The amount of each legacy is 55 , 275 , 385 , 605.
What is linear equation ?Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on. Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.
Calculationequations:
a + b + c + h = 1320
a+h = b+c
b+h = 2(a+c)
c+h = 3(a+b)
---------------------
Rearrange:
a + b + c + h = 1320
a - b - c + h = 0
2a- b +2c - h = 0
3a+3b -c - h = 0
--------------------------
I used my TI-84 to get:
a = 55
b = 275
c = 385
h = 605
learn more about linear equations here :
brainly.com/question/11897796
#SPJ4
What do you do for this question
Answer:
= 197.5 [tex]cm^{2}[/tex]
Step-by-step explanation:
1) first split the shape into two shapes (a rectangle and trapezium)
2. find the area of the rectangle
10 x 6 = 60 [tex]cm^{2}[/tex]
3. find the missing sides for the trapezium and substitute it into the formula for finding the area of trapezium
([tex]\frac{a+b}{2}[/tex])xh
a=10
b= 15
h = 11 (17-6=11)
( [tex]\frac{10+5}{2}[/tex])x 11
this gives you 137.5 [tex]cm^{2}[/tex]
4. add both the areas together
60 [tex]cm^{2}[/tex] + 137.5 [tex]cm^{2}[/tex] = 197.5 [tex]cm^{2}[/tex]
5 so your final answer is 197.5 [tex]cm^{2}[/tex]
Evaluate the expression when c=12 and d=112. 3(14 c2) 2d enter your answer as a mixed number in simplest form in the box.
The value of the expression is 698.
What is an expression?
A mathematical expression is a phrase containing a minimum of two numbers or variables and a minimum of one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression)
The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication, and division (left to right), addition and subtraction (from left to right).
Given expression 3*(14+c²) +2d
3*(14+12²)+2*112
= 42+3*12²+224
= 42+3*144+224
= 42+432+224
= 698
To learn more about the expression from the given link
https://brainly.com/question/25968875
#SPJ4
3. Because it is so popular, a store owner increases the cost of a toy by $4.99. The new cost of the toy is $14.84. (a) Write an equation that represents the situation. Use c to represent the original cost of the toy. (b) Solve the equation using a related equation. Show your work. (c) What does the solution of the equation represent? HELP ASAPPP
The equation that represents the situation is c + 4.99 = 14.84, and the store owner increased the original price of the toy by adding $5.
What is the percent increase?
The formula for percentage increase is the ratio of the increased value to the original value multiplied by 100. It is expressed as a percentage. If the price of something rises, the percentage rises as well.
a) c + 4.99 = 14.84.
c = 14.84.- 4.99
c = 9.84
(b) 14.84 - 9.84 = 5
(c) Store owner increased the original price of the toy by adding $5.
hence, the equation that represents the situation is c + 4.99 = 14.84, and the store owner increased the original price of the toy by adding $5.
To learn more about the percent increase visit,
https://brainly.com/question/24753098
#SPJ1
5x+-3=-18 (pls help me)
Answer: x = 3
Step-by-step explanation:
5x+-3=-18
5x + -3 + 3 = -18 + 3 (add 3 to both sides)
5x = 15
5x/5 = 15/5
x = 3
Answer: x =3
Step-by-step explanation:
HELPPP MATH 30 pointsss
Answer:
Step-by-step explanation:
h(x) = 3x - 5
h(-2) = 3*(-2) - 5 = -6 -5 = - 11
a fair coin is tossed five times, and each time the coin lands tails up. if the coin is then tossed 1990 more times, how many tails are most likely to appear for the 1990 additional tosses?
Probability of getting tails are most likely to appear for the 1990 additional tosses will be 1/32.
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Here,
The coins gets tail always,
=(1/2)^5
=1/32
For the 1990 additional tosses, there is a 1/32 chance that a tail will appear.
To know more about probability,
https://brainly.com/question/11234923?referrer=searchResults
#SPJ4
please help me answer this worksheet (Geometry Worksheet 3.3)
As per the reference document attached thereby along with the question statement, if (∠SOX = 160°), [∠1 = (x + 14)], and [∠2 = (3x – 10)], then the measure of ∠2 in degrees will be 113°
As per the reference document attached thereby along with the question statement, (∠SOX = 160°), and it's constituent angles
[∠1 = ∠SOW = (x + 14)], and [∠2 = ∠WOX = (3x – 10)],
And we are required to determine the measure of ∠2.
Since, [(∠SOW + ∠WOX) = ∠SOX],
Therefore, [{(x + 14) + (3x – 10)} = 160°]
Or, [{(x + 3x) + (14 - 10)} = 160°]
Or, [(4x - 4) = 160°]
Or, [4x = (160 + 4)°]
Or, (4x = 164°)
Or, [x = (164/4)°]
Or, (x = 41°)
Or, [(3x – 10) = {(3 * 41) - 10}°]
Or, [∠2 = (123 - 10)°]
Or, (∠2 = 113°)
That is, if (∠SOX = 160°), and it's constituent angles (∠1) and (∠2) measure as [∠1 = ∠SOW = (x + 14)], and [∠2 = ∠WOX = (3x – 10)], then the measure of ∠2 in degrees will be 113°
To learn more about Measures in Degrees, click on the link below.
https://brainly.com/question/12362603
#SPJ1
what kinds of images are based on mathematical instructions that define lines, curves, text, ovals, and other geometric shapes?
The mathematical instructions that define lines, curves, text, ovals, and other geometric shapes is vector graphics
The vector graphics is defined as the computer graphics that the visual images are created directly from geometric shapes. It is defined on the Cartesian plane such as lines, curves, texts, ovals and other geometric shapes
The vector artworks are the artwork that created by vector graphics. There will be lines curves, text, oval and other geometric shapes according to the mathematical expression
Therefore, the vector graphics is the mathematical instruction that defines the geometric shapes
Hence, the mathematical instructions that define lines, curves, text, ovals, and other geometric shapes is vector graphics
Learn more about geometric shape here
brainly.com/question/13704812
#SPJ4
help asaap
7.2.1 Prove that AABC and ALMN are congruent.
7.2.2 Given that AFGH|||ALMN.
Calculate the value of x.
The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate. And the value of the variable 'x' will be 6 cm.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
In triangles ΔABC and ΔLMN, we have
AB = LM = 8 cm
∠B = ∠M = 90°
AC = LN = 12 cm
The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate.
The triangles ΔFGH and ΔLMN are similar triangles, then we have
x / 12 = 4 / 8
x / 12 = 1 / 2
x = 12 / 2
x = 6 cm
The triangles ΔABC and ΔLMN are congruent triangles by the SAS postulate. And the value of the variable 'x' will be 6 cm.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ1
Find the angle measure (15x+12)°=(19x–24)°
The measurement of angle is 147°
Equation is combination of mathematical operation , numbers and variables.
Solving the equation involves finding the unknown variable by the given equation . The condition that two expression are equal is only satisfied by value of that unknown variable.
Solving given equation to find x ,
=> (15x+12)°=(19x–24)°
Bring x terms together and changing their signs,
=> 15x - 19x = -24 - 12
=> -4x = -36
=> x = -36 / -4
Cancelling the negative signs and dividing,
=> x = 9
Substituting the value of x
Angle = 15(9) + 12
=> 135 + 12
=> 147°
To know more about Equation here
https://brainly.com/question/15707224
#SPJ9
an ostrich farmer wants to enclose a rectangular area and then divide it into six pens with fencing parallel to one side of the rectangle (see the figure below). there are 900 feet of fencing available to complete the job. what is the largest possible total area of the six pens?
The largest possible total area of the six pens is 33750 square feet.
Given:
An ostrich farmer wants to enclose a rectangular area and then divide it into six pens with fencing parallel to one side of the rectangle (see the figure below). there are 900 feet of fencing available to complete the job.
Let L and W be the length and width.
900 = L + 6W
L = 900 -6W
Area = A = LW = (900-6W)W = 900W -6W^2
A' = 990-12W = 0
W = 900/12 = 75 feet wide
L = 900 -6W = 900 - 6(75)
L = 900 - 450 = 450 feet.
Maximum area = 450 * 75
= 33750 square feet.
Therefore the largest possible total area of the six pens is 33750 square feet.
Learn more about the total area here:
https://brainly.com/question/8419462
#SPJ4
(x+5) is a factor of R(x)=x^4+5x^3-16x^2-80x. What are the zeros of the function R(x)?
A) 2, 3, -4, -5 B) 0, 3, -3, -5
C) 0, 3, 4, -5 D) 0, 4, -4, -5 E) 0, 16, -16, -5
The zeros of the function R(x) will be 0 , 4 , -4 , -5.
The equation given to us is
[tex]x^{4}[/tex] + 5[tex]x^{3}[/tex] - 16[tex]x^{2}[/tex] - 80x = 0
Take x common
x( [tex]x^{3}[/tex] + 5[tex]x^{2}[/tex] - 16x - 80 ) = 0
from here we get one factor of x as 0.
Now
[tex]x^{3}[/tex] + 5[tex]x^{2}[/tex] - 16x - 80 = 0
It is given that x + 5) is a factor of this equation. so we will divide the equation by (x + 5).
After dividing it by (x + 5) we get [tex]x^{2}[/tex] - 16
Which can be written as [tex]x^{2}[/tex] - [tex]4^{2}[/tex] = (x + 4) (x - 4)
From here we get rest of the two roots of the equation.
Therefore four zeros of the function will be 0 , 4 , -4 , -5.
to know more about zeros of function
https://brainly.com/question/28668134
#SPJ1
Answer:
D) 0, 4, -4, -5
Step-by-step explanation:
Given polynomial:
[tex]R(x)=x^4+5x^3-16x^2-80x[/tex]
Given (x + 5) is a factor of R(x), use long division to find the other factor:
[tex]\large \begin{array}{r}x^3-16x\phantom{)}\\x+5{\overline{\smash{\big)}\,x^4+5x^3-16x^2-80x\phantom{)}}}\\{-~\phantom{(}\underline{(x^4+5x^3)\phantom{-b))))))))))))}}\\-16x^2-80x\phantom{)}\\-~\phantom{()}\underline{(-16x^2-80x)\phantom{}}\\0\phantom{)}\\\end{array}[/tex]
Therefore:
[tex]R(x)=(x^3-16x)(x+5)[/tex]
Factor out x from the first factor:
[tex]R(x)=x(x^2-16)(x+5)[/tex]
Apply the Difference of Two Square Formula: a²-b²=(a-b)(a+b)
[tex]\begin{aligned}\implies x^2-16&=x^2-4^2\\&=(x-4)(x+4)\end{aligned}[/tex]
Therefore:
[tex]R(x)=x(x-4)(x+4)(x+5)[/tex]
Zero Product Property
If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
To find the zeros of the function, apply the zero-product property by setting each factor equal to zero and solving for x:
[tex]\implies x=0[/tex]
[tex]\implies x-4=0 \implies x=4[/tex]
[tex]\implies x+4=0 \implies x=-4[/tex]
[tex]\implies x+5=0 \implies x=-5[/tex]
Therefore, the zeros of the function R(x) are:
0, 4, -4, -5Bao is the oldest of four siblings whose ages are consecutive even integers. If the sum of their ages is 60, find Bao's age.
Answer:
:)......................
Bao's age is 12 years old.
What are Integers?Integers are defined as the collection of Whole Numbers and the negative values of Natural Numbers make up an integer. Fractional numbers are not included in integers. Integers are represented by the symbol Z.
Let's call Bao's age "x".
Since their ages are consecutive even integers, the next sibling's age would be x + 2, the next one x + 4, and the last one x + 6.
The sum of all their ages is x + (x + 2) + (x + 4) + (x + 6) = 4x + 12 = 60.
Solving for x, we get 4x + 12 = 60, and subtracting 12 from both sides gives 4x = 48.
Dividing both sides by 4 gives x = 12.
Therefore, Bao's age is 12 years old.
To learn more about the integers click here:
https://brainly.com/question/1768254
#SPJ2
Himesh has blocks like the one shown below. 6 cm -8 cm- -7 cm- He wants to build a 40 cm high tower with such blocks. What is the LEAST number of blocks with which he can do this?
The least number of blocks with which he can do is 168 blocks.
What is the least Common Multiple (LCM)?
The Least Common Multiple (LCM) is a method for determining the smallest common multiple of two or more numbers. A common multiple is a number that is the product of two or more numbers.
Least number of blocks = LCM of 6cm, 7cm, and 8cm.
Multiples of 6 - 6,12,18,24,30,36,42,48,54,60
Multiples of 7 - 7,14,21,28,35,42,49,56,63,70
Multiples of 8 - 8,16,24,32,40,48,56,64,72,80
Common Multiples - 168
Least Common Multiple - 168
So the least number of blocks with which he can do is 168 blocks.
To learn more about the Least Common Multiple (LCM) visit,
https://brainly.com/question/233244
#SPJ9
Planes m and n intersect at line d. line a forms a right angle with line d. line b is diagonal and crosses line d. line c is on plane n and is diagonal. line e is on plane m and is slightly diagonal at the top of the plane. which are skew lines? check all that apply. a and b c and b b and e e and c a and e a and c
the answers are option 2 4 6
Answer:
B,D,F
Step-by-step explanation:
The time it takes to wash all the windows on a large building w(z) varies inversely with the number of workers assigned to the job x.
It takes 6 hours to complete the job when 4 workers are assigned to it.
Which equation can be used to find the time to complete the job when x workers are assigned to it?
a.)w(x) = 24/x
b.)w(x)= 1.5x
c.)w(x)=10/x
d.)w(x)=24
The equation that can be used to find the time to complete the job can be expressed as w (x) = 1.5x, so option B is correct.
What is the equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
The time taken to complete the work = 6 hrs,
The no of worker = 4,
The no of workers = The time taken by four workers / no of workers,
w (x) = 6 /4x
w (x) = 1.5x
Therefore, the equation that can be used to find the time to complete the job can be expressed as w (x) = 1.5x.
To know more about equation:
https://brainly.com/question/12788590
#SPJ1
Help please! Find the slope of the line that goes through these two points.
(–6, −3), (–19, 16)
The slope of the line that goes through these two points is -19/13.
Given points:
(–6, −3), (–19, 16)
slope:
Slope is the steepness of a line as it moves from LEFT to RIGHT. Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line. The slope of a line is always constant (it never changes) no matter what 2 points on the line you choose.
slope m = y2-y1 / x2-x1
= 16-(-3) / -19-(-6)
= 16+3/-19+6
= 19/-13
= -19/13
Therefore The slope of the line that goes through these two points is -19/13.
Learn more about the slope here:
https://brainly.com/question/3605446
#SPJ1
Mr Pilgrim has a turkey farm. He has one male turkey for evey 17 female turkeys. if he has 289 females, how many male turkeys does he have? can the number of female turkeys be expressed using exponents? if so, how?
There are in total 17 Male Turkey in the farm
What is Division?
Division is one of the four basic operations of arithmetic, which are the methods through which numbers are joined to form new numbers. Addition, subtraction, and multiplication are the other operations.
Solution:
Here we will use the concept of basic division
Since, there is 1 male turkey for every 17 female turkey
Therefore, it can be said that
Total Male Turkeys for 289 Female Turkey = 289 / 17
Total Male Turkey = 17
Yes we can express the number of female turkey in exponent as [tex]17^{2}[/tex]
To learn more about Division from the given link
https://brainly.com/question/24662212
#SPJ1
Graph AXYZ with vertices X(2, 4), Y(6, 0) and Z(7, 2) and its image after the composition.
Translation: (x,y) → (x-6.y)
Translation: (x, y) → (x+2y+7)
After 1st Translation (x,y) → (x-6.y) = X(-4,4), Y(0,0), Z(1,2)
After 2nd Translation (x, y) → (x+2y+7) = X(4,11), Y(8,7), Z(9,9)
What is translation?
Translation is a transformation where all points of the figure are moved the same distance in the same direction. The distance and direction are indicated by a ray sometimes called the translation vector. A vector is a quantity that has both length and direction, and can be thought of as a line segment with a starting point and an endpoint. A translation is an isometry, so the image of a translated figure is congruent to the preimage.And image After Composition means resultant image after you plot the translated points.
So, Given Vertices are X(2,4), Y(6,0), Z(7,2)
Then after 1st Translation = X(-4,4), Y(0,0), Z(1,2)
After 2nd Translation = X(4,11), Y(8,7), Z(9,9)
To know more about translation check below link:
https://brainly.com/question/12861087
#SPJ9
X
The following question has two parts. First, answer part A.
Then, answer part B.
Part A
Hailey is making floral centerpieces for a wedding. Each
centerpiece has 17 flowers. She has 430 flowers for the project.
She estimates that she can make between 20 and 30 complete
centerpieces. Is her estimate reasonable?
Use your knowledge of place value and division to explain the
reasonableness of her answer.
18
▾ Math symbols
centerpieces
+
010
II
=
LA
I
08 (-)
v
X
O
>
?
+
[-]
H
Part B
How many complete centerpieces can she make? Find the
exact answer.
a subset bb of the set of integers from 11 to 100100, inclusive, has the property that no two elements of bb sum to 137137. what is the maximum possible number of elements in bb?
The maximum possible number of elements in B = 68.
A subset B of the set of integers from 1 to 100, inclusive, has the property that no two elements of B sum to 137.
Maximum possible number of elements in B =?
Set of integers = {1, 2, 3, 4, 5......100}
If we divide 137/2 = 68.5
If we add 68+69 = 137
So, we cannot consider number 69 in the subset, it gives us the total numbers we can consider are till 68.
Set B = {1,2,3,4,5,6,7....60,61,68}.
The maximum possible number of elements in B = 68.
Learn more about elements:
https://brainly.com/question/14347616
#SPJ4
Nathaniel's car used 2/3 of a gallon to travel 11 miles. How many miles can the car go
on one gallon of gas?
Nathaniel’s travel 16.5 miles with one gallon gas
Arithmetic generalization in which letters representing numbers are combined using arithmetic rules. Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions.
Given that Nathaniel's car used 2/3 of a gallon to travel 11 miles
We have to find how many miles can the car goon one gallon of gas
2/3 gallons = 11 miles
1 gallon = ?
= (11x 1)/(2/3)
= 33/2
= 16.5 miles
Therefore Nathaniel travel 16.5 miles with one gallon gas
To learn more about algebra visit
https://brainly.com/question/12130720
#SPJ1
Explain how to find the distance between 1 and -3 on a number line.
Answer: Distance can't be negative, so it must be positive. That's the first thing you need to know. To find the distance, you take the difference between the two points.
1 - (-3) = 4
(second point on the number line) - (first point on the number line)
4
Convert the mixed number to an improper fraction. -5-
5
=
Answer:
+1
Step-by-step explanation:
So, you just first multiply the denominator to whole then add to the numerator after that the denominator will remain the same and the numerator will be the remainder
Use a model in 2006, the average ticket price for a national football league game was $62. 38. Since then the cost has increased an average of $2. 54 per year. Write a linear equation to represent the cost c of an nfl ticket y years after 2006.
The linear equation to represent the cost of C of an NFL ticket y years after 2006 is y=2.54x+62.38.
Given that the average ticket price for a national football league game was $62. 38 and the cost has increased an average of $2. 54 per year.
we want to write a linear equation to represent the cost c of an nfl ticket y years after 2006.
A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The equation can be written in the form y=mx+b.
Let us assume x represent the duration or stipulated years after the year 2006, y represent the amount of ticket that is sold and m represent the average increase in the price every year.
y=mx+c
y=2.54x+62.38
Hence, a linear equation to represent the cost c of an nfl ticket y years after 2006 is y=2.54x+62.38 when the average ticket price for a national football league game was $62. 38 and the cost has increased an average of $2. 54 per year.
Learn more about the linear equation from here brainly.com/question/4074386
#SPJ4
Please anyone I need and explanation and just h and c solving them and explaining how that it please.
Answer: h = 19, c = 132
Step-by-step explanation:
Oooh! This is a toughie!
Okay, first of all, there's a straight line on top. A straight line is 180 degrees.
This means we have to subtract 48 from 180.
180 - 48 = 132.
This means both a and b are 132.
F is equal to 151.
180 - 151 = e
e = 29
d = 29
g = 29
132 + 29 = 161
180 - 161 = 19
h = 19
19 + 29 = 48
180 - 48 = 132
c = 132
Sorry that this answer isn't so clear...
(BTW, it'd make me happy if you gave me the brainliest reward)
Which problem can be solved by determining 5 ÷ 1/4?
Answer:
[tex]20[/tex]
Explanation:
[tex]5[/tex] ÷ [tex]\frac{1}{4}[/tex]
To change the division sign into a multiplication sign, you need to change (1/4) into its reciprocal.
[tex]5[/tex] × [tex]\frac{4}{1}[/tex]
[tex]5[/tex] × [tex]4[/tex]
[tex]20[/tex]
1. Which is the solution of 8 -3(1-x) = 2(x + 1)-3? Ax=-6 B © x= D x = 9/10 6550 x=4 204
We are given the following:
[tex]8-3(1-x)=2(x+1)-3[/tex]
To solve for x, simplify both sides of the equation, then isolate the variable.
Option A; [tex]x = -6[/tex] ← Our Solution
Hope this helps!
Kayden invested $6,300 in an account in the year 2006, and the value has been growing exponentially at a constant rate. The value of the account reached $8,200 in the year 2010. Determine the value of the account, to the nearest dollar, in the year 2019.
The answer to the expositional growing account will be $14838.
What is exponential function?
The mathematical formula for an exponential function is f (x) = ax, where x is a variable and a constant known as the base of the function, which must be greater than zero. The transcendental number, or e, which is roughly equivalent to 2.71828, is the most frequently used exponential function base.
Let suppose in the xth year, the value of the money is 6300* [tex]a^{4}[/tex]
⇒8200 = 6300* [tex]a^{4}[/tex]
⇒a = 1.068
So 6300 *[tex]a^{13}[/tex]
= $14838
Hence the value of the account will be $14838.
Learn more about expositional, by the following link
https://brainly.com/question/2456547
#SPJ1
if the rvr equipment is inoperative for an iap that requires a visibility of 2,400 rvr, how should the pilot expect the visibility requirement to be reported in lieu of the published rvr? a. as an rvr of 2,400 feet. b. as a ground visibility of 1/2 sm. c. as a slant range visibility of 2,400 feet.
The correct answer is the pilot should expect the visibility required to be reported in lieu of the published RVR as a ground visibility of 1/2SM.
Visibility is half of a statute mile (SM). Persuading visibility is described in statute miles and fractions. The visibility having 15+ is encrypted as 15SM. Lower visibilities which are half or less of the visibility are detailed in the remarks section. Low visibility procedures (LVP) refer to procedures related to an aerodrome for the cause of ensuring safe operations in the course of lower-than-standard value and low visibility take-offs.
Reduced visibility operations are operations that take place at an aerodrome during the visibility is lower than Runway Visual Range which is 2600 RVR and 1/2 statute mile sm down to and including 1200 RVR and 1/4 statute mile sm.
To know more about Runway Visual Range RVR:
https://brainly.com/question/29382382
#SPJ4
