Answer:
Step-by-step explanation:
To construct an infinite set of sets of natural numbers such that all of their pairwise symmetric differences are infinite, we can define the following sequence of sets:
S_1 = {1, 2, 3, ...}
S_2 = {2, 3, 4, ...}
S_3 = {1, 3, 5, ...}
S_4 = {2, 4, 6, ...}
S_5 = {1, 4, 7, ...}
S_6 = {2, 5, 8, ...}
...
In general, S_n is the set of natural numbers that are congruent to n mod 2. For example, S_1 is the set of all odd natural numbers, S_2 is the set of all even natural numbers, and so on.
To show that all of their pairwise symmetric differences are infinite, we can consider any two distinct sets S_n and S_m. Without loss of generality, assume that n < m. Then, the symmetric difference between S_n and S_m is the set of natural numbers that are congruent to n or m mod 2, but not both:
S_n Δ S_m = {k ∈ N : (k ≡ n mod 2) XOR (k ≡ m mod 2)}
Since n < m, we can see that every other natural number is in this set, and therefore it is infinite. Hence, the sequence {S_n} is a set of sets of natural numbers such that all of their pairwise symmetric differences are infinite
a large company is being sued for false advertisement because 18% of the flashlights in its shipping boxes are defective, but the company claims that only 8% are defective. you plan to use hypothesis testing to determine whether there is significant evidence that the company is falsely advertising. part a: state the null and alternative hypotheses for the significance test. (2 points) part b: in the context of the problem, what would a type i error be? a type ii error? (2 points) part c: if the hypothesis is tested at a 10% level of significance instead of 5%, how will this affect the power of the test? (3 points) part d: if the hypothesis is tested based on the sampling of 100 boxes of flashlights rather than 1,000 boxes of flashlights, how will this affect the power of the test? (3 points) source stylesformatfontsize
The required solution for the hypothesis testing is shown.
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Here, we have,
Part A:
The null hypothesis (H0) is that the company's claim is true, and the proportion of defective batteries is 5% or less.
The alternative hypothesis (Ha) is that the company's claim is false, and the proportion of defective batteries is greater than 5%.
H0: p ≤ 0.05
Ha: p > 0.05
where p represents the proportion of defective batteries.
Part B:
A Type I error in this context would be rejecting the null hypothesis (i.e., finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually true (i.e., the proportion of defective batteries is 5% or less). This would be a false positive result.
A Type II error would be failing to reject the null hypothesis (i.e., not finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually false (i.e., the proportion of defective batteries is greater than 5%). This would be a false negative result.
Part C:
If the hypothesis is tested at a 5% level of significance instead of 1%, this means that the criteria for rejecting the null hypothesis will be less stringent. In other words, it will be easier to find significant evidence that the company's claim is false. Therefore, increasing the level of significance from 1% to 5% will increase the power of the test.
Part D:
If the hypothesis is tested based on the sampling of 500 boxes of batteries rather than 100 boxes of batteries, this means that the sample size is larger. As a result, the standard error of the estimate will be smaller, and the test will be more precise. This increased precision will increase the power of the test.
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The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 34 minutes of calls is $14.69 and the monthly cost for 57 minutes is $17.68 . What is the monthly cost for 39 minutes of calls?
The monthly cost for 39 minutes of calls is $15.34.
According to given conditions :We can use the two given data points to form two equations and then solve for the unknown coefficients of the linear function.
Let the monthly cost (in dollars) be denoted by C, and let the total calling time (in minutes) be denoted by T. Then we can write:
C = aT + b
where a is the slope of the line (representing the rate of change of cost per minute of calling time), and b is the y-intercept of the line (representing the fixed monthly cost).
Using the given data points (34, 14.69) and (57, 17.68), we can form the following two equations:
14.69 = 34a + b (equation 1)
17.68 = 57a + b (equation 2)
Subtracting equation 1 from equation 2, we get:
17.68 - 14.69 = 57a - 34a + b - b
2.99 = 23a
a = 2.99/23
a = 0.13 (rounded to two decimal places)
Substituting the value of a into equation 1 (or 2), we get:
14.69 = 34(0.13) + b
b = 14.69 - 4.42
b = 10.27
Therefore, the linear function that represents the monthly cost in terms of total calling time is:
C = 0.13T + 10.27
To find the monthly cost for 39 minutes of calls, we can substitute T = 39 into this function:
C = 0.13(39) + 10.27
C = 5.07 + 10.27
C = $15.34 (rounded to two decimal places)
Therefore, the monthly cost for 39 minutes of calls is $15.34.
What is cost price ?The cost price (CP) is the original price paid to purchase a product or asset. It is the total cost incurred to acquire or produce the item, including all direct and indirect costs such as the cost of raw materials, labor, overhead expenses, transportation, taxes, etc.
The cost price is an important factor in determining the profitability of a business or investment, as it directly affects the profit margin. The profit margin is the difference between the selling price (SP) and the cost price (CP), expressed as a percentage of the cost price.
Profit Margin = (SP - CP) / CP * 100%
For example, if a product is sold for $100 and the cost price is $70, then the profit margin is:
Profit Margin = ($100 - $70) / $70 * 100%
Profit Margin = 30%
This means that for every $1 of cost, the business makes a profit of $0.30. The profit margin can be used to evaluate the efficiency and competitiveness of a business, and to compare the profitability of different products or investments.
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Lauren is working two summer jobs, making $24 per hour tutoring and making $8
per hour clearing tables. In a given week, she can work no more than 13 total hours
and must earn no less than $160. Also, she must work no more than 8 hours tutoring
and a maximum of 5 hours clearing tables. If a represents the number of hours
tutoring and y represents the number of hours clearing tables, write and solve a
system of inequalities graphically and determine one possible solution.
The system of inequalities of the given question is x>0, y>0 and 24x+8y=160
What are system of inequalities?
When mathematical expressions are compared, with non-strict equality, then such mathematical statements are called mathematical inequalties.
A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.
We are given that;
Price per hour for tutoring=$24
Price per hour for clearing tables=$8
Earning no less than $160
Work no more than in tutoring= 8hr
Maximum working for clearing table=5hr
Now,
x = number of hours tutoring y = number of hours landscaping
We cannot have negative values for either x and y, so xo and
x+y= total hours worked for both jobs combined
This total cannot exceed 11 hours
x+y≤11
Either x+y= 11 or x+y < 11
22x amount of money made from tutoring only = By amount of money made from landscaping only 22x+8y = total amount made from both jobs
24k+By 160 since he must make at least $160 Either 24x+8y = 160 or 24x+8y> 160
Therefore, the system of inequalities will be x>0,y>0,24x+8y=160
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My teacher gave me an extra credit assignment with 25 minutes left of class. It is extra credit, not a timed assessment.
need done as soon as possible
Figure Q was rotated about the origin (0,0) by 270 degrees counterclockwise.
Check the picture below.
Find the area and the circumference for the circle below. Use the math tools to get the correct symbols.
Answer:
Area = 78.54 sq. ft. (25π)
Circumference = 31.42 ft. (10π)
Step-by-step explanation:
Diameter of circle d = 10 ft
Radius r = Diameter/2 = 5
Area = πr² = π x 5² = π x 25 = 78.54 sq. ft. rounded to 2 decimal places
Circumference = πd = π x 10 = 31.42 ft. rounded to 2 decimal places.
The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude,
in feet, of the airplane and x represents the number of minutes the plane has been descending:
y= -1025x + 30,750
Part A:
Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B:
Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and
describe what is happening to the ajrplane at these time intervals.
Part C:
Which ordered pair(from the table in part A) represents the initial value? What does the initial value represent in this problem?
Part D:
What is the rate of change in this equation? What does the rate of change represent in this problem?
Answer:
Step-by-step explanation:
Part A:
To create the table, we substitute each of the given values of x into the equation and solve for y:
x y = -1025x + 30,750
0 30,750
5 25,375
8 21,050
10 18,725
30 -7,500
Part B:
The altitude after 5 minutes can be found by substituting x=5 into the equation:
y = -1025(5) + 30,750 = 25,375
The altitude after 30 minutes can be found by substituting x=30 into the equation:
y = -1025(30) + 30,750 = -7,500
After 5 minutes, the altitude of the airplane is 25,375 feet. After 30 minutes, the altitude of the airplane is -7,500 feet, which means the airplane is on the ground. This is because the altitude is decreasing by 1,025 feet every minute, and after 30 minutes, the altitude has decreased to 0 feet, which is the ground level.
Part C:
The ordered pair (0, 30,750) represents the initial value, where x=0. The initial value represents the altitude of the airplane before it started descending. In this problem, the initial value of 30,750 feet represents the altitude of the airplane when it was at cruising altitude.
Part D:
The rate of change in this equation is -1025. The rate of change represents the speed at which the altitude of the airplane is changing per minute. In this problem, the rate of change of -1025 feet per minute means that the altitude of the airplane is decreasing by 1025 feet every minute it descends.
What is the value of the digit 3 in 4693?
Answer:
Step-by-step explanation:
The digit 3 in the number 4693 has a place value of 3 tens or 30. Therefore, the value of the number 3 in the number 4693 is 30.
( 20 points!!) \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ simplify:
The value of the expression is -3/2, So correct option is A.
Describe Fraction?In mathematics, a fraction represents a part of a whole. A fraction consists of two numbers separated by a horizontal line called a fraction bar or a division sign. The number above the bar is called the numerator, and the number below the bar is called the denominator.
The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator. This fraction represents three parts out of a total of four equal parts.
Fractions can be written in different forms, such as proper fractions, improper fractions, and mixed numbers.
A proper fraction has a smaller numerator than the denominator, such as 2/3 or 5/8.
An improper fraction has a numerator that is equal to or greater than the denominator, such as 7/4 or 11/6.
A mixed number consists of a whole number and a proper fraction, such as 2 1/3 or 3 2/5.
Fractions are used in many real-life situations, such as cooking, measuring, and financial calculations. They are also an essential part of mathematics and are used in operations such as addition, subtraction, multiplication, and division.
We can start by simplifying the expression inside the absolute value bars:
|1/6 - 3/4| = |(2/12) - (9/12)| = |-(7/12)| = 7/12
Now we can substitute this back into the original expression and simplify:
(7/4 - 8/3) - |1/6 - 3/4|
= (21/12 - 32/12) - 7/12 (converting fractions to have a common denominator)
= -11/12 - 7/12
= -18/12
= -3/2
Therefore, the value of the expression is -3/2.
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Answer:
What is Fraction ?
A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fractio" which means 'to break'.
A proper fraction has a smaller numerator than the denominator, such as 2/3 or 5/8.
An improper fraction has a numerator that is equal to or greater than the denominator, such as 7/4 or 11/6.
A mixed number consists of a whole number and a proper fraction, such as 2 1/3 or 3 2/5.
Fractions are used in cooking, measuring, and financial calculations.
We can start by simplifying the expression inside the absolute value bars:
|1/6 - 3/4| = |(2/12) - (9/12)| = |-(7/12)| = 7/12
Now we can substitute
(7/4 - 8/3) - |1/6 - 3/4|
= (21/12 - 32/12) - 7/12 (converting fractions to have a common denominator)
= -11/12 - 7/12
= -18/12
= -3/2
Therefore, the value of the expression is -3/2.
Solve for l if V = 120 w = 5 and h = 4
Answer:
The value of l is 48. The formula to calculate volume (V) is V = l * w * h, so we can rearrange the equation to solve for l, or l = V/(w * h). In this case, l = 120/(5 * 4) = 48.
Answer:
125
Step-by-step explanation:
w
100 POINTS HELP PLEASE
Answer:
C
Step-by-step explanation:
Figure 1 and Figure 2 below are similar. Which point corresponds to point V?
Answer:
Point Q
Step-by-step explanation:
Point Q corresponds to Point V, because if you turn the green triangle around, it matches almost exactly the same.
A square has an area of 400 square miles. What is the length of each side of the square? 10 mi 20 mi 30 mi 40 mi
Answer: The side of the square is 20 miles
Step-by-step explanation:
Since the area of square= side *side
given, area =400 square miles
400 = side *side
400= side²
√400=side
20 miles=side
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Which rule can be used to describe the x-coordinates in the translation below?.
-5-4-3-2
5
--3-
2
1-
14
2
तुलने
3.
4
L5
-A.
B'
B
C'
2 3 4
C
5 X
A
Answer:
translation point a cross the coordinator
Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank. About _____% of the area is between zequalsnegative 2. 2 and zequals2. 2 (or within 2. 2 standard deviations of the mean)
The area under the curve of the standard normal distribution is 98.61% of the area between equals negative 2. 2 and zequals2. 2
The area under the curve of a standard normal distribution between z = -2.2 and z = 2.2 is given by the integral of the normal distribution function from -2.2 to 2.2. This can be calculated using a table of standard normal probabilities or using a calculator with a normal distribution function.
The result is approximately 0.9861. To convert this to a percentage, simply multiply by 100: 0.9861 * 100 = 98.61%. Therefore, about 98.61% of the area is between z = -2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is also known as the z-distribution or the unit normal distribution. It is often used in statistical tests, such as the z-test, t-test, and chi-square test. It is also used to determine confidence intervals, to calculate probabilities, and to measure the probability of a given event.
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After a 66% increase your salary is now $75,000. What was your original salary?
The original salary was approximately $45,180.72.
What is the formula for the starting amount?Prior to a percentage increase or decrease, one must ascertain the beginning value of an amount: The amount must be represented as a percentage of the initial sum. Determine one percent of the starting sum. The original value may be obtained by multiplying by 100 because 100% is the original sum.
We can use algebra to resolve this issue. Let x represent the starting wage.
The issue states that following a 66% raise, the new compensation is $75,000 Mathematically, this can be expressed as:
x + 0.66x = 75000
By merging similar phrases to simplify the left side, we obtain:
1.66x = 75000
Finally, by multiplying both sides by 1.66, we can find the value of x:
x = 75000/1.66
x ≈ 45,180.72
Hence, the initial wage was roughly $45,180.72.
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what is the area of a trapezoid with a height of 5 ft and bases of 10 ft and 14 ft?
The area of the Trepezium will be 60 feet².
What is a trepezium, exactly?
Trapezoids have two parallel sides and two oblique sides. It is also known as a Trapezium. A trapezoid is a four-sided closed shape or figure having a space-filling perimeter. It is a 2D figurine, not a 3D figure. The bases of a trapezoid are the sides that are parallel to one another. Legs, also known as lateral sides, are non-parallel sides. Its height is determined by the distance between its parallel sides.
Area of a trepezium=1/2*(a+b)*h
where h=height or distance between two parallel lines
a and b are two parallel lines.
Now,
Given that a=14 feet, b=10 feet and h=5 feet
then area=1/2*(10+14)*5
=24/2*5
=12*5
=60 ft²
hence,
The area of the Trepezium will be 60 feet².
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What is the answer to this problem?
3x+6+x-2+8(x-3)+-4-4+x+1+-2(x+2)+6+7x+-8x=?
Answer:
10x -25
Step-by-step explanation:
You want to simplify the expression ...
3x+6+x-2+8(x-3)+-4-4+x+1+-2(x+2)+6+7x+-8x
SimplifyFirst, we use the distributive property to eliminate parentheses:
3x+6+x-2+8x-24+-4-4+x+1+-2x-4+6+7x+-8x
Now, we group x-terms and constant terms:
(3 +1 +8 +1 -2 +7 -8)x +(6 -2 -24 -4 -4 +1 -4 +6)
Finally, we perform the sums:
10x -25
__
Additional comment
This sort of problem can be described as "tedious, but not difficult."
The bike store marks up the wholesale cost of all of the bikes they sell by 30%.
1. Andre wants to buy a bike that has a price tag of $125. What was the wholesale cost of this bike?
2. If the bike is discounted by 20%, how much will Andre pay (before tax)?
Answer:
1. The wholesale cost of the bike is $93.75.
2. Andre will pay $100 before tax.
A person walks 1/4 miles in 1/12 hour. What is the person’s speed in miles per hour?
The speed of the person in miles per hour is S = 3 mph
What is Speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the speed of the person in miles per hour be S
Now , the distance traveled by the person D = 1/4 miles
The time taken by the person to travel ( 1/4 ) miles = 1/12 of an hour
Now , speed of the person in miles per hour S = distance traveled by the person D / time taken by the person to travel ( 1/4 ) miles
On simplifying , we get
The speed of the person in miles per hour S = ( 1/4 ) / ( 1/12 )
The speed of the person in miles per hour S = ( 1/4 ) x 12
The speed of the person in miles per hour S = 3 miles per hour
Hence , the speed is 3 mph
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Given w=-68, e=-3, f=-4 what is e4-df?
Answer:
-12 + 4d
Step-by-step explanation:
(-3)4 - d(-4)
-12 - -4d
Triangle XYZ is mapped onto triangle X′Y′Z′ by a dilation with a scale factor of 3 and center (2,1). What are the coordinates of triangle X′Y′Z′ when X(-3,2), Y(0,0), Z(2,1).
Don't forget that your ordered pairs need to be in parentheses and the coordinates separated by a comma!
X'=
Y'=
Z'=
30 points
Answer:
Step-by-step explanation:
To find the image of each point under the dilation, we need to apply the scale factor of 3 to the distances between the point and the center, and then add the coordinates of the center to get the new coordinates.
The center of dilation is (2,1), so we subtract 2 from the x-coordinates and 1 from the y-coordinates to get the distances from the center to each point:
X: (-3 - 2, 2 - 1) = (-5, 1)
Y: (0 - 2, 0 - 1) = (-2, -1)
Z: (2 - 2, 1 - 1) = (0, 0)
Next, we apply the scale factor of 3 to each distance:
X': (-5 × 3, 1 × 3) = (-15, 3)
Y': (-2 × 3, -1 × 3) = (-6, -3)
Z': (0 × 3, 0 × 3) = (0, 0)
Finally, we add the coordinates of the center (2,1) to each image:
X': (-15 + 2, 3 + 1) = (-13, 4)
Y': (-6 + 2, -3 + 1) = (-4, -2)
Z': (0 + 2, 0 + 1) = (2, 1)
Therefore, the coordinates of the image triangle X'Y'Z' are:
X' = (-13, 4)
Y' = (-4, -2)
Z' = (2, 1)
pls give diple working out :))
Answer:
x = 132°
Step-by-step explanation:
x and y lie on a straight line and sum to 180° , that is
x + y = 180°
x + 48° = 180° ( subtract 48° from both sides )
x = 132°
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The constant of proportionality of the equation y = 1 / 3 x is 1/3.
How to find constant of proportionality?Proportional relationships are relationships between two variables where their ratios are equivalent. In other words, proportional relationship is one in which two quantities vary directly with each other.
Therefore, proportional relationship can be represented as follows:
y ∝ x
y = kx
where
k = constant of proportionalityTherefore, the constant of proportionality of y = 1 / 3 x is 1 / 3
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How can $60,000 be invested, part at 10% annual simple interest and the remainder at 5% annual simple interest, so that the interest earned by the two accounts will be equal?
Answer:
Step-by-step explanation:
Let's assume that the amount invested at 10% is x, and the amount invested at 5% is (60000 - x), since the total investment is $60,000.
The interest earned on the 10% investment after one year would be 0.10x, and the interest earned on the 5% investment after one year would be 0.05(60000 - x).
We are given that the interest earned by the two accounts is equal, so we can set up an equation:
0.10x = 0.05(60000 - x)
Simplifying this equation, we get:
0.10x = 3000 - 0.05x
Adding 0.05x to both sides, we get:
0.15x = 3000
Dividing both sides by 0.15, we get:
x = 20000
Therefore, the amount invested at 10% is $20,000, and the amount invested at 5% is ($60,000 - $20,000) = $40,000.
To check that the interest earned is equal for both investments, we can calculate:
Interest earned on 10% investment = 0.10($20,000) = $2,000
Interest earned on 5% investment = 0.05($40,000) = $2,000
As expected, the interest earned on both investments is equal.
4x−1<11 what is the answer
Answer:
Add 1 to both sides. Add 11 and 1 to get 12. Divide both sides by 4. Divide 12 by 4 to get 3.
let us suppose that some article investigated the probability of corrosion of steel reinforcement in concrete structures. it is estimated that the probability of corrosion is 0.1 under specific values of half-cell potential and concrete resistivity. the risk of corrosion in five independent grids of a building with these values of half-cell potential and concrete resistivity is investigated now. let the random variable x denote number of grids with corrosion in this building. determine the probability mass function of x.
The probability mass function for the random variable would be 0.38742049.
What is probability mass function {P.M.F}?In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value.
Probability mass function is the probability distribution of a discrete random variable, and provides the possible values and their associated probabilities. It is the function [tex]{\displaystyle p:\mathbb {R} \to [0,1]}[/tex] defined by -
[tex]${\displaystyle p_{X}(x)=P(X=x)}[/tex].
Given is that the probability of corrosion is 0.1 under specific values of half-cell potential and concrete resistivity. the risk of corrosion in five independent grids of a building with these values of half-cell potential and concrete resistivity is investigated now.
We can write the
[tex]$f(x;n,p) = \frac{n!}{x!(n-x)!}\; p^{x} \;(1-p)^{n-x}[/tex]
where -
{x} = number of successes
{n} = number of trials
{p} = probability of a successful outcome
Substituting the values, we get -
[tex]$f(1;10,0.1) = \frac{10!}{1!(10-1)!}\; (0.1)^{x} \;(1-0.1)^{10-1}[/tex]
[tex]$f(1;10,0.1) = 0.38742049[/tex]
Therefore, the probability mass function for the random variable would be 0.38742049.
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f(x) = 4x − 12 what is the inverse
Answer:
f-1(x)=x4+3 this is your answer
can someone please help me
Using trigonometric ratio, the value of tan V is √7 / 8
What is the value of tan VTo find the value of tan V, we have to use trigonometric ratio.
In the triangle, we have the opposite side and the hypothenuse. We can find the adjacent side using Pythagoras theorem.
Substituting the values into the formula;
w² = v² + x²
(√71)² = (√7)² + x²
71 = 7 + x²
x² = 71 - 7
x² = 64
x = √64
x = 8
The value of tan V;
tan V = opposite /adjacent
tan V = √7 / 8
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Jamaica from Jammin' Candles is trying to arrange 40 candles on a table. She wants them arranged as close to a square shape. Which way should she arrange the candles?
2 rows of 20 candles
10 rows of 4 candles
5 rows of 8 candles
4 rows of 10 candles