Final answer:
To set up a profitable computer repair business, assuming $50 for parts per repair and a service fee of $150, the weekly expenses equation is y = 50x + 500, and income equation is y = 150x, where x is the number of repairs.
Explanation:
When starting a computer repair business with estimated expenses of $500 per week, it's crucial to set average costs for replacement parts and fees for services to ensure profitability. Let's assume an average cost of $50 for parts per computer repaired and a service fee of $150 per repair. If x represents the number of computers you repair each week, your total weekly expenses for parts would be 50x plus the fixed expenses of $500, resulting in a total expense equation of y = 50x + 500. Your total weekly income can be modeled by the equation y = 150x, with each repair contributing $150 to the income.
To break even or make a profit, the total income must exceed total expenses, leading to an analysis based on the number of repairs done weekly. This practical application of linear equations in a business setting helps in budgeting, pricing strategies, and understanding economic principles behind running a service-based business. Monitoring these variables is key to achieving sustainability.
Ivan's favorite colors are \blue{\text{blue}}blue and \green{\text{green}}green. He has \blue{\text{1 blue shirt}}1 blue shirt, \green{\text{1 green shirt}}1 green shirt, \blue{\text{1 blue hat}}1 blue hat, \green{\text{1 green belt}}1 green belt, \blue{\text{1 blue pair of pants}}1 blue pair of pants, and \green{\text{1 green pair of pants}}1 green pair of pants. Ivan selects one of these garments at random. Let A be the event that he selects a green garment and B be the event that he chooses a pair of pants. What is P(A\text{ or }B)P(A or B), the probability that the garment Ivan chooses is either green or a pair of pants?
Answer:
P(A or B) = 2/3
Step-by-step explanation:
Blue Garments = 1 blue shirt, 1 blue hat, 1 blue pair of pants
Total blue garments = 3
Green garments= 1 green shirt, 1 green hat, 1 green pair of pants
Total green garments = 3
Total no. of garments = blue garments +green garments = 6
A = event that Ivan selects a green garment
P(A) = Favourable outcomes/Total no. of outcomes
P(A) = 3/6
B = event that Ivan chooses a pair of pants
P(B) = 2/6
We need to find P(A or B) = P(A∪B)
By formula, P(A∪B) = P(A)+P(B)-P(A∩B)
P(A∩B) = Probability that a green pair of pant is chosen = 1/6
P(A∪B) = 3/6+2/6-1/6
= 4/6
=2/3
Answer:
1/2
Step-by-step explanation:
Vanessa earns a base salary of \$400.00$400.00 every week with an additional 5\%5% commission on everything she sells. Vanessa sold \$1650.00$1650.00worth of items last week. What was Vanessa's total pay last week?
Answer:
Total pay = 400+ 1650* 5/100= 482,5 $
Step-by-step explanation:
Patty earns a raise of 4precent each year .If her starting salary is 24,812.00 , what will be her salary after one year?
Saul simplifies the expression 2x3 + 4x3 to 6x6. Use the drop-down menus to complete the statements below to explain why Saul's solution is correct or incorrect.
Answer:
Saul is incorrect. The proper answer should be 6x^3
Step-by-step explanation:
Think of "x^3" as "x". So we have 2x+4x = 6x. Similarly, 2x^3+4x^3 = 6x^3. The exponents of the like terms do not change.
As a more real world example, let's say that we replace "x^3" with "dogs". Saying "2x^3" could mean "2 dogs". Same goes for "4x^3" meaning "4 dogs". So "2x^3+4x^3" turns into "2 dogs + 4 dogs", and you can see that leading to 6 dogs total. The last step is to replace "dogs" with "x^3" to end up with 6x^3. The x^3 stays the same the whole time in much the same way that "dogs" do not change either.
Answer:
saul is incorrect
2x3 + 4x3 is the same as (2 . x^3) + (4 . x^3)
6x6 is the same as 6x . x. x. x. x. x
2x3 + 4x3 simplifies to 6x^3
Step-by-step explanation:
Which of the following functions best describes this graph
Answer: Choice C)
y = (x-2)(x-2)
note: This is the same as y = (x-2)^2
======================================================
The x intercept or root is x = 2, so x-2 is a factor. There is only one root visible, but this is a parabola, so it's technically a double root (it repeats itself). That is why (x-2) shows up twice giving (x-2)(x-2)
If the equation was simply y = x-2, then it would be a linear equation instead of a curved parabola.
Note how plugging in x = 2 leads to the following y value
y = (x-2)(x-2)
y = (2-2)*(2-2)
y = 0*0
y = 0
So (2,0) is the only x intercept.
Find the coordinates of the midpoint of the segment whose endpoint are H(9,4) and K(7,2)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad K(\stackrel{x_2}{7}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{7+9}{2}~~,~~\cfrac{2+4}{2} \right)\implies (8,3)[/tex]
Solve f/a+r=m/s for m
Answer:
d. m = fs/ (a+r)
Step-by-step explanation:
f/ (a+r) = m/s
We want to isolate m, so we will multiply both sides by s
f/ (a+r) *s= m/s*s
fs/ (a+r) = m
[tex]\dfrac{m}{s}=\dfrac{f}{a+r}\qquad\text{multiply both sides by}\ s\neq0\\\\\boxed{m=\dfrac{fs}{a+r}}[/tex]
If a town with a population of 10,000 doubles every 14 years, what will the population be in 42 years and is it modeled by a linear function or an exponential function? A) 30,000; linear function B) 60,000; exponential function C) 72,000; linear function D) 80,000; exponential function
Answer: D) 80000; exponential function
Step-by-step explanation:
It would double 3 times in total; first from 10k to 20k, then from 20k to 40k, and finally from 40k to 80k. Hope this helps
Answer:
D)80,000; exponential function
Step-by-step explanation:
We are given that a town with a population of 10,000 doubles every 14 years
So, Initial Population = 10,000
Now we are given that what will the population be in 42 years
First determine how many times population will double : [tex]\frac{42}{14} = 3[/tex]
So, In 42 years it doubles three times .
Now Linear functions change at a constant rate per unit interval while An exponential function changes by a common ratio over equal intervals.
So, the given situation will be modeled by exponential function
So, Using exponential function : [tex]y=ab^x[/tex]
Where a is Initial Population = 10,000
b is rate of change
x = time = 3 times
So, the population will be in 42 years=[tex]10000 (2)^3[/tex]
=[tex]80000[/tex]
So, the population will be 80,000 after 42 years.
Thus Option D is correct.
D)80,000; exponential function
A company manufactured 1,287 drones last year. The company shipped 2 percent of those drones to Australia. How many drones did the company ship to Australia? Round your answer to the nearest whole drone.
A school board has determined that there should be 4 teachers for every 50 students. How many teachers are needed for an enrollment of 2,650 students?
Answer:
212 teachers are needed for an enrollment of 2,650 students.
Step-by-step explanation:
This is a kind of question that can be solved using proportions.
Proportions are used when we are asked about finding one unknown value, knowing the value of others that keep a ratio among all of them, including the unknown value.
In this case, we know that a school board estimated that 4 teachers are needed for every 50 students:
[tex]\\ \frac{4_{teachers} }{50_{students}}=ratio[/tex]
If we divide 4 teachers by 50 students, we obtained a ratio, or a constant relationship that remains between teachers and students, that is, how many teachers are needed for the number of students, or more generally "how many times the first number contains the second" [Wikipedia, 2019].
We can also notice that more students require more teachers (which is a relation of direct proportionality), that is, if we require more students, more teachers are also required in the same ratio or constant already mentioned.
Then, we can make a proportion among these values because they keep the same ratio of teachers to students (but can also be students to teachers).
So, we can pose the following question:
If four (4) teachers are needed for every 50 students, how many teachers are needed to attend 2,650 students? Then,
[tex]\\ \frac{4_{teachers}}{50_{students}} = \frac{X_{teachers}}{2650_{students}} [/tex] = the same ratio or constant.
To know the amount of teachers needed for 2,650 students:
[tex]\\ X_{teachers} = \frac{2650_{students} * 4_{teachers} }{50_{students}}[/tex].
or,
[tex]\\ X_{teachers} = \frac{2650 * 4_{teachers} }{50}[/tex].
[tex]\\ X_{teachers} = 212_{teachers}[/tex].
So, for an enrollment of 2,650 students there should be 212 teachers, according to the ratio (teachers/students) previously determined by the school board.
Please help! Im so dumb ( -̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥᷄ ω-̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥̥᷅ )
Look at both pictures!
I need two answers!
ANSWER:
For the first picture, it is the first answer. This is because of the Exterior Angle Theorem.
For the second picture, use the Exterior Angle Theorem again, but this time, solve for x.
[tex]132 = x + (3x-24)\\132 = 4x - 24\\156=4x\\x=39[/tex]
The m∡B = 39°
Amanda put $1500 in her savings account. After five years she had $1833 in the account. What rate of interest did she earned use the formula a equals PE to the power of rt and t is time and
Answer: 4.01% interest rate
This value is approximate. It is rounded to the nearest hundredth of a percent.
============================================
Work Shown:
A = P*e^(r*t)
1833 = 1500*e^(r*5)
1833/1500 = e^(5r)
1.222 = e^(5r)
e^(5r) = 1.222
5r = Ln(1.222)
5r = 0.2004888607494
r = 0.2004888607494/5
r = 0.04009777214989
r = 0.0401
r = 4.01%
Paul uses 2 and 1/4 cups of raisins to make 4 servings of trail mix. How many cups raisins are in each serving?
Answer:
9/16
Step-by-step explanation:
(2+1/4)/4=(8/4+1/4)/4=(9/4)(1/4)=9/16
What is the area of this parallelogram? 4.9 cm? 12.25 cm? 17.15 cm? 24.01 cm? Parallelogram A B C D is composed of a square and two triangles. The square has a length and height of 3.5 centimeters each. There are two identical triangles. Each triangle has a base of 1.4 centimeters and a height of 3.5 centimeters.
Answer:
(C) 17.15
Step-by-step explanation:
The graph shows calories compared to grams of protein.
What information can you draw from the point (3, 12) on the graph?
A. There are 12 calories in 3 grams of protein.
B. There are 3 calories in 1 gram of protein.
C. There are 3 calories in 12 grams of protein.
D. There is 1 calorie in 4 grams of protein.
Answer:
By the looks of it i would assume 3 grams of protein and 12 calories burned but i am not sure either i am stuck on the same question
Step-by-step explanation:
Shelly is trying to improve her running time for a track race she ran the first race in 43.13 seconds her time was 43.1 seconds in the third race of this pattern continues what will Shelly time will be inthe fourth race
Answer:
The time in the fourth race is 43.04 seconds.Step-by-step explanation:
Shelly's first race time is 43.13 seconds.
Shelly's second race times is 43.1 seconds.
Basically, she improved 0.03 seconds, because 43.13 - 43.1 = 0.03.
If she keeps this patterns that means she will improve 0.03 each race.
So, the third race times is 43.1 - 0.03 = 43.07 seconds.
The fourth race time is 43.07 - 0.03 = 43.04 seconds.
Therefore, the time in the fourth race is 43.04 seconds, because she's improving at a constant rate of 0.03 seconds per race.
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
The polynomial function y = x^3 -3x^2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros of the function?
Answer: B
Step-by-step explanation:
x³ - 3x² + 16x - 48 = 0
→ x²(x - 3) + 16(x - 3) = 0
→ (x² + 16) (x - 3) = 0
→ (x² - (-16)) (x - 3) = 0
→ (x - 4i)(x + 4i)(x - 3) = 0
→ x - 4i = 0 x + 4i = 0 x - 3 = 0
→ x = 4i x = -4i x = 3
2 imaginary roots and 1 real root
An experiment consists of randomly selecting a marble from a bag, keeping it, and then selecting another marble. The bag contains 4 blue marbles, 3 green marbles, 7 red marbles, and 1 yellow marble. What is the probability of selecting a red marble and then a blue marble? SHOW ALL WORK!
Answer:
2/15
Step-by-step explanation:
How many marbles are in the bag
4blue + 3 green + 7 red + 1 yellow = 15 marbles
On the 1st draw:
red/total = 7/15
Since we keep the marble, there are only 14 marbles left
4blue + 3 green + 6 red + 1 yellow = 14
On the 2nd draw:
blue/total = 4/14 = 2/7
To find the probability of the two draws, we multiply them together
1st draw * 2nd draw
7/15 * 2/7 = 2/15
I need help with this question 15 points
Answer:
Third option
Step-by-step explanation:
You are correct, right angle forms a 90°
Hope that helps
Answer:
The third option.
Step-by-step explanation:
The first option is acute becuase the angle is less that 90 degrees.
The second options is obtuse because it is more than 90 degrees.
The third option is a right angles becuase it makes an 90 degree angle.
The fourth option is also obtuse because it is more than 90 degrees.
What is the domain of f/g, given f(x)=x+2 and g(x)=x-7?
Answer:
(-∞,7) U (7,∞)
Step-by-step explanation:
f(x)= x+2
g(x) = x-7
[tex]\frac{f(x)}{g(x)} =\frac{x+2}{x-7}[/tex]
Here we have x-7 in the denominator
To find domain we set the denominator =0 and solve for x
x-7=0
Add 7 on both sides
x=7
x=7 makes the denominator 0 that is undefined
So we ignore 7 for x
Hence domain is
(-∞,7) U (7,∞)
Answer:
The correct answer i believe is A.
Mr. Ramirez receives 4 sets of books each set has 16 fiction books and 14 nonfiction books he puts 97 books in his lilbarry and donates the rest how many books does he donate
Mr. Ramirez donates 23 books.
Explanation:To find the number of books that Mr. Ramirez donates, we first need to calculate the total number of books he receives. Since each set has 16 fiction books and 14 nonfiction books and he receives 4 sets, the total number of books he receives is 4 sets * (16 fiction books + 14 nonfiction books) = 4 * (16 + 14) = 4 * 30 = 120 books.
Since Mr. Ramirez puts 97 books in his library, he donates the remaining books. To find the number of books he donates, we subtract the number of books he keeps from the total number of books he receives: 120 books - 97 books = 23 books.
Therefore, Mr. Ramirez donates 23 books.
Learn more about Number of books donated here:https://brainly.com/question/7392128
#SPJ12
Mr. Ramirez donates 23 books.
Explanation:To find out how many books Mr. Ramirez donates, we need to first calculate how many books he receives in total.
Each set has 16 fiction books and 14 nonfiction books, so each set contains 16 + 14 = 30 books.
Since Mr. Ramirez receives 4 sets, he receives a total of 4 x 30 = 120 books.
We know that Mr. Ramirez keeps 97 books in his library, so he donates the rest.
To find out how many books he donates, we subtract the number of books kept from the total number of books received:
120 - 97 = 23 books.
Learn more about Donation of books here:https://brainly.com/question/15502833
#SPJ12
A shoe store marks up it's merchandise by 8 percent what was the selling price of a pair of shoes whose wholesale price is 24.50
The answer is 26.46. I got it correct on my GoFormative.
The price of shoe store merchandise after markup price will be equal to 26.46.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given data given in the question,
The wholesale price of merchandise = 24.50
Markup percentage on merchandise = 8%
Then, the amount of increment in the price will be,
(24.50 × 8)/100
= 196/100
=1.96
Then, the price of merchandise after markup will be,
= 24.50 + 1.96
= 26.46
To know more about Percentage:
https://brainly.com/question/29306119
#SPJ5
Which input value produces the same output value for the two functions on the graph?
X= -3
X= -1
X= 1
X= 3
Answer:
X=3
Step-by-step explanation:
We have two linear functions which intersect at a point. Linear functions are lines which are made of points that satisfy the function or relationship. This means at the intersection, this point (3,-1), both functions have values. An input of x=3 produces y=-1 in both functions.
Answer:
The correct option is 4.
Step-by-step explanation:
If the graph of a function represent in coordinate plane, then x-axis represents the domain of the function and y-axis represents the range of the function.
We have to find the input value that produces the same output value for the two functions on the graph.
From the given graph it is clear that the intersection point of both functions is at (3,-1).
At x=3 the output value of f(x) is -1.
At x=3 the output value of g(x) is -1.
It means both functions have same output -1 at x=3.
Therefore the correct option is 4.
HELP!!!!!!! 100 POINTS PLS HALP
Isaac is purchasing two pairs of shoes—one pair for $37.00 and the second pair for $42.00. The state sales tax applied to Isaac’s bill is 7%. How much is Isaac’s total bill? Show your work.
ANSWERED^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 84.53
If Isaac uses a coupon entitling him to a 25% discount off the purchase price before tax, how much will his bill be? Assume that a 7% sales tax is applied to the discounted price. Using words, explain how you found the discounted price.
ANSWERED ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 63.4
The shoe store’s clerks are paid on commission. If the clerk receives a 12% commission on total purchase amounts before tax is applied, how much would the commission be for Isaac’s purchase with and without a coupon?
NOT ANSWERED^^^^^^^^^^^^^^^^^^^^^^^ Pls help
Answer:
7.11 and 9.48
Step-by-step explanation:
.12 is equal to 7.11
with out coupon
.12 is equal to 9.48
with the coupon
a. Isaac's total bill is $84.53
b. Isaac's price after the discount is $63.40
c. The shoe store clerk's commission before the coupon is $9.48 and $7.11 after the coupon
Solution to the first question
Total bill = cost of shoes + tax paid
Tax paid = tax rate + cost of shoes
Cost of shoes = $37.00 + $42.00. = $79
Tax paid = $79 + 0.07 = $5.53
Total bill = $5.53 + $79 = $84.53
Solution to the second question
The discounted price of the shoes can be found by subtracting the value of the discount from the price of the shoes
Discounted price = cost of the shoes = value of the 25% discount
Value of the 5% discount = 0.25 x $79= $19.75
Discounted price = $79 - $19.75 = 59.25
Bill = discounted price x ( 1 + tax rate)
59.25 x 1.07 = $63.40
Solution to the third question
Commission before the coupon
Commission = 12% x price before the coupon
0.12 x $79 = $9.48
Commission after the coupon
Commission = 12% x price after the coupon
0.12 x 59.25 = $7.11
A similar question was solved here : https://brainly.com/question/19096727?referrer=searchResults
What is the relationship between the ratios? 48/72 and 6/9 Drag and drop to complete the statement.
a. proportional
b. not proportional
write the first five terms of the geometric sequence with a1=-2 and common ratio r=-5/2
Answer:
option D
Step-by-step explanation:
First term is -2
common ratio = -5/2
To get second term we multiply first term -2 by common ratio -5/2
[tex]-2 * \frac{-5}{2} =\frac{10}{2} = 5[/tex]
To get third term we multiply second term 5 by common ratio -5/2
[tex]5 * \frac{-5}{2} =\frac{-25}{2}[/tex]
To get fourth term we multiply third term -25/2 by common ratio -5/2
[tex]\frac{-25}{2}*\frac{-5}{2} =\frac{125}{4}[/tex]
Option D is correct
The first five terms of the geometric sequence with a first term of -2 and a common ratio of -5/2 are -2, 5, -12.5, 31.25, and -78.125.
To find the terms of a geometric sequence, we start with the first term and multiply each subsequent term by the common ratio. In this case, the first term, a1, is -2 and the common ratio, r, is -5/2.
The first term (a1) is -2
The second term (a2) is -2*(-5/2) = 5
The third term (a3) is 5*(-5/2) = -12.5
The fourth term (a4) is -12.5*(-5/2) = 31.25
The fifth term (a5) is 31.25*(-5/2) = -78.125
Therefore, the first five terms of the sequence are -2, 5, -12.5, 31.25, and -78.125.
For more such questions on geometric sequence, click on:
https://brainly.com/question/34721734
#SPJ6
Carl rode a horse about 15 f ode a horse about 15 feet from the center of the car om the center of the carousel. Allison r ousel. Allison rode a horse about 10 f a horse about 10 feet from the center om the center. How much fur . How much further did Carl' ther did Carl's horse s horse travel in one complete turn of the carousel?
Carl's horse traveled approximately 31.4 feet further than Allison's horse in one complete turn of the carousel. The distances were calculated using the circumference formula for each horse based on their distance from the centre of the carousel.
Explanation:The question involves comparing the distances traveled by horses on a carousel based on their distance from the center of the ride. To find out how much further Carl's horse traveled compared to Allison's, we need to calculate the circumference of the circular paths each horse took during one complete turn of the carousel and then find the difference between these two distances.
To calculate the circumference (C) of a circle, we use the formula C = 2πr, where π (pi) is approximately 3.14159 and r is the radius of the circle, in this case, the distance from the center of the carousel to the horse.
For Carl's horse:
CCarl = 2π(15 feet) ≈ 2π×15 ≈ 94.2 feet
For Allison's horse:
CAllison = 2π(10 feet) ≈ 2π×10 ≈ 62.8 feet
The difference in the distances traveled by the horses in one complete turn is CCarl - CAllison, which is approximately 94.2 feet - 62.8 feet = 31.4 feet. Therefore, Carl's horse travelled about 31.4 feet further than Allison's horse in one complete turn.
Ms. Miller wants to give each of her students 1/4 of a pound of modeling clay. She has 26 students. How many pounds of modeling clay does she need?
A) 6
1
2
B) 8
3
4
C) 13
D) 26 what the answer
Answer:
she give each kid about 6
Step-by-step explanation:
26/.25=104
104/16= 6.5
From 19801980 to 20002000, the annual profit of a company was determined by subtracting from \$625{,}000$625,000 the product of \$25{,}000$25,000 and the number of years either before or after 19901990. Which of the following equations below could be used to determine in which year, xx, the profit was \$550{,}000$550,000?
a.550−25∣x−1990∣=625
b.625 - 25 | x - 1990 | = 550625−25∣x−1990∣=550
c.625 +25 | x - 1990 | = 550625+25∣x−1990∣=550
d.625 +25 | x + 1990 | = 550625+25∣x+1990∣=550
Answer: b) 625 - 25 |x - 1990| = 550
Step-by-step explanation:
According to the question,
The annual profit of a company was determined by subtracting from $625,000 the product of $25,000 and the number of years either before or after 1990.
That is, On x year the total profit is,
P(x) = 625,000 - 25,000 |x - 1990|
But again according to the question,
On x years the profit is $ 550,000
Thus, 625,000 - 25,000 |x - 1990| = 550,000
⇒ 625 - 25 |x - 1990| = 550 ( by dividing both sides by 1000)
Therefore, Option b) is correct.
The correct equation for determining the year when the profit was $550,000 is 625 - 25 | x - 1990 | = 550, where x represents the year, option B.
The annual profit of the company can be determined by the equation that subtracts the product of a certain amount ($25,000) and the number of years before or after 1990 from $625,000. If we are given that the profit was $550,000 in year x, we need to find the value of x that satisfies this condition. We will represent the difference in years as the absolute difference from 1990, which accounts for years before and after 1990 equally.
The correct equation based on this would be the one that represents the profit ($550,000) after subtracting the product of $25,000 and the absolute difference in years from $625,000. Thus, the correct equation should subtract from $625,000 (not add to it), and it should involve the absolute value of x - 1990 to denote the number of years before or after 1990.
The equation that fits these criteria is:
625 - 25 | x - 1990 | = 550
Here, when we solve for x, we're trying to find the year in which the profit was $550,000. Therefore, option (b) is the correct choice.
Which table shows a proportional relationship between x and y?
x 3 9 10 15
y 1 3 4 5
x 4 6 8 10
y 6 8 10 12
x 1 5 8 10
y 15 75 120 150
x 2 3 5 6
y 3 4 7 9
Answer:
the third table listed here
Step-by-step explanation:
A "proportional" relationship has the same y/x ratio for all values of x and y.
... first table: all entries but one have y/x = 1/3. The 3rd entry has y/x = 0.4—not the same.
... second table: 6/4 ≠ 8/6
... third table: all entries reduce to y/x = 15
... fourth table: 3/2 ≠ 4/3