathematical operations such as negative numbers and decimal fractions.
The two purposes of numerals or digits are to show the cardinal value (how many) and to show the place value (10s, 100s, 1000s). The cardinal value is the actual quantity of a number, while the place value is the position of a digit in a number, which determines its value in relation to other digits.
The natural numbers are the numbers used in a counting process and do not include 0. They include the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on to infinity. The principle of closure is the idea that certain operations, such as addition and multiplication, will always result in a natural number when performed on natural numbers. However, subtraction and division do not result in natural numbers in all cases.
Integers are positive and negative numbers that start at 0 and expand infinitely in both directions. They are closed under addition, multiplication, and subtraction. However, division is not closed under integers.
Rational numbers are numbers that can be expressed as the quotient of two integers. Irrational numbers are non-terminating, non-repeating decimals.
The three axioms of equality are the reflexive property (A = A), the symmetric property (if A = B, then B = A), and the transitive property (if A = B and B = C, then A = C).
The commutative property states that the order of the numbers does not affect the result in operations such as addition and multiplication. The associative property states that the grouping of numbers does not affect the result in operations such as addition and multiplication. The distributive property states that multiplication can be distributed over addition.
The unity element for multiplication is the number 1, which serves as the identity element for multiplication. The zero element for addition is 0, which serves as the identity element for addition. Dividing by 0 is an error and not allowed.
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4 Which number is included in the set of integers that when added to –4 gives a sum of less than zero? Select all that apply. A 3 B 7 C 9 D –2 E 4 F 0
The number included in the set of integers that when added to -4 gives a sum less than zero are 0, -2 and 3
How to find the integers in a word expression?The question wants us to find the numbers included in the set of integers that when added to -4 gives a sum less than zero.
The options are 3, 7, 9, -2, 4 and 0.
Therefore,
let
the number added = x
Hence,
-4 + x < 0
Base on the options, the numbers that fits into the inequality are as follows:
The numbers are 0, -2 and 3.
Therefore,
-4 + 0 < 0
-4 + -2 < 0
-4 + 3 < 0
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the sum of fifteen and three times a number is equal to 24. find the number
Answer:
The number is 6Step-by-step explanation:
The equation given:
[tex]15 + \left(3x\right) = 24[/tex]
Our goal is to find x. To find x, what I like to do is add the given values together, then subtract them by 24 to find x's value.
[tex]15 + 3 = 18\\24 - 18 = x\\x = 6[/tex]
Hope this helps!
State the center point and radius of the circle. Write the equation of the circle in standard and general form.
The equation of the circle is [tex](x-2)^2+(y+1)^2=16[/tex].
What is equation of the circle?
A closed curve that is drawn from a set point known as the center and has all of its points at exactly the same distances from it is termed a circle. The formula for a circle with the coordinates (h, k) in its center and radius is [tex](x-h)^2+(y-k)^2=r^2[/tex]
This represents the equation's conventional form. As a result, the equation for the circle is simple to find if we also know the coordinates for the radius of the circle.
Here according to the graph the center of the circle is (2,-1) and radius of the circle = 2+2=4 unit.
Now using circle equation then
=> [tex](x-p)^2+(y-q)^2=r^2[/tex]
Where p=2 , q=-1 and r=4 then
=> [tex](x-2)^2+(y-(-1))^2=4^2[/tex]
=> [tex](x-2)^2+(y+1)^2=16[/tex]
Hence the equation of the circle is [tex](x-2)^2+(y+1)^2=16[/tex].
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An experienced bricklayer can work twice as fast as an apprentice bricklayer. after the bricklayers work together on a job for 4 hours, the experienced bricklayer quits. the apprentice requires 14 more hours to finish the job. how long would it take the experienced bricklayer, working alone, to do the job?
The total time taken by the experienced bricklayer to complete the job as per given condition is equal to 13 hours.
As given in the question,
Let the time taken by experienced bricklayer be 't' hours
Then time taken by apprentice bricklayer be '2t' hours
Time to complete 1 complete work is
Experienced bricklayer worked for 4 hours
Apprentice bricklayer worked for ( 4 + 14 ) = 18 hours
Required equation to complete 1 work is :
( 4/x) + ( 18 /2x) = 1
⇒( 8 + 18 )/ 2x = 1
⇒26/2 = x
⇒ x = 13 hours
Therefore, time taken by the experienced bricklayer to complete the job is equal to 13 hours.
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In a class of 100 students, 30 are computer science majors, 49 are mechaincal engineering majors, 13 are civil engineers and the rest are general engineering majors. Assume students only have one major.Suppose five students from the class are chosen at random what is the probability none are mechanical engineering majors?My info I know: The mechanical engineers account for 49% of the students, making 51% not mechanical engineers? Do I take five out of the 51, so 0.05 X 0.51?
The probability that none of the five students chosen at random are mechanical engineering majors is 0.0111 or about 1.11%.
The probability that none of the five students chosen at random are mechanical engineering majors is
=(51/100) * (50/99) * (48/98) * (47/97) * (46/96)
= 0.0111
This means that the probability is about 1.11%
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
The probability means that the chances of an event to occur or do not occur and it lies between the range of 0 and 1.
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A forest covers 51,000 acres. A survey finds that 0.4% of the forest is old-growth trees. How many acres of old-growth trees are there?
If a forest covers 51,000 acres. A survey finds that 0.4% of the forest is old-growth trees. The number of acres of old-growth trees that are there is: 204 acres.
How to find the number of acres?Using this formula to find the number of acres that are there.
Number of acres = Number of forest covers acres × Forest old growth tree percentage
Where:
Number of forest covers acres = 51,000 acres
Forest old growth tree percentage = 0.4% or 0.004
Let plug in the formula
Number of acres = 51,000 acres × 0.004
Number of acres = 204 acres
Therefore we can conclude that the number of acres is 204 acres.
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What does the statement T(60(>T(10)+T(30) mean
T(60) > T(10) + T(30) means that the number of tenants living on 60th floor is greater than the sum of tenants that are living in 10th and 30th floor.
What is meant by n, T(n) and tenant:
n = number of floor of the Princess Tower (Floor Number)
T(n) is a function of n (floor number) which tells how many tenants are beings living on the nth floor
Tenant means a person occupying a rented land or property (A resident for simple understanding)
Therefore:
T(60) means the number of tenants living on 60th floorT(10) means the number of tenants living on 10th floorT(30) means the number of tenants living on 30th floorThus using the above information, it should be clear that:The statement: T(60) > T(10) + T(30)
Means that: The number of tenants living on 60th floor is greater than the sum of tenants living on 10th and 30th floor.
Just for an example If we have T(60) = 30, T(10) = 10, T(30) = 5
Then T(60) > T(10) + T(30) means that 30 > 10 + 5 which becomes 30 > 15
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Think About the Process At a supermarket, a 6-ounce bottle of brand A salad dressing costs $1.56. A 14-ounce bottle costs $3.36. A 20-ounce bottle costs $5.60. What unit prices do you need to know to find the best buy? What is the best buy?
a) The unit prices to determine the best buy are as follows:
6-ounce bottle = $0.2614-ounce bottle = $0.2420-ounce bottle = $0.28.b) The best buy is the 14-ounce bottle of salad dressing with a unit cost of $0.24 since they are all Grade A products.
What is the unit price?The unit price or cost is the cost for an item or a unit.
The unit price can be compared to the unit rate, which is the quotient of the total cost and the number of units.
6 ounces 14 ounces 20 ounces
Total costs $1.56 $3.36 $5.60
Unit cost $0.26 $0.24 $0.28
($1.56/6) ($3.36/14) ($5.60/20)
Thus, buying a 14-ounce bottle of salad dressing is more economical than others.
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Math
B8.18 Evaluate a linear function: word problems
c = 18h + 63
4) This equation shows how the cost of renting a moving van depends on how many hours
it is rented for.
The variable h represents the number of hours the moving van is rented for, and the
variable c represents the cost in dollars. For $81, what is the maximum amount of time that a
moving van can be rented for?
Quizzes
DELL
pls help!!
Therefore , the solution of the given problem of equation comes out to be 1 hour is required to generate 81$ .
Clarify Equation.The equal symbol (=) is used to indicate equivalency in a statement for a mathematical model, which combines two statements. In algebra, an equation is a claim that establishes the similarity of two mathematics. The formula 78x + 5 = 14 connects the two numbers, for example. The statements on either face of a letter form a mathematical connection. Typically, the symbol is the lone element and the only variable. For example, 9x – 4 = 2.
Here,
Given :c = 18h + 63
Where c is cost in dollars
and h is hour spend.
Thus ,
To find the maximum amount of time to generate $81
So,
Using equation:
81 = 18h + 63
=> 18h = 81-63
=> 18h = 18
=> h =1
Therefore , the solution of the given problem of equation comes out to be 1 hour is required to generate 81$ .
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50% of what number is 140?
Answer:280
Step-by-step explanation:
determine whether the series is convergent or divergent. 1 + 1 2 2 + 1 3 3 + 1 4 4 + 1 5 5 ⋯
We can see from the provided data that it is obviously divergent.
What in mathematics is convergent and divergent?Convergent sequence occurs when, as n approaches infinity, you arrive at a final as well as constant term through a number of terms. Divergent sequences are those in which individual terms never stabilize; instead, they constantly grow or decrease as n approaches infinity, approaching either infinity or -infinity.
Is divergence equivalent to infinity?A series diverges when it moves up, down, to infinity or minus infinity without settling on a value.
The series' parts are becoming larger and larger while being interrupted by some constant "1" (however they are useless in this situation since the series is divergent because there are always two numbers that follow an intercepting "1" that are greater by 1 than the two that came before it).
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You are using a 9-inch paint roller to paint a wall of your bedroom. The roller has a diameter of 158 inches and a nap thickness of 14 inch, as shown. The nap is the fuzzy material on the surface of the roller.
The area covered by the roller in one full revelation is 1674 square inches.
Step-by-step explanation:
Given that You are using a 9 inch paint roller to paint a wall of your bedroom. The roller has a dimension of 158 inches as diameter and a nap thickness of 14 inch, as shown,
The nap is the fuzzy materials on the surface roller. How much area does the roller cover in one full revelation
The parameters to be considered are:
Diameter = 158 inches
Thickness = 14 inches
After one revolution rolling, the dimensions of the length will be:
L = 14 + 158 + 14
L = 186 inches.
Let the width be equal to 9 inches
The area covered = L × W
Substitute L and W into the formula
Area = 186 × 9
Area = 1674 square inches.
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During the summer, 1.3% of the water in the kiddie pool evaporates every day. if the kiddie pool holds 8,000 gallons of water and is not refilled for 10 days, how many gallons of water will be in the pool?
7019 gallons of water will be in the pool.
Initial volume of water = 8000 gal
Daily reduction = 1.3%
Time = 10 days
Required equation:
=8000*(1- 0.013)^10
=8000*0.987^10
=7018.7781 ≈ 7019 rounded to the nearest gallon.
An expression that uses constant algebraic numbers, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
In contrast, since they are not derived from integer constants and algebraic operations, transcendental numbers like and e are not algebraic. The definition of e necessitates an infinite number of algebraic operations, while the construction of is typically done as a geometric relationship.
Any expression that can be converted into a rational fraction using the properties of the arithmetic operations is said to be rational (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).
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I got a word problem for you maths people that I need help with
Answer: sometimes
Step-by-step explanation:
nine times the sum of a number and 4 is equal to 7
Use the variable w for the unknown number. Write it into an equation
Answer:
9(w+4)7
Step-by-step explanation:
I got this answer too, just like the person before me
(a) A parallelogram has base (2x - 1) metres and height (4x-7) metres.
The area of the parallelogram is 1 m².
(i) Show that 4x² - 9x +3=0.
Answer (a)(i)
“please show steps and thank you”
Answer:
See below.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a parallelogram}\\\\$A=bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
Given:
[tex]b = (2x - 1)\;\sf m[/tex][tex]h = (4x - 7)\;\sf m[/tex][tex]A=1\;\sf m^2[/tex]Substitute the expressions for b and h and the value of A into the formula for area:
[tex]\implies 1=(2x-1)(4x-7)[/tex]
[tex]\implies (2x-1)(4x-7)=1[/tex]
Expand the brackets:
[tex]\implies 8x^2-14x-4x+7=1[/tex]
[tex]\implies 8x^2-18x+7=1[/tex]
Subtract 1 from both sides of the equation:
[tex]\implies 8x^2-18x+7-1=1-1[/tex]
[tex]\implies 8x^2-18x+6=0[/tex]
Factor out 2 from the left side:
[tex]\implies 2(4x^2-9x+3)=0[/tex]
Divide both sides by 2:
[tex]\implies 4x^2-9x+3=0[/tex]
Hence, showing that 4x² - 9x + 3 = 0.
if xy + 8ey = 8e, find the value of y'' at the point where x = 0.
The value of y'' at the point where x = 0 is 8.
A derivative is a mathematical concept that measures how much a function changes as its input (or independent variable) changes. It is often represented by the symbol "dy/dx" or "f'(x)", and is used to calculate the slope of a function at a particular point.
To find the value of y'' at the point where x = 0, we first take the derivative of the equation with respect to x. This gives us y' + 8exy' = 0. Then, we take the derivative of this equation with respect to x again, which gives us y'' + 8exy'' + 8ey' = 0. Substituting x = 0 into this equation gives us y'' + 0 + 8e(0) = 0, which simplifies to y'' = 8.
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