go step by step with this problem.

The common ratio of the second geometric progression is 1/5.

A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant (which is non-zero) to the preceding term. It is represented by:

a, ar, ar2, ar3, ar4, and so on.

Let the common ratio of the second geometric progression be r. Then the sum to infinity of the first progression is:

S1 = a1/(1 - r1), where a1 = 25 and r1 = 1/2

And the sum to infinity of the second progression is:

S2 = a2/(1 - r), where a2 = 40 and r is the common ratio of the second progression

We know that S1 = S2, so we can set the two expressions equal to each other:

S1 = S2

a1/(1 - r1) = a2/(1 - r)

Substituting the given values:

25/(1 - 1/2) = 40/(1 - r)

Simplifying:

50 = 40/(1 - r)

Multiplying both sides by (1 - r):

50 - 50r = 40

Subtracting 50 from both sides:

-50r = -10

Dividing both sides by -50:

r = 1/5

Therefore, the common ratio of the second geometric progression is 1/5.

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Answer:

The answer to your problem is, There are total 55 counters out of which 11 are green and 44 are other color.

Step-by-step explanation:

This is a ratio and proportion question. There are c amount of counters in the box

same ratio as in the box

Green : total

4:         20

11:          x

Use cross product rule

x * 4= 20 *11

x= 20*11/4

x= 55. Which is the answer.

So there are total 55 counters out of which 11 are green and 44 are other color. Benedict take 20 counters out of which 4 are green. 

Thus the answer to your problem is, There are total 55 counters out of which 11 are green and 44 are other color.

In exponential function , after 7 moths approximate user is 45542.

What is exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Here Number of current used = 37,030.

A new social media site is increasing its user base by approximately 3% per month then after 7 month,

Using exponential growth formula then,

=> f(x)=a([tex]1+r)^x[/tex]

=> 37030(1+3%[tex])^7[/tex]

=> 37030[tex](1+\frac{3}{100})^7[/tex]

=> 37030[tex](1+0.03)^7[/tex]

=> 37030[tex](1.03)^7[/tex]

=> 45542

Hence in 7 moths approximate user is 45542.

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The probability that the proportion of persons more than 6 feet tall will differ from the population proportion by more than 5%  is approximately 0.0456.

The standard error of the sample proportion is:

SE = √[(p × (1 - p)) / n]

where p is the population proportion, and n is the sample size.

Substituting the given values, we get:

SE = √[(0.56 × 0.44) / 643] ≈ 0.025

To find the probability that the sample proportion differs from the population proportion by more than 5%, we need to find the z-scores for the upper and lower bounds of the interval:

Lower bound: 0.56 - 0.05 = 0.51

Upper bound: 0.56 + 0.05 = 0.61

z_lower = (0.51 - 0.56) / 0.025 ≈ -2.00

z_upper = (0.61 - 0.56) / 0.025 ≈ 2.00

Using a standard normal distribution table or calculator, we can find the probabilities for these z-scores:

P(Z < -2.00) ≈ 0.0228

P(Z > 2.00) ≈ 0.0228

The probability that the sample proportion differs from the population proportion by more than 5% is the sum of these two probabilities:

P(|p - 0.56| > 0.05) = P(Z < -2.00) + P(Z > 2.00) ≈ 0.0456

Therefore, the probability that the proportion of persons more than 6 feet tall in a random sample of size 643 will differ from the population proportion by more than 5% is approximately 0.0456, rounded to four decimal places.

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The error the student made was not correctly distributing the -3 to the second term (1/3y) inside the parenthesis in Step 1. The student incorrectly wrote -3(1/3y) as -3y instead of -y.

By correctly distributing the -3, the proper simplification would lead to the final answer of y = -12x.

The error the student made in simplifying the equation occurred in Step 1.

To solve the equation 9x = -3(x + 1/3y) for y is as follows:
Step 1: Distribute the -3 to both terms inside the parenthesis:
9x = -3x - y
Step 2: Add 3x to both sides of the equation to isolate the term with y:
9x + 3x = -y
Step 3: Simplify the equation by combining like terms:
12x = -y
Step 4: To solve for y, multiply both sides of the equation by -1:
y = -12x.

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The probability that the Yankees will lose when they score less than 5 runs is 0.805.

What exactly is probability?

Probability is a measure of the possibility of an event to be occurred. It is a numerical value between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain.

Now,

Let's denote the event "Yankees win a game" by W, and the event "Yankees score 5 or more runs in a game" by S. Then, we are given:

P(W) = 0.51

P(S) = 0.59

P(W' and S') = 0.33, where W' denotes the complement of the event W (i.e., Yankees lose a game), and S' denotes the complement of the event S (i.e., Yankees score fewer than 5 runs).

We can use the following formula to find the probability that the Yankees lose when they score fewer than 5 runs:

P(W' | S') = P(W' and S') / P(S')

Using the given values, we have:

P(W' | S') = 0.33 / (1 - 0.59)

= 0.33 / 0.41

≈ 0.805

Rounding to the nearest thousandth, we get:

P(W' | S') ≈ 0.805

Therefore, the probability that the Yankees will lose when they score fewer than 5 runs is approximately 0.805.

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Answer:

The equation of the given circle is (x-2)^2 + (y+3)^2 = 9, which is in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

Comparing the given equation with the standard form, we can see that the center of the circle is (2, -3) and the radius is 3.

Therefore, the radius of the circle is 3 units.

we can multiply 6561m⁴ by 1 to get the final answer of 6561m⁴.

How to solve the problem?

In mathematics, an exponent refers to a numerical representation of repeated multiplication. An exponent is usually written as a small number that appears to the right and above a larger number, called the base. The exponent indicates how many times the base should be multiplied by itself. For example, in the expression 3², the base is 3, and the exponent is 2. This means that 3 should be multiplied by itself 2 times, resulting in 3 multiplied by 3, which equals 9.

Exponents are a shorthand way of representing repeated multiplication and can be used to simplify complicated expressions. They are widely used in algebra, calculus, and other branches of mathematics. Exponents can be positive, negative, or zero, and they can be fractions or irrational numbers. The rules of exponents, such as the product rule and power rule, allow for easy manipulation of expressions involving exponents.

To write (9m)⁴ without exponents, we need to perform the multiplication four times.

First, we can multiply 9m by 9m to get 81m².

Next, we can multiply 81m² by 9m to get 729m³.

Then, we can multiply 729m³ by 9m to get 6561m⁴.

Finally, we can multiply 6561m⁴ by 1 to get the final answer of 6561m⁴.

In summary, (9m)⁴ can be written as 6561m⁴ by performing multiplication four times using the distributive property of multiplication. It is important to note that exponents are a shorthand way of writing repeated multiplication, but the same result can always be obtained by performing the multiplication explicitly. This process may become more cumbersome for larger exponents, which is why exponents are a useful notation for expressing repeated multiplication in a more concise way.

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Answer:

a

Step-by-step explanation:

A tree should therefore have 38,900 leaves on average by the eighth week of spring.

An equation that depicts a linear model on a graph is referred to as a linear equation. This polynomial equation has a factor whose greatest power is one. The formula for a linear equation is y = mx + b, were x and y are factors, m is the line's gradient or slope, and b is the y-intercept, or the place where the line crosses the y-axis. The line's steepness is determined by its slope, and its point of intersection with the y-axis is indicated by its y-intercept. Science and mathematics both frequently model and examine relationships between variables using linear equations.

given

B is the right response for the linear equation y = 4700x + 1500, which can be used to approximate the data distribution.

We may enter x = 8 into the calculation to get the predicted average number of leaves on a tree 8 weeks after spring has begun:

y = 4700(8) + 1500

y = 38,900

A tree should therefore have 38,900 leaves on average by the eighth week of spring.

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The surface area of the square or other shaped barn will be in unit ft² i.e. D.

What are squares?

In mathematics, a square is a geometric shape that has four equal sides and four right angles. It is also known as a regular quadrilateral or a square polygon. The sides of a square are also called edges or vertices. The area of a square is given by the formula A = s², where s is the length of one of its sides.

Now,

Let the barn to be a square or any type of shape.

The farmer can expect to calculate the surface area of the barn in square units, such as square meters or square feet. This means that the correct option is d) ft².

Surface area is the measure of the total area that the surface of an object occupies. It is measured in square units because it involves calculating the area of multiple faces or surfaces of an object. In the case of the barn, the farmer will need to measure the area of each face of the barn that will be painted, such as the walls and roof, and add them together to get the total surface area. This calculation will give the farmer the total area of the barn that needs to be painted and the amount of paint needed to cover the area.

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Answer:

1834 ÷ 334 ≈ 5.49

Since we can't make a fraction of a batch, we can make 5 batches of gumbo. therefore, the solution is

5 batches: 1834÷334

Part B:

For the smaller batches, each batch requires 334 pounds of shrimp. For the larger batches, each batch requires 614 pounds of shrimp.

subtract

614-334 = 280 pounds

divide

1834÷614 ≈ 2.99

Since we can't make a fraction of a batch, we can make 2 larger batches of gumbo.

So, the solution is: 2 fewer larger batches can be made than smaller batches.

The coordinates of the triangle's image in the question serve as an example of transformation and are A(-2,4), B (-3,7), and C (0,6).

The triangle's coordinates are as follows:

(-6,-1), (-5,2) and (-3,0) (-3,0)

The new points are created when the triangle is mirrored over the line y = 2.

(-6,5), (-5,2) and (-3,4) (-3,4)

Then, we use the translation to translate the triangle's picture.

(x,y) -> (x + 3, y +2)

We thus have:

(-6,5) => (-6 + 3, 5 + 2) = (-3,7) (-3,7)

(-5,2) => (-5 + 3, 2 + 2) = (-2,4) (-2,4)

(-3,4) => (-3 + 3, 4 + 2) = (0,6) (0,6)

Hence, the triangle's image's coordinates are A(-2,4), B (-3,7), and C (0,6) respectively.

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Answer:

y= 2 (x - -5/2)^2-39/2 ?

Answer:

No, drawing four aces from a deck of cards does not have the same probability as drawing four 3s.

Step-by-step explanation:

To see why, consider the number of ways to draw four aces from a deck of cards. There are only four aces in the deck, so the first card drawn must be an ace, which has a probability of 4/52 (or 1/13). After the first ace is drawn, there are only three aces left in the deck, so the probability of drawing a second ace is 3/51. Similarly, the probability of drawing a third ace is 2/50, and the probability of drawing the fourth ace is 1/49.

Therefore, the probability of drawing four aces from a deck of cards is:

(4/52) x (3/51) x (2/50) x (1/49) = 0.0000185

On the other hand, there are four 3s in the deck, so the first card drawn must be a 3, which has a probability of 4/52 (or 1/13). After the first 3 is drawn, there are only three 3s left in the deck, so the probability of drawing a second 3 is 3/51. Similarly, the probability of drawing a third 3 is 2/50, and the probability of drawing the fourth 3 is 1/49.

Therefore, the probability of drawing four 3s from a deck of cards is:

(4/52) x (3/51) x (2/50) x (1/49) = 0.0000185

The probabilities are the same for drawing four aces and drawing four 3s because the same process is followed for each scenario: a specific card is drawn, the number of remaining cards decreases by one, and the probability of drawing the next card changes accordingly.

In summary, the probability of drawing four aces from a deck of cards is the same as the probability of drawing four 3s, but they are both very low probabilities because they require drawing specific cards in a specific order from a large deck of cards.

3. The measure of angle S in the given pentagon is 155.33 degrees. 4. The value of x is 9. 5. The value of x is 40 degrees. 6. The value of angle C is 33 degrees. 7. The polygon has 30 sides.

A polygon having 5 sides and 5 angles is called a pentagon. Two terms, Penta and Gonia, both of which denote five angles, combine to form the word "pentagon." End to end, the sides of a pentagon come together to form a shape. Every side of a regular pentagon has the same length, and its five angles are all the same size. A pentagon is said to as irregular if its side length and angle measurement are not equal.

The sum of angles of a pentagon is equal to 540 degrees.

Thus,

5x + 2 + 10x - 3 + 8x - 19 + 13x - 31 + 7x - 11 = 540

42x - 62 = 540

42x = 602

x = 14.33

The angle of s is:

13(x) - 31 = 13(14.33) - 31 = 155.33

Hence, the measure of angle S in the given pentagon is 155.33 degrees.

4. In a regular hexagon, each angle is equal, and the sum of all the angles is equal to 720 degrees.

6A = 720

A = 120

11x + 21 = 120

x = 9

5. The angle of a nonagon is 140 degrees.

Now, 140 + x = 180

x = 80 degrees.

6. For the given triangle we have:

exterior angle of C = D + E

Substituting the value of D and E as:

7x - 2 = 180 - 9x + 31 + 180 - 4x + 33

7x - 2 = 360 - 13x + 64

20x = 426

x = 21.3

Angle C = 180- (7(21.3) - 2) =  33 degrees.

7. single angle = (n-2) x 180 / n

168n = (n - 2) 180

168n = 180n - 360

360 = 12n

n = 30

The polygon has 30 sides.

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The parallelogram therefore has a 3/4 square inch area.

A parallelogram is a geometric figure with four equal sides that are parallel to one another. It has equal opposed angles and two sets of parallel sides.

The base length and height of a parallelogram must be multiplied to determine its area. In this instance, the parallelogram's shorter side is specified as 1 inch and its longer side as 4 inches. It states that the height is 3/4 inch.

Hence, the parallelogram's area is:

Area = base x height

= 1 inch x 3/4 inch

= 3/4 square inches

3/4 square inches is equal to 1 inch by 3/4 inch by the base and height.

The parallelogram therefore has a 3/4 square inch area.

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Answer:

There are multiple statements that can be made about the function y = x^2 - 6x + 8. Here are a few examples: 1. The function is a quadratic function, meaning it is a polynomial of degree 2. 2. The coefficient of the x^2 term is positive, which means the function opens upwards and has a minimum value. 3. The function intersects the y-axis at y = 8. 4. To find the x-coordinate of the vertex of the parabola, we can use the formula x = -b/(2a), where a is the coefficient of the x^2 term and b is the coefficient of the x term. In this case, a = 1 and b = -6, so x = 3. This means the vertex is at the point (3, 1). 5. The function can be factored

Answer:I only know that number 4 is yards i hope that is enough for now

Step-by-step explanation: in a game of soccer there are numbers that represent yards or any sport.

Step-by-step explanation:

a) The appropriate unit of measurement for the surface area of a tissue box could be square inches or square centimeters.

b) The appropriate unit of measurement for the amount of space in a gift box of earrings could be cubic inches or cubic centimeters.

c) The appropriate unit of measurement for the area of a parking lot could be square meters, square feet, depending on the size of the parking lot.

d) The appropriate unit of measurement for the length of a soccer field could be meters, yards or feet.

e) The appropriate unit of measurement for the volume of a medium-sized fish tank could be liters or cubic feet.

1. The cannonball is at 70 meters before it is launched.

2. The cannonball reaches its maximum height at about 3 seconds.

3. The maximum height of the cannonball is about 115 meters.

4. It takes about 8 seconds for the cannonball to reach the ground.

I don't know the answer to number 5 - sorry :(

I hope the rest are correct

[tex]f(-2) = -4[/tex] for the given piecewise function by using the equation [tex]f(x) = x - 2[/tex]  if   [tex]x < 3.[/tex]

A piecewise function is a mathematical function that is defined differently on different parts of its domain.

Instead of having a single formula that applies to the entire domain, a piecewise function has multiple formulas, each applying to a specific interval or subset of the domain.

To find f(-2) for the given piecewise function, we need to determine which piece applies to the input value o  [tex]f -2[/tex], which is less than 3. Therefore, we use the first piece of the function, which is[tex]f(x) = x - 2 if x < 3.[/tex]

Substituting x = -2 into this piece, we get:

[tex]f(-2) = (-2) - 2 = -4[/tex]

Therefore, f(-2) = -4 for the given piecewise function.

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Value of variable x in the given triangle is 10 units.

Triangle proportionality refers to the relationship between the sides of two similar triangles. Similar triangles are those that have the same shape but may differ in size.

In similar triangles, the corresponding sides are in proportion, which means that the ratio of the lengths of any two corresponding sides is equal to the ratio of the lengths of any other pair of corresponding sides.

In the given figure;

Two lines of the triangle are parallel

By triangle proportionality rule,

AB/AC=AD/AE

7.6/11.6=19/19+x

7.6(19+x)=19×11.6

x=29-19

x=10

hence, value of variable x in the given triangle is 10 units.

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Answer:

We can use the formula for the average (arithmetic mean) of a set of numbers to solve this problem:

Let's call the missing number x. Then the sum of the numbers in the list is:

We want the average of this list to be 12, so we can set up the following equation:

Multiplying both sides by 6, we get:

Subtracting 52 from both sides, we get:

Therefore, the missing number is 20, and the complete list is:

The average of this list is:

So, the hose can complete the job alone in approximately 2.62 hours, and the inlet pipe can complete the job alone in approximately 1.62 hours.

Let the time it takes for the hose alone to fill the pond be H hours, and the time it takes for the inlet pipe alone be P hours. According to the given information:

1) P = H - 1 (The inlet pipe alone can complete the job in one hour less time than the hose alone)

2) In one hour, the hose fills 1/H of the pond, and the inlet pipe fills 1/P of the pond. Together, they can fill the pond in one hour, so: (1/H) + (1/P) = 1

Now, substitute the value of P from equation 1 into equation 2:

(1/H) + (1/(H-1)) = 1

To solve for H, first find a common denominator (H*(H-1)):

(H-1) + H = H*(H-1)

Combine the terms on the left:

2H - 1 = H^2 - H

Rearrange to form a quadratic equation:

H^2 - 3H + 1 = 0

Now, solve the quadratic equation using the quadratic formula:

[tex]H = (3 + sqrt(5))/2 or H = (3 - sqrt(5))/2[/tex]

However, since H > 0, the only valid solution is H = (3 + sqrt(5))/2 ≈ 2.62 hours.

Now, find the time it takes for the inlet pipe alone to complete the job:

P = H - 1 = 2.62 - 1 = 1.62 hours

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Answer:

444 in

Hope this helps!

Step-by-step explanation:

Area of a triangle is [tex]\frac{1}{2}[/tex] × B × H

Already given, the base is 12 and the height is 12.5, [tex]\frac{1}{2}[/tex] and 12 can simplify to get 6 so 6 × 12.5 is 75. One triangle has the area of 75, the 4 triangles have a total area of 300.

The base is a square, so the formula for that is L × W, which would be 12 × 12 = 144. Add that to 300 and the surface area of the pyramid is 444.

Answer:

(2,1)          (2,1)

1=5(2)-9   1=-2(2)+5

1=10-9      1=-4+5

Step-by-step explanation:

Hope this helps!!

Mark me brianliest :))

The total commission Sylvia will earn over the first three years is $1,500.

Let's assume the commission rates are X% for the first year, Y% for the second year, and Z% for the third year.

Calculate the yearly commission amounts
To calculate Sylvia's yearly commission, we'll multiply the insurance plan cost (6,000) by the respective commission rate for each year.
First-year commission = 6,000 * (X / 100)
Second-year commission = 6,000 * (Y / 100)
Third-year commission = 6,000 * (Z / 100).

Calculate the total commission over three years
To find the total commission Sylvia will earn over the first three years, we'll add the yearly commission amounts calculated.
Total commission = First-year commission + Second-year commission + Third-year commission.

To calculate the commission Sylvia will earn over the first three years, we need to use the commission rates for each year:

In the first year, Sylvia will earn a 10% commission on the $6,000 plan, which is $600.

In the second year, Sylvia will earn an 8% commission on the $6,000 plan, which is $480.

In the third year, Sylvia will earn a 7% commission on the $6,000 plan, which is $420.

Therefore, the total commission Sylvia will earn over the first three years is:

$600 + $480 + $420 = $1,500

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Question: Sylvia earns commission on insurance sales. She sold a plan that costs 6,000 per year. Based on the chart, how much commission will Sylvia earn from this sale over the first three years?

Commission Schedule.

Year         Rate

1 st                10

2 nd              8%

3 rd               7%

We can follow these steps using the points provided in the table and for Terrance to determine which diver ascended at a faster rate and by how much.

To determine which diver ascended at a faster rate, we need to calculate the slope of the line for each diver's ascent. The slope represents the rate of change in depth over time.

A steeper slope indicates a faster ascent.
Step 1: Find the slope of Bailey's ascent using the points given in the table.

we can use the slope formula:

(y2 - y1) / (x2 - x1).
Step 2: Find the slope of Terrance's ascent using the two points given for Terrance.
Step 3: Compare the slopes of both divers.

The diver with the steeper slope (greater slope value) ascended at a faster rate.
Step 4: To determine how much faster the faster diver ascended, subtract the smaller slope value from the larger slope value.
Without the actual data points, I cannot provide specific calculations.

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Part A : From Angle Angle similarity, ΔMBR and ΔZLP are similar.

Part B.: As the ratios of sides are not equal, triangles are not similar.

Congruent triangles and similar triangles are two different  but closely related concepts. Similar triangles are any two or more triangles having the identical proportions of their corresponding sides, an equal pair of corresponding angles, and their similar shape.

Part A:

using the equal sides property of triangle:

In ΔRBM,

side BM  = side RM

So,

angle B = angle R    (eq 1)

In triangle ZLP and  PL =  LZ

So, angle P = angle Z        (eq 2)

And angle B  =  angle P

∠B = ∠R = ∠P = ∠Z

By Angle Angle similarity, triangle RBM and triangle ZLP are similar.

Part 16.:

In right angle triangle:  KLN.

(KL)² = LN² + KN²

(KL)² = 8² + 15²

(KL)² = 64 + 225

(KL)² = 289

(KL) = 17

taking the ratios of sides:

27/8 = 30.6/17

3.375 ≠ 1.8

As the ratios of sides are not equal, triangles are not similar.

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Part A:The volume of cat food in the can is approximately 9.62 cubic inches.

Part B:The ratio of cubic inches to ounces is approximately 1.66:1.

Volume is a measure of the amount of space occupied by an object or a substance. It is the quantity of three-dimensional space enclosed by a closed surface or bounded by a given set of points. Volume is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).

PART A:

The volume of a cylinder can be calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height. Since the diameter of the can is 3.5 inches, the radius is half of that, or 1.75 inches. The height of the can is 1 inch.

Plugging these values into the formula, we get:

V = π(1.75)²(1)

V ≈ 9.62 cubic inches

Therefore, the volume of cat food in the can is approximately 9.62 cubic inches.

PART B:

To write a ratio of cubic inches to ounces, we need to divide the volume of the can (in cubic inches) by the weight of the cat food (in ounces):

Ratio = Volume of cat food in can (cubic inches) / Weight of cat food (ounces)

Ratio = 9.62 cubic inches / 5.8 ounces

Ratio ≈ 1.66 cubic inches per ounce

Therefore, the ratio of cubic inches to ounces is approximately 1.66:1.

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