The factor of 36 in order from smallest to largest is 2 × 2× 3× 3.
Prime factor:
Factors are the numbers you multiply together to get another number. In simple words, a prime factor is finding which prime numbers multiply together to make the original number.
Here we have to find the prime factor 36.
That is we have to find the smallest multiplication of digits to get the value.
36 = 2 × 2 × 3 × 3
Therefore the prime factor is 2 × 2×3×3.
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25pts. URGENT: What is the classification of each system?
Drag the answers into the boxes to match each system.
It is found that the first system of equations is consistently independent, the second one is inconsistent, and the third one is consistently dependent.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
We are given the first system of equations:
4x + y = 8
x + 3y = 8
thus 4/1 ≠ 1/3 = 1 is consistently independent.
The second system of the equation is;
-4x + 6y = 2
2x - 3y = 1
Therefore, -4/2 = -6/3 = 2 is inconsistent.
The third system of equations is;
5x - 2y = 4
5x - 2y = 6
Thus, 5/5 = -2/-2 ≠ 4/6 is consistent dependent.
Thus, It is found that the first system of equations is consistently independent, the second one is inconsistent, and the third one is consistently dependent.
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Write an equation of the line that passes through (4,-1) and is parallel to the line y = 3x +7
An equation of the parallel line is
Answer:
[tex]y=3x-13[/tex]
Step-by-step explanation:
Parallel lines have the same slope. So, the equation is:
[tex]y+1=3(x-4) \\ \\ y+1=3x-12 \\ \\ y=3x-13[/tex]
PLEASE HELP FAST
A cylindrical jar has a radius of 6 inches and a height of 10inches. The jar is filled with marbles that have a volume of 20 in3. Use 3.14 for pi. Show work. Complete sentences.
a. What is the volume of the jar?
b. How many whole marbles can fit in the jar? *Each marble has the volume of 20 cubic inches
The volume of the cylindrical jar be 1130.97 in³.
Also, 56 whole marbles can fit in the jar.
Given, a cylindrical jar has a radius of 6 inches and a height of 10 inches.
The jar is filled with marbles that have a volume of 20 in³.
(a) The volume of the cylindrical jar be,
Volume = πr²h
Volume = (3.14)(6)²(10)
Volume = 1130.97 in³
(b) Now, if each marble has the volume of 20 in³
then, the number of marbles that can be fit in the jar be,
The number of marbles = 1130.97/20
The number of marbles = 56.
Hence, the volume of the cylindrical jar be 1130.97 in³.
Also, 56 whole marbles can fit in the jar.
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How to solve X + 3 <6
The value of the inequality X + 3 < 6 is x < 3.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Based on the information given, the inequality will be illustrated thus:
x + 3 < 6
Collect like terms
x < 6 - 3
x < 3
The value is x < 3.
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Geometry Question help?
Measure of all angles must equal 180 degrees.
Therefore,
(4x+20) + (2x+34) + x = 180
6x + 54 + x = 180
7x + 54 = 180
7x = 126
x = 18
4(18)+20 = 92
Angle A = 92
2(18)+34 = 60
Angle C = 60 degrees
Unknown angle is 18 degrees because the "x" represents the third angle.
Is r=5 a solution to the inequality below? r<11
Yes, r=5 is a solution of inequality r<11.
Given the inequality is r<11
Given the value of r is, r=5
Since 5<11
So yes r=5 is the solution of the inequality r<11.
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An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3500 feet and Plane B is at an altitude of 1970 feet. Plane A is gaining altitude
at 40.25 feet per second and Plane B is gaining altitude at 65.75 feet per second.
How many seconds will pass before the planes are at the same altitude
What will their height be when they’re at the same altitude
60 seconds long will it take for the planes to reach the same altitude.
Given that,
Two planes are being monitored by an air traffic controller. Plane A is initially at an altitude of 3500 feet, while Plane B is initially at a height of 1970 feet. The altitude of Plane A is increasing at a rate of 40.25 feet per second, while Plane B is doing so at a rate of 65.75 feet per second.
We have to find how long will it take for the planes to reach the same altitude.
Let us take x as the number of seconds in time.
We get,
3500+40.25x for Plan A.
1970+65.75x for Plan B.
Take,
3500+40.25x=1970+65.75x
3500-1970=65.75x-40.25x
1530=25.5x
x=1530/25.5
x=60
Therefore, 60 seconds long will it take for the planes to reach the same altitude.
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3(5a+4b)-3a+b I need help with this problem. I just am really confused
Answer:
12a + 13b
Step-by-step explanation:
3(5a + 4b) - 3a + b
multiply 3 by 5a and 4b
15a + 12b - 3a + b
Now add the a terms together and b terms together
15a - 3a + 12b + b
12a + 13b
Answer:
12a + 13b
Step-by-step explanation:
3(5a+4b)-3a+b
To simplify the expression, we need to distribute the 3 to all terms inside the parentheses
3*5a+3*4b-3a+b
15a+12b-3a+b
Combine like terms
12a + 13b
HELP ASPPP SHOW UR WORK PLEASE
Answer:
Step-by-step explanation:
y + 8= 2(x-1)
y+8=2x-2
y=2x-10
Slope equals 2
36x + 31 = 535
A.
none of these
B.
1
C.
17
D.
12
Answer:
A
Step-by-step explanation:
36x = 535 - 31
36x = 504
36/36 x = 504/36
x = 14
[tex]{ \green{ \boxed{ \red{ \sf{x = 14}}}}}[/tex]
Step-by-step explanation:
[tex]{ \purple{ \tt{36x + 31 = 535}}}[/tex]
[tex]{ \purple{ \tt36x = 535 - 31}}[/tex]
[tex]{ \purple{ \tt{36x = 504}}}[/tex]
Divide both the sides by 36 then,
[tex]{ \purple{ \tt{ \frac{ \cancel{36}}{ \cancel{36}}}}} = { \purple{ \tt{ \frac{ \cancel{504}} { \cancel{36}}}}}[/tex]
[tex]{ \red{ \boxed{ \green{ \sf{x = 14}}}}}[/tex]
Jamal wants to save $54,000 for a down payment on a home. How much will he need to invest in an account with 8. 2% apr, compounding daily, in order to reach his goal in 5 years?.
Jamal need to invest $35838.77 in an account.
What is compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
As given Jamal wants to save $54,000 for a down payment on a home with 8.2% APR, compounding daily for 5 years.
The compound interest formula is,
[tex]A = P(1+\frac{r}{n})^n^t[/tex]
where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Here, A = $54000, r = 8.2% = 0.082, t = 5, n = 365
Plug the values in the above formula,
[tex]54000 = P(1+\frac{0.082}{365} )^(^3^6^5^)^(^5^)\\54000 = P(1.0002246575)^1^8^2^5\\54000= P(1.5067483068)\\P = \frac{54000}{1.5067483068} \\P = 35,838.766\\P = 35838.77[/tex]
Hence, Jamal need to invest $35838.77 in an account.
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An exercise machine with an original price of $565 is on sale at 6% off.
a. What is the discount amount?
b. What is the exercise machine's sale price?
a. The discount amount of the exercise machine is $3.39.
b. The exercise machine's sale price will be $561.61
What is a percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since the exercise machine with an original price of $565 is on sale at 6% off. The discount will be:
= Discount percentage × Price
= 6% × $565
= $3.39
The exercise machine's sale price will be:
= Original price - Discount
= $565 - $3.39
= $561.61
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Kiran is competing in a bike race. The function rule t(s)=40/s relates the time in hours of a bike race with the average speed, s, in miles per hour. Identify the constant of proportionality and explain what it means in this situation.
Answer:
Step-by-step explanation:
so, I was just commenting about word problems to another person and here is a great example of a word problem that is too complex. They are using the term "function rule" that is too broad. They have probably defined it in some text somewhere and the teacher has mentioned in super briefly, but it's what the question is all about. We need to understand what "function rule" really means. They have also used the varible "s" which is mostly reserved for Laplace / Fourier transformations. This is just a really badly written question. Don't feel bad if you don't get what it's asking. it's messy at best. t(s) is then name of our function, it's rule ( the function rule) is 40/s it's constant of proportionality is 40 , This rule would also mean that at the very very start of the race... at .001 into the race, you'll be going 40,000 MPH , which is obviously not correct. There probably needs to be some more rule descriptions saying that s is an integer, and it can't be negative. Also note that after 4 hours of racing , the speed would be 40/4 or 10 MPH, this function rule is probably not accurate after some time. the speed probably starts out fast, slows down till the close to the very end of the race... they jumps up dramatically to the finish. Watch the Tour de France writer of this question. :D The riders slow down as the race progress according to this function rule. But I don't think that's at all accurate for a real bike race. they slow down only to a point... after the start.... then hold at that speed ... till close to the end.. then speed up a lot... like 50 MPH :0
If 4x is one factor of 4x^2 - 12x, what is the other factor?
Answer:
(x - 3)
Step-by-step explanation:
4x² - 12x ← factor out 4x from each term
= 4x(x - 3)
the factors are 4x and (x - 3)
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
x² + (y – 3)² = 36 and x² + (y + 8)² = 36 are equations that represent circles having a diameter of 12 units and a center that lies on the y-axis
How to find the equations of circles?Given : x² + (y – 3)² = 36, x² + (y – 5)²= 6, (x – 4)² + y² = 36, (x + 6)² + y² = 144 and x² + (y + 8)² = 36
and x² + (y + 8)² = 36
The standard form of the equation of a circle is
(x-a)² + (y-b)² = r²
where (a, b) is the center and r is the radius
Let's compare the given equations with the standard equation:
x² + (y – 3)² = 36 can be written as:
(x-0)² + (y – 3)² = 6²
This has a center (0, 3), radius r = 6 and diameter = 12 units
x² + (y – 5)²= 6 can be written as:
(x-0)² + (y – 5)² = (√6)²
This has a center (0, 5), radius r = √6 and diameter = 2√6 units
(x – 4)² + y² = 36 can be written as:
(x-4)² + (y – 0)² = 6²
This has a center (4, 0), radius r = 6 and diameter = 12 units
(x + 6)² + y² = 144 can be written as:
(x+6)² + (y – 0)² = 12²
This has a center (6, 0), radius r = 12 and diameter = 24 units
x² + (y + 8)² = 36 can be written as:
(x+0)² + (y + 8)² = 6²
This has a center (0, -8), radius r = 6 and diameter = 12 units
Therefore, the equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are x² + (y – 3)² = 36 and x² + (y + 8)² = 36
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[Legitimately giving away like, 40 points, & mark brainliest.]
1. The point plotted on graph A is located at (__, __). When using the ratio y/x and changing it to a decimal, that means the constant of proportionality is __ and the equation of the line is y=__.
NOTE!: The rest is basically asking the same question, but different graphs. (ex. The point plotted on graph B is located at (___, __). To be more specific)
Question 5:
Since graph ___ has a different constant of proportionality and different equation, it is different than other three graphs.
[I'd appreciate it if someone were to answer quickly...]
The different proportional relationship is given by:
Relationship B.
The justification is:
Since graph B has a different constant of proportionality and different equation, it is different than other three graphs.
What is a proportional relationship?The definition of a proportional equation is given as follows:
y = kx.
Which means that the output variable y is obtained with the multiplication of the constant of proportionality k and the input variable x.
The constant is obtained as the division of y by x of a point (x,y) different of the origin, as follows:
k = y/x.
Hence, for each relationship, the constant is given as follows:
Relationship A: k = 4/0.8 = 5.Relationship B: k = 55/10 = 5.5. -> different due to the different constant.Relationship C: k = 20/4 = 5.Relationship D: k = 50/10 = 5.More can be learned about proportional relationships at https://brainly.com/question/10424180
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what does a linear graph with a negative slope indicate? responses as the independent variable decreases, the dependent variable increases. as the independent variable decreases, the dependent variable increases. there is no relationship between the independent and dependent variables. there is no relationship between the independent and dependent variables. as the independent variable increases, so does the dependent variable. as the independent variable increases, so does the dependent variable. as the independent variable increases, the value of the dependent variable remains the same. as the independent variable increases, the value of the dependent variable remains the same.
A linear graph with a negative slope indicates that as the independent variable decreases, the dependent variable increases.The line with a negative slope is sloping down to the right.
This relationship is represented by a line sloping down to the right. A line with a negative slope indicates that there is a negative correlation between the two variables. This means that as one variable decreases, the other variable increases.
This is because the line is going down from left to right, which means that the y-value is increasing as the x-value decreases. This relationship is known as a negative correlation.It is also known as an inverse relationship. In an inverse relationship, the two variables move in opposite directions. As one variable decreases, the other variable increases.
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Write an equation of the line passing through the point A (8, 2) that is perpendicular to the line y = 4x - 7.
The equation of line perpendicular to line y = 4x – 7 and passing through point A (8, 2) is y + (1/4)x = 4.
What does the point slope form of a line equation look like?A line's point slope form equation is y - y₁ = m(x - x₁). Consequently, y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.How do you figure out the slope of a line that is perpendicular to another line?The slope of a line that is perpendicular to another line is equal to the negative reciprocal of that line's slope.
Given: A line is perpendicular to line y = 4x – 7 and passes through point A (8, 2).
We know that,
Slope of line perpendicular to another line is negative reciprocal of its slope.
So, m(slope) = -1/4
Equation of line is given as follows:
y - y₁ = m(x - x₁)
y - 2 = -1/4(x - 8)
y + (1/4)x = 4
Therefore, the equation of line perpendicular to line y = 4x – 7 and passing through point A (8, 2) is y + (1/4)x = 4.
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3. Candice eats six egg whites a day with a protein
content of 21.6 grams. Calculate her protein intake, if
he consumes 9 egg whites a day.
Protein intake, if he consumes 9 egg whites a day is 32.4 grams.
Given:
Candice eats six egg whites a day with a protein content of 21.6 grams.
6 egg white = 21.6 grams.
1 egg white = 21.6/6
= 216/10/6
= 216/10*6
= 216/60
= 3.6 grams.
9 eggs white = 9 * 3.6
= 9 * 36/10
= 324/10
= 32.4 grams.
Therefore protein intake, if he consumes 9 egg whites a day is 32.4 grams.
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Harold solved a division problem in the following way. Check his work. Is the solution valid. Why or why not?
Harold's solution for the given division problem is not valid because it is not accurate.
We are given two numbers. The numbers are given in scientific notation. The first number is 8.4×10^(-7). The second number is 3.6×10^(-2). We need to find the result of the division of the first number by the second number. Let the result of division be denoted by the variable "Q".
Q = [8.4×10^(-7)] ÷ [3.6×10^(-2)]
Q = [(8.4/3.6)×10^(-7 - (-2))]
Q = [(8.4/3.6)×10^(-7 + 2)]
Q = 2.33×10^(-5)
Harold solved this division problem by first rounding the numbers. His result is 2×10^(-5).
Harold's result differs a lot from the actual result. So, his result is not accurate. Hence, his solution is not valid.
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Hey! I don’t understand this proof. Can anyone help me thank you!
Proved that the length of AB ≅ the length of CD
The conditions are given that
The line BC and the line AD are parallel lines
The parallel lines are two coplanar straight lines are at equal distance from each other and never intersect each other
Similarly
The measure of angle BAD is equal to the measure of angle DCB
If angle BAD = angle DCB, then we can say that the given shape is a parallelogram
In the parallelogram the opposite sides will be equal
Then the length of the length of AB equal to the length of CD
Hence, proved that the length of AB ≅ the length of CD
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Help!! Question Solve. 2 1/3−1/2x=−2/3 Enter your answer in the box. x =
Answer:
x = 6
Step-by-step explanation:
2 [tex]\frac{1}{3}[/tex] - [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] ( subtract 2 [tex]\frac{1}{3}[/tex] from both sides )
- [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] - 2 [tex]\frac{1}{3}[/tex] = - 3 ( multiply both sides by - 2 to clear the fraction )
x = - 3 × - 2 = 6
x = 6
How to isolate Y when y - 3 = 2/5 (x+4) is the problem
Explanation:
To isolate the Y from y - 3 = 2/5 (x+4), you need to add 3 from both sides to move it to the right side of the equation:
y - 3 = 2/5 (x+4)
+3 +3
y = 2/5 (x+4) + 3
Answer:
add 3 to both sides
or move 3 across the equal sign, which will change its sign from - to +
= y = 2x + 8 / 5 +
a theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let represent the cost of 1 adult ticket, and represent the cost of 1 child ticket. which system of equations can be used to determine the cost of each type of ticket? a. b. c. d.
The system of equations that can be used to represent the cost of each type of ticket is 2a + 3c = 30.75 and 3a + 2c = 33 .
In the question ,
it is given that ,
a theater sells adult and child tickets for its play .
the cost for 2 adult ticket and 3 child ticket is = $30.75
and the cost for 3 adult tickets and 2 child tickets = $33.00
let the cost of 1 adult ticket = "a" and
let the cost of 1 child ticket = "c"
So, According to the question ,
the equation to represent both the situation is
2a + 3c = 30.75 and
3a + 2c = 33
Therefore , The system of equations that can be used to represent the cost of each type of ticket is 2a + 3c = 30.75 and 3a + 2c = 33 .
The given question is incomplete , the complete question is
A theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let "a' represent the cost of 1 adult ticket, and "c" represent the cost of 1 child ticket . Write a system of equations can be used to determine the cost of each type of ticket ?
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Explain how you can tell if the data in a table is a function
use the words input and output in your response
please if you don't know this font look it up and copy the and past it they will look it up and see if you copied and pasted it
Answer:
Okay, sorry for answering a few minutes late!
Step-by-step explanation:
So, for data in a table to be a function, the input must only have one output.
Short and sweet answer, hope this helps!
a cylindrical can that has a capacity of 20 m 3 will be made. the metal used to build the top costs $10 per square meter while the bottom costs $20 per square meter. the material used for the side costs $15 per square meter. what are the dimensions that will minimize the cost?
The dimensions that will minimize the cost is
h= 2.82876 and r = 1.06078
Given That, C₁ = $10 and C₂= $10 and C₃ = $15
lets multiply the top and bottom, we get,
C₁ × C₂ = $10 ×$ 20 = $ 30
The total cost is,
C = (2πr²) C₁ + (2πrh)C₂
Here, r is base radius and h is the side length.
The volume is given by and the volume to 20 m³
∴ V = πrh² ⇒ πr²h = 20
So, h = 20/πr²
Now, the problem can be stated as
minimum h, r C(h, r) restricted to V(h, r) = V₀
Using language multiplier it reads,
L(h ,r,λ) = C(h, r) + λ [ V(h ,r) - V₀]
Solving for h, r, λ, we get,
h = ∛(2 C₁/C₂)² V₀ /π , r = ∛ (C₂/C₁) (v₀/2π)
λ = -2 ∛2πC₁C₂² /V₀
or, h= 2.82876 , r= 1.06078 with associated cost C= 424.214
We know that is a minimum because,
(C₀ V) = 2 ( C₁πr³ + C₂V₀) /r
d²/dr² (C₀V) (r) = 4 (C₁πr³+ C₂V₀)/ r³
and for the found solution has the value
d²/dr² (C₀V) (r) = 240 π > 0
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can you substitute y=2x+4 and 6x-3y=-12
Using the table, give the percentage associated with each unit of standard deviation in the standard normal curve to the nearest hundredth.
Standard Deviation Percentage Area
-2 to -1 ____________%
0 to +1 ____________ %
0 to +2 _____________%
+1 to +3 _____________%
-1 to +2 _____________%
The corresponding standard deviation percentage area for -2 to -1, 0 to +1, 0 to +2, +1 to +3 and -1 to +2 are 13.59%, 34.13%, 47.72%, 15.74% and 81.85%
How to find the percentage associated with standard deviation?To find the Standard Deviation Percentage Area, you have to consider the lower and upper points:
-2 to -1
The gap between -2 and -1 is 1 step, you will subtract -1 from -2:
-2 to -1 => 0.4772 - 0.3413 = 0.1359 = 13.59%
Note: the values for -2 and +2 are the same. The same also applies to -1 and +1 and others
0 to +1
Check the value under 1. That is 0.3413 = 34.13%
0 to +2
Check the value under 2. That is 0.4772 = 47.72%
+1 to +3
The gap between +1 and +3 is 2 steps, you will subtract 1 from 3:
+1 to +3 => 0.4987-0.3413 = 0.1574 = 15.74%
-1 to +2
-1 to +2 is the same as moving -1 to 0 and then moving from 0 to +2, you will add the values for -1 and +2:
-1 to +2 => 0.3413 + 0.4772 = 0.8185 = 81.85%
Therefore, the Standard Deviation Percentage Area for -2 to -1, 0 to +1, 0 to +2, +1 to +3 and -1 to +2 are 13.59%, 34.13%, 47.72%, 15.74% and 81.85% respectively
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Help my with this problem please 23 points
Answer:
4x² +4x -20
Step-by-step explanation:
You want the difference between 6x² -5x -12 and 2x² -9x +8.
DifferenceThe difference is found by subtraction. This is the same as adding the opposite.
(6x² -5x -12) - (2x² -9x +8)
= 6x² -5x -12 -2x² +9x -8
= (6 -2)x² +(-5 +9)x +(-12 -8)
= 4x² +4x -20
<95141404393>
pleace is my testing
The value of [tex]\sqrt{13}[/tex] is between 3 and 4 on the number line.
What is a number line?A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
[tex]\sqrt{13}[/tex] = 3.60
The value 3.6 is going to be between 3 and 4 because it is seen to be more than 3 while the value is also seen to be less than 4.
Hence the solution to the problem is the locations are 3 and 4.
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