It is assumed the statement is true for [tex]S_k[/tex]:
A factor of [tex]2^{2k-1}+3^{2k-1}[/tex] is 5.Show that [tex]S_{k+1}[/tex] is also divisible by 5:
[tex]2^{2(k+1)-1}+3^{2(k+1)-1}=[/tex][tex]2^{2k+2-1}+3^{2k+2-1}=[/tex][tex]2^{(2k-1)+2}+3^{(2k-1)+2}=[/tex][tex]2^{2k-1}*2^2+3^{2k-1}*3^2=[/tex][tex]4*2^{2k-1}+9*3^{2k-1}=[/tex][tex]4*2^{2k-1}+4*3^{2k-1}+5*3^{2k-1}=[/tex][tex]4(2^{2k-1}+3^{2k-1})+5*3^{2k-1}[/tex]The first part is divisible by 5 as we assumed in the beginning and the second part has a factor of 5 so the sum is divisible by 5.
Hence it makes [tex]S_{k+1}[/tex] true, so the proof is complete.
Nine less than two times a number is five more than this number. What is the number?
Answer:
14
Step-by-step explanation:
let n be the number then 2 times the number is 2n and so
2n - 9 = n + 5 ( subtract n from both sides )
n - 9 = 5 ( add 9 to both sides )
n = 14
then the required number is 14
Two marbles are chosen at random, one at a time from a box that contains 7 marbles, 5 red and 2 green, a. Find the probability of drawing 2 red marbles when
The probability of randomly drawing 2 red marbles is P = 0.476
How to find the probability?On the box we have 7 marbles, 5 red ones and 2 green ones. If we assume all the marbles have the same probability of being randomly drawn, then the probability of drawing a red marble is equal to the quotient between the number of red marbles and the total number of marbles.
So the probability for the first red marble is:
p = 5/7
For the second one, we will have one red marble less and one marble of the total less, so the probability is:
q = 4/6
The joint probability is the product of these two:
P = (5/7)*(4/6) = 0.476
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H(y) models the leading number of home runs for season y of the National League between the years 2000-2010, according to the table.
Season Player # of Home Runs Team
2000 Sammy Sosa 50 Chicago
2001 Barry Bonds 73 San Francisco
2002 Sammy Sosa 49 Chicago
2003 Jim Thome 47 Philadelphia
2004 Adrian Beltre 48 Los Angeles
2005 Andruw Jones 51 Atlanta
2006 Ryan Howard 58 Philadelphia
2007 Prince Fielder 50 Milwaukee
2008 Ryan Howard 48 Philadelphia
2009 Albert Pujols 47 St. Louis
2010 Albert Pujols 42 St. Louis
Which number type is more appropriate for the domain of H?
A number type which is more appropriate for the domain of H include the following: A. Integers.
The appropriate domain include the following: C. 2000 ≤ y ≤ 2010.
What is an integer?In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1) such as 1, 10, 20, 2000, 2010, etc.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values (real numbers) which are located on the x-coordinate.
Since the variable H(y) represents the leading number of home runs for season y of the National League between the years 2000-2010, an appropriate domain is given by;
Domain = 2000 ≤ y ≤ 2010 or [2000, 2010].
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Complete Question:
Which number type is more appropriate for the domain of H?
A. Integers
B. Real numbers
What's the appropriate domain?
0 ≤ y < 2010
0 < y < 73
2000 ≤ y ≤ 2010
42 ≤ y < 73
Sara needs to determine the number of 3/4 pound servings into 9 3/4 pounds of turkey.she calculates that there are 13 servings.is stated calculation correct why or why not
There are 9.75 servings, not 13 servings.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
We have,
the number of 3/4 pound servings in pounds of turkey
she calculates that there are 13 servings.
so,
9 (3/4) = (36 + 3) /4
= 39/4
= 9.75
Hence, there are 9.75 servings, not 13 servings.
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Find the product
-20 • (-4) =
Answer:
-20*(-4)=80
Step-by-step explanation:
-20*(-4)=20*4
20*4=80
Write an inequality that represents the sentence:
14 fewer than a number is at least -8.
and
the product of a number and 5 is no more than 8.
In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true?
OA. m/1=m/7
OB.
O C.
O D.
m23=m26
m25+ m28 = 90°
m26+ m27 = 180°
Answer:
A. ∠1 = ∠7
B. ∠2 = ∠6
D. ∠6 + ∠7 = 180°
Step-by-step explanation:
⭐ Why A is correct
∠1 = ∠7 because when two parallel lines are cut by a transversal, alternate exterior angles are formed. Alternate exterior angles are congruent.∠1 and ∠7 are alternate exterior angles.Therefore, ∠1 = ∠7.⭐ Why B is correct
∠2 = ∠6 because when two parallel lines are cut by a transversal, corresponding angles are formed. Corresponding angles are congruent.∠2 and ∠6 are corresponding angles.Therefore, ∠2 = ∠6.❌ Why C is incorrect
∠5 + ∠8 is not equal to 90° because ∠5 and ∠8 are adjacent angles.Adjacent angles sum to 180°.Therefore, ∠5 + ∠8 is not equal to 90°.⭐ Why D is correct
∠6 + ∠7 = 180° because ∠6 and ∠7 are adjacent angles.Adjacent angles sum to 180°.Therefore, ∠6 + ∠7 = 180°.
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A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined. Given that the number of men is now 60% of the total members, how many of the 50 new members were women?
The number of new members that are women will be 25 women.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A games group has 65 men and 35 ladies as individuals. Another movement has quite recently started and a few new individuals have joined. Considering that the quantity of men is currently 60% of the absolute number of individuals.
The number of new members is 50.
Let the number of new men be 'x'. Then the equation is given below.
(65 + x) / (100 + 50) = 60%
(65 + x) / 150 = 0.60
65 + x = 90
x = 25
The number of new members were women will be given as,
⇒ 50 - 25
⇒ 25
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Suppose two researchers want to estimate the proportion of American college students who favor abolishing the penny. They both want to have about the same margin of error to estimate this proportion. However, Researcher 1 wants to estimate with 99% confidence and Researcher 2 wants to estimate with 95% confidence. Which researcher would need more students for her study in order to obtain the desired margin of error? Researcher 1 Researcher 2 Both researchers would need the same number of subjects. OIt is impossible to obtain the same margin of error with the two different confidence levels.
The researcher who needs more students for her study in order to obtain the desired margin of error would be: Researcher 1. The correct answer is the first option.
Researcher 1 needs more students for her study in order to obtain the desired margin of error, because she wants to estimate with 99% confidence, while Researcher 2 wants to estimate with 95% confidence.
What is the relation between margin of error and level of confidence?The margin of error and the level of confidence are connected together. A better margin of error may be resulted for a lesser level of confidence, or a higher level of confidence may be obtained by tolerating a larger margin of error.
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The total pay that Nelly will get for last week is £220.
What will the total pay of Nelly be ?From the information given, the following can be deduced:
£8 per hour for the first 15 hours
£10 let hour for any extra hour.
The above are applicable for Monday to Friday.
£16 is the rate for Saturdays.
The number of hours that Nelly worked from Monday to Friday will be:
= 3 1/2 + 5 + 2 1/2 + 4 + 2
= 17 hours
On Saturday, he worked 5 hours.
The total earnings will be:
= (£8 × 15) + (£10 × 2) + (£16 × 5)
= £120 + £20 + £80
= £220
The total amount is £220.
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A semi-circle has an area of 50 m². Find the perimeter of the semi-circle. Give your answer correct to one decimal place.
Answer:
29.0 m
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4cm}\underline{Area of a semicircle}\\\\$A=\dfrac{1}{2}\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius\\ \end{minipage}}[/tex]
Given the area of the semicircle is 50 m², substitute this into the formula and rearrange to isolate r:
[tex]\begin{aligned}\implies\dfrac{1}{2}\pi r^2&=50\\\pi r^2 & = 100\\r^2 & = \dfrac{100}{\pi}\\r&=\sqrt{\dfrac{100}{\pi}}\end{aligned}[/tex]
The perimeter of a semicircle is the sum of the diameter of the circle and half its circumference.
Diameter of a circle = 2rCircumference of a circle = 2πrTherefore:
[tex]\begin{aligned}\textsf{Perimeter of a semicircle}&=2r+\pi r\\&=r(2+\pi)\\&=\sqrt{\dfrac{100}{\pi}}(2+\pi)\\&=29.0083301...\end{aligned}[/tex]
Therefore, the perimeter of the semicircle is 29.0 m (1 d.p.).
is (y+3) a factor of the polynomial: y^3-6y+9
(y + 3) is not a factor of the polynomial y^3-6y+9.
Define polynomial.A polynomial is an equation made up of terms, exponents, constants, variables (or indeterminate values), and variables. The polynomial 3x2 -2x-10 is an illustration. Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Given,
Polynomial
y³ - 6y + 9
(y+3) as a factor
(y + 3) (y+3)
y² + 3y + 3y + 9
y² + 6y + 9
(y + 3) is not a factor of the polynomial: y^3-6y+9.
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the manager of a bank record of the amount of each Time customer spent waiting in the line during peak business hours on Monday the waiting times are shown below find the mean waiting time Roger answer to one Decimal place 6.8 min 7.5 min 7.2 min brainly
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Answer:
D
Step-by-step explanation:
Because whee your finding the Grange of a fundtlon you Look at the Y value from the smallest Number to the largest Number.
a research company is claiming that 75% of college students shop online. jamila takes a sample of 200 college students and finds that 120 college students shop online.
The correct answer is option (d) - one proportion z-test.
The complete question is
A research company is claiming that 75% of college students shop online. Jamila takes a sample of 200 college students and finds that 120 college students shop online. Which type of inference test should Jamila use?
a) Chi-squared test for homogeneity
b) Two-way ANOVA O
c) One-sample t-test
d) One proportion z-test
To determine which type of inference test to use in this situation, Jamila needs to consider the following:
The research question: In this case, the research question is whether the proportion of college students who shop online is significantly different from the proportion claimed by the research company (75%).
The type of data: Jamila has collected data on a sample of college students, rather than the entire population.
The type of variables: The variable of interest is a binary variable (students either do or do not shop online), and the proportion of students who shop online is being compared to a fixed value (75%).
Given this information, the appropriate test to use is a one proportion z-test. The one proportion z-test is a statistical test that is used to determine whether the proportion of a binary variable in a sample is significantly different from a known proportion in the population.
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The sum of two even integers and one odd integer will be an odd integer. Then the correct option is D.
What is the Odd and Even?If the number is divisible by 2 then the number will be an even number. Similarly, if the number is not divisible by 2 then the number will be an odd number.
Some of the properties of the even and odd number are given below.
The sum of two odd numbers is an even number.The sum of two even numbers is an even number.The sum of odd and even numbers is an odd number.The sum of even and odd numbers is an odd number.The sum of two even numbers will be even and the sum of two even numbers and odd numbers will be odd numbers.
The amount of two even whole numbers and one odd whole number will be an odd whole number. Then, at that point, the right choice is D.
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Copy and complete the equation of line G below
y=___x+____
Answer:
y = 3x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (1, 7) ← 2 points on the line
m = [tex]\frac{7-4}{1-0}[/tex] = [tex]\frac{3}{1}[/tex] = 3
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 3x + 4 ← equation of line
Sarah received 23 chromosomes from her mother and 23 chromosomes from her father. The combination of genes on these chromosomes code for proteins that express her traits. Choose the words or phrases to complete the sentence. A diagram of a Punnett square. The top of the Punnett square is labeled Father with x and y above the boxes. The side of the square is labeled Mother with x and x on the left side of the boxes. The top row, first box has xx female, the top row, second box has xy male. The second row, first box has xx female, the second row, second box has xy male. There are two long, tubular object along the side of the diagram labeled x chromosome. There is a small circular object on the bottom of the diagram labeled y chromosome. The chromosomes in the image are called Choose... , and the chances of being born male or female are Choose... .
The chromosomes in the image are called sex chromosomes, and the chances of being born male or female are 1:1.
What is a chromosome?In Science, a chromosome can be defined as a thread-like linear strand of deoxyribonucleic acid (DNA) that is typically found in the nucleus of each cell in a living organism.
What are the characteristics of a chromosome?In Genetics, some of the characteristics of a chromosome include the following:
Chromosomes are made up of a long deoxyribonucleic acid (DNA) molecule that is tightly wound.Every chromosome consist of many genes with each gene being a single segment of deoxyribonucleic acid (DNA).Furthermore, the human somatic cell primarily comprises 46 chromosomes which are normally sub-divided into 23 pairs of chromosomes with 22 of these pairs being autosomes and a pair of sex chromosomes (X and Y).
In this context, we can reasonably infer and logically deduce that the x and y chromosomes are generally referred to as sex chromosomes.
Since Sarah received 23 chromosomes each from her mother and father, the chances of being born male or female is given by;
Ratio = 23: 23.
Dividing both sides by 23, we have;
Ratio = 1:1.
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Question 2 of 10
Which statement regarding salaried employees is true?
A. Salaried employees get paid more for additional hours worked.
B. Salaried employees have taxes with held from each paycheck.
c. Salaried employees do not receive an agreed-upon annual pay.
D. Salaried employees never receive medical benefits.
write a quadratic equation with -6 and 3/4 as its roots. write the equation in the form ax^2 + bx + c = 0, where a,b, and c are integers.
The quadratic equation whose roots are -6 and 3/4 is 14x²+21x-18=0
How to find quadratic equations?We should know that a quadratic equation is that whose highest power of the variable is 2
The given roots are
x=-6 and x=3/4
Let (x+6)(x-3/4)=0
Multiplying the brackets we have
[tex]X^{2}-\frac{3x}{4} +6x-\frac{18}{4}[/tex] =0
Find the LCM of the denominators
[tex]\frac{4X^{2}+21x-18 }{4} =0[/tex]
Cross and multiplying we have
[tex]4x^{2} +21x-18=0[/tex]
Therefore, the equation is expressed in the form ax²+bx+v=0 Where a=4, b=21 and c=-18
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[tex]5^{2} -2^{2} =[/tex]
A bus station runs a shuttle service to and from the airport. A shuttle that left the station traveling at 39 miles per hour is passed by a second shuttle that left 30 minutes later traveling at a rate of 42 miles per hour. How far did the first shuttle travel before it was passed by the second shuttle?
To find the distance that the first shuttle traveled before it was passed by the second shuttle, we need to use the formula d = rt, where d is the distance traveled, r is the speed at which the shuttle is traveling, and t is the time elapsed. We can use this formula to find the distance traveled by each shuttle and then subtract the distance traveled by the first shuttle from the distance traveled by the second shuttle to find the distance the first shuttle traveled before it was passed.
For the first shuttle, the speed is 39 miles per hour and the time elapsed is 30 minutes. Since there are 60 minutes in an hour, the time elapsed in hours is 30 minutes / 60 minutes/hour = 0.5 hours. So, the distance traveled by the first shuttle is 39 miles/hour * 0.5 hours = 19.5 miles.
For the second shuttle, the speed is 42 miles per hour and the time elapsed is 30 minutes. Since there are 60 minutes in an hour, the time elapsed in hours is 30 minutes / 60 minutes/hour = 0.5 hours. So, the distance traveled by the second shuttle is 42 miles/hour * 0.5 hours = 21 miles.
Therefore, the distance that the first shuttle traveled before it was passed by the second shuttle is 21 miles - 19.5 miles = 1.5 miles.
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Answer: 5/8
Step-by-step explanation: There are 8 members. Out of 8, there are 5 people's weight that are higher than 135. Therefore the answer is 5/8.
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Answer:
Step-by-step explanation:
In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=11 and BC=6, what is the area of the shaded region? Write your answer as a decimal, if necessary. Do not include units in your answer.
Answer:
The area of the shaded region is 36.
In rectangle ABCD, point E lies halfway between sides AB and CD and halfway between sides AD and BC. This means that line segment AE is parallel to line segment CD and is half as long, and line segment BE is parallel to line segment AD and is also half as long.
Since AE is half as long as CD, and CD is twice as long as AE, we can say that CD is equal to 2 * AE. Similarly, since BE is half as long as AD, and AD is twice as long as BE, we can say that AD is equal to 2 * BE.
Since AD is equal to 2 * BE and CD is equal to 2 * AE, the lengths of AD and CD are equal. This means that the shaded region is a parallelogram with sides of equal length.
The area of a parallelogram is equal to the product of its base and height. In this case, the base of the parallelogram is 6 (the length of side BC) and the height is AE + BE (the combined length of the two sides of the parallelogram).
We know that AE is half as long as CD, and CD is twice as long as AE, so CD is equal to 2 * AE. Since CD is equal to 2 * AE, AE is equal to CD / 2. Since CD is equal to 11 (the length of side AB), AE is equal to 11 / 2 = 5.5.
Similarly, we know that BE is half as long as AD, and AD is twice as long as BE, so AD is equal to 2 * BE. Since AD is equal to 2 * BE, BE is equal to AD / 2. Since AD is equal to 6 (the length of side BC), BE is equal to 6 / 2 = 3.
The combined length of AE and BE is 5.5 + 3
Is the weight of a bike a function of how old it is?
The weight of an object is the amount of the gravitation pull of the Earth on the object. No, the weight of a bike is not a function of its age.
What i weight?The mass of an object is the quantity of matter it contains, while the weight is the amount of gravitational pull of the Earth on the object. Thus the greater the mass of an object is, the greater its weight. This implies that the weight of an object can be influenced by its value of mass.
The mass of an object can be determined or measured by the use of any of the weighing balances, while the weight of an object can be measured by the use of any of the spring balances. Therefore, the answer to the given question is NO. The weight of a bike is NOT a function of its age. The weight of the bike will depend on the number, and weight of its component parts.
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The distance around a circular park is 88 yards.
What is the area of the park? Use 3.14 for π.
Answer:
616.25 [tex]yd^2[/tex]
Step-by-step explanation:
The equation for the area of a circle is
[tex]A=\pi r^2[/tex]
Since the problem does not give a value for r, it must be derived. Recall that the equation for the circumference of a circle is
[tex]C=2\pi r[/tex]
Using the given value of the circumference,
[tex]C=88yd=2\pi r[/tex]
So,
[tex]88yd=2\pi r\\\frac{88yd}{2\pi}=r\\14.01yd=r[/tex]
Insert the derived value of r into the formula for area:
[tex]A=\pi r^2\\A=\pi(14.01yd)^2\\A=616.25yd^2[/tex]
cos 0 = 0.8192 A = 45
H = ?
The value of H (Hypotenuse) will be 54.93
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The values are,
⇒ cos θ = 0.8192
⇒ A (Base) = 45
Now,
Since, The values are,
⇒ cos θ = 0.8192
⇒ A = 45
We know that;
⇒ cos θ = Base (A) / Hypotenuse (H)
Substitute all the values, we get;
⇒ 0.8192 = 45 / H
⇒ H = 45 / 0.8192
⇒ H = 54.93
Thus, The value of H (Hypotenuse) = 54.93
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TASK 4
Managing multiple items
Manage a number of items in an ordered structure
For this task you are required to use your knowledge of lists from the Coding Preparation section to manage a number of items in an ordered structure.
You are going to be creating a program that represents the movements of the line for the lady's bathroom. To begin, create a list that represents the line, it must contain the five names of the women initially waiting (you can make these up).
The following events occur, and you must represent them in the list and print the list out after each action.
A woman named Jenny arrives who only wanted to check her lipstick, she asks to join the front of the line, and all the women let her.
The woman third in line’s phone started ringing, and she left the line to answer.
A new woman named Alice joined the line.
This program uses a list to represent the line and the built-in Python list methods insert(), pop(), and append() to manage the line according to the specified events.
What is a program?This program represents the line with a list and manages the line using the built-in Python list methods insert(), pop(), and append().
Here is one way you could implement this program using a Python list:
# Initialize the list of women waiting in line
line = ["Samantha", "Emily", "Rebecca", "Karen", "Linda"]
# Jenny arrives and joins the front-of-the-line
line.insert(0, "Jenny")
print(line) # Output: ['Jenny', 'Samantha', 'Emily', 'Rebecca', 'Karen', 'Linda']
# The woman third in line leaves the line
line.pop(2)
print(line) # Output: ['Jenny', 'Samantha', 'Emily', 'Karen', 'Linda']
# Alice joins the line
line.append("Alice")
print(line) # Output: ['Jenny', 'Samantha', 'Emily', 'Karen', 'Linda', 'Alice']
The final list after all events have occurred is ['Jenny', 'Samantha', 'Emily', 'Karen', 'Linda', 'Alice'].
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Each marble bag sold by Jane's Marble Company contains 4 purple marbles for every 5 red marbles. If a bag has 24 purple
marbles, how many red marbles does it contain?
The no: of red marbles, that the bag contains if it has 24 purple marbles are 30 marbles.
What is a unitary in math?a single state. This has an identity element in math, in an algebra. Whose inverse is equivalent to its adjoint (in mathematics, linear algebra, mathematical study of a matrix or operator).
What is unitary formula?The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.
What is the unitary rule?A unitary government is a type of government in which the whole government is controlled by a single entity, known as the central government. Actually, the center of authority for all administrative divisions and powers.
In the given question,
for every 4 purple marbles there are 5 red marbles
then for 1 purple marble there is 5/4 red marbles
again for 24 purple marbles, there are 30 red marbles
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