Answer:
[tex]\frac{6}{5}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} *\frac{9}{5} =\frac{18}{15} =\frac{6}{5}[/tex]
The value of the product of 2/3 × 9/5 is 6/5.
In the given question, we have to attempt fraction multiplication.
For fraction multiplication, we simply multiply the respective numerators and denominators with each other.
Here, in 2/3 × 9/5 ⇒ 18/15 (since 2×9=18) (since 3×5=15)
Now, since we can see that both the numerator and denominator in the solution can get divided by 3, we can simplify the fraction by dividing both the numerator and denominator by 3.
On dividing by 3, we get ⇒ 6/5
So, on multiplying 2/3 and 9/5, we get 18/15 which we later simplify into 6/5.
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A runner completed a 26.2-mile
marathon in 210 minutes.
a. Estimate the unit rate, in miles per minute.
b. Estimate the unit rate, in minutes per mile.
c. Another runner says, “I averaged 10-minute miles in the
marathon.” Is this runner talking about the unit rate
described in part (a) or in part (b)? Explain your reasoning.
Step-by-step explanation:
The answer is: A=210÷26.2=8.2
B=now we have to turn minutes in to haurs 210:60=3.5 now 26.2÷3.5=29.7
Answer:
A) 26.2/210= .125 miles per minute
B) 210/26.2= 8.02 minutes per mile
C) the other runner talks about the same rate as b), not a).
Step-by-step explanation:
A)[tex]\frac{26.2}{210\\}[/tex] and B)[tex]\frac{210}{26.2}[/tex] :)
C)the runner was referring to the time they took to run one mile, so the other runner ran 10 minutes to cover one mile, or as they say, "10 minute miles", which is the rate in minutes per mile.
If they were referring to the rates in a), that would imply the other runner ran 10 miles per minute... which is very unlikely.
Find m∠1 and m∠2. Tell which theorem can be used.
According to the vertical angles theorem, m∠1 = 117°.
Based on the corresponding angles theorem, m∠2 = 117°.
What is the Vertical Angles Theorem?The set of angle pairs formed that are directly opposite each other when two straight lines intersect or when two parallel lines are crossed by a transversal are said to be vertical angles, and therefore congruent to each other based on the vertical angles theorem.
What is the Corresponding Angles Theorem?When two lines are intersected by a transversal, the angles that are on the same transversal and lie in relative position or corner in the two parallel lines are said to be corresponding angles which are congruent based on the corresponding angles theorem.
Using the information given in the diagram attached below, angles 1 and 117° are vertical angles.
Therefore:
m∠1 = 117° [vertical angles theorem]
Angles 1 and 2 are corresponding angles. Therefore:
m∠2 = m∠1
Substitute
m∠2 = 117° [corresponding angles theorem]
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Trapezoid G is a scaled copy of trapezoid F.
Answer:
yes it is???
Step-by-step explanation:
You go out to eat with 3 friends and your meal was $72.50. There is 6.75% sales tax and you plan to tip the server 15%. How much should each person pay?
The amount that each person should pay is $22.06 .
in the question ,
it is given that
total number of persons = 3 person + 1 = 4 persons
cost of the meal = $72.50
sales tax percent = 6.75%
tip percent = 15%
So , the amount of sales tax = 6.75% of cost = 0.0675 * 72.50 = $4.89
and , the amount of tip is = 15% of cost
= 0.15 * 72.50
= 10.87
So , the total amount payable is = cost + sales tax + tip
= 72.50 + 4.89 + 10.87
= 88.26
since the total number of persons is 4 ,
the amount per person is = 88.26/4 = 22.06
Therefore , The amount that each person should pay is $22.06 .
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How to subtract 27 minus 9.9 using mental math
Answer: you are left with 17.1 or 17.10
HOW TO: picture this. i'ma going to go to your store and you have 27 dollars. you owe me 9.90 for some reason. you give me the money and i go on my way. how much money are you left with?
The equation below describes a function of x . y=−4x+12
The solution for x in the function when the equation y=−4x+12 equals -12 is -6
How to determine the solution for x in the function?From the question, we have the following equation that can be used in our computation:
y=−4x+12
To make the equation legible, we need to rewrite it
So, we have the following representation
y = −4x + 12
Also from the question, we have
y = -12
This means that we calculate x when y = -12
Substitute the known values in the above equation, so, we have the following representation
-12 = -4x + 12
So, we have the following equation
-4x + 12 = -12
Add -12 to both sides of the equation
So, we have the following representation
-4x + 12 - 12 = -12 - 12
Evaluate the like terms in the equation
-4x = -24
Divide both sides of the equation by -4
x = 6
Hence, the solution is 6
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Possible question
The equation below describes a function of x . y=−4x+12
Solve for x when y = -12
What is the zero of g?
(-6,0)
(-3, -4.5)
(-8, 0)
(0,-9)
Answer: Either C. or D.But I'm sure it's D.
Step-by-step explanation:
what is the definition of pi
and multiply it to a decimal number
(any equation)[tex]\pi[/tex]
Pi written as 3.l4 and π in mathematics is the ratio for the diameter of a circle to the circumference of that circle. The value is unending
What is Pi?Pi, which is represented by the Greek letter p, or, is a shorthand for the ratio of a circle's diameter to its circumference. No matter how big the circle is, this ratio will always be equal to pi. The value of pi is about 3.14 in decimal notation.
We are to multiply Pi to any equation
let the equation be (20.5 + 3x)[tex]\pi[/tex]
pi is represented in numbers by 3.14
Hence we would have the equation to be of the form
(20.5 + 3x)3.14
multiply through the bracket
64.37 + 9.42x
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In a company, 85% of the workers are women. If 675 people work for the company who aren't women, how many workers are there in all?
Answer:
so there are 3825 worker in total
Step-by-step explanation:
675=15%
women=85%
how much workers are 5%=675/3 =225
225=5%
how many workers is 85%= 85/5=17
85%=225x17=3825
y = 1,000x is that a constant proportionality
During the problem disaggregation process, the logic trees should have branches that are?.
During the problem disaggregation process, the logic trees should have branches that are both mutually exclusive and collectively exhaustive.
Problem disaggregation refers to the process of breaking down the larger higher-level operation into smaller plans and shorter periods. It refers to the use of analysis, logic, and facts to evaluate and understand each element of the problem in terms of causes and driver of the situation using logic trees. Logic trees improve the problem definition and aid in understanding an issue in more detail. There are different types of logic trees used in the process – factor logic tree, inductive logic tree, deductive logic tree, hypothesis tree, and decision tree. The logic trees should have branches that are MECE – mutually exclusive and collectively exhaustive. It is the second and an important step in the seven steps bulletproof problem-solving process used for complex solving.
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d) The rent of a room for 4 months is Rs 20,000. (i) What is the rent for 7 months? (ii) How long would a tenant hire the room for Rs 55,000 at the same rate of rent?
The rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months
The rent of a room for 4 months is Rs 20,000.
The rent of a room for 1 month is Rs 20,000./4
The rent of a room for 1 month is Rs 5000
The rent of a room for 7 months is Rs 5000 x 7
The rent of a room for 7 months is Rs 35000
Now we need to calculate the number of month a tenant hire the room for Rs 55,000 at the same rate of rent
The rent is 5000 for 1 month
The rent will be 55000 for 1/5000 x 55000 = 11 months
Therefore, the rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months
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two trains leave a station at the same time and travel in opposite directions. one train travels 20 kph faster than the other train. after 3 hours, they are 810 miles apart. what is the speed of each train?
The speed of each train is 125kph and 145kph.
Here it is given that the distance between the two trains is 810 miles after traveling for 3 hours.
The difference in their speed is 20 kph.
Let x be the speed of one train. So by this, we get the speed of the second train that is x + 20.
Formula to calculate speed is:
Speed = Distance / Time
Distance = Speed × Time
Distance covered by first train = x × 3
Distance covered by second train = (x + 20) × 3
Total distance = 810
So we get;
3x + (x + 20)3 = 810
3x + 3x + 60 = 810
6x = 750
x = 125
x + 20 = 125 + 20 = 145
Therefore we get the speed of both trains which is 125kpp and 145 kph.
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A car originally is worth $3000. It is decreasing in value by 3% every year. How much is it worth in 3 years.
(Round to the nearest cent)
Answer:
$2825,32
Step-by-step explanation:
Value of the car after 1 year
$3000 * 3% = 3000 * 0.03 = 90
3000 - 90 = $2910
Value of the car after 2 year
$2910 * 3% = 2910 * 0.03 = 87.3
2910 - 87.3 = $2912,7
Value of the car after 3 year
$2912,7 * 3% = 2912,7 * 0.03 = 87.381
2912,7 - 87.381 = $2825,319
"Round to the nearest cent"
$2825,32
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry. In words, describe the graph of the proportional relationship.
The proportional relationship between the cost and weight is given as y = 0.89x.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The absolute expense for clothing administration, in dollars, relies upon the heaviness of the clothing, in pounds. This relationship is corresponding, as it costs $22.25 for 25 pounds of clothing and $36.49 for 41 pounds of clothing.
The equations are given below.
22.25 = 25m + c ...1
36.49 = 41m + c ...2
From equations 1 and 2, then we have
41m - 25m = 36.49 - 22.25
16m = 14.24
m = 0.89
Then the value of c will be given as,
22.25 = 25 (0.89) + c
c = 0
The proportional relationship between the cost and weight is given as y = 0.89x.
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A triangle has an angle that measure 36.6° and a second angle that measures 59.3°. What is the
measure of the third angle?
2 pts
Answer: 82 is the answer
Step-by-step explanation: I just did this question and worked it out and it said it was right
very stuck please help
The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5 .
In the question ,
it is given that
the required line is perpendicular to the line passing through (6, -2) and (-8 ,5) .
the slope is = (5 -(-2))/(-8 -6)
= 7/(-14)
= -1/2
so , the slope of the required line is = 2 .
The equation of the line passing through the point (3,1) with slope 2 is
(y - 1) = 2*(x-3)
y -1 = 2x - 6
y = 2x - 6 + 1
y = 2x - 5
the equation of line is y [tex]=[/tex] 2x - 5
the perpendicular slope is = 2
the y intercept is -5 .
Therefore , The equation of the line through (3,1) and is perpendicular to a line through (6, -2) and (-8 ,5) is y = 2x - 5 .
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The population of a state was estimated to be
about 38,332,521 people. Write the estimated
population as a single digit times a power of 10.
The state population as a single-digit time power of 10 is approximately 4 × 10⁷.
What is estimation?Calculations are made easier and more realistic when a number is estimated, which is a plausible estimation of its true value.
To estimate something is to approximate it as accurately as possible.
To acquire a quick and approximate response is obtained by rounding down the values used in the computation.
Given the state estimated population = 38,332,521
Divide and multiply by 10
So,
= 3,833,252.1 × 10¹
= 383,325.21 × 10²
So, similarly, we can write
= 3.8332521 × 10⁷
So, we can write the state population as approximately 4 × 10⁷
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The functions f(x)=−34x+2 and g(x)=(14)x+1 are shown in the graph. What are the solutions to −34x+2=(14)x+1? Select each correct answer. Responses −1 negative 1 0 0 1 1 2 2 3
A solution to −34x+2=(14)x+1 is x = 1/48
In this question, we have been given functions f(x) = -34x + 2 and g(x) =(14)x + 1
We need to find the solutions to −34x + 2 = (14)x + 1
i.e., we need to find the solution to f(x) = g(x)
Consider, f(x) = g(x)
-34x + 2 = (14)x + 1
-34x + 2 - 14x = 14x + 1 - 14x
-48x + 2 = 1
-48x = -1
x = 1/48
Therefore, a solution to −34x+2=(14)x+1 is x = 1/48
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Ester sarai and kurry chose a number esters number is 1/10 of saris kurrys number is 10 times as much as sarais sarais number is 0.09. what number did each person choose?
Ester, Sarai, and Kurry each selected a number: 0.009, 0.09, and 0.9, respectively.
One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical sizes. For instance, 3+3+3+3+3 can be expressed as 3 5.
the ester's number is equal to one-tenth of the Sarai number.
= 1 / 10 × 0.09 = 0.009
to determine Kurry's number, multiply Sarai's number by 10
= 10 × 0.09 = 0.9
Therefore, it can be inferred that Kurry chose 0.9, Ester chose 0.009, and Sarai chose 0.09.
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suppose 44% of politicians are lawyers. if a random sample of size 853 is selected, what is the probability that the proportion of politicians who are lawyers will be less than 40%? round your answer to four decimal places.
The probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .
Given :
Population Proportion ( p ) = ( 44 % ) = 0.44
Sample proportion ( p hat ) = ( 40 % ) = 0.4
Size of sample ( n ) = 853
To find : P ( p hat < 0.4 )
Formula : ( p hat - p ) / [tex]\sqrt{ p * ( 1 - p ) / n }[/tex]
Substituting values in the above formula ,
z = ( 0.4 - 0.44 ) / [tex]\sqrt{ 0.44 * ( 1 - 0.44 ) / 853}[/tex]
z = - 2.3535
z - score = -2.3535
Finding the p - value :
p - value = 0.009299
Therefore , the probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .
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PLEASE HELP!! WILL GIVE BRAINLIEST
The mass of a test sample is 10g, and it has the volume of 2.5cm^3 . What is its density?
A. 10g/cm^3
B. 2.5cm^3/g
C. 4g/cm^3
D. 4cm^3/g
E. 0.25g/cm^3
Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.
Define density.The ratio of an object's mass to its volume is its density. Grams per cubic centimeter, or g/cm³, are frequently used to measure density. Keep in mind that a volume is measured in cubic centimeters, not gram (the same volume as 1 milliliter). More particles will make a box denser than fewer particles in the same box. Despite the fact that the SI unit of density is kg/m³, we instead use g/cm³ for solids, g/ml for liquids, and g/L for gases out of convenience. The relationship between a substance's mass and the volume it occupies is known as its density.
Given,
Volume = 2.5 cm³
Mass = 10 g
For density:
Mass ÷ volume
10 ÷ 2.5
4
Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.
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help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The length of the shorter leg is 9 mm.
The length of the longer leg is 12 mm.
The length of the hypotenuse is 15 mm.
Pythagoras theory applies to every right triangle. If
The shorter leg = aThe longer leg = bThe hypotenuse = c[tex]a^2 + b^2 = c^2[/tex]Step-by-step explanation:
Known
Longer leg = shorter leg +3 mmAsked
a?b?c?Answer
[tex]a^2 + b^2 = c^2[/tex]
[tex]a^2 + (a+3)^2 = (a+6)^2[/tex]
[tex]a^2 + a^2 + (2 \times a \times 3) + 3^2 = a^2 + (2 \times a \times 6) + 6^2[/tex]
[tex]2a^2 + 6a + 9 = a^2 + 12a + 36[/tex]
[tex]2a^2 - a^2 + 6a - 12a + 9 - 36 = 0[/tex]
[tex]a^2 - 6a - 27 = 0[/tex]
[tex]a^2 - 9a + 3a - 27 = 0[/tex]
[tex]a \times (a - 9) + 3 \times (a - 9) = 0[/tex]
(a-9) (a+3)=0
a-9=0 or a+3= 0
a=9 or a=-3 (impossible)
Shorter leg
a=9 mm
Longer leg
b = a+3
b = 9+3
b = 12 mm
Hypotenuse
c = a+6
c = 9+6
c = 15 mm
is y=4x-8, continuous or discrete?
The equation y = 4x - 8 is discrete
What are discrete data?Discrete data is a sort of numerical information that consists of full, concrete numbers with predetermined, set values that can be counted.
While complex numbers and fluctuating data values taken over a predetermined period of time are examples of continuous data.
The difference between discrete and continuous dataThe main distinction between continuous and discrete data is that the former has a finite value that can be counted while the latter has an endless number of possible values that can be measured.
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question 1 a sample random sample of 6 bulbs was selected from a lot of 100 for the purpose of estimating its quality. the life of each bulb selected was measured by letting the bulb until it burned out. the results from the test are as follows: bulb number life duration (hours) 1 950 2 1210 3 1070 4 840 5 1420 6 980 a.) estimate the average life of the bulbs in the lot. b.) estimate the total life bulbs in the lot c.) estimate the proportion of bulbs in the lot with life exceeding 1000 d.) estimate the number of bulbs in the lot with life exceeding 1000
a) The average life of the lot is 1078.33 hrs, b) the total life is 107833.33 hours, c) a proportion of 1/2 bulbs have a life exceeding 1000 hrs while d) an estimation of 50 bulbs have a life exceeding 1000 hours.
It is given that the number of bulbs in a given lot is 100.
The number of bulbs in the sample selected is 6
The life of the sample bulbs was
no. life (hours)
1 950
2 1210
3 1070
4 840
5 1420
6 980
a)
The average life of the bulbs can be calculated by
the sum of the lives of the sample/ no. of samples
= (950 + 1210 + 1070 + 840 + 1420 + 980) / 6
= 1078.3333 hrs
b) The total lives of the bulbs in the lot will be
average life X no. of bulbs
= 1078.3333 X 100
= 107833.33 hrs
c)
We can gain the proportion of the bulbs that have a life exceeding 1000 hrs by the given sample
The bulbs
2, 3, and 5 have lives exceeding 1000 hrs.
Hence, out of 6 bulbs, 3 have lives exceeding 1000 hrs.
Therefore the proportion
= 3/6
= 1/2
d)
The number of bulbs in the lot with a life exceeding 1000 will be
proportion X no. of bulbs
= 1/2 X 100
= 50 bulbs
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Latisha wants to buy pumpkins and autumn squash for a fall display. She has a budget of $117 but wants to buy more than 10 vegetables. The pumpkins are $5. 59 each. The squash are $3. 50 each. List THREE possible combinations of pumpkins and squash that latisha can purchase to represent the situation
(x,y) = (8,20), (6,24), and (10,17).are three alternative combinations of pumpkins and squash that Latisha may buy to depict the circumstance.
Latisha's total wealth is $17.
More than 10 veggies are the number of vegetables that Latisha wants to purchase.
A pumpkin costs $5.50.
An autumn squash costs $3.50.
Let n pumpkins purchased equal x.
Purchased number of autumn squash = y
There are three alternative squash and pumpkin combination that Latisha might buy to symbolize the circumstance.
With x acting as the independent variable, we may identify many y's.
x ( Pumpkin) y(Autumn squash) (integral value)
8 20
6 24
10 17
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2.8x + 10 + 5.7x = 70+x
Answer:
Step-by-step explanation a=0.32
The required simplified value of x in the given expression is 8.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
2.8x + 10 + 5.7x = 70+x
Simplifying,
8.5x + 10 = 70 + x
8.5x - x = 70 - 10
7.5x = 60
x = 60 / 7.5
x = 8
Thus, the required simplified value of x in the given expression is 8.
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Walt Disney Co paid a $1.42 annual dividend on a day it closed at a price of $96 per share.
What was the annual dividend for 500 shares?
The annual dividend for 500 shares was $710.
How is the annual dividend computed?The annual dividend is a function of the dividend per share and the number of shares held by a stockholder.
Dividends are always declared per share with a stated dollar amount or percentage.
Dividends represent the portion of the profits earned by an entity that it decides to distribute to the shareholders.
Dividends are a kind of financial reward to stockholders for their investment in the entity.
The dividend per share = $1.42
Market price per share = $96
The number of shares held = 500
The dividend received for the year = $710 ($1.42 x 500)
Thus, the holder of 500 shares in Walt Disney Co. will get $710 in a year the company declared and paid a $1.42 annual dividend.
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What is the equation in standard form of the line that passes through the point (6,-1) and is perpendicular to the line represented by 8x + 3y=1
The required equation of line in standard form that passes through the point (6,-1) and is perpendicular to the line represented by 8x + 3y = 1 is
y = (3/8)x - 13/4
How to find equation of line if one point and equation of perpendicular line is given?
To find the equation of line which is perpendicular to another line
Find slope of the required line using m₁. m₂ = -1Using the given point find y-intercept by substituting in the equation of line.According to the given question:
Let the required equation of line be y = mx + b
where m is the slope of line and b is the y-intercept
Now, 8x + 3y = 1 is perpendicular to the line. Hence, the slopes of both line will satisfy m₁. m₂ = -1
Standard form of the given line is
y = (-8/3)x + 1/3
∴ m₁ = -8/3
Finding m₂, (-8/3). m₂ = -1
∴ m₂ = 3/8 ------ (1)
Using the given point (6, -1) to find y-intercept in the equation
y = (3/8)x + b
-1 = (3/8)(6) + b
∴ b = -13/4
Therefore the required equation of line in standard form is
y = (3/8)x - 13/4
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twelve fair dice are rolled. what is the probability that the product of the numbers on the top faces is prime?
Probability that the product of the numbers on the top faces is prime is 1/2(1/6)⁴.
Define probability.In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution. Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.
Given,
12 fair dice rolled,
Probability that the product of the numbers on the top faces is prime:
⁶C₅ × (1/6)⁵ × ³C₁/⁶C₁
6 × (1/6)⁵ × 3/6
1/2(1/6)⁴
Probability that the product of the numbers on the top faces is prime is 1/2(1/6)⁴.
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