If Shapera mowed 7 lawns and worked for 36 hours at pet store and delivered newspapers 7 days , then she earned $497 which is not enough to buy the computer .
the amount that she earns in mowing each lawn is = $15 ;
So , the amount earned for mowing 7 lawns is = [tex]15\times 7[/tex] = $105 ;
the amount that she earns per hour working at pet store is = $7 ;
So , amount earned for working 36 hours is = [tex]36\times 7[/tex] = $252 ;
the amount that she earns by delivering newspapers per day is = $20 ;
So , amount earned by delivering newspapers for 7 days =[tex]20\times7[/tex] = $140 ;
The total amount earned by Shapera is = [tex]\$ 105 + \$252+\$140[/tex]
On adding all the amount earned ,
we get ;
= $497 ;
The amount earned by Shapera is $497 .
Therefore , Shapera will not be able to buy the $499 computer as she is $2 less than the price .
The given question is incomplete , the complete question is
Shapera has three sources of income. She earns $15 for each lawn she mows. She earns $7 per hour working part-time at a pet store She earns $20 each day she delivers newspapers.
In the six weeks, Shapera mowed 7 lawns, worked 36 hours at the pet store, and delivered newspapers 7 days. Did she make enough to buy the $499 computer ?
Learn more about Equations here
https://brainly.com/question/29293303
#SPJ4
Totally T's is a company that makes t-shirts. Workers go on strike and the factory is closed. What will happen to the supply of t-shirts?
Answer the 3 questions below related to this scenario.
Complete sentences are not required. Please number each answer.
1. Will there be an increase or decrease?
2. Which way will the graph shift?
3. What is the determinant?
Can u please help ………….
Answer:
x = 17
Step-by-step explanation:
the midsegment of a triangle is half the length of the third side, that is
DE = [tex]\frac{1}{2}[/tex] × BC = [tex]\frac{1}{2}[/tex] × 34 = 17
so x = 17
One year ago, Farid spent $16,600 on a new pizza oven for his restaurant, The Dough Zone.
He checked the value of his oven online and discovered it is worth $15,770 today. The
website also predicts that the oven's value will continue to decrease each year.
Write an exponential equation in the form y = a(b)* that can model the value of the pizza
oven, y, x years after purchase.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
Exponential equation in the form y = a(b)* that can model the value of the pizza oven, y, x years after purchase is y = 16000(0.985625)ˣ.
The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour. After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.
The exponential equation is y = a(b)ˣ
The value of y = 15770, a = 16000 and x = 1
b = 0.985625
y = 16000(0.985625)ˣ
To learn more about Exponential function from given link
https://brainly.com/question/2456547
#SPJ1
Anyone pls help :) I'll give brainliest
Answer:
B. -5/2
Step-by-step explanation:
(0, -7) and (-4, 3)
m = 3+7/-4-0
m = 10/-4
m = -10/4
m = -5/2
Answer:
b
Step-by-step explanation:
Will Give Brainliest!!! 1. For the circle with equation , answer each question.
(a) What are the coordinates of the center?
(b) What is the radius of the circle?
(c) What is the diameter of the circle?
a) The coordinates of the center is (2 ,-3)
b) The radius of the circle is 3
c) The diameter of the circle is twice the radius = 2(3) = 6
Now, According to the question:
a) The equation of a circle is given by
[tex](x-h)^2 + (y-k)^2 =r^2[/tex]
where (h, k) is the center and r is the radius
(x - 2)² + (y+3)² = 9
(x - 2)² + (y- -3)² = 3^2
The coordinates of the center is (2 ,-3)
b) The radius of the circle is 3
c) The diameter of the circle is twice the radius = 2(3) = 6
Learn more about Circle at:
https://brainly.com/question/29142813
#SPJ4
The complete question is this:
For the circle with equation (x - 2)² + (y+3)² = 9 , answer each question.
(a) What are the coordinates of the center?
(b) What are the radius of the circle?
(c) What is the diameter of the circle?
The ruthless queen has asked the royal pharmacist to create a concoction which will straighten her curly hair. If the pharmacist combines a mixture containing 10% milkweed with another mixture containing 50% milkweed to create a 5 ounce mixture containing 30% milkweed, how many ounces of the 10% mixture will the pharmacist use?
The pharmacist utilized a 10% percentage mixture, according to the solution, in a quantity of 2 ounces.
The formula for calculating percentages?To calculate the percentage, we must first determine the value's ratio to the sum of its parts. We must then multiply the result by 100.
Since when do we utilize percentages?Comparing two quantities while rebasing the second quantity to 100 is the most fundamental use of percentages. If the proportion of employed women who are women is of relevance to us, let's say.
According to the given information:We are aware that m = CV, where
V = volume and c = concentration
Let
M is equal to 6.5%, m' is equal to 7.9%, and m = 3.7%.
It is known that m + m' = M.
where cv + c'v' = CV
Since cv + c'v' = CV, the formula is:
c = 3.7% concentration = 0.037;
v = volume of 3.7% = 1 ounce;
c = 7.9% concentration = 0.079;
v' = volume of 7.9%;
C = 6.5% concentration = 0.065;
and V = volume of 6.5% = v + v'
We obtain by altering the values of the variables in the equation
3.7% × 1/3.7% + 7.9 %v' = 6.5%(v + v')
3.7% + 7.9 %v' = 6.5%(1 + v')
3.7% + 7.9 %v' = 6.5% + 6.5%v'
7.9%v' - 6.5%v' = 6.5% - 3.7%
1.4%v' = 2.8%
v' = 2.8%/1.4%
2 ounces are v'.
To know more about percentage visit:-
brainly.com/question/29306119
#SPJ1
Question 1 : (2.3 × 10^4) × (1.5 × 10^-2)
Question 2: (3.6 × 10^-5) ÷ (1.8 × 10²)
The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expressions are given below.
(2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²)
Simplify the expression (2.3 × 10⁴) × (1.5 × 10⁻²), then the value of the expression will be given as,
⇒ (2.3 × 10⁴) × (1.5 × 10⁻²)
⇒ 345
Simplify the expression (3.6 × 10⁻⁵) ÷ (1.8 × 10²), then the value of the expression will be given as,
⇒ (3.6 × 10⁻⁵) ÷ (1.8 × 10²)
⇒ 2 × 10⁻⁷
The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
Seacausus stadium has a seating capacity for 25,000 spectators. The stadium has 25 exits and can be vacated in 20 minutes. The time taken to exit the stadium varies directly with the number of spectators and inversely with the number of exits. Determine the time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional.
The time taken for 21,000 spectators to vacate the stadium, if only 15 exits are functional is 28 minutes
How to determine the time taken for 21,000 spectators to vacate the stadium?
A variation is a relation between a set of values of one variable and a set of values of other variables
Let E, N and T represent the number of exits, the number of spectators and the time taken to exit the stadium respectively
We can write the variation as:
T α N/E
T = kN/E (where k is constant of proportionality)
when N = 25,000, E = 25, T = 20:
T = kN/E
k = TE/N
k = (20×25)/25000 = 0.02
when N = 21,000 and E = 15:
T = kN/E
T = (0.02×21,000)/15 = 28 minutes
Learn more about variation on:
brainly.com/question/2375770
#SPJ1
Select the interval where the graph h is increasing.
Answer: B
Step-by-step explanation:
Based on the graph, we know that it is increasing if it is going up from left to right.
A: incorrect
Looking at choice A, it says the interval is from -5<x<-4. This means we have to find x=-5 and x=-4. On the graph, that interval is going down from left to right, so it is decreasing.
B: correct
Looking at choice B, it says the interval is from -2<x<2. This means we have to find x=-2 and x=2. On the graph, that interval is going up from left to right, so it is increasing.
C: incorrect
Looking at choice C, it says the interval is from 3<x<4. This means we have to find x=3 and x=4. On the graph, that interval is going down from left to right, so it is decreasing.
Therefore, B is the correct answer.
Using a number line, find both the intersection and the union of the following
intervals:
(-3,∞) and (4,∞)
Answer:
The intersection of the two intervals = 4, 5, 6,.......∞ = (4, ∞)
The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞ = (-3, ∞)
Step-by-step explanation:
The given intervals are;
First interval = (-3, ∞)
Second interval = (4, ∞)
Using the number line, we therefore, the first interval includes, -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,∞
The second interval includes 4, 5,.....,∞
Which gives the intersection as 4, 5, 6,.......∞
The union is the interval that combines the two sets of intervals which is given as follows;
The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,∞
Isaac buys 17 anti-pollution masks for £5. 25 each
He pays with five £20 notes.
a) How much change should Isaac get?
Write your answer in £.
The normal price of an e-scooter is £370
1
In a sale, there is off the normal price of the e-sc
4
hlork out the nice of the e-scooter in the sale
a) Issac get £10.75 as change after buying all masks
b) The price of the e-scooter in the sale is £277.50
a)
Isaac buys 17 anti-pollution masks for £5.25 each, so the total cost is
17 * 5.25 = £89.25
He pays with five £20 notes, which is a total of 5 * 20 = £100
So, the change he should get is £100 - £89.25 = £10.75
Therefore, Isaac should get £10.75 as change.
b)
In the sale, there is 1/4 off the cost price of the e-scooter, which means that the scooter is discounted by 1/4 * £370 = £92.50.
To work out the price of the e-scooter in the sale, you need to subtract the discount from the normal price, so
£370 - £92.50 = £277.50
Therefore, the price of the e-scooter in the sale is £277.50
To know more about cost price click below:
https://brainly.com/question/29511226#
#SPJ4
How many incas did the spanish kill on november 16 1532 o 100 o 600 o 1000 6000?
Spanish killed nearly 6000 Incas.
The Spanish conquistador and explorer Francisco Pizarro springs a trap on Atahualpa, the monarch of the Incas, in the year 1532. Atahualpa allowed roughly 6,000 unarmed men to attend the feast despite having almost 80,000 soldiers with him in the mountains. It took the Spanish a long time and much violence to conquer the Inca Empire. Pizarro's soldiers massacred the 6,000 Incans in approximately one hour.
The lone Spanish wounded were received by Pizarro himself, who injured his hand while saving Atahualpa's life. Pizarro retained Atahualpa in captivity while he prepared plans to conquer his empire because he understood that the emperor was worthy alive than dead. Atahualpa responded by appealing to his hostages' avarice and supplying them with money and silver in exchange for their release.
Read more about Incas on:
https://brainly.com/question/1699679
#SPJ4
PLEASE HELP NOW IM BEGGING AND PLEADING PLEASE AND THANK YOU
Linear sequences & graphs 206 - Straight line graphs 1 Quiz 1 2 3 4 5 6 7 8 6 of 8 Use the table to work out the values of a , b , c , and d . x y = 5 − 3 x − 3 a − 2 11 − 1 b 0 5 1 c 2 d a = b = c = d =
The values of a, b, c and d are -5, -1, 3 and 5.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is y=2x+1
Substitute (-3, a) in y=2x+1, we get
a=2(-3)+1
a=-6+1
a=-5
Substitute (-1, b) in y=2x+1, we get
b=2(-1)+1
b=-1
Substitute (1, c) in y=2x+1, we get
c=2(1)+1
c=3
Substitute (2, d) in y=2x+1, we get
d=2(2)+1
d=5
Therefore, the values of a, b, c and d are -5, -1, 3 and 5.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ1
"Your question is incomplete, probably the complete question/missing part is:"
Use the table to work out the values a, b, c and d.
x y=2x+1
-3 a
-2 -3
-1 b
0 1
1 c
2 d
Which linear equation shows a proportional relationship?
y equals two thirds times x
y equals negative 3 times x minus one seventh
y equals three fourths times x minus 5
y equals 3 times x plus 7
The linear equation that shows a proportional relationship is y equals two thirds times x.
A proportional relationship is a relationship between two variables in which one variable is a constant multiple of the other. In other words, if y is directly proportional to x, then y = kx for some constant k. This can also be written as y/x = k, where k is the constant of proportionality.
The linear equation that shows a proportional relationship is y = 2/3x.
It shows a direct relationship because the coefficient of x (2/3) is constant, and there is no constant term (y-intercept) which breaks the proportionality.
The other equations do not show a proportional relationship because they have a coefficient that varies with x or a constant term.
Learn more about proportional relationship here: https://brainly.com/question/20374537
#SPJ4
Question Show that the binomial is a factor of the polynomial. Then factor the polynomial completely. f(x)=x4−6x3−8x+48; x−6
Answer:
(x-2)(x²+2x+4)(x-6)
Step-by-step explanation:
6 | 1 -6 0 -8 48
_____6_0_0_-48__
1 0 0 -8 | 0
As we can see, our remainder is 0, so x-6 is indeed a factor of the polynomial. Also, we can see that the factored polynomial is [tex]x^4-6x^3-8x+48=(x^3-8)(x-6)=(x-2)(x^2+2x+4)(x-6)[/tex]
Aiden is a spice trader.
The price he charges for an order of cumin (in dollars) as a function of the size of the order (in kilograms) is graphed.
What is the approximate average rate at which the total cost increases, as the order size increases from 100 to 600 kilograms?
Approximately $2.40 per kilogramme is the average rate that the total cost rises as the order size does, from 100 to 600 kg.
How much is the average rate?The average rate of change is the average change rate of one thing in respect to another. Simply explained, a computation that divides the amount of change in one thing by the comparable amount of change in another is known as an average rate of change function.
How are average rates calculated?Divide the y-value change by the x-value change to determine the average rate of change. When analyzing changes in observable parameters like average speed or average temperature, finding that average rate of change is especially helpful.
To know more about average rate visit:
https://brainly.com/question/29383345
#SPJ1
12x+105=55x+0 solve for x
12y=155 sovle for y
Answer:
Step-by-step explanation:
12x + 105 = 55x + 0
=> 12x + 105 = 55x
=> 55x - 12x = 105
=> 43x = 105
=> x = 105/43
12y = 155
=> y = 155/12
Charlie sold 100 tickets for his show.
An adult ticket costs £6.50 and a child ticket costs £2.50.
Charlie's ticket sales totalled £410.
a) How many adult tickets did he sell?
b) How many child tickets did he sell?
#SPJ1
For adults, there were 40 tickets sold, and for kids, there were 60 tickets sold.
What are the three algebraic rules?There are several laws that regulate the sequence in which you should do the operations in math and algebra. The Commutative, Associative, and Distributive Laws are the three that are most frequently discussed.
Let x be the total number of adult tickets sold.
6.50 × x + 2.50 × (100 - x) = 410
6.50 × x + 250 - 2.50x = 410
4x = 410 - 250
x = 40
Hence,
a) 40 tickets were sold by adults, according to item
and
b) 100-40=60 tickets were sold to children.
To know more about algebra visit:-
brainly.com/question/24875240
#SPJ1
Find the equation of a line in General form passes through the points (7,5) and (-9,5)
Answer:
Step-by-step explanation:
54×54
The total number of laps anitia swims, d, is proportional to the total timethat she swims, t, at constant pace, r. Which of the following equations best represents this situation.?
a circular fish pond has a diameter of 14 m the pond is surrrounding by a concrete path 1.75 meters wide. Find the ponds area. take pi as 22/7
Area of the pond is 86.625 m²
What is the area formula to a circle?The following formulae can be used to determine a circle's area: Area is equal to r2, where r stands for radius. Area is equal to (/4) d2, where d stands for diameter.The region encircled by a circle of radius r is known as r2 in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.A circle's area is equal to pi times the radius squared (A = r2). Discover how to apply this formula to determine a circle's area given its diameter.Pi () is a unique mathematical constant that expresses the relationship between a circle's circumference and diameter.Given data :
Diameter of the pond = 14m
Radius of the inner circle (pond), r = 7 m
Width of the concrete path = 1.75m
Radius of outer circle (Including pond + Path), R = 7 + 1.75 = 8.75 m
Area of the path = Area of the outer circle − Area of the inner circle.
= πR² - πr²
= 22 / 7 x ( 8.75 + 7) ( 8.75 − 7 )
= 86.625 m²
Learn more about circle's area refer to :
https://brainly.com/question/14068861
#SPJ4
What is the vector equivalent to the directed line segment from the point?
The vector equivalent to the directed line segment from the point (x1, y1) to the point (x2, y2) is the vector <x2-x1, y2-y1>.
The vector of a directed line segment is the difference between the two endpoints of the line segment. In this case, the endpoints are the points (x1, y1) and (x2, y2). Therefore, the vector of the directed line segment is equal to the vector <x2-x1, y2-y1>.
The vector equivalent of a directed line segment from the point (x1, y1) to the point (x2, y2) is the vector with initial point (x1, y1) and terminal point (x2, y2). This vector is equal to the vector form <x2-x1, y2-y1>, which describes the displacement from the initial point to the terminal point. This vector can also be written in component form, meaning the magnitude of the vector in the x-direction is x2-x1, and the magnitude of the vector in the y-direction is y2-y1.
Learn more about vector here
https://brainly.com/question/15709504
#SPJ4
•18 POINTS• don’t explain
a.) neither
b.)SAS
c.)HL
SAS congruence theorem should be used.
Option (B) is correct.
What is the SAS congruence theorem?
In Euclidean geometry, the SAS congruence theorem states that if two triangles have two sides of one triangle congruent (equal in length) to two sides of the other triangle, and the included angle is congruent, then the triangles are congruent. This theorem is often abbreviated as SAS, and is used in combination with other congruence theorems, such as ASA and SSS, to prove that triangles are congruent.
In the given picture, we can say both triangles has the same side of length 7 and along with it, one more side is of equal length.
and both triangles are having the right-angle,
so we can say that we can prove these triangles congruent by using SAS congruence theorem.
Hence, SAS congruence theorem should be used.
To learn more about the SAS congruence theorem, visit:
https://brainly.com/question/16986516
#SPJ1
BROO PLS SOMEONE HELP IM SO CONFUSED
The start of an arithmetic sequence is shown below.
Work out the nth term
Work out the 30th term in this sequence.
4 - 13 - 22 - 31
The 30th term of the arithmetic sequence is 265
What is an arithmetic sequence in math?
Arithmetic sequences are those in which each term is increased by the addition or subtraction of a constant k. In contrast to a geometric sequence, where each term rises by being multiplied by or divided by a constant k,A series of numbers is considered to be an arithmetic progression or sequence if there is a constant difference between the terms. Consider the mathematical progression with a common difference of 2 in the numbers 5, 7, 9, 11, 13, and so on.An is equal to a1 + d(n - 1), where d is the common difference across terms in the series, and a1 is the first term in the sequence.This is an arithmetic sequence since there is a common difference between each term. In this case, adding 9 to the previous term in the sequence gives the next term. In other words, [tex]a_{n}[/tex]= [tex]a_{1}[/tex]+ d ( n - 1 )
Arithmetic Sequence: d = 9
This is the formula of an arithmetic sequence.
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )
Substitute in the values of [tex]a_{1}[/tex] = 4 and d = 9
[tex]a_{n}[/tex]= 4 + 9 ( n - 1 )
[tex]a_{n}[/tex]= 4 + 9n - 9
[tex]a_{n}[/tex] = 9n - 5
.30th term = [tex]a_{n}[/tex] = [tex]a_{1}[/tex]+ d ( n - 1 )
= [tex]a_{30}[/tex]= 4 + 9 ( 30 -1 )
[tex]a_{30}[/tex]= 4 + 9 x 29
[tex]a_{30}[/tex]= 265
Learn more about arithmetic sequence refer to :
brainly.com/question/6561461
#SPJ1
Jessica works 7 days a week at an internship in Paris, France. She makes 70 Euros per day. When she comes back to America she needs to know how many dollars per week she was making. What is the correct amount? ( 1 Euro = 1.17 dollars)
A. $573.30/week
B. $335.65/week
C. $479.50/week
D. $357.66/week
Answer: D
Step-by-step explanation:
i got this question before
In the triangle below, with right angle R, suppose that m is Angle Q=(5x-13) and m is Angle S=(4x-5) Find the degree measure of each angle in the triangle.
Answer:
Degree measure of each angle is 90⁰, 47⁰ and 43⁰
Step-by-step explanation:
since the triangle is right angled, we assume that Q and S are the other angles of this triangle R
Thus using the concept that angles inside a triangle add up to 180⁰ and we already have one angle as 90⁰( since the triangle is right angled). we therefore know that Q + S = 90⁰
5x - 13 + 4x - 5 = 90⁰
9x = 108
x = 12
We now replace x in Q and S to get the angles
Q = 5(12) -13
= 47⁰
S = 4(12) - 5
= 43⁰
What 3 numbers make a right triangle?
Answer:
A right triangle equals to 90 degress, and has 2 equal angles.
Example: 20 degress, 20 degrees and 50 degress could make a right triangle.
I hope this helps you!
which values from the set (2,4,6,8,10) make the inequality n + 5 > 10 true ?
Answer: Values; 6,8,10
Step-by-step explanation:
❌ 2 + 5 > 10
❌ 4 + 5 > 10
✔️ 6 + 5 > 10
✔️ 8 + 5 > 10
✔️ 10 + 5 > 10
a)
b)
2
Complete the prime factor trees for 24 and 84:
24
2
||||
6
2
84
7
2
3
What is the Lowest Common Multiple of 24 and 84?
4
6
The prime factor trees for 24 and 84 are attached in the image below. The Lowest Common Multiple of 24 and 84 is 168.
What are prime factors?A natural number other than 1 whose only factors are 1 and itself is said to be a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth. The lowest of two or more natural numbers' common multiples is referred to as the Lowest Common Multiple (LCM). A prime factor is a natural integer, other than 1, whose sole factors are itself and 1. Actually, 2, 3, 5, 7, 11, and so forth are the first few prime numbers. The term "Lowest Common Multiple" refers to the common multiple of two or more natural integers that is the lowest (LCM).
The prime factors of 24 are: 2,2,2 and 3.
The prime factors of 84 are: 2,2,3 and 7.
Now, The Lowest Common Multiple (LCM) of 24 and 84 is calculated using the prime factors of both the numbers.
LCM= 2*2*2*3*7= 168
Hence, The Lowest Common Multiple of 24 and 84 is 168.
To know more about prime factors visit:
brainly.com/question/18187355
#SPJ1
What is the y-intercept of 6x 3y =- 12?
The y-intercept of the equation 6x + 3y = -12 is -4.
Therefore the answer is -4.
The y-intercept of a linear equation is the point at which the line crosses the y-axis. In other words, it's the point at which x = 0.
To find the y-intercept of the equation 6x + 3y = -12, we can set x = 0 and solve for y.
Substituting x = 0 into the equation:
6(0) + 3y = -12
3y = -12
To find the y-intercept, we divide both sides by 3:
y = -4
So the y-intercept of the equation 6x + 3y = -12 is (0, -4). This means that when x = 0, y = -4 and the graph of this equation will cross the y-axis at the point (0, -4).
To know more on intercept
https://brainly.com/question/14180189
#SPJ4