The eight letters in the word DECEIVED may be arranged in 4200 distinct ways, with two Ds grouped together and three Es not all together.
The following approach may be used to determine how many different ways there are for the eight letters in the word DECEIVED to be arranged such that two Ds are together and three Es are not altogether:
Treat the two Ds as a single object, which we can call DD. Now we have 7 objects to arrange: DD, E, E, C, V, I, and E.First, we count the total number of arrangements of these 7 objects, without considering any restrictions. This is simply the number of permutations of 7 objects, which is 7! = 5040.Next, we count the number of arrangements in which the three Es are all together. We can treat the three Es as a single object, which we can call EEE. Now we have 6 objects to arrange: DD, EEE, C, V, I, and an extra E. The number of arrangements of these objects is 6!, since we can treat the EEE as a single object.However, we have overcounted the arrangements in which the two Es are together with the EEE object. To correct for this, we can treat the two Es as a single object, which we can call EE. Now we have 5 objects to arrange: DD, EEE, EE, C, V, and I. The number of arrangements of these objects is 5!, since we can treat the EEE and EE as single objects.Therefore, the number of arrangements in which the three Es are not all together is the difference between the total number of arrangements and the number of arrangements in which the three Es are all together, minus the number of arrangements in which the two Es are together with the EEE object:7! - 6! - 5! = 5040 - 720 - 120 = 4200
Therefore, there are 4200 different arrangements of the 8 letters in the word DECEIVED, in which two Ds are together and the three Es are not all together.
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The function = 50 − 1.6 can be used to determine the amount, in fluid ounces, of laundry detergent remaining after x loads of laundry have been done. What is the rate of change amount of laundry in fluid ounces with respect to the number of loads of laundry that have been done?
The rate of change of the amount of laundry with respect to the number of loads is a constant value of -1.6 fluid ounces per load.
What is linear equation?Any equation that has terms that are either constants or the product of a constant and a variable of the first degree (exponent 1) is said to be linear. In other words, the equation's greatest degree for any variable is 1. One way to express a linear equation is as follows:
ax + b = 0
If an is not equal to zero, a and b are constants, and x is the variable. This is how a linear equation is typically expressed.
The given function is f(x) = 50 - 1.6x.
Now, the rate of change is the slope of the equation.
Comparing the equation with that of the linear equation y = mx + c we see that the slope is -1.6.
Hence, the rate of change of the amount of laundry with respect to the number of loads is a constant value of -1.6 fluid ounces per load.
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type 43 words per minute. If she maintains her typing speed without a break, how many words can she type in 2 hours and 15 minutes?
Answer: 6,450 words per minute
Step-by-step explanation:
Each hour is 60minutes long, making your total number of minutes 150.
The last step would be to multiply 150 by the wpm (43) and making the total number typed 6,450
1) Calculate the area of this triangle. (if h = 4m; b = 7m)
A.
B.
C.
n
28cm
14cm2
28cm2
b
Answer:
B
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = 7 and h = 4 , then
A = [tex]\frac{1}{2}[/tex] × 7 × 4 = [tex]\frac{1}{2}[/tex] × 28 = 14 cm²
In the diagram below DE is parallel to XY what is the value of X
Since this is about the angle theorem and the angle theorem is a theorem that helps us know the relationship between angles. Being a corresponding angle, x = 105°. Hence option A is correct.
What are corresponding angles?A corresponding angle is an angle that occupies the same relative position as another angle elsewhere in the diagram. The corresponding angle in planar geometry occurs when a transverse line crosses his two straight lines. Two angles correspond or relate to each other by being on the same side of the horizontal line. One is the exterior angle (outside the parallel lines) and the other is the interior angle (inside the parallel lines).
You can see that the transversal line intersects two parallel lines DE and XY. From the transversal theorem of angles in mathematics, we know that when a transversal line intersects two parallel lines, the corresponding angles formed are congruent and therefore equal to each other.
In this question we see that one of the angles is 105°. Therefore x° is congruent to it, x = 105°.
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The complete question is as follows:
Question content area top
Part 1
For the statement below, write the claim as a mathematical statement. State the null and alternative hypotheses and identify which represents the claim.
An amusement park claims that the mean daily attendence at the park is people.
Mathematical statement μ = 18000 where μ is the mean, Null hypothesis H₀ : μ = 18000, Alternate hypothesis Hₐ : μ ≠ 18000.
What does a mathematical statement mean to you ?A mathematical statement is a meaningful string of words that can be either true or false.
For instance , 3+4=7 is always true. Consequently, it is a true statement.
Similar to this , 3+4=8 is never true Therefore, it is a false statement.
Here the amusement park makes the claim that the mean daily attendence at the park is 18000 people
∴ μ = 18000 is the statement .
What is a null hypothesis ?A null hypothesis is known as statistical hypothesis that proposes that no statistical significance exists in a set of given observations. Hypothesis testing is used to assess the credibility of a hypothesis by using sample data. Sometimes referred to simply as the "null," it is represented as H₀.
∴ Here the null hypothesis is μ = 18000
What do you understand by alternate hypothesis ?The alternative hypothesis is an assertion used in statistical inference experiment. It is contradictory to the null hypothesis and indicated by Ha or H₁ . We can also say that it is simply an alternative to the null. In hypothesis testing, an alternative theory is a statement which a researcher is testing.
For instance : A school principal claims that students in her school score an average of seven out of 10 in exams. The alternate hypothesis is μ ≠ 7.0.
Similarly here in this question alternate hypotesis will be μ ≠ 18000.
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The trifecta at most racetracks consists of selecting the first-, second-, and third-place finishers in a particular race in
their proper order. If there are ten entries in the trifecta race, how many tickets must you purchase to guarantee a win?
You would need to purchase 720 different tickets to guarantee a win.
how many finishers must be selected?You must pick the first three finishers in the correct order to win a trifecta race with 10 entries.
Since there are ten participants in the race, there are ten ways to select the winner of the first place prize. In the wake of choosing the primary spot finisher, there are just 9 passages remaining, so the quantity of ways of choosing the second-place finisher is 9.
Finally, since there are only eight entries left after selecting the first two, there are 8 ways to select the third-place finisher.
Therefore, the total number of possible winning trifecta combinations is:
10 x 9 x 8 = 720
This indicates that in order to guarantee a win, you would need to purchase 720 distinct tickets. However, it is essential to keep in mind that betting on a race in this manner may not always be the most profitable or efficient option, and that purchasing each and every possible combination can be very costly. It's vital to painstakingly think about the chances, payouts, and your financial plan prior to putting down any wagers.
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Find the range of the list of values. 3, 16, 22, 25, 24, 23, 16, 16
Answer:
range = 22
Step-by-step explanation:
the range is the difference between the largest and smallest values in the data set.
largest value = 25 , smallest value = 3
range = 25 - 3 = 22
What is m∠a?
A straight angle divided by a ray into two angles. The smaller angle has a measure of 50 degrees.
40°
50°
90°
130°
5. Jennifer solved a math problem. The answer. to her problem was in square inches. Which formula did Jennifer most likely use to solve her problem?
A P=(2xl) + (2xw)
B V=SxSxS
C P= 4xs
D A= SXS
Answer:
D. A = s × s
Step-by-step explanation:
D. A = s × s is an area formula. Area is side times side. This is an area formula for a square. The units of area are square units. Since Jennifer has square inches in her answer, she was working on an area problem.
A. and C. are perimeter formulas. Perimeter is the distance around the outside of a shape. The units of perimeter are straight up plain, one-dimensional units like inches (or feet, meters, miles, km)
B. is a volume formula. The units of volume is cubic units or units to the third power.
The answer is D.
2. Select all the equations that
describe the situation and then
find the solution.
Each notebook contains
60 sheets of paper. Andre
has 5 notebooks. How
many sheets of paper do
Andre's notebooks
contain?
i.y = 60÷5
ii. y = 5 times 60
iii. Y/5 = 60
iv. 5y = 60
Answer: i. y = 60÷5
Step-by-step explanation: If he has 60 sheets of paper and 5 notebooks, it would only make sense to divide the number of sheets by the number of notebooks to get the sum. Which is 12 btw! <33
Which expressions are equivalent to...
The equivalent expression of log4 ( 1/4x²) is log4(1/4) + log4(x²) ( option D)
What are laws of logarithm?The logarithm is the inverse function to exponentiation. For example log2 (8) = 3 and 2³ = 8
The following are math logarithm rules:
loga (MN) = loga M + loga N.
loga (M/N) = loga M - loga N.
IogaMn = n Ioga M.
For example Log5 (5²) = Log5 (5) + Log5 (5)
= 1+1 = 2
this means Log5 ( 5²) = log5 ( 25) = 2
Therefore if loga (MN) = loga M + loga N.,
we can say that,
log4( 1/4x²) can also be written as ;
log4 (1/4) + log4 (x²) .
therefore the equivalent expressions for
log4 ( 1/4x²) is log4 (1/4) + log4 (x²) .
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. Labor Variances Ellen Chenoweth, the manager of the city of St. Paul road maintenance shop, uses standards to judge performance. Because a clerk mistakenly discarded some labor records, however, Ellen has only partial data for April. She knows that the total direct-labor flexible-budget variance was $1,643 favorable. Moreover, a recent pay raise produced an unfavorable labor price variance for April of $1,157. The actual hours of input were 1,780 and the standard labor price was $20 per hour. 1. Find the actual labor rate per hour 2. Determine the standard hours allowed for the output achieved.
Labor Variances Ellen Chenoweth, the manager of the city of St. Paul road maintenance shop, uses standards to judge performance, the actual labor rate per hour for April was $19.35.
1. Actual Labor Rate per Hour:
The labor price variance formula is:
Labor Price Variance = (Actual Labor Rate - Standard Labor Rate) x Actual Hours
We are given that the labor price variance for April was unfavorable and equal to $1,157. We also know that the standard labor rate was $20 per hour. Using the formula above and plugging in the known values, we can solve for the actual labor rate:
-1,157 = (Actual Labor Rate - 20) x 1,780
-1,157 = 1,780Actual Labor Rate - 35,600
1,780Actual Labor Rate = 34,443
Actual Labor Rate = 19.35
Therefore, the actual labor rate per hour for April was $19.35.
2. Standard Hours Allowed for the Output Achieved:
The flexible-budget variance formula is:
Flexible-Budget Variance = (Actual Hours - Standard Hours) x Standard Labor Rate
We are given that the flexible-budget variance for April was favorable and equal to $1,643. We also know that the standard labor rate was $20 per hour.
Using the formula above and plugging in the known values, we can solve for the standard hours allowed:
1,643 = (1,780 - Standard Hours) x 20
1,643 = 35,600 - 20Standard Hours
20Standard Hours = 33,957
Standard Hours = 1,697.85
Therefore, the standard hours allowed for the output achieved in April was 1,697.85.
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You rented a sedan for 37.45 per day and unlimited miles. she paid a CDW fee of 19.40 per day. Her total rental cost was 646.50. She spend 78 for gasoline and her final cost per mile was 0.77. How many days did You rented the car?
You rented the car for 10 days.
Mathematical word problemLet's begin by setting up the equation to solve for the number of days:
Total rental cost = (daily rental cost + CDW fee) x number of days + gasoline cost
We know that the daily rental cost is 37.45, and the CDW fee is 19.40, so we can substitute those values into the equation:
646.50 = (37.45 + 19.40) x number of days + 78
Simplifying the equation:
646.50 = 56.85 x number of days + 78
Subtracting 78 from both sides:
568.50 = 56.85 x number of days
Dividing both sides by 56.85:
number of days = 10
Therefore, You rented the car for 10 days.
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PLEASE HELP! A man in a lighthouse looks out straight in front of him at the birds in the sky. Then he looks down at an angle of depression of 24 degrees and sees a boat in the ocean. If the distance to throw a rope from the top of the lighthouse to the boat is 45 feet, find how far from land the boat is.
What is the equation for this problem?
Using the given angle of depression the equation (D) cos(24) = x/45 will be used to find the answer.
What is the angle of depression?The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item.
When we know the angles and the distance of an object from the ground, it is primarily utilized to find the distance between the two objects.
The angle from the horizontal downward to an item is referred to as the "angle of depression."
The line of sight of an observer would be below the horizontal.
So, in the given situation:
We will find the base which is the distance of the boat from the land.
Which means:
hypotenuse/Base
Which is represented by Cosx.
The angle is 24°.
Then, the equation for a solution would be:
cos(24) = x/45
Therefore, using the given angle of depression the equation (D) cos(24) = x/45 will be used to find the answer.
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3. "Frank has four different credit cards, the balances and interest information of which are outlined in the table below.
He would like to consolidate his credit cards to a single credit card with an APR of 18% and pay off the balance in 24 months.
What will his monthly
credit card payment be?
Hint use the monthly payment formula where PV = (all balances combined), i=0.18/12, and n=24
A. $390.00
B. $462.91
C. $454.31
D. $52.00
Answer:
Therefore, Frank's monthly credit card payment will be $454.31.
Step-by-step explanation:
Monthly payment = (PV * r) / (1 - (1 + r)^-n)
PV = $2,500 + $1,000 + $3,000 + $1,500
= $8,000
r = 0.18 / 12
= 0.015
Monthly payment = ($8,000 * 0.015) / (1 - (1 + 0.015)^-24)
= $454.31
Is (3, 5) a solution to this system of equations?
y = 5
Y= -5/3x+10
yes
no
Yes, (3, 5) is a solution to this system of equations.
How do you calculate the equation system?
The system has a single solution if the m-values of the two equations differ. The system has no solution if the two equations have the same m-value but distinct b-values.
Substituting x = 3 and y = 5 into the equations, we get:
y = 5 (which is already given)
y = (-5/3)x + 10
y = (-5/3) * 3 + 10
y = -5 + 10
y = 5
Therefore, both equations are satisfied by the point (3, 5), making it a solution to the system of equations.
Yes, (3, 5) is a solution to this system of equations.
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A checkout clerk at a department store is expected to complete 16 transactions every hour.
In the past 20 minutes, he completed 6 transactions.
Choose True or False for each statement.
Statements:
If the clerk continues at the same rate, he will meet his goal of 16 transactions in 1 hour.
At his current rate, the clerk will complete 12 transactions in 1 hour.
At his current rate, the clerk will complete 9 transactions every half hour.
If the clerk continues at this rate for a 6-hour shift, he will complete 96 transactions.
✓ - True If the clerk continues at the same rate, he will meet his goal of 16 transactions in 1 hour.
➜ This is true. The clerk is currently going at 6 transactions per 1/3 hours. 6 * 3 = 18, and 18 > 16.
✗ - False At his current rate, the clerk will complete 12 transactions in 1 hour.
➜ This is false. As stated above, he will complete 18.
✓ - True At his current rate, the clerk will complete 9 transactions every half hour.
➜ Let us set up a proportion to check. Then we will cross-multiply and solve.
[tex]\frac{20\;min}{6} =\frac{30\;min}{x}[/tex]
180 = 20x
x = 9
➜ Yes, he will complete 9 every half hour.
✗ - False If the clerk continues at this rate for a 6-hour shift, he will complete 96 transactions.
➜ We can utilize a proportion again. 6 hours is equal to 360 minutes. Then, we will cross-multiply and solve.
[tex]\frac{20\;min}{6} =\frac{360\;min}{x}[/tex]
20x = 2,120
x = 106
➜ He will complete 106 transactions, not 96. It depends on if they're asking for exactly 96 or at least 96.
100 POINTS !!! Will give brainiest. Which equation is the imposter??
Answer:
C.
Step-by-step explanation:
C. is an impossible equation.
Can anybody help me on the question.
ASAP
The hanger in the illustration will have the value x = 6, and it will remain balanced.
Define equations?Mathematical expressions with two algebraic expressions on either side of the equals (=) sign are called equations. It demonstrates the equality of the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in each mathematical equation. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved.
Here's the query,
Considering the graph,
The hanger's equation is as follows:
4x= 24
There are 4 numbers here that represent the value of the hanger.
So, x+x+x+x will be 24.
The equation is thus:
4x = 24.
Now, by resolving the equation, we can determine the value of x that balances the hanger:
4x = 24.
When you divide 4 on both sides:
x = 24/4
x = 6.
As a result, the hanger will remain in equilibrium for x = 6.
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4 ft
6 ft
T4ft-
8 ft
1. List the shapes that make up the front of the house.
The answer on shape of house is , (1) A rectangle for the main structure of the house. (2) A triangle for the roof. (3) A rectangle for the front porch. (4) Two trapezoids for the roof of the front porch. (5) A rectangular door.
What is Trapezoid?A trapezoid is a four-sided geometric shape with two parallel sides, called the bases, that are of different lengths, and two non-parallel sides that connect the bases. The non-parallel sides are also called legs, and they may or may not be equal in length.
Trapezoids are often encountered in geometry and in real-life situations, such as in construction and architecture. They can be classified as either right trapezoids or oblique trapezoids depending on whether one of the angles formed by the bases and a leg is a right angle or not.
Based on the image provided, the shapes that make up the front of the house are:
A rectangle for the main structure of the house. A triangle for the roof.A rectangle for the front porch.Two trapezoids for the roof of the front porch.A rectangular door.To know more about Oblique trapezoids visit:
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Perimeter of rectangle is 306 one dimension is 6 cm
Answer:
the other two sides of the rectangle is 147
Step-by-step explanation:
because since u told us that there is a side with a length of 6 cm and u also gave us the preimeter which can help us do this so what I did is 6 x 2 why because if one side is 6cm then the other side will also be 6cm and then 6 x 2 = 12 and this is what I did 306 - 12 = which equalls 294 and then divide that by 2 = 147 please mark as brainliest bye have a great day :D
Describe a real-world problem that can be modeled by a circle.
A circle-based model is highly suitable for the design and construction of roundabouts, which present themselves as practical solutions to tackle traffic-related issues.
Describe a real-world problem that can be modeled by a circle.Roundabout intersections involve vehicles circulating around a central island in a counterclockwise direction. The circular form guarantees fluidity in traffic movements and significantly reduces the requirement for traffic lights and stops signs while enhancing security.
This model entails using a circle, ascertaining that the diameter corresponds with the width of the roadway, with its center accommodating the location of the island at equidistant distances from all contact points on the circle's periphery, thus ensuring optimal functionality.
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Use slopes and y-intercepts to determine if the lines 15x−6y=−5 and 5x−2y=5 are parallel.
The two lines are parallel because they have thesame slope and different y intercept
How do we know parallel lines?If two non-vertical lines that are in the same plane has the same slope. However the lines will have different y intercept.
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Therefore putting the equations 15x−6y=−5 and 5x−2y=5 into that form.
15x-6y = -5
-6y = -15x-5
y = 5x/2 +5/6
for the second equation,
5x-2y =5
-2y = -5x-5
y = 5x/2 +5/2
therefore , the two lines are parallel because they have the same slope( 5/2) and different y intercept.
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At the school's holiday craft fair, Colette and her classmates get to make gingerbread houses. Their teacher divides a bag of licorice ropes evenly among the 9 students at the table. Each student gets 3 licorice ropes to decorate the roof of his or her gingerbread house.
Answer: So, what are you asking?
Step-by-step explanation:
√ x 2 = x 2 4 = x 1 2 = √ x Based on this, the student claims that 4 √ x 2 = √ x for all values of x.
Answer:
The student's claim is incorrect. While it is true that √x^2 = x for all non-negative values of x, this property does not apply to expressions with multiple terms, such as 4√x^2.
Step-by-step explanation:
consider the case where x = -1. Then, √x^2 = √(-1)^2 = 1, but 4√x^2 = 4√1 = 4. On the other hand, √x = √(-1) is undefined, so the equation 4√x^2 = √x is not true for this value of x.
Therefore, the student's claim is not true for all values of x, and it is important to be careful when applying algebraic properties to expressions with multiple terms.
What is the incorrect statement? Show your work
The incorrect statement regarding the dilation is given as follows:
2. The transformation can be represented by (7x/3, 7y/3).
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
For this problem, we have that:
The original circle has a radius of 7 units.The dilated circle has a radius of 3 units.Hence the scale factor is given as follows:
k = 3/7.
And the rule is then given as follows:
(3x/7, 3y/7).
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The number of bacteria in a culture is n(t) after t hours. n(t)=500e0.15t How many bacteria are present after 12 hours. Round to the nearest whole number.
The requried, 3025 bacteria are present after 12 hours.
To find the number of bacteria present after 12 hours, we simply need to substitute t=12 in the given equation:
[tex]n(12) = 500e^{(0.15*12)}[/tex]
[tex]n(12) = 500e^{1.8}[/tex]
n(12) ≈ 3024.82
Rounding this to the nearest whole number, we get:
n(12) ≈ 47,416 ≈ 3025
Therefore, there are approximately 3025 bacteria present after 12 hours.
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You need to cut the strongest beam out of a log with a diameter of 18 in. The strength of a wooden beam is directly proportional to the product of its width and the square of its height. What are the dimensions of the strongest beam? Find the exact value and then round your answer to the nearest hundredth.
Need answers ASAP
The dimensions of the strongest beam are 27 inches x 13.5 inches.
What is a dimension?In general, dimension refers to a measurable extent of a physical quantity, such as length, width, height, depth, or time. These dimensions provide a framework for describing and measuring objects and events in the physical world. In geometry, dimension are refers to the number of coordinates needed to specify a point in a space. In physics, the concept of dimension is used to describe the properties of space and time.
We know that the strength of the beam is directly proportional to its width multiplied with the square of its height. Let's call the width of the beam "w" and the height "h". Then we can write the strength of the beam as:
S = kwh², where "k" is the constant of proportionality.
We want to find the dimensions of the strongest beam, which means we want to find the values of "w" and "h" that will maximize the strength "S". To do this, we need to find the maximum value of the function S = kwh² subject to the constraint that the diameter of the log is 18 inches.
The diameter of the log is equal to the width of the beam plus twice the height of the beam:
d = w + 2h
Since the diameter of the log is 18 inches, we can write:
w + 2h = 18
or
w = 18 - 2h
Substituting this expression for "w" into the equation for the strength of the beam, we get:
S = k × w(18-2h) × h²
Expanding and simplifying this expression, we get:
S = 36kh³ - 2kh⁴
To find the maximum value of S, we take the derivative of S with respect to h and set it equal to zero:
dS/dh = 108kh² - 8kh³ = 0
Simplifying this expression, we get:
h²(108 - 8h) = 0
This equation has two solutions: h = 0 and h = 13.5.
Since a beam with height equal to zero would have zero strength, we reject the solution h = 0. Therefore, the maximum strength is achieved when h = 13.5 inches.
To find the corresponding width, we can use the equation we derived earlier:
w = 18 - 2h = 18 - 27 = -9
Since the width of the beam cannot be negative, we reject this solution as well.
Therefore, the required dimensions of the strongest beam are:
Width = 2h = 2(13.5) = 27 inches
Height = h = 13.5 inches
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ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°. Find AB?
Answer:
We can use trigonometry to find AB.
First, we can use the fact that the sum of the angles in a triangle is 180° to find angle A:
A + B + C = 180°
A + 90° + 30° = 180°
A = 60°
Now, we can use the sine function to find AB:
sin A = opposite/hypotenuse
sin 60° = AB/96
AB = 96 * sin 60°
AB = 96 * √3/2
AB = 48√3
Therefore, AB is approximately 83.14 cm (rounded to two decimal places).
The frequency table represents the fraction of an hour
Rita spends writing in her journal each night. Represent
this data in the line plot.
16. What fraction of an hour did Rita spend most days
writing?
17. What is the difference between the greatest amount
of time spend writing and the least?
A line plot that represents the data is shown in the image attached below.
A fraction of an hour which Rita spend most days writing is 3/4.
The difference between the greatest amount of time spend writing and the least is 3/4.
What is a line plot?In Mathematics and Statistics, a line plot is a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a line plot as shown in the image attached below.
Additionally, we can logically deduce that the mode of the data set is equal to 3/4 (the fraction of an hour Rita spend most days writing) because it has the highest frequency of 5.
Difference = greatest amount of time - least amount of time
Difference = 1 - 1/4
Difference = 3/4.
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