So for the maximum area, the values of the width and length of the rectangle will be 2.121.
Since we know that the formula for the area of a rectangle is:
A = XY, where x and y are the width and length
since we are given the are, y=√(9-x²), so
A = √(9-x²)
taking the derivative on both sides and considering it to be zero, we get
A' = (x/√(9-x²)(-2x) + √(9-x²) = 0, after multiplying by √(9-x²)
A' = -x² + 9 -x² = 0
=>-2x² =-9
=>x² = 9/2
=> x = 3/√2
so x=2.121 so the for y = √(9-(2.121)^2) = √(9-4.498) = 2.121
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A rectangle is bounded by a semicircle y = radical 9 − x^2 and the x-axis. What length and width should the rectangle be to maximize the area
Which system of linear equations has a solution of (1, –1)? y1 and y2 y1 and y3 y2 and y3 y2 and y4
The system of linear equations which has a solution of (1,-10) is y2 and y4
What are the 3 types of systems of a linear equation?Dependent: There are countless possible solutions to the system. The same lines are depicted on the equation graphs.
Independent: There is only one solution to the problem. The equations' graphs come together at a single point.
Inconsistent: There is no fix for the system.
What are the 3 solutions of systems of linear equation?There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method
line y2 cross line y4 at (1,-1)
Hence the solution is y2 and y4
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I do not know
how to do fractions please help
Answer:
should be the first one because 12 is the common factor between the two of them(had to be 20 characters long so i could answer your question)
A group of friends wants to go to the amusement park. They have $69. 75 to spend on parking and admission. Parking is $17. 25, and tickets cost $17. 50 per person, including tax. Write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.
The equation to determine the number of persons is x/(y+z) and total 2 people are there in total.
What does a math equation mean?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.Given: Several buddies want to visit the theme park. Spending money for parking and entry totals $69.75. Tickets cost $17.50 per person, tax included, and parking is $17.25.
Let,
x = total amount for parking and admission fee
y = ticket per person
z = parking cost per person
Total number of people who can go to the amusement park is given as:
= x/(y+z) =69.75/(17.50+17.25)
= 2
Therefore, the equation to determine the number of persons is x/(y+z) and total 2 people are there in total.
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describe the relationship between the variables in the graph and equation
The equation that describes the proportional relationship between the variables on the graph is given as follows:
y = 12x.
What is the proportional relationship?The general format of a proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality, and hence the output variable y is obtained as the multiplication of the input x and the constant of proportionality k.
One point from the graph given at the end of the answer is given as follows:
(8, 96).
Hence the constant of the proportional relationship is given as follows:
k = 96/8 = 12.
Then the equation is of:
y = 12x.
Meaning that the output variable y is obtained by the multiplication of the input variable x and the constant of proportionality k.
Missing InformationThe graph is given by the image presented at the end of the answer.
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Marta buys x candles and y books at a store.
• Each candle costs $6, and each book costs $14.
• She spends no more than $65.
• She buys more than 8 items total.
Create two inequalities using x and y to model the situation.
The two inequalities that models the situation are as follows:
6x + 14y ≤ 65
x + y > 8
How to use inequalities to model a situation?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.
Marta buys x candles and y books at a store.
Each candle costs $6, and each book costs $14.She spends no more than $65.She buys more than 8 items totalTherefore,
x = number of candlesy = number of booksHence, the inequalities are as follows:
6x + 14y ≤ 65
x + y > 8
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If ƒ(x) = 2x³ – 11x² + 13x − 4 and x − 4 is a factor of f(x), then find all of the
zeros of f(x) algebraically.
Answer:
The zeros of ƒ(x) are 4, 1, and -2.
Complete the program so that it takes in 4 integers (a, b, c, and d) as arguments, stores them in the 2D array nums, and then prints their row, column, and total sums. The program should print the integers according to this formula:
(a) (b) (a+b)
(c) (d) (c+d)
(a+c) (b+d) ((a+b)+(c+d)+(a+c)+(b+d))
// (a+b) is the first row's sum
// (c+d) is the second row's sum
// (a+c) is the first column's sum
// (b+d) is the second column's sum.
// ((a+b)+(c+d)+(a+c)+(b+d)) is the total sum of all rows and columns
The program should print the integers according to this formula is
nums[0][0]=a;
nums[0][1]=b;
nums[1][0]=c;
nums[1][1]=d;
nums[0][2]= nums[0][0] + nums[0][1]; //a+b
nums[1][2]= nums[1][0] + nums[1][1]; //c+d
nums[2][0] = nums[0][0] + nums[1][0]; //a+c
nums[2][1] = nums[0][1] + nums[1][1]; //b+d
//sum = (a+b) + (c+d) + (a+c) + (b+d)
nums[2][2] = nums[0][2] + nums[1][2] + nums[2][0] + nums[2][1];
The nums array is 2 dimensional as shown below.
row, column column 0 column 1 column 2
row 0 a b a+b
row 1 c d c+d
row 2 a+c b+d (a+b)+(c+d)+(a+c)+(b+d)
The first index of an array always starts from 0.
Thus, nums[rows][columns] is used to access each element of the array.
The sum of first row elements is to be stored in the last index of row0, that is in nums[1][2].
Thus we equate nums[0][2] = nums[0][0] + nums[0][1]
Similarly, for 2nd row; nums[1][2] = nums[1][0] + nums[1][1]
The sum of first column is to be stored in last index of column0.
Thus, nums[2][0] = nums[0][0] + nums[1][0]
and for 2nd column,
nums[2][1] = nums[0][1] + nums[1][1].
Thus, the answer is--
-------------------------------------------------------------------------------------------------------------------------------------
nums[0][0]=a;
nums[0][1]=b;
nums[1][0]=c;
nums[1][1]=d;
nums[0][2]= nums[0][0] + nums[0][1]; //a+b
nums[1][2]= nums[1][0] + nums[1][1]; //c+d
nums[2][0] = nums[0][0] + nums[1][0]; //a+c
nums[2][1] = nums[0][1] + nums[1][1]; //b+d
//sum = (a+b) + (c+d) + (a+c) + (b+d)
nums[2][2] = nums[0][2] + nums[1][2] + nums[2][0] + nums[2][1];
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Please! I don't understand this question! Help!
Zachary purchased a computer for $ on a payment plan. months after he purchased the computer, his balance was $. months after he purchased the computer, his balance was $. What is an equation that models the balance y after x months?
write a paragraph explaining any similarities and differences for series solutions about ordinary points and series solutions about singular points.
Ordinary points: Point an is a regular point whenever functions p1(x) having p0(x) are logical at x = a.
Singular points: There are two types of singular points: regular and irregular.
Define the term series solutions for ordinary points?All those other points are common points except for the singular point x0=0.Every point is a regular point if P0 is a nonzero constant, as in Airy's equation, y″−xy=0. P1/P0 and P2/P0 are continuous at every point x0 that is not a zero of P0 for polynomials are continuous everywhere.Whenever functions p1(x) with p0(x) are analytical at x = a, point an is an ordinary point.
Define the term series solutions for singular points?Use the steps below to get a series solution centered on a regular solitary point x0. enter ∞ n=0 cn(x − x0)n+rinto the formula.
Since functions p1(x) with p0(x) are analytical at x = a, point an is an ordinary point. If p1(x) has a pole up to receive 1 at x = a and p0 has a pole with order up to 2 at x = a, then point an is a regular unique point. Point A is just an irregular singular point if left untreated.To know more about the singular point, here
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Carmen made 6 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 6 necklaces was $31.80 . If the beads cost a total of $21.60, how much did each pendant cost?
Answer:
The answer is $1.70
Step-by-step explanation:
What I did is $31.80-21.60=$10.20. $10.20 is the amount of money for all 6 pendants, so to find how much 1 pendant is I just divided $10.20 by 6 which got me $1.70. Hope that helped you. :)
I’ll give you points and brainlest answer if you answer with a legit answer!
answer:
(1/y)^3(1/z)^4
step-by-step explanation:
negative exponents just move the number to the denominator. so all you have to do is move the y & z to the denominator to change the exponents to positive. hope that helps!
state a recursive definition for 2, -2, 2, -2
Answer:
Step-by-step explanation:
Chinese people eat beans so it would be Chinese
people
Given the following piecewise function,
f(3) =
f(8) =
f(-1) =
Answer:
f(3) = 5
f(8) = 3
f(-1) = 0
Step-by-step explanation:
Just plug in the number from the parentheses into the inequalities and whichever makes the inequality true plug into that equation so for example f(3) = ?
first plug 3 into the inequalities: 3 ≤ 0, 0 < 3 ≤ 5, 3 > 5
then find the one that's true which is: 0 < 3 ≤ 5
then plug into the equation that corresponds to that inequality: 2(3) - 1 → 6 - 1 = 5
If a circular flower bed has a diameter of 18ft.
What is the area of the flower bed?
A local deli makes turkey sandwiches and salami sandwiches at a weekly ratio of 2 salami sandwiches for every 5 turkey sandwiches. If the deli makes 60 turkey sandwiches this week, how many salami sandwiches did they make?
1. 5 salami sandwiches
2. 16 salami sandwiches
3. 30 salami sandwiches
4. 24 salami sandwiches
Please answer :)
Answer:
1.5
Step-by-step explanation:
there are unknown number of oranges in a bag. seven oranges in the bag are stale. now you need to pick two oranges out of the bag. the probability to pick two stale oranges is 2/21. what is the total number of the orange in the bag?
The total number of oranges present in the bag was 21.
Explain the term probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages extending from 0% through 100% can be used to describe probabilities.For the stated question.
Let the total number of oranges in the bag be 'x'.
Total stale oranges = 7.
Thus,
Probability (first orange is stale) = Total stale oranges/ Total oranges.
Probability (first orange is stale) = 7/x
Probability (second orange is stale) = 6/(x - 1).
But, probability to pick two stale oranges is 2/21
7/x . 6/(x - 1) = 2/21
On solving,
x ² - x - 441 = 0
x = 21
Thus, the total number of oranges present in the bag was 21.
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let x denote the number of canon slr cameras sold during a particular week by a certain store. the pmf of x is x 0 1 2 3 4 px(x) 0.1 0.2 0.3 0.25 0.15
P(X = 4, Y = 2) = 0.055131
P(X = Y) = 0.35607
From the information given:
X represent no of Canon SLR
The PMF is given as:
X : 0 1 2 3 4
p(x) : 0.1 0.2 0.3 0.25 0.15
p = P(customers that purchase the camera & also purchase an extended warranty.
As a result, the conditional distribution Y provided X approaches a Binomial distribution with n = x and p = 0.55 as the parameter.
[tex]\frac{Y}{X}[/tex] ~ Bin ( n= x , p =0.55) y
= 0.1 ........ x and X = 0,1,2,3,4.
The condition probabilities Y given X is:
[tex]P (\frac{Y = 0}{X = 0} ) =1[/tex]
[tex]P (\frac{Y = 0}{X = 1} ) = 0.45 and P (\frac{Y = 1}{X = 1} ) =0.55[/tex]
[tex]P (\frac{Y = 0}{X = 2} ) = 0.2025 and P (\frac{Y = 1}{X = 2} ) =0.495, P (\frac{Y = 2}{X = 2} ) =0.3025[/tex]
[tex]P (\frac{Y = 0}{X = 3} ) = 0.091125 and P (\frac{Y = 1}{X = 3} ) =0.334125, \\P (\frac{Y = 2}{X = 3} ) =0.408375 and P (\frac{Y = 3}{X = 3} ) = 0.166375[/tex]
[tex]P (\frac{Y = 0}{X = 4} ) = 0.0.041006 and P (\frac{Y = 1}{X = 4} ) =0.0.200475, P (\frac{Y = 2}{X = 3} ) =0.367538[/tex]
[tex]P (\frac{Y = 3}{X = 4} ) = 0.299475 and P (\frac{Y = 4}{X = 4} ) =0.091506[/tex]
Now, the joint P.D (probability Dist.) of X & Y is expressed as:
[tex]P (\frac{Y = y}{X = x} ) = P (\frac{Y = y. X = x}{X = x} )[/tex]
[tex]P( X = x , Y = y) = P(\frac{Y = y}{X =x} ) * P(X =x)[/tex]
The Joint P.D is;
Y Total
0 1 2 3 4
X 0 0.1 0 0 0 0 0.1
1 0.09 0.11 0 0 0 0.2
2 0.06075 0.1485 0.09075 0 0 0.3
3 0.022781 0.083531 0.102094 0.041594 0 0.25
4 0.006151 0.030071 0.055131 0.044921 0.013726 0.15
Total 0.279682 0.372103 0.247974 0.086515 0.013726 1
(a)
P(X=4,Y=2)
From the table above:
P(X=4,Y=2)
= 0.055131
(b)
P(X= Y)
= (P = 0 , Y = 0) + P( X =1, Y =1) + P( X=2, Y=2) + P(X=3,Y=3) + P(X=4,Y=4)
= 0.1 + 0.11 + 0.09075 + 0.041594 + 0.013726
= 0.35607
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a researcher is interested in whether or not a significant trend exists regarding the popularity of certain music played at restaurants. a random sample of 50 customers from each of three restaurants is selected. the customers are asked to indicate which of three music types: country, jazz, and classical they preferred. the results are given for each restaurant by music category. do the results deviate significantly from what would be expected due to chance?
No the results did not deviate significantly from what would be expected due to chance.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
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Patrice is a star player for the UNC women's basketball team. She has injured her ankle and it is doubtful that she will be able to play. If she can play, the coach estimates they will score 78 points. If she is not able to play, the coach estimates they will score 62 points. The team doctor estimates there is a 60-40 chance she will play. Determine the number of points the team can expect to score. Play Not Play P(x) Outcome Expected Value:
If she can play, the coach estimates they will score 78 points. If she is not able to play, the coach estimates they will score 62 points. The team doctor estimates there is a 60-40 chance she will play.
Therefore, P(x) Outcome Expected Value: 71.6 %
Given in the question:
If she is playing, estimate score is 78 points.
If she is not playing, estimated score is 62 points.
chances : 60% to 40%
Therefore, the expected outcome value is :
P(X) = 78 × 60% + 62× 40%
= 71.6%
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HELP FAST WILL GIVE BRAINIEST
Answer:
first this is English
providential
slow congealed
innovative, effectual
more easy to
a local amateur ice skater estimates that the probability she will place first in the next regional competition is 0.56. what are the odds she will win this competition? a) 14 to 39 b) 11 to 14 c) 33 to 17 d) 39 to 14 e) 14 to 11 f) none of the above.
The odds she will win this competition is 14 to 11.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. The potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.Odds in favor of an event is ratio of probability of an event to its completion:
Probability =0.56 / 1-0.56
= 0.56/0.44
= 56/44
= 14/11
Hence, the odds she will win this competition is 14 to 11.
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What is the average rate of change of the functionf(x)=20(14)x from x = 1 to x = 2? enter your answer, as a decimal, in the box. Do not round your answer.
The average rate of change of the function f(x) from x = 1 to x = 2 is, -3.75 when the function f(x)=20(1/4)ˣ.
Given that,
We have to find what is the function f(x)=20(1/4)ˣ average rate of change from x = 1 to x = 2.
We know that,
Average rate of change(A(x)) of f(x) over a interval [a,b] is given by:
A(x)=(f(b)-f(a))/b-a
We get the function:
f(x)=20(1/4)ˣ
Now, the average rate of change from x = 1 to x= 2
At x = 1
Then;
f(1)=20(1/4)¹=5
At x = 2
Then;
f(2)=20(1/4)²=1.25
Substitute these in above formula we have;
A(x)=f(2)-f(1)/2-1=-3.75
Therefore, The average rate of change of the function f(x) from x = 1 to x = 2 is, -3.75 when the function f(x)=20(1/4)ˣ.
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Write a linear function g with the values g(2) = 3 and g(6) = 5
Answer:
g(x)=1/2x+2
Step-by-step explanation:
the coordinates provided here are (2,3) and (6,5)
slope intercept form is g(x)=mx+b
m is slope and b is y intercept
We use slope formula to find slope y2-y1/x2-x1
5-3/6-2
2/4
1/2
Now we can find b by putting the values in
g(x)=1/2x+b
5=1/2(6)+b
5=3+b
-3 -3
2=b
g(x)=1/2x+2
Hopes this helps please mark brainliest
Which of the following binary operations are closed? a. subtraction of positive integers b. division of nonzero integers c. function composition of polynomials with real coefficients d. multiplication of 2×2 matrices with integer entries ​
The goal is to determine whether or not the following binary operations are closed.
A. Subtraction of positive integers: Under normal substation operation, a set of positive integers is not near. Since 1∈Ζ⁺ and 2∈Ζ⁺ but (2-1) = ₋1∉Z⁺.
B. A division of nonzero integers: Non-zero integer set Z/{0} is not closed under the operation. Since 1∈Z/{0} and 2∈ Z/{0} but 1/2 ∉ Z/{0}.
C. Function composition of polynomials with real coefficients: The set of polynomials with real coefficients is closed when using the typical binary operator. Use the obvious conclusion that a polynomial is a combination of two polynomials [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since every polynomial coefficient is real, every polynomial's composition will also have real coefficients.
D. The multiplication of 2×2 matrices with integer entries: Under the action of standard matrix multiplication Μ₂ₓ₂ (Z), the collection of matrices with integer elements, is close.
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in a random sample of 38 restaurants it was found that the mean number of employees was 12.6 with a standard deviation of 2.4 employees. find the critical value used to test the claim that the mean number of restaurant employees is less than 15 at the 1% significance level.
Critical value used to test the claim that the mean number of restaurant employees is less than 15 at the 1% significance level is - 2.431
What is standard Deviation ?The square root of the variance is used to calculate the standard deviation, a statistic that gauges a dataset's dispersion from its mean. The variation from the mean of each data point is used to determine the standard deviation, which is equal to the square root of variance.
What is mean ?It is basically the average of the given numbers.
The given data is
Sample Size = n = 38
Sample mean = X = 12.6
Sample Standard deviation = S = 2.4
= n - 1 = 38 - 1 = 37
μ₀ = μ ≥ 15
μ₁ = μ < 15 ( left tailed )
d = 0.01
Hence, Critical value = - 2,431
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Give a big-o estimate for the number additions used in this segment of an algorithm. T := 0 for i := 1 to n for j := 1 to n t := t + i + j.
The big oh notation for the given algorithm that is T := 0 for i := 1 to n for j := 1 to n t := t + i + j will be O(n).
What is big oh notation?Big O notation is a type of mathematical notation that expresses how a function limits itself when the argument goes to zero or infinity. Big O Notation is a technique for expressing how time-consuming an algorithm is. As the input increases, it calculates how long it will take to perform an algorithm. In other words, it determines an algorithm's worst-case time complexity. The maximum runtime of an algorithm is expressed using the Big O Notation in data structures.
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In the first week of July, a record 1,060 people went to the local swimming pool. In the second week,105 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 199 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
The percent decrease in the number of people who went to the pool over these four weeks is 15%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
The number of people by the fourth week will be:
= 1060 - 105 + 145 - 199
= 901
The percentage decrease will be:
= (1060 - 901) / 1060 × 100
= 159/1060 × 100
= 15%
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S
How could you show QR SR?
O A.
OB.
O C.
OD.
Use SAS to show triangle PRQ is congruent to triangle SRP
Use SAS to show triangle PRQ is congruent to triangle PRS
Use AAS to show triangle PRQ is congruent to triangle PRS
Use ASA to show triangle PRQ is congruent to triangle PRS
We prove that QR≅SR, using SAS to show triangle PRQ is congruent to triangle PRS. So option B is correct.
In the given question;
Given: PR bisects ∠QPS. PQ=12 units, and PS=12 units.
Prove: QR≅SR
We have to find how we prove QR≅SR.
As we can see that;
PQ = PS
Since PR is bisector.
So PR is common in both triangles PRQ and PRS.
PR=PR
Since PR is bisector.
So ∠PRQ=∠PRS
As we know that if two sides and one angle are congruent, then using the Side-Angle-Side (SAS) Theorem, the both triangle is congruent.
So ∠PRQ≅∠PRS
So QR≅SR
Hence, we prove that QR≅SR, using SAS to show triangle PRQ is congruent to triangle PRS. So option B is correct.
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PLEASE HELP ME WITH THIS QUESTION!!!
QUESTION ATTACHED BELLOW
THANKS IN ADVANCE!
Christopher says that whenever you multiply a whole number by a fraction the product is either greater or less than the whole number. Do you agree with Christopher? Why or why not. If not provide an example.
Christopher's statement "whenever you multiply a whole number by a fraction the product is either greater or less than the whole number" is correct.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The statement made by Christopher is correct, this is because a fraction is always either greater or lesser than 1. And multiplying a fraction to a whole number will give result either greater or less than the whole number, depending upon the type of fraction it is.
If the fraction is a proper fraction, than the result will be less than the whole number.If the fraction is a improper fraction, than the result will be greater than the whole number.For example let's take the number 100,
Let's take a proper fraction, 2/5. Therefore, the result will be,
100 × (2/5) = 40
Let's take an improper fraction, 7/5. Therefore, the result will be,
100 × (7/5) = 140
Hence, Christopher's statement is correct.
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