The false statement is that the membership rates are increasing 20% each year.
What are exponential functions?When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.
We are given the equation models the number of members, M, of a gym t years after the gym opens.
[tex]M = 1,800 (1.02) ^t[/tex]
Now if the t time is 3 year then;
[tex]M = 1,800 (1.02) ^t\\\\M = 1,800 (1.02) ^3\\\\M = 1910.14[/tex]
So the last option is True.
Now we can see that the model shows exponential growth. so it is true also.
From the equation the inital part is that 1,800 members joined the gym when it first opened. that is also true.
Hence, the statement is false.
•The membership rates are increasing 20% each year.
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how tall will each candle be at 11:00 PM when johnsons put the candles out for the night
Answer:
3.5 inches
Step-by-step explanation:
From the information given, it can be deduced that the length of the candle at 11:00PM will be 3.5 inches tall. Since the family lights candles
What is the value of the product 3 2i?
The product of 3 and 2i is 6i. This means that the real component of the product is 0, and the imaginary component value is 6.
The product of two complex numbers, such as 3 and 2i, can be calculated by multiplying their real and imaginary components separately. The real component of 3 is 3 and the imaginary component of 2i is 2. So, the real component of the product is 3 x 0 = 0, and the imaginary component is 2 x 3 = 6. Therefore, the product of 3 and 2i is 0 + 6i or 6i. This means that the real component of the product is 0, and the imaginary component is 6. To calculate the product of two complex numbers, simply multiply their real and imaginary components separately and add the results together.
step by step calculations
Real component of 3 x Real component of
2i = 3 x 0 = 0
Imaginary component of 3 x Imaginary component of
2i = 2 x 3 = 6
Therefore, the product is 0 + 6i or 6i.
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Which property will need to be used to solve the equation below? -5x = 15
The property that will be used to solve the equation given, is the Division Property of Equality.
What is the Division Property of Equality?According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0.
An example is:
6 / 3 = 6 / 3
2 = 2
This means that to find the value of x in -5x = 15, the Division Property of Equality, allows us to divide both sides by - 5:
- 5 x / - 5 = 15 / - 5
x = - 3
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The teacher gave a true and false quiz where P(true) = 0.8 for each question. Interpret the likelihood that the first question will be true.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
The interpretation that the likelihood that the first question will be true is (a) Likely
How to interpret the likelihood that the first question will be true.From the question, we have the following parameters that can be used in our computation:
Probability value
The value of the probability and the notation is given as
P(true) = 0.8
As a general rule of probability, we have
Range of probability value = 0 to 1 (inclusive)Unlikely = less than 0.5Equally likely and unlikely = 0.5Likely = greater than 0.5Using the above as a guide, we have the following:
The value of P(true) = 0.8 is greater than 0.5
This that the probability is likely
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Answer: A its that easy
Step-by-step explanation:
Find the area of the region bounded by the hyperbola 9x2-4y2=36 and the line x=3.
Begin by solving the equation for y.
Sketch only the right half of the hyperbola.
Use symmetry to evaluate the trigonomic integral.
Draw a reference rectangle.
First, we will solve the equation of the hyperbola for y:
9x^2 - 4y^2 = 36
4y^2 = 9x^2 - 36
y^2 = (9/4)x^2 - 9
y = ±√((9/4)x^2 - 9)
In math, what is a parabola?
Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.
We only need to consider the right half of the hyperbola because of the symmetry,
the line x=3 is the vertical asymptote of the hyperbola, so we need to find the y-coordinates of the hyperbola when x=3
y = ±√((9/4)3^2 - 9)
y = ±√(9/49 - 9)
y = ±√(27 - 9)
y = ±√18
The area of the region is given by the definite integral of y with respect to x between the limits of x = 3 and x = infinity.
∫y dx = ∫√18 dx = 3/2 * √18 * x^(3/2) from 3 to infinity
The area of the region is infinite as the integral is evaluated from x = 3 to infinity.
It's important to note that the method of evaluating the definite integral is not valid in this case as the integral is of an improper kind and it does not converge to a finite value.
It's impossible to draw a reference rectangle for this problem as the area of the region is infinite.
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42. How many lines of symmetry does the figure have? (1 point)
04
3
02
01
Answer:
yES, THIS IS CORRECT THE ANSWER IS 2
Step-by-step explanation:
If f(x)=x^2 sin(2x), then dy/dx = ?
A Small Publishing Company is planning to publish a new look. The Production Costs will include one-time fixed cost (such as edition) andVariable Casts (such as Printing). The One-time fixed Costs will total $10,300. The Vouciable Casts will be $12 per book. The Publisher Will Sell the finished froduct to bookstores at a price of $118.25 per bookHow Many books must the Publisher Produce and sell So that the producation Costs will equal the money from Sales?
Using the provided values and making an equivalent equation and equating the equation to solve for the number of books required to break even, The answer is 97 books should be produced and sold.
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.
What are the methods to solve system of equations?There are three ways to solve systems of linear equations :
GraphingSubstitution methodElimination methodrequired equation,
10300 + 12x = 118.25x
solving for x , we get,
106.25x = 10300
x=10300/106.25
=97
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Examine the equation and the table, each of which represent a different linear function. Function A: y=3x−6 Function B: Input (x) Output (y) 3 3 6 13 9 23 12 33 Which statement is true about the two functions? Responses Function B has a greater rate of change. Function B has a greater rate of change. - no response given Function B has a greater output when the input is 3. Function B has a greater output when the input is Function A has a greater rate of change. Function A has a greater rate of change. Function A has a greater output when the input is 6.
The statement which is true about the two functions include the following: A. Function B has a greater rate of change.
What is the rate of change?In Mathematics, the rate of change is sometimes referred to as slope or gradient and it can be calculated by using this formula;
Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, m = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the value of y with respect to the value of x in function B, which represents a line that is passing through the data points (3, 3) and (6, 13):
Rate of change, m = (13 - 3)/(6 - 3)
Rate of change, m = 10/3 or 3.33.
From function A (y = 3x - 6), we can logically deduce that the rate of change is equal to 3.
In conclusion, we can logically deduce that the rate of change of function B (m = 3.33) is greater than the rate of change of function A (m = 3).
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Bank account starts with $10 and doubles each week.Bank account D starts with $1000 and grows by $500 each week.
When will account c contain more money than account D.
0 weeks
3 weeks
9 weeks
11 weeks
15 weeks
89 weeks
Answer:
9 weeks
Step-by-step explanation:
set y as how much money they have
set x as how many weeks spend
Bank account C:
y = 10 * 2^x
Bank account D:
y = 1000 + 500x
Set this two equations equal to find the point of two bank account have the same amount of money:
10 * 2^x = 1000 + 500x
Solve the equation:
2^x = 100 + 50x
Let f and g be differentiable functions with the following properties (i) g(x)>0 for all x (ii) f(0)=1 if h(x)=f(x)g(x) and h'(x)=f(x)g'(x) , then f(x)= :.
If h(x) = f(x)g(x) and h'(x) = f(x)g'(x), then f(x) = 1.
Let f and g be differentiable functions such that g(x)>0 for all x and f(0)=1.
We can then write h(x) = f(x)g(x). Taking the derivative of h(x) with respect to x, we get:
h'(x) = f'(x)g(x) + f(x)g'(x)
Since h'(x) is equal to f(x)g'(x), then we can cancel out f(x)g(x) from both sides to get:
f'(x)g(x) = 0
Since g(x) is always greater than 0, this implies f'(x) = 0. This means that f(x) is a constant function. Since f(0) = 1, then f(x) = 1 for all x.
Therefore, if h(x) = f(x)g(x) and h'(x) = f(x)g'(x), then f(x) = 1.
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T Raiderlink Bb Blackboard SPC Blackboard TTU -/1 Points] DETAILS HARMATHAP12 9.4.011. Find the derivative of the function. w = 2? - 326 + 14 w= 1-/1 Points) DETAILS HARMATHAP12 9.4.014.MI. Find the derivative of the function. +(x) = 16x12 + 6x6 - 2x + 19x - 7 h'(x) = [-/1 Points] DETAILS HARMATHAP12 9.5.002.MI. Find the derivative and simplify. y = (8x + 5)(x2 – 3x).
The derivative of the function is
A) dw/dz=z^5 (7z-18)
B) dh/dx=192x^11+36x^5-6x^2+19
C) dy/dx=24x^2-38x-15
In mathematics, the derivative of a function measures the sensitivity to change of the function value with respect to a change in its argument. It is the rate of change of a function with respect to a variable.
A) w = z^7 – 3z^6 + 14
dw/dz=7z^6-18z^5
dw/dz=z^5 (7z-18)
B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7
dh/dx=192x^11+36x^5-6x^2+19
C) y = (8x + 5)(x^2 – 3x)
dy/dx= d/dx [8x+5]*〖(x〗^2-3x)+(8x+5)*d/dx[x^2-3x]
dy/dx=(8* d/dx [x}+d/dx[5])*〖(x〗^2-3x)+(8x+5)*(d/dx[x^2]-3 d/dx[x])
dy/dx=(8*1+0)(x^2-3x)+(8x+5)(2x-3*1)
dy/dx=8(x^2-3x)+(2x-3)(8x+5)
dy/dx=24x^2-38x-15
Note: The question is incomplete. The complete question probably is: Find the derivative of the following function: A) w = z^7 – 3z^6 + 14 B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7 C) y = (8x + 5)(x^2 – 3x).
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George is planning a dinner party for three other couples, his wife, and himself. He plans to seat the four couples around a circular table for 8, and wants each husband to be seated opposite his wife. How many seating arrangements can he make, if rotations and reflections of each seating arrangement are not considered different
Seating arrangements that can be made, if rotations and reflections of each seating arrangement are not considered different is 24.
The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.
Total number of couples = 3
No. of seating in Circular table = 8
Total number of ways they can be seated =3*8 = 24
Thus, Seating arrangements that can be made, if rotations and reflections of each seating arrangement are not considered different is 24.
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The number of possible arrangements he can make = 24
Assume that George and his wife seated opposite to each other.
Then there would be six open seats for three other couples.
The first woman of them can be seated in six ways.
Using combination formula, we can write it as
6C1 = 6
And her husband sits opposite to her.
Now the next woman can be seated in six ways.
Using combination formula, we can write this as
4C1 = 4
And her husband sits opposite to her.
Now the last woman can be take any seat from the remaning 2 seats and her husband sits opposite to her.
Since rotations and reflections of each seating arrangement are not considered different, there are 6 × 4 = 24 possible seating arrangements.
Therefore, there would be 24 possible seating arrangements.
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I need help with this. Could someone explain how to solve this question? A simple explanation, please. The explanations I'm seeing seem to confuse me a lot.
Step-by-step explanation:
given
a(-23) &b(5)
if you take this as a continuous graph
AB+BC =28
ATQ,
AB/BC=2/5
28-bc/BC=2/5
140-5BC=2BC
140=7BC
BC=20
B is -15
A line that includes the points (-10, W) and (10, 6) has a slope of I. What is the value of w?
Can someone please help me?
Thank you!
Step-by-step explanation:
(6 - W)/(10+10)= (6 - W)/20= 2
6 - W= 40
-W= 34
W= -34
Answer:
line can be described by the equation y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
Since we are given that the line has a slope of 1 and includes the point (10, 10), we can plug these values into the equation to solve for the y-intercept. We get:
10 = 1 * 10 + b
b = 10 - 10
b = 0
So the equation of the line is y = x + 0, or simply y = x.
Since we are also given that the line includes the point (u, 9), we can substitute this value for y in the equation of the line to solve for u. We get:
9 = x
x = 9
Therefore, the value of u is 9.
Uday Tahlan
line that includes the points (-10, W) and (10, 6) has a slope of I. What is the value of w?
Can someone please help me?
Thank you!
To find the value of W, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Since we are given that the line includes the points (-10, W) and (10, 6) and has a slope of I, we can use these two points to find the value of W.
First, we can plug in the coordinates of one of the points and the value of the slope into the equation to solve for the y-intercept. Let's use the point (10, 6):
6 = I * 10 + b
b = 6 - 10I
Then, we can plug the values of the slope and y-intercept into the equation and solve for W using the coordinates of the other point (-10, W):
W = I * (-10) + (6 - 10I)
= -10I + 6 - 10I
= 6 - 20I
Therefore, the value of W is 6 - 20I.
Daren can run 8.55 kilometers in one hour. Umberto can run 9.5 kilometers in one hour. If Daren plans to run for 3.5 hours and Umberto plans to run for 3 hours who will run more kilometers assuming their running pace stays the same for the entire time? How do you know?
Answer: Daren
Step-by-step explanation:
The rate for Daren is 8.55 kph, while Umberto is 9.5 kph.
Find the total miles for Daren and Umberto:
8,55 x 3,5 = 29,925
9,5 x 3 = 28,5
Daren will run more kilometers than Umberto because the distance running is more than Umberto's.
Find the value of x
The value of {x} in the given geometrical figure is 7.
What are angles?In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection.Given is a pair of intersected lines.
We can write, as observed from the image that -
6x + 3 = 45 {Vertically opposite angles}
6x = 42
x = 7
Therefore, the value of {x} in the given geometrical figure is 7.
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Which action can be taken to the expression in step 3 to give an expression for step 4? divide both the numerator and denominator by sin(x)sin(y) divide both the numerator and denominator by sin(x)cos(y) divide both the numerator and denominator by cos(x)sin(y) divide both the numerator and denominator by cos(x)cos(y)
The step which is to be taken to get the required result is to divide both the numerator and denominator by cos(x)cos(y).
The given question is incomplete, I am answering as per my general knowledge.
The values of all trigonometric functions depends on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.
Sides of a triangle for which we can calculate these ratios are ,
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Divide both the numerator and denominator by cos(x)cos(y) with expression is (sin(x)sin(y) + cos(x)cos(y)) / (sin(x)sin(y))
Step 3: (sin(x)sin(y) + cos(x)cos(y)) / (sin(x)sin(y))
Step 4: (sin(x)sin(y) + cos(x)cos(y)) / (cos(x)cos(y))
In Step 3, the expression is (sin(x)sin(y) + cos(x)cos(y)) / (sin(x)sin(y)) which is a fraction. In order to obtain the expression for Step 4, both the numerator and denominator must be divided by cos(x)cos(y). This will result in the expression (sin(x)sin(y) + cos(x)cos(y)) / (cos(x)cos(y)) for Step 4.
In order to obtain the expression for Step 4, both the numerator and denominator must be divided by cos(x)cos(y).
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(-2/3)^-4, Evaluate without using a calculator
[tex]\left(-\cfrac{2}{3} \right)^{-4}\implies \left(-\cfrac{3}{2} \right)^{+4}\implies \left(-\cfrac{3}{2} \right)\left(-\cfrac{3}{2} \right)\left(-\cfrac{3}{2} \right)\left(-\cfrac{3}{2} \right)\implies \cfrac{81}{16}[/tex]
Who is right, and why?
Neither Kurt nor Maria is right, because 3,500 should be used instead of 3,600.
Kurt is right, because finding One-fifth of 3,600 is not a good way to approximate 21% of 3,585.
Maria is right, because finding 10% of 3,600 and multiplying the result by 2 is not a good way to approximate 21% of 3,585.
Both Kurt and Maria are right, because 3,585 should be rounded up to 3,600, and 21% of this amount can be approximated by either finding 10% of 3,600 and multiplying the result by 2 or by finding One-fifth of 3,600.
The correct statement regarding the proportion is given as follows:
Both Kurt and Maria are right, because 3,585 should be rounded up to 3,600, and 21% of this amount can be approximated by either finding 10% of 3,600 and multiplying the result by 2 or by finding One-fifth of 3,600.
How to obtain the correct proportion?A proportion is a fraction of a total amount.
The total amount is of 3585, and 21% of the goal has been reached, hence the amount reached is obtained as follows:
0.21 x 3585 = $752.85.
Both Kurt or Maria took different routes, rounding the amount to 3600, and then obtaining 20% of it, which is equivalent to one-fifth. 20% can also be obtained as twice of 10%, hence both are correct, and the fourth statement is correct.
Missing InformationThe missing text is given as follows:
Kurt and Maria’s high school is having a newspaper drive.The goal is to collect 3,585 pounds of newspapers. So far, 21% of the goal has been reached.
Kurt estimated the number of pounds of newspapers collected by finding 10% of 3,600 and then multiplying the result by 2.
Maria estimated the number of pounds of newspapers collected by finding One-fifth of 3,600.
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F(x)=2+3x²; find f(3)
Answer:
29
Step-by-step explanation:
[tex]f(3)[/tex] represents the value of [tex]f(x)[/tex] when [tex]x=3[/tex].
[tex]f(3)=2+3(3)^2=29[/tex]
what is 53x-2=43+31x-1?
Answer:
x=2.05
Step-by-step explanation:
To solve for x, we start by adding 2 to both sides of the equation:
53x - 2 + 2 = 43 + 31x - 1 + 2
53x = 45 + 31x
Then, we subtract 31x from both sides of the equation:
53x - 31x = 45 + 31x - 31x
22x = 45
Finally, we divide both sides of the equation by 22:
22x/22 = 45/22
x = 2.05
Therefore, the value of x is 2.05.
Why is it called tangent function?
The tangent function is a trigonometric function used to calculate angles and the relationships between them.
This function is also known as the “slope of a curve” and measures the rate of change of the angle with respect to the x-axis. In its most basic form, the tangent function is expressed as tanθ, which is interpreted as the ratio between the length of the opposite side of angle θ and the length of the adjacent side. The graph of the tangent function is a periodic curve with a range of [-π/2,π/2]. It has many uses in mathematics and physics, such as the calculation of derivatives, integration, and interpolation.
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Fill in the table using this function rule.
y=6x+4
X Y
4
7
8
10
Does anyone know what the answer is? Thanks!
Answer:
D
Step-by-step explanation:
An obtuse angle is one over 90. They both have one of them.
Each situation can be modeled using a linear equation. Describe the rate of change for each situation.
1. Andre started his no-interest savings account with $1,000. He makes the same deposit each week, and there is $1,600 in the account after 6 weeks.
2. Kiran starts with $748 in his checking account. After 4 weeks of spending the same amount each week, he has $716 left.
1. The rate of change, in this case, is $100 per week.
2. The rate of change, in this case, is $-8 per week.
1. In this situation, the rate of change of Andre's savings account can be modeled using a linear equation of the form - y = mx + b
where
y represents the balance in the account,
x represents the number of weeks,
m represents the rate of change (i.e., the amount of money added to the account each week), and
b represents the starting balance.
To find the rate of change, you can use the point-slope form of a linear equation, which is y - y1 = m(x - x1).
In this case, y represents the balance in the account after 6 weeks (i.e., $1,600),
y1 represents the starting balance (i.e., $1,000),
x represents the number of weeks (i.e., 6), and
x1 represents the number of weeks at the starting balance (i.e., 0).
Substituting these values into the point-slope form gives 1600 - 1000 = m(6 - 0), which simplifies to 600 = 6m.
Dividing both sides of the equation by 6 gives m = 100, so the rate of change is $100 per week.
2. In this situation, the rate of change of Kiran's checking account can also be modeled using a linear equation of the form y = mx + b,
where
y represents the balance in the account,
x represents the number of weeks,
m represents the rate of change (i.e., the amount of money spent from the account each week), and
b represents the starting balance.
To find the rate of change, you can again use the point-slope form of a linear equation, which is y - y1 = m(x - x1).
In this case, y represents the balance in the account after 4 weeks (i.e., $716),
y1 represents the starting balance (i.e., $748),
x represents the number of weeks (i.e., 4), and
x1 represents the number of weeks at the starting balance (i.e., 0).
Substituting these values into the point-slope form gives 716 - 748 = m(4 - 0), which simplifies to -32 = 4m.
Dividing both sides of the equation by 4 gives m = -8, so the rate of change is $-8 per week.
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how many degrees does the minute hand of a clock turn in 45 minutes
In 45 minutes the minutes of the clock turns 270 degrees
How to find the angular measure of the hands of clockThe hands of clock while rotating is observed to be rotating 6 degree per minute
This can be calculated based on the fact that in 60 minutes a clock makes a 360 degrees rotation, using this concept we have that
if 60 minutes = 360 degrees then 1 minute will be
1 minute = 360 degrees / 60 minutes
1 minute = 6 degrees
To calculate for 45 minutes we have
number of degrees in 45 minutes = 45 * 6
number of degrees in 45 minutes = 270 degrees
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What does it mean when an observational study is retrospective' When does it mean when an observational study is prospective? What does it moan when an observational study is retrospective? A retrospective study requires that individuals look back in three or require the researcher to look at existing records A retrospective study collects the data over time A retrospective study is a list of all individuals in a population along with certain characteristics of each individuals What does it mean when an observational study is prospective? A prospective study requires that individuals took hack in time or require the researcher to look at existing records A prospective study collects the data over time. A prospective study is a list of all individuals in a population along with certain characteristics of each individual.
A. Prospective observational studies involve collecting data from participants before an event or outcome occurs, while retrospective observational studies collect data after the event has already taken place.
A prospective observational study is a type of observational study that involves collecting data from participants before an event or outcome occurs. This type of study is used to predict and measure outcomes in the future.
In this type of study, the researcher can control the variables, such as when and how the data is collected, and can also observe the effects of any changes in the environment.
On the other hand, a retrospective observational study is a type of observational study that involves collecting data after an event or outcome has already taken place. This type of study is used to study the causes of a given outcome.
In this type of study, the researcher looks back in time and collects data from the past. This type of study is more limited than a prospective observational study, since the researcher cannot control the variables of the study or observe any changes in the environment.
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Segment VU is parallel to segment LM. Find the missing length.
L
M24 U
44
27
24
39
?
11
8
N
Segment VU is parallel to segment LM. The missing length is 16.
What parallel segments are there?If the matching lines formed by two segments are parallel, then the segments are parallel. In other words, two segments are considered to be parallel if they are in the same plane and do not cross even when stretched indefinitely in both directions.
Two line segments are parallel if any pair of matching angles, alternate interior angles, alternate exterior angles, or consecutive interior angles are supplementary. On a coordinate plane, parallel lines have the same slope.
If the matching lines formed by two segments are parallel, then the segments are parallel.
Segment VU is parallel to segment LM. The missing length is 16.
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WRITE Math Suppose there was 1 centerpiece
for every 5 tables. Use counters to show the ratio of
centerpieces to tables. Then make a table to find the
number of tables if there are 3 centerpieces.
Answer: 15 tables.
Step-by-step explanation:
To show the ratio of centerpieces to tables using counters, we can use 1 blue counter to represent 1 centerpiece and 5 yellow counters to represent 5 tables. The ratio of centerpieces to tables can then be represented as 1:5, or 1/5.
To find the number of tables if there are 3 centerpieces, we can set up the following proportion:
3 centerpieces / 1 centerpiece = X tables / 5 tables
Cross-multiplying this proportion gives us:
3 * 5 tables = 1 centerpiece * X tables
Solving for X gives us the number of tables:
X = 15 tables
Therefore, if there are 3 centerpieces, there are 15 tables.
