9514 1404 393
Answer:
1333.3 N
Step-by-step explanation:
The centripetal acceleration is given by ...
a = v^2/r
a = (100m/s)^2/(3 m) = (10^4)/3 m/s^2
Then the force on the ball is ...
F = Ma = (0.4 kg)(10^4)/3 kg·m/s^2 ≈ 1333.3 N
Find the z-score such that the area under the standard normal curve to its left is 0.2
The z-score such that the area under standard normal curve to its left is 0.2 is found as -0.84.
Explain the term Z-score?A mathematical table known as the Z table, also known as the Z-score table or the standard normal table, is used to determine the likelihood that the z-score number is below, above, or in between the values just on standard normal distribution.
Z-scores are the most used name for standard scores. Its similar concepts, like as z-values, standardized factors, and normal scores, are utilized in this article.A positive Z score score implies that the raw score is higher than the distribution's mean.For instance, a z-score of 2 indicates that the result is two standard deviations above the mean.If the Z score is negative, the distribution's mean is below the raw score value.For the stated question,
You simply need to discover the location of 0.2 on the z-score table and then its z-score. (The area to the left of a z-score is shown in the table)
Our z-score is -(0.8 + 0.04) = - 0.84 as a result.
Thus, the z-score such that the area under the standard normal curve to its left is 0.2 is found as -0.84.
To know more about the Z-score, here
https://brainly.com/question/12553378
#SPJ1
1. What is the vertical distance between (5, –12) to (5, 17)?
2. What is the volume of a rectangular prism with a length of fourteen and one-fifth yards, a width of 7 yards, and a height of 8 yards?
3. The point (–7, 6) was reflected over an axis to become the point (7, 6). Which axis was it reflected over? Explain.
The required solutions for each of the questions are obtained as 29 units, 235.2 cubic yards and y axis respectively.
What is the distance formula?The distance formula in coordinate geometry is used to find the distance between two points whose coordinates are given as (x₁, y₁) and (x₂, y₂) as √((x₁ - x₂)^2 + (y₁ - y₂)^2).
By knowing the sides, the area of different polygons can be found.
(1) The vertical distance between points (5, –12) and (5, 17) is given by distance formula as below,
√((5 - 5)² + (-12 - 17)²) = 17
(2) The volume of the rectangular prism is given as,
Volume = Area of base × Height of the prism
= 14(¹/₅) × 7 × 8
= 21/5 × 56 = 235.2
(3) The given points are (–7, 6) and (7, 6).
It is clear that after reflection y coordinate does not change.
Which implies that the axis of symmetry is y axis.
Thus, the axis of reflection is y axis.
Hence, the vertical distance between points, the volume of the prism and the axis of reflection are 29 units, 235.2 cubic yards and y axis respectively.
To know more about distance formula click on,
brainly.com/question/28956738
#SPJ1
I really need help with these questions please help
The area, lengths and dimensions of the plot of land and the situation picture are as follows;
a. 282.2 ft
b. 2330 ft²
c. 42.8 ft
Exercise 364
The true statements are;
The perimeter of ΔPQU is greater than 13 units
The perimeter of ΔPQR is 12 units
The area of ΔPST is 7.5 square units
What is the perimeter of a shape or figure?The perimeter of a shape or figure is the length or distance of the edge boundary of the shape.
a. The perimeter of the plot of land, P, can be found as follows;
P = (70 - 0) + (60 - 0) + (80 - 0) + √((80 - 60)² + (0 - 70)²) ≈ 282.8
The perimeter of the fencing is approximately 282.8 feet
b. The shape of the plot of land is a trapezium
Area of the plot of land is therefore; A = 0.5 × (60 + 80) ×70 = 4900
The shape of the Parking Area is a trapezium, therefore;
Area of the Parking Area = 0.5 × ((49 - 8) + (60 - 8)) ×(70 - 50) = 930
The shape of the Warehouse is a square, therefore;
Area of the Warehouse = (49 - 8) × (50 - 10) = 1640
Area of the plot of land that does not include the warehouse and the parking area is therefore;
Required area = 4900 - (930 + 1640) = 2330
The area of the plot of land that does not include the warehouse and the parking area is 2330 ft²
c. The sum of the length of the legs of the parking area trapezoid, L, can be found as follows;
L = (70 - 50) + √((70 - 50)² + (60 - 49)²) ≈ 42.8
The total length of fence needed is about 42.8 ft
Exercise 364
The true statements are found as follows;
The perimeter of the ΔPQU = 4 + 4 + 4·√2 ≈ 13.66 > 13The perimeter of the ΔPQR = 3 + 4 + √(3² + 4²) = 12The perimeter of QRSTU = 3 + √(5² + 2²) + √(3² + 4²) + 4·√2 + √(5² + 2²) ≈ 24.43
The perimeter of QRSTU > 24
The area of ΔPRS = 0.5 × 3 × 5 = 7.5
The area of triangle ΔPST = 0.5 × 3 × 5 = 7.5Learn more about finding the area of shapes on the coordinate plane here:
https://brainly.com/question/19293493
#SPJ1
Which of these expressions is equivalent to 5.8 ÷ 1.15 ?
0.58÷115 5.8÷115 58÷115 580÷115
The expression that is equivalent to 5.8 ÷ 1.15 is 580 ÷ 115
What are equivalent expressions?Equivalent expressions are expressions that have equal values when compared
How to determine the equations that are equivalent?From the question, we have the following parameters that can be used in our computation:
5.8 ÷ 1.15
Divide both sides of the equation by 1/10
So, we have the following representation
5.8 ÷ 1.15 = 5.8/(1/10) ÷ 1.15/(1/10)
Evaluate the quotients
So, we have the following representation
5.8 ÷ 1.15 = 58 ÷ 11.5
Multiply both sides of the equation by 10
So, we have the following representation
5.8 ÷ 1.15 = 580 ÷ 115
Hence, the equivalent equation is 580 ÷ 115
Read more about equivalent equation at
https://brainly.com/question/15775046
#SPJ1
Mr Jenkins runs a large arable farm.
He grows three times as much wheat than barley,
and three times as much barley than corn. Farmer
Jenkins grows twice as much corn as pumpkins.
Mr Jenkins's farm has an area of 270 acres.
Set
that
x acres.
wood to
then
2x
are
used
to grow
and 6x acres. are
used
to grow barley.
and
16x
acres
Ore
used
to
grow
where.
§ set up
riddles
according
to quation
x +
2x
+6
x
+ 16x
=
270
{total oven is
270
acres?
252
=270
x = 10.8
solve
equersion
for 23
So
10.8
acnes
are
used
to
grow
pumpkins.
what is the measure of angle x
Answer:
61 degrees
Step-by-step explanation:
sum of all angles of a triangle is 180 degrees
82+37+x=180
119+x=180
-119. -119
x=61
hopes this helps
180 Degrees
[tex]37+82+x=180[/tex]
[tex]119+x=180[/tex]
[tex]x+119=180[/tex]
Subtract 119 from both sides:
[tex]x+119-119=180-119[/tex]
[tex]\fbox{x = 61}[/tex]
Question 1 of 10
What is the slope formula?
OA. ₂-₁,
Y/₂-1/₁
OB. -
X₂-X₁
O c. 2-₁
X₂-1/₁
D. +₁
Y/₂+1/₁
SUBMIT
Answer:
(y2-y1)/(x2/x1)
Step-by-step explanation:
Well uh I hope you get it
Using the year 2000 as the base year, compute
- nominal GDP [1 point]
- real GDP [1 point]
- GDP de
ator [1 point]
1) Nominal GDP = Current year price* Current year quantity
= 500*3000 + 400,000*20
= 1,500,000 + 8,000,000
= $9,500,000
2) Real GDP = Base year price* Current year quantity
= 500*2000 + 400,000*10
=1,000,000 + 4,000,000
= $5,000,000
3) GDP Deflator = Nominal GDP/Real GDP
=9,500,000/5,000,000
Choose the function whose graph is given by:
A. y=-3.5cos x
B. y=3.5sin x
C. y=sin(3x)
D. y=2.5sin x
Answer:
A a option is right because cause 3 is near to zero that's value one and y 3.5 x 1near equal to 3 something
Can somebody please tell me how do i solves these. Thank you.
1. The statement is false, as the differential equation is of the second order but it is nonlinear.
2. The statement is false, as the differential equation is linear.
3. The third statement is correct, as the differential equation is of the fourth order and nonlinear.
How to classify the differential equations?Regarding to linearity, the differential equations are classified as follows:
Linear: the derivatives of y are multiplied only by terms that do not contain the variable y.Non-linear: the derivatives of y are multiplied by terms that contain the variable y.Regarding the order, it is given by the order of the highest derivative in the differential equation.
For question 1, the differential equation y''y + (y')² = sin(x) is in fact of the second order, as the highest derivative is y'' (second derivative), but it is nonlinear, due to the multiplication of y by y''.
Hence the differential equation for question 2 is linear, as the multipliers to the derivatives are of x and -1, neither of which contains the variable y.
For question 3, we have that:
The differential equation is of the fourth order, as y''' x y' = y''''.The differential equation is nonlinear, due to the multiplication of y by xy'''.More can be learned about differential equations at https://brainly.com/question/18760518
#SPJ1
A rectangular walkway is 38 feet long and has a perimeter of 80 feet the department of public works wants to spread gravel on the walkways how many square feet of gravel are needed to cover the entire walkway ?
Answer:
76 [tex]ft^{2}[/tex]
Step-by-step explanation:
We are looking for the area of the walkway.
Area = length times width.
We know the length, we need to find the width.
Perimeter is the distance around the rectangle. It is two length and two widths.
p = 2l + 2w
80 = 2(38) + 2W
80 = 76 + 2W Subtract 76 from both sides.
80 - 76 = 76 - 76 + 2w
4 = 2w Divide both sides by 2
[tex]\frac{4}{2}[/tex] = [tex]\frac{2w}{2}[/tex]
2 = w
Now that we know the width we can find the area
a = 38 x 2
a = 76 [tex]ft^{2}[/tex]
Answer:
Length=38 ft
breadth=?
Perimeter=80 ft
we know,
Perimeter= 2(length+breadth)
or,80ft=2(38 ft + breadth)
or,40 ft=38ft + breadth
or,breadth=40 ft-38 ft
:. breadth=2 ft
Now,
Area of walkway= length ×breadth
=38 ft×2 ft=76 ft²
Hence,72 square feet of gravel is required to cover the entire walkway.
A large rectangular prism is 12 inches long, 9 inches wide, and 6 inches tall. A small rectangular prism is also 12 inches long, but it's only 3 inches wide and 3 inches tall.
How many small prisms would it take to fill the large prism?
The required number of small prism that would be fill in the large prism is given as 6
As mentioned in the question, a large rectangular prism is 12 inches long, 9 inches wide, and 6 inches tall. A small rectangular prism is also 12 inches long, but it's only 3 inches wide and 3 inches tall.
Here,
The volume of the large prism = 12 × 9 × 6
= 648 inches cube
The volume of the small prism = 12 × 3 × 3
= 108 inches cube,
The ratio of the volume of the large prism to a small prism will give the number of small prisms needed to fill the large prism. So,
n = 648 / 108 = 6 / 1
Thus, the required number of small prism that would be filled in the large prism is given as 6.
Learn more about Ratio here:
brainly.com/question/13419413
#SPJ1
Santa Santa can deliver presents to 15 children per hour. What is the maximum number of presents Santa can deliver to children’s in three hours?
Answer:
45
Step-by-step explanation:
15(3) = 45
Which of the following functions is graphed below?
Answer:
D
Step-by-step explanation:
Looking at the graph, when x <= 1, the line is x + 6. Only one answer has this option.
{20 PTS}
4/6 = ??? x 1/6
what number makes this equation true? fill in the blank
Kimberly’s whole family has colds so she makes a 6-quart pot of chicken noodle soup and serves everyone a bowl. Her family has a total of 4 people. If each of Kimberly’s bowls hold about 2 cups how many bowls of soup are left in the pot
The quantity of bowls of soup are left in the pot aftee serving her family is 16 cups
How many cups are left?Quantity of chicken noodle soup made = 6-quartNumber of people in Kimberly's family = 4Volume of bowl = 2 cupsConvert quarts to cups:
1 quarts = 4 cups6 quarts = 24 cupsTotal quantity of soup served = Number of people in Kimberly's family × Volume of bowl
= 4 × 2
= 8 cups
Quantity of bowls of soup are left in the pot = Quantity of chicken noodle soup made - Total quantity of soup served
= 24 cups - 8 cups
= 16 cups
In conclusion, 16 cups of soup are left in the pot after serving.
Read more on quarts to cups:
https://brainly.com/question/3071800
#SPJ1
determine the equation of the parabola that opens up, has vertex (7,7) and a focal diameter of 16.
The equation of a parabola that opens up and has a vertex at (7,7) can be written in the form
y = a(x - 7)^2 + 7.The focal diameter of the parabola is 16, which means that the distance from the vertex to the focus is 8 (since the focal diameter is the sum of the distances from the vertex to the focus and from the vertex to the directrix).
To find the equation of the parabola, we need to determine the value of a that will give us the correct focal diameter. The distance from the vertex to the focus is given by the equation sqrt(4a(y - 7)), so we can set this equal to 8 and solve for a:
sqrt(4a(y - 7)) = 8
4a(y - 7) = 64
a(y - 7) = 16
a = 16 / (y - 7)
Substituting this value of a back into the equation for the parabola gives us:
y = (16 / (y - 7))(x - 7)^2 + 7
This is the equation of the parabola that opens up, has a vertex at (7,7), and a focal diameter of 16.
Learn more about focal diameter here:
https://brainly.com/question/27357773
#SPJ4
the value of y varies exponentially with respect to x and the 1 -unit growth factor is 1.8 . which of the following is the best explanation for the meaning of this growth factor?
We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.
Given that,
With respect to x, the value of y varies exponentially, and the 1-unit growth factor is 1.7.
We have to find which of the following best describes the significance of this growth factor.
We know that,
The required expression for y with respect to x is
y=(1.8)ˣ------>equation(1)
1.8=1- unit growth factor.
Whenever x changes by 1.
x=x-1----->equation(2)
Putting equation (2) in (1)
y'=1.8ˣ⁺¹
y'=1.8ˣ×1.8----->equation(3)
Here [ y is new value after increase]
Taking ratio of (3) and (1)
y'/y= (1.8)ˣ×(1.8)/(1.8)ˣ
y'=(1.8)y
Therefore, We can say that whenever x changes by 1, the value of y becomes 1.8 times as large as its previous value.
To learn more about growth factor refer to:
brainly.com/question/12052909
#SPJ4
y=(1.8)ˣ equation(1)
1.8=1- unit growth factor.
Whenever x changes by 1.
x=x-1 equation(2)
y'=1.8ˣ⁺¹
y'=1.8ˣ×1.8 equation(3)
Here [ y is new value after increase]
Taking ratio of (3) and (1)
y'/y= (1.8)ˣ×(1.8)/(1.8)ˣ
y'=(1.8)y
Therefore, We can say that whenever x changes by 1, the value of y becomes 1.8 times as large as its previous value.
Tim has 42 marbles. He divides them equally into 7 bags. How many marbles are in each bag?
Answer:
6 marbles per bag
Step-by-step explanation:
42 marbles * 1 bag / 7 bags =
42 * 1/7 =
42/7 = 6 marbles per bag
1 bag represents each bag of the 7 total bags.
Multiply 1 bag / 7 bags with 42 marbles(total amount of marbles) to get the marbles in EACH bag.
Answer:
let x = marbles in a bag
x = 42/7
x = 6
There are 6 marbles in each bag for 7 bags(6) + (6) + (6) + (6) + (6) + (6) + (6)
This is 7 bags, total of 42 marbles
this is my own explanation moderator, please dont delete just because its almost the same with previous answer. well its because its the only way to solve it hehe but i add another explanation, i really dont want to get warnings for this kind of questions you knoww..
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Charlie starts to sove a system of linear equations graphically. he puts both equations into slope-intercept form and notices that the lines have the same slope. based on this information only, which of the following statements is true?A. The system could have no solution, one solution, or infinitely mani solutionsB. The system has no solution because two equations with the same slope never intersectC. The system has either no solution or infinitely many solutions, depending on the y-interceptsD. The system has infinitely many solutions because two equations with the same slope represent the same lineHx - 4y = -10Kx + 3y = -15
C. The system has either no solution or infinitely many solutions, depending on the y-intercepts
what is linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
If the slopes of both lines are same then the lines are parallel. Now, both the equations can represent same line or two different lines. If the equations represent the same line, then they are coincident and have infinite number of solutions, else if the equations represent two different lines with same slope then they are parallel and hence will never intersect, and therefore won't have any solution
to know more about linear equation visit : brainly.com/question/29739212
#SPJ4
The system has either no solution or infinitely many solutions, depending on the y-intercepts
If the slopes of both lines are same then the lines are parallel. Now, both the equations can represent same line or two different lines. If the equations represent the same line, then they are coincident and have infinite number of solutions, else if the equations represent two different lines with same slope then they are parallel and hence will never intersect, and therefore won't have any solution
Realiza las siguientes potencias
The powers is 5 - 1/2³.
What is Exponents and Powers?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
The number of times a number has been multiplied by itself is referred to as an exponent.
Given:
(5 - [tex]2^{-3}[/tex])
As, we know that
[tex]a^{-m[/tex] = 1/ [tex]a^m[/tex]
Then, (5 - [tex]2^{-3}[/tex])
= 5 - 1/2³
= 5-1/8
= 40-1/8
= 39/8
Learn more about Exponents and power here:
https://brainly.com/question/15722035
#SPJ1
The Translation of attached question is
Make the following powers
What is the value of x in the triangle?
3√2
A. 3√2
B. S
C. 6
D. 6√2
E. 2√2
Answer: D
Step-by-step explanation:
Olivia and liam paint their houses. Olivia can paint her house in 9 hours while liam paints his in 7 hours. If olivia and liam painted together, write an equation that would find the time in hours t it. would take them to paint a house.
Answer:
t = 7/9 * 9 + 7/9 * 7 = 14 hours
Step-by-step explanation:
statistics that specify how likely findings are to be true for other populations or in other locales is called statistics.
The study of data collection, analysis, presentation, and interpretation is known as statistics.
Given,
What is statistics?
Data collection, analysis, presentation, and interpretation are all part of the science of statistics. Much of the early motivation for the subject of statistics came from governmental needs for information on a variety of economic activity and census data.
Types of statistics;
Based on the characteristics, the various statistical kinds are divided: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as using pie charts, bar graphs, or tables.
Learn more about statistics here;
https://brainly.com/question/6907663
#SPJ4
How many positive integers have distinct prime digits?
Answer:
64
Step-by-step explanation:
There are 4 prime digits: 2, 3, 5, and 7.
If the number is one digit, there are 4 possible numbers.
If the number is two digits, there are 4(3)=12 possible numbers.
If the number is three digits, there are (4)(3)(2)=24 possible numbers.
If the number is four digits, there are (4)(3)(2)(1)=24 possible numbers.
Taking the sum, the answer is 64.
The sum of heart rate readings taken five times for of Kundaval and Kulazhi are 400 and 360 respectively. And their projected deviations are 3,16 and 2.0 respectively. If you were. a doctor, who would you treat immediately?.
If i were a doctor, the person I would treat immediately is; Kundaval because he has higher heart rate and larger projected deviation.
We are given that;
Sum of heart rates taken 5 times for Kundaval = 400
Sum of heart rates taken 5 times for Kulazhi = 360
Projected deviation for Kundaval = 3.16
Projected deviation for Kulazhi = 2.0
Now, mean simply means the average of a set of given data while standard deviation is defined as a measure of how dispersed the data is in relation to the mean.
Thus, as a doctor, I would prioritize the treatment of the patient that has higher heart rate and larger projected deviation. Thus, we would conclude that Kundaval, whose sum of heart rate readings is 400 and whose projected deviation is 3.16 would be the one that should be treated first.
Read more about Mean and Standard deviation at; https://brainly.com/question/26941429
#SPJ1
Give slope for these points blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah blah
The slope equation is: [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
The slope of the points (0, 2) and (1, -3) is: -5
The slope of the points (-5, -8) and (10, 12): 4/3
First graph: m = 1
Second graph: m = -2/3.
What is the Slope of a Line?The slope of a line is calculated using the formula below:
Slope (m) = rise/run = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Therefore, the equation of the slope is expressed as: [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
Find the slope of the points (0, 2) and (1, -3):
m = change in y / change in x = (-3 - 2) / (1 - 0)
m = -5/1
Slope (m) = -5
Find the slope of the points (-5, -8) and (10, 12):
Slope (m) = (12 -(-8)) / (10 - (-5))
m = 20/15
m = 4/3
Find the slope of the first graph:
Slope (m) = rise/run = 1/1
m = 1
The slope of the second graph = rise/run = -2/3.
Learn more about the slope of a line on:
https://brainly.com/question/29044610
#SPJ1
I'm not sure about this question DO NOT MIND THE TEXT IN THE BOX JUST ANSWER PLEASEEE!!
DONT ASNWER IF YOU DONT KNOW!
Answer:
You had it right, now all you have to do it add 18 and 30 and 4 and 3 and you should get your answer, than you take the answer and write 48r+7w=55rw
Step-by-step explanation:
I added 18, 30, 4, and 3. I got 48 for the 18 and 30 and 7 for the 4 and 3
Let ƒ(x) = 8(1/4)^X+³ — 4.
The graph of f(x) is translated 4 units down to form the graph of g(x).
The function f(x) is translated by 4 units down to form a function g(x) will be written below.
[tex]g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 8\\[/tex]
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
[tex]f(x) = 8 \times \left (\dfrac{1}{4} \right )^{x^3} - 4[/tex]
Simplify the equation, then we have
[tex]f(x) = 8 \times \left (\dfrac{1}{4} \right )^{x^3} - 4\\\\\\f(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 4[/tex]
The function f(x) is translated by 4 units down to form a function g(x) will be given as,
[tex]g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 4-4\\\\\\g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 8[/tex]
The function f(x) is translated by 4 units down to form a function g(x) will be [tex]g(x) = 8 \times \left (\dfrac{1}{4} \right )^{3x} - 8\\[/tex]. The graph is drawn below.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ1
Based on the relative frequency histogram below , which of the following statements is supported by the plot? i. The IQR of the distribution is roughly 10
ii. There are no outliers in the distribution.
iii. It is not possible to estimate the median without knowing the sample size. iv. The distribution is multimodal v. The mean of the distribution is smaller than its median.
The statement supported by the plot is that the IQR of the distribution is roughly 10. It is possible to estimate the median from the plot, and the distribution appears to be unimodal, with the mean being smaller than the median. There are no outliers shown in the plot.
The relative frequency histogram provides a visual representation of the distribution of the data. From the plot, it is possible to estimate the median, which is the middle value of the distribution, as well as the interquartile range (IQR), which is the difference between the upper and lower quartiles. The IQR of the distribution is roughly 10, which can be seen by the distance between the upper and lower quartiles in the plot. Additionally, the distribution appears to be unimodal, which means that it has only one mode or peak. It is also apparent that the mean of the distribution is smaller than its median, as the peak is shifted to the left of the median. Finally, there are no outliers shown in the plot, as all of the values appear to be within the range of the distribution.
Learn more about median here
https://brainly.com/question/28060453
#SPJ4