According to the empirical rule -
a) About 95% of organs will be in range of weights of organs 230 grams and 430 grams.
b) 68% percentage of organs weighs between 280 grams and 380 grams.
c) 32% percentage of organs weighs less than 280 grams or more than 380 grams.
d) 97.35% percentage of organs weighs between 180 grams and 430 grams.
What is empirical rule?
The empirical rule 68-95-99.7 tells us that:
68% of the data is expected to be within 1 standard deviation from the mean.
95% of the data is expected to be within 2 standard deviation from the mean.
99.7% of the data is expected to be within 3 standard deviation from the mean.
There is a bell shaped distribution ( assume as approximately normal) with mean of 330 g and standard deviation of 50 g.
a) This happens for an interval with ±2 standard deviations from the mean.
That is:
X1 = μ + z1 × σ X2 = μ + z2 × σ
X1 = 330 - 2 × 50 X2 = 330 + 2 × 50
X1 = 330 - 100 X2 = 330 + 100
X1 = 230 X2 = 430
Therefore, the range of weights of organs is 230 grams and 430 grams.
b) Calculate the z-scores for each value to know how many standard deviations are from the mean.
z1 = (x1 - μ)/σ z2 = (x2 - μ)/σ
z1 = (280 - 330)/50 z2 = (380 - 330)/50
z1 = -50/50 z2 = 50/50
z1 = -1 z2 = 1
The values are 1 standard deviations from the mean each.
Therefore, the expected percentage is 68%.
c) This is the complementary of the point b.
Then, it is expected that (100 - 68)% = 32% of the organs weigh less than 280 grams or more than 380 grams.
d) Calculate the z-scores for each value to know how many standard deviations are from the mean.
z1 = (x1 - μ)/σ z2 = (x2 - μ)/σ
z1 = (180 - 330)/50 z2 = (430 - 330)/50
z1 = -150/50 z2 = 100/50
z1 = -3 z2 = 2
The values are 1 standard deviations from the mean each.
Therefore, the expected percentage is 68%.
The values are 3 standard deviations from the mean each. Between 180 and 330 there is 99.7%/2 = 49.85% of the data.
The values are 2 standard deviations from the mean each. Between 330 and 430 there is 95%/2 = 47.5% of the data.
Then, between 180 grams and 430 grams there is (49.85% + 47.5)% = 97.35% of the data.
Therefore, the expected percentage is 97.35%.
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BENCHMARK ASSESSMENT - 2/20
Which of the ratios below has a unit rate of 8? Select all that apply.
A) 40:5
B) 24:16
C) 96:12
D) 48:6
E) 2:24
Answer: So Here you go I got the perfect answer with a explanation
Step-by-step explanation:
A unit rate is a rate in which the second term is 1. To find a unit rate, we need to divide the first term by the second term.
A) 40:5 has a unit rate of 8 (40/5 = 8)
C) 96:12 has a unit rate of 8 (96/12 = 8)
D) 48:6 has a unit rate of 8 (48/6 = 8)
So options A, C and D has a unit rate of 8.
Answer:
the ration has a unit rate of 8 A - 40:5C - 96:12 D - 48:6Dividable by 8
Step-by-step explanation:
Write the expression as a single power of b.
open parentheses b to the power of begin display style 3 over 4 end style end exponent over b to the power of begin display style 1 fourth end style end exponent close parentheses to the power of 1 half end exponent
The simplified form of the given expression is x raise to the power of one-thirty.
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
Simplifying indices expressions
Given the indices expression (x^1/2/(x^1/3)^1/5
Using the indices law below:
a^m/a^n = a^m-n
(a^m)^n
Applying the law above to the given equation
(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5
(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5
(x^1/2/(x^1/3)^1/5 = x^1/30
Hence the simplified form of the given expression is x raise to the power of one-thirty.
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Solve 2 4/5x=−1 1/4 . Write your answer as a fraction in simplest form.
Answer: -56/55
Step-by-step explanation:
2 4/5x = -11/4
14/5x = -11/4
Cross multiply:
-55x = 14 * 4 = 56
x = -56/55
HELP!
which is the graph of g(x) = [x+3]?
Answer:
Step-by-step explanation:
O gráfico de g(x) = [x+3] é uma Reta que passarum pelo pno (3,0) e tem inclinação 1.
2. Write an equation to represent f(e)
Absolute Value Functions
The absolute value function for f(e) is given as follows:
f(e) = |e|
The piece-wise definition of the function is given as follows:
f(e) = e, e >= 0.f(e) = -e, e < 0.What is the absolute value of a number?The absolute value of a number is the number without the signal, representing the difference between the number and zero.
This means that the elevation function gives just elevation, without considering if the elevation is positive or negative, and thus the function is defined as follows:
f(e) = |e|
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How do i solve for the value of s
Sample Spaces and Probabilities (18 points) For each of the following scenarios first describe the sample space and indicate how big it is (i.e., what its cardinality is) and then answer the question. (a) [3 Points] You flip a fair coin 50 times. What is the probability of exactly 20 heads? (b) [3 Points] You roll 2 fair 6-sided dice, one red and one blue. What is the probability that the sum of the two values showing is 4? (c) [3 Points] You are given a random 5 card poker hand (selected from a single deck). What is the probability you have a full-house (3 cards of one rank and 2 cards of another rank)? (d) [3 Points] 20 labeled balls are placed into 10 labeled bins (with each placement equally likely). What is the probability that bin 1 contains exactly 3 balls? (e) [3 Points] There are 30 psychiatrists and 24 psychologists attending a certain conference. Three of these 54 people are randomly chosen to take part in a panel discussion. What is the probability that at least one psychologist is chosen? What is the probability that exactly three psychologists are chosen? (f) [3 Points] You buy ten cupcakes choosing from 3 different types (chocolate, vanilla and caramel). Cupcakes of the same type are indistinguishable. What is the probability that you have at least one of each type?
(a) Sample space: 2^50 (1,024,000). Probability of exactly 20 heads: 0.000244140625.
(b) 6^2 (36). Probability of a sum of 4: 1/9.
(c) C(52,5) (2,598,960). Probability of a full house: 0.001441.
(d) 10^20 (10^19). Probability of bin 1 containing exactly 3 balls: 1/10^19.
(e) C(54,3) (19,323). Probability of at least one psychologist: C(24,1)/C(54,3) (0.841). Probability of exactly three psychologists: C(24,3)/C(54,3) (0.037).
(f) 3^10 (590,490). Probability of at least one of each type: 0.001690.
(a) The sample space consists of all the possible outcomes of flipping a fair coin 50 times, which is 2^50 (1,024,000). There are only two possible outcomes for each flip, heads or tails. The probability of getting exactly 20 heads is 0.000244140625.
(b) The sample space consists of all the possible outcomes of rolling a red and a blue 6-sided die, which is 6^2 (36). The probability of getting a sum of 4 is 1/9.
(c) The sample space consists of all the possible 5 card poker hands (selected from a single deck), which is C(52,5) (2,598,960). The probability of getting a full house (3 cards of one rank and 2 cards of another rank) is 0.001441.
(d) The sample space consists of all the possible ways of placing 20 labeled balls into 10 labeled bins, which is 10^20 (10^19). The probability of bin 1 containing exactly 3 balls is 1/10^19.
(e) The sample space consists of all the possible ways of selecting 3 of the 54 people attending the conference, which is C(54,3) (19,323). The probability of at least one psychologist being chosen is C(24,1)/C(54,3) (0.841). The probability of exactly three psychologists being chosen is C(24,3)/C(54,3) (0.037).
(f) The sample space consists of all the possible ways of buying ten cupcakes from the 3 different types, which is 3^10 (590,490). The probability that you have at least one of each type is 0.001690.
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The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
The likelihood of randomly selecting a chocolate chip cookie from the batch is unlikely. Therefore, option C is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Given that, the baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies.
P(chocolate chip) = 0.25
In probability, larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 0.5 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
Here, 0.25<0.5
Therefore, option C is the correct answer.
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Answer:unlikely
Step-by-step explanation:
You go to the grocery store and purchase the items listed in the table. What is your total if
the sales tax is 7%?
The total price is obtained following these two steps:
Adding the price of all the products in the table.Multiplying the total by 1.07, due to the sales tax of 7%.How to obtain the total price?The first step is obtain the price without taxes, which is done adding the price of all the items in the data-set.
Then the proportion is applied, relative to the sales tax of 7%.
The percentage of a sales tax of 7% is given as follows:
107%.
Hence the multiplier relative to this sales tax is given as follows:
1.07.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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Please help to answer this qns.. 6th grade algebra
The linear function that gives the number of matchsticks required to make the nth pattern is given as follows:
M(n) = 15n.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.When a linear function represents a proportional relationship, it means that the intercept is of zero.
As for each pattern the number of sticks is increased by 15, the slope is of 15 and the equation is given as follows:
M(n) = 15n.
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The rule for the glide reflection that maps △ABC with vertices A(–4, –2), B(–2, 6), and C(4, 4) to △A′B′C′ with vertices A′(–2, –2), B′(0, –10), and C′(6, –8) is T⟨a, b⟩ ∘ Rx-axis where
The ΔABC reflects across x-axis with point a=2 and scale factor of x+2 to form the ΔA'B'C'.
What is reflection?
A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
The vertices of ΔABC is given as -
A(–4, –2), B(–2, 6), and C(4, 4)
The vertices of ΔA'B'C' is given as -
A′(–2, –2), B′(0, –10), and C′(6, –8)
To find the scale factor of the reflection use the formula -
x + a = x' and y + b = y'
Substitute the values in the equation.
For vertex A and A' -
x1 + a = x1'
-4 + a = -2
a = -2 + 4
a = 2
y1 + b = y1'
-2 + b = -2
b = -2 + 2
b = 0
For vertex B and B' -
x2 + a = x2'
-2 + a = 0
a = 0 + 2
a = 2
y2 + b = y2'
6 + b = -10
b = -10 - 6
b = -16
For vertex C and C' -
x3 + a = x3'
4 + a = 6
a = 6 - 4
a = 2
y3 + b = y3'
4 + b = -8
b = -8 - 4
b = -12
It can be seen that the values of a is constant whereas the values of y varies. This happens due to reflection of coordinates across the x-axis.
Therefore, the reflection happens across the x axis.
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There are two different pathways around a circular lake. The circular pathway is inscribed inside of a square pathway. The circular pathway has an area of 768 square feet. How far would a person walk if she walked around the square pathway? Use 3 for pi.
The person walks 128 feet if she walked around the square pathway.
What are the 2D shapes?The plane forms that can be sketched on a flat (or plane) surface or a piece of paper are known as 2D shapes. Every 2D shape has different attributes, like area and perimeter. Some of the two-dimensional objects have sides and corners, while others have curved edges.
Given two pathways,
circular and square, and the circular pathway is inscribed inside of a square pathway,
area of circular pathway = 768 square feet
area of circle = π/4*d²
where d is the diameter
768 = π/4*d²
768*4 = πd² (π = 3)
3072/3 = d²
d = √1024
d = 32 feet
since the circle is inscribed in a square the length of a side of square is equal to the diameter of the circle,
d = a = 32 feet
to find the perimeter of the square path,
perimeter of square = 4a
perimeter of square = 4*32
perimeter of square = 128 feet
Hence the person has to cover 128 feet if she walked around the square pathway.
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75,232 = ___ in
expanded form
Answer:
seventy-five thousand two hundred thirty-two
Step-by-step explanation:
-8.8/x = 1.5/10
Pls help
Answer:
x = 58.67
Step-by-step explanation:
[tex]\frac{-8.8}{x}[/tex] = [tex]\frac{1.5}{10}[/tex]
Cross multiply
1.5x = (-8.8)(10)
1.5x = -88
Divide, solve for x
x = -88/1.5 = -58.6666667 = around -58.67
Explain weather there is a possible transformation of f in the form g(x) =f(x)+k, where k is a constant for which the graph y=g(x) will have no x-intercepts. Enter your answer and your justification in the space provided.
Answer:
Yes, a transformation of f in the form g(x) =f(x)+k can have no x-intercepts. This will occur if the constant k is added to the y-value of every point on the f(x) graph, resulting in the chart of g(x) being shifted upward by k units. If the original diagram of f(x) had no x-intercepts, then the graph of g(x) would also have no x-intercepts because the x-coordinate of each point on the graph of f(x) is unchanged by the transformation.
Step-by-step explanation:
The list below gives the location of 3 friends who are scuba diving together. Mallory is exploring at an elevation of -25 feet. Jacob is standing on the boat, at an elevation of 15 feet. Eva just jumped in and is 5 feet below the surface of the water.
Which inequality correctly compares the distance of the scuba divers from the surface of the water?
Which one of these?
1- Eva > Mallory
2- Mallory < Jacob
3- Jacob < Eva
4- Mallory > Eva
Mallory is further from the surface than Eva. So, Mallory > Eva. Therefore, option D is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, Mallory is exploring at an elevation of -25 feet.
So, distance between Mallory and the surface of water is 25 feet
Jacob is standing on the boat, at an elevation of 15 feet.
Distance between Jacob and the surface of water is 15 feet
Eva just jumped in and is 5 feet below the surface of the water.
Distance between Eva and the surface of water is 5 feet
In this case, the person closest to the surface is Eva, who is 5 feet from the surface.
So, the inequality is Mallory > Eva
Therefore, option D is the correct answer.
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Manny drives 2 times the hours that Tabria does. Manny and Tabria drive for a total of 9 hours. How
long did each person drive?
Answer:
4.5
Step-by-step explanation:
4.5 times 2 = 9
9 divided by 2 =4.5
Need help with question number 3
Using what we know about lines and vertical angles we will see that:
m∠3 = 35°.
How to find the measure of angle 3?Remember that when two lines intercept and 4 angles are formed, the vertical angles (these ones connected only by the vertex) have the same measure.
For example, 2 and 5 are vertical angles in this case.
Angles 6 and 3 also are vertical angles, and if both white lines are parallel, then the measures of angle 1 and 6 will be equal (because both are on the same quadrant) then:
m∠6 = 35°
Then the measure of angle 3 is:
m∠3 = 35°.
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6. Write a polynomial function of the least degree that has the root x = (5+ i).
Factors:
Polynomial Function:
To much to right but have it in pic: \/ \/
please help with linear function equations
Answer:
f(x) = 0.5x
Step-by-step explanation:
For this problem, we simply have to find the constant of proportionality between x and f(x). In other words, what x is multiplied by to get f(x).
Since this proportion is constant (meaning it doesn't change), all we have to do is divide an f(x) value in the table by its corresponding x value.
p = f(x) / x
p = -2 / -4
p = 1/2 = 0.5
We can show the relationship of x to f(x) with the equation f(x) = px, which can be simplified using the constant of proportionality that we just solved for.
f(x) = 0.5x
One number is six less than three times another number. If the sum of the numbers is 38, find the numbers.
Answer: Let's call the first number "x" and the second number "y".
From the problem statement, we know that:
x = 3y - 6 (because one number is six less than three times the other number)
x + y = 38 (because the sum of the numbers is 38)
We can substitute the first equation into the second equation to solve for one of the variables:
3y - 6 + y = 38
4y - 6 = 38
4y = 44
y = 11
Now we can substitute this value of y back into the first equation to find the value of x:
x = 3(11) - 6
x = 29
So the two numbers are:
x = 29
y = 11
Step-by-step explanation:
Suppose b is a constant and that f(x) is a function defined when x = b. Complete the following sentences.
1. If f(b) is large, then 1/f(b) is __
2. If f(b) is small, then 1/f(b) is __
3. If f(b) = 0 then
1/f(b) is __
4. if f(b) is positive, then
1/f(b) is __
5. If f(b) is negative, then 1/f(b) is __
(i) 0
(ii) inifinity(very large value)
(iii) undefined
(iv) positive value
(v) negative value
What is limiting value of a function?A limiting value of a function is a value that the function approaches as the input (or independent variable) approaches a certain value. It is also called the function's limit at that point. This concept is used in calculus to understand the behavior of functions and their derivatives.
so in all the cases we have to find the limiting value of f(x)
1. if the value of f(b) is very large the 1/f(b) is very small.
2. if f(b) is small then the value of 1/f(b) is very large
3. if f(b) is 0 then 1/f(b) is not defined.
4. if f(b) is positive then its reciprocal is also positive.
5. if f(b) is negative then its reciprocal is also negative.
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(I) 0
(ii) The infinite (very large value)
IIII, undefinable
(iv) A favorable value
(v) negative value
What does a function's limiting value mean?A function's limiting value is a point that the function approaches as the input (or independent variable) gets closer to a particular value. At that time, it is also known as the function's limit. Calculus makes use of this idea to comprehend how functions behave and how their derivatives work.
Therefore, we must always determine the limiting value of f. (x)
1. The value of 1/f(b) is very small if the value of f(b) is very large.
2. The value of 1/f(b) is very large if f(b) is tiny.
3. 1/f(b) is not defined if f(b) is 0.
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Lisa is traveling to Greece this summer and needs to exchange 500 US Dollars to Euros.
How many Euros will Lisa receive with the following exchange rate?
1 USD = 0.95 Euros
Answer: Lisa will receive 475 Euros.
Step-by-step explanation: 500x0.95 = 475.
Answer:
Step-by-step explanation:
2
Write True if the statement is correct and Faise if the statement is incorrect
1. Every composite number can be expressed as a product of primes
, 2. Some quadratic equation has infinite solution
3. For any two real numbers x andythenix-yl=ly=xl
4. 2(3+√7)-2√7 = 6√7
5. 25,471,287 is not divisible by 3 and 9,
6. √6 is not rational number,
7. Between every two real numbers there is another real number,
8. For any natural numbers a and b GCF (a, b) * LCM(a,b) = a*b.
9. Integer is not closed under division,
10. The product of non zero rational number and irrational number is rational⁹
1. Every composite number can be expressed as a product of primes - True
2. Some quadratic equation has infinite solution - True
3. False (ix-yl = |x-y|, which may not equal ly = |y|)
What is Rational Number?A rational number is a number that can be expressed as the ratio of two integers.A rational number can be written in the form p/q, where p and q are integers and q ≠ 0.Examples of rational numbers include -3/4, 0, 1/2, and 5.Every integer is a rational number, since it can be expressed as the ratio of the integer and 1.Every fraction can be represented as a rational number, since it is the ratio of two integers.The decimal representation of a rational number will either terminate (e.g. 1/4 = 0.25) or repeat (e.g. 1/3 = 0.3333...).The set of rational numbers is dense, meaning that between any two rational numbers, there is another rational number.4. 2(3+√7)-2√7 = 6√7 - False
5. False (25,471,287 is divisible by 3)
6. √6 is not rational number - True
7. Between every two real numbers there is another real number -True
8. For any natural numbers a and b GCF (a, b) * LCM (a, b) = a*b. -True
9. Integer is not closed under division -True
10. False (The product of a non-zero rational number and an irrational number is not necessarily rational)
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graph the equation y=2/3x-1 iready quiz graph linear equations
Answer: To graph the equation y = 2/3x - 1, we can start by finding some points that satisfy the equation.
We can pick any value for x and substitute it into the equation to find the corresponding y-value.
For example:
When x = 0, y = (2/3)(0) - 1 = -1
When x = 1, y = (2/3)(1) - 1 = -1/3
When x = 2, y = (2/3)(2) - 1 = 1/3
When x = 3, y = (2/3)(3) - 1 = 2/3
We can plot these points on a coordinate plane and then connect them with a straight line to graph the equation.
The graph will be a line that passes through the points (0, -1), (1, -1/3), (2, 1/3), and (3, 2/3).
Step-by-step explanation:
Solve the system by substitution {2x−3y=12 −12y+8x=48
If there is one solution, type the answer as an ordered pair. If there is no solution, type ∅. If there are infinitely many solutions, type ∞.
The solution to the system is (7.5, 1)
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
2x−3y=12
−12y+8x=48
divide the first equation by 2
So, we have
x - 1.5y = 6
This gives
x = 6y + 1.5
By substitution, the second equation becomes
-12y + 8 (6y + 1.5) = 48
So, we have
-12y + 48y + 12 = 48
Evaluate
36y = 36
Divide by 36
y = 1
So, we have
x = 6 + 1.5
x = 7.5
Hence, the solution is (7.5, 1)
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simplify
(-4x^2)(3x^5)/2x^-4
The expression after simplification is -6x¹¹.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is (-4x²) (3x⁵) / (2x⁻⁴).
We have the rule for exponents,
xᵃ . xᵇ = xᵃ⁺ᵇ
xᵃ / xᵇ = xᵃ⁻ᵇ
(-4x²) (3x⁵) = (-4 × 3) x²⁺⁵ = -12x⁷
-12x⁷ / 2x⁻⁴ = (-12 / 2) x⁷⁻⁻⁴
= -6x¹¹
Hence the simplification of the expression (-4x²) (3x⁵) / (2x⁻⁴) is -6x¹¹.
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Help please and thank you and please explain how you got it. It’s #13!
Answer:
-13a +10b
Step-by-step explanation:
[tex]-3a-4b-2(5a-7b)[/tex]
[tex]=-3a-4b-10a+14b[/tex]
[tex]=-13a+10b[/tex]
Hope this helps
Find the quartile
49, 27,10,76, 91, 86, 40, 38, 15, 33, 12, 87, 60, 9, 80
Answer:
uh 6
Step-by-step explanation:
10??????????????????????????6????
The interquartile range?
I believe it is 65.
4
What is angle G?
70°
Step-by-step explanation:
based on you input, I would suggest you divide 70 by 4 to get 17.5.
that is the answer. trust.
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