Round 472.529996081 to the nearest ten.

The 12.5% of the data values fall between 114 and 133, inclusive,  37.5% of the data values are 119 or greater and 40% of the data values are 128 or less.

To create a frequency distribution table, we first need to determine the range of the data and the number of classes. The range of the data is the difference between the maximum and minimum values. In this case, the minimum value is 104, and the maximum value is 143. The range is therefore 143 - 104 = 39.

To determine the number of classes, we can use a rule of thumb suggested by Sturges' formula: k = 1 + 3.322 log(n), where k is the number of classes and n is the number of data points. In this case, we have 40 data points, so k = 1 + 3.322 log(40) ≈ 6. We can choose to use 8 classes to provide a more detailed distribution.

Based on the range and the number of classes, we can create the following frequency distribution table:

Class     Frequencies    Class Midpoints   Class Boundaries    Relative                               Frequencies

----------------------------------------------------------------------------------------------

104-108       2                106                103.5-108.5                5

109-113        4                111                108.5-113.5                   10

114-118         5                116                113.5-118.5                  12.5

119-123        2                121                118.5-123.5                    5

124-128       3                126                123.5-128.5                7.5

129-133       4                131                128.5-133.5                   10

134-138       3                136                133.5-138.5                  7.5

139-143       3                141                138.5-143.5                   7.5

(b) The class that includes the values between 114 and 133, inclusive, is the class 114-118. The frequency for this class is 5. To find the percentage of data values in this range, we divide the frequency by the total number of data points and multiply by 100: (5/40) * 100 = 12.5%. Therefore, 12.5% of the data values fall between 114 and 133, inclusive.

(c) The classes that include the values of 119 or greater are 119-123, 124-128, 129-133, 134-138, and 139-143. The sum of the frequencies for these classes is 2 + 3 + 4 + 3 + 3 = 15. To find the percentage of data values in this range, we divide the frequency by the total number of data points and multiply by 100: (15/40) * 100 = 37.5%. Therefore, 37.5% of the data values are 119 or greater.

(d) The classes that include the values of 128 or less are 104-108, 109-113, 114-118, 119-123, and 124-128. The sum of the frequencies for these classes is 2 + 4 + 5 + 2 + 3 = 16. To find the percentage of data values in this range, we divide the frequency by the total number of data points and multiply by 100: (16/40) * 100 = 40%. Therefore, 40% of the data values are 128 or less.

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Answer:

\(2 \div \frac{8}{9} = 2 \times \frac{9}{8} = \frac{9}{4} = 2.25\)

I hope I helped you^_^

Answer:

Step-by-step explanation:

Use KCF method for fraction division.

K- Keep the first fraction.

Change the division to multiplication.

Flip the second fraction

2 ÷ 8/9 = \(2 * \dfrac{9}{8}\)

             \(= 1*\dfrac{9}{4}=\dfrac{9}{4}\\\\= 2\dfrac{1}{4}\)

The mass of all the worker bees in the hive together is 4 kg given that the mass of one worker bee is given as 1 x 10⁻⁴ kg.

To find the mass of all the worker bees in the hive, we can multiply the mass of one worker bee by the total number of worker bees in the hive.

The mass of one worker bee is given as 1 x 10⁻⁴ kg.

The total number of worker bees in the hive is given as 4 x 10⁴ bees.

To multiply these numbers in scientific notation, we need to multiply the coefficients (1 x 4) and add the exponents (-4 + 4).

1 x 4 = 4
-4 + 4 = 0

Therefore, the mass of all the worker bees in the hive together is 4 x 10⁰ kg.

Since any number raised to the power of zero is equal to 1, the mass can be simplified as 4 kg.

In conclusion, the mass of all the worker bees in the hive together is 4 kg.

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The son is 30 years and the father is 65 years.

Let x represent the present age of the son and y represent the present age of the father.

Hence:

y = x + 35

-x + y = 35    (1)

In 5 years time:

y + 5 = 2(x + 5)

y + 5 = 2x + 10

-2x + y = 5  (2)

Solving equations 1 and 2 simultaneously gives:

x = 30, y = 65

The son is 30 years and the father is 65 years.

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Son   =  30 years

Father  =  65 years

Present Details:

Son: "s" years                    (lets consider son's present age to be s)

Father: "s + 35"                  (father is 35 years older than the son)

After 5 years:

Son: "s + 5"                [son will be 5 years older]

Father: 2(s + 5)     [twice the son's age]  and  (s + 35) + 5 = (s + 40) years

Solve father's age simultaneously:

⊕ Thus, the Son is 30 years old.

Father's age:

Answer:

Both the mean and median are greater for Plot A than for Plot B

Step-by-step explanation:

✔️Mean and Median of Plot A:

Write out each data value represented on the dot plot:

3, 4, 4, 5, 5, 6, 6, 7, 7, 10

\( Mean = \frac{3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 + 7 + 10}{10} = \frac{57}{10} = 5.7 \)

Median = (5 + 6)/2 = 11/2 = 5.5

✔️Mean and Median of Plot B:

Write out each data value represented on the dot plot:

3, 4, 4, 5, 5, 5, 6, 6, 6, 7

\( Mean = \frac{3 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7}{10} = \frac{51}{10} = 5.1 \)

Median = (5 + 5)/2 = 10/2 = 5

✅Therefore, we can conclude that:

Both the mean and median are greater for Plot A than for Plot B.

Answer:

A

Step-by-step explanation:

I made 100 on my quiz, all credit goes to the other person

The population of an island in 1950 was 2 million. The population grew exponentially for 63 years and reached 6.5 million in 2013. The carrying capacity of the island is estimated to be 10 million.

If the population growth rate in the future is similar to the last 50 years, what will the population be in 2050

The population is given to be increasing exponentially, which means it will follow the equation:

\($P(t) = P_0 e^{rt}$\)Here,\($P(t)$\) is the population after a period of time \($t$, $P_0$\) is the initial population, $r$ is the annual growth rate (which we are given is the same as the growth rate of the last 50 years), and \($t$\) is the time.

We can find the annual growth rate $r$ using the formula:\($$r = \frac{\ln{\frac{P(t)}{P_0}}}{t}$$\)
We know\($P_0 = 2$ million, $P(t) = 6.5$ million, and $t = 63$\) years. Substituting these values, we get:

\($r = \frac{\ln{\frac{6.5}{2}}}{63} = 0.032$\) (rounded to 3 decimal places)

Since the carrying capacity of the island is 10 million, we know that the population will not exceed this limit.

Therefore, we can use the logistic model to find the population growth over time. The logistic growth model is:

\($$\frac{dP}{dt} = r P \left(1 - \frac{P}{K}\right)$$\)

where $K$ is the carrying capacity of the environment. This can be solved to give:\($P(t) = \frac{K}{1 + A e^{-rt}}$\)

where \($A = \frac{K-P_0}{P_0}$. We know $K = 10$ million, $P_0 = 2$ million, and $r = 0.032$\). Substituting these values, we get:\($A = \frac{10-2}{2} = 4$\)

Therefore, the equation for the population of the island is:\($P(t) = \frac{10}{1 + 4 e^{-0.032t}}$\)

To find the population in 2050, we substitute\($t = 100$\) (since 63 years have already passed and we want to find the population in 2050, which is 100 years after 1950):

\($P(100) = \frac{10}{1 + 4 e^{-0.032 \times 100}} \approx \boxed{8.76}$ million\)
Therefore, the estimated population of the island in 2050, assuming constant carrying capacity and consumption per capita, is approximately 8.76 million.

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Answer:

179

Step-by-step explanation:

180- 2=189 this is because 2 of the students the 180 received a or b

The given question is incorrect. The correct question is:

Of the 180 students in a college course, 1/4 of the students earned an A for the course, 1/3 of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?

A. 75

B. 90

C. 105

D. 120

E. 135

The number of students who earned a C for the course can be represented by the fraction of 5/12 of the total number of students and is equal to 75. Hence, option A is the right choice.

A fraction in general means a part of. We represent a part of the whole using fractions. The total number of parts is taken as the denominator, while the parts used are taken as the numerator.

Fraction = Numerator/Denominator.

We are given that there are 180 students in a college course. 1/4 of them get an A for the course while 1/3 get a B. Rest of the students to get a C for the course.

We need to find the number of students who get a C.

Let the fraction of students getting a C be x.

We know that a whole fraction is always = 1.

∴ Fraction of students getting an A + Fraction of students getting a B + Fraction of students getting a C = Whole fraction.

or, 1/4 + 1/3 + x = 1

or, x = 1 - 1/4 - 1/3 = (12 - 3 - 4)/12 = 5/12

∴ 5/12 of the students get a C for the course.

Number of Students who get a C for the course = 5/12 of 180 = 5*15 = 75.

∴ The number of students who earned a C for the course can be represented by the fraction of 5/12 of the total number of students and is equal to 75. Hence, option A is the right choice.

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Answer:

D

Step-by-step explanation:

Answer:

The correct answer is D

Step-by-step explanation:

pls put me as brainly

Answer:

85

Step-by-step explanation:

You can set this up as an algebraic equation by assigning variables to each part of the question.      So you could say  Y - 13 = 72    If you are in middle school they will expect all that.  

If you want the easy way you could say,  72 + 13= 85 because we beat you by 13 and you only scored 72 points.   So I add 13 to their lame score and we  get my great score.  

Answer:

the answer is 85

Step-by-step explanation:

Answer:

time greater than 6 hours

Step-by-step explanation:

For this problem, we are given the rate at which the refrigerator's temperature increases and the rate at which the oven's temperature decreases along with the initial temperatures for both.  Using this information, we can determine the amount of time that will need to pass for the two to have equal temperature, or pass each other in opposite directions of temperature.  Let's write the inequality using the information:

40 + 5t > 340 - 45t

Let t be the amount of time passed in hours.  So, we simply need to solve the inequality for t.

40 + 5t > 340 - 45t

40 + 50t > 340

50t > 300

t > 6

Given this information, we know that after 6 hours have passed, the temperature of the fridge and oven will be equal.  So we can say that any time greater than 6 hours, the fridge will have a higher temperature than the oven.

Cheers.

Let the original amount be x

Then According to the question,

15.5 % of x is 713

15.5% * x = 713

(15.5 / 100 ) * x = 713 ( as 1 Percent =1/100)

x = 713 * 100/15.5

x = 4600

So, the original amount is 4600.

The original amount is calculated by setting up an equation using percentages, representing the original amount as X: 15.5 / 100 * X = 713. This equation is then solved to find X = (713 * 100) / 15.5, which results in X = 4600. Thus, the original amount is 4600.

The subject of the question is percentage calculation. In this situation, we can understand that 15.5 percent of an original amount equates to 713.

To find the original amount, we can set up an equation with the values provided. If we represent the original amount as X, then: 15.5 / 100 * X = 713.

To isolate X and hence find the original amount, we can solve this equation by dividing both sides by 15.5 and multiplying by 100: X = (713 * 100) / 15.5.

Calculating this gives us X = 4600. So, the original amount was 4600.

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Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Number of recipes already known = 4

Number of new recipes learnt per week = 3

Relationship between number of weeks and appetizer recipe :

y = 3w

number of weeks = w

Number of appetizer recipe = y

B.) Linear equation:

y = mx + c

x and y are the independent(x = number of weeks) and dependent variables (y = number of recipes learnt)

C = intercept, value of y, when x = 0 ; number of recipes already known before learning ; 4

m = gradient change in y per change in x; number of recipes Learnt per week ; m = 3

y = 3x + 4

Number of recipes known after 18 weeks :

x = 18

y = 3(18) + 4

y = 54 + 4

y = 58

58 recipes

After 18 weeks, Tara would have learnt (18 * 3) = 54 new recipes plus the already known 4 = (54 + 4) = 58

Answer:

use distance formula

\(\qquad\quad {:}\longmapsto\sf AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\qquad\quad {:}\longmapsto\sf \sqrt {(4-8)^2+(9-1)^2}\)

\(\qquad\quad {:}\longmapsto\sf \sqrt{(-4)^2+(8)^2}\)

\(\qquad\quad {:}\longmapsto\sf \sqrt {16+64}\)

\(\qquad\quad {:}\longmapsto\sf \sqrt {80}\)

\(\qquad\quad {:}\longmapsto\sf AB=4\sqrt{5} \:or \:8.94\)

Answer:

A

Step-by-step explanation:

If 1 gallon contains 128 fluid ounces, and you have 10 gallons. That would mean you have 1280 fluid ounces of water. Each cup takes 8 fluid ounces. 1280/8 = 160 which is your answer.

The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments 500x + 900y + 1500z = 750,000

formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv

500x + 900y + 1500z = 750,000 - - - (1)

x + y + z = 1000 - - - - (11)

x = 200 + y + z - - - - (111)

x + 2y + 3z = 1550 - - - (1V)

I bedroom = x

2 bedroom = y

3 bedroom = z

All the condition s gjvbbs'

500x + 900y + 1500z = 750,000 - - - (1)

x + y + z = 1000 - - - - (11)

x = 200 + y + z - - - - (111)

x + 2y + 3z = 1550 - - - (1V)

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Rolle's Theorem can be applied on \(-x^2 + 9x\) on [0, 9]

What is Rolle's Theorem?

Rolle's Theorem states that

1) If f is continuous on [a, b]

2) f is differentiable on (a, b)

3) f(a) = f(b)

Then there exist a point c in (a, b) such that \(f^{'}(c) = 0\)

Here, f(x) = \(-x^2 + 9x\)

f is continuous on [0, 9] as it is a polynomial function.

f is differentiable on (0, 9)

f(0) = \(-0^2+9\times 0 = 0\)

f(9) = \(-9^2+9 \times 9 = 0\)

f(0) = f(9)

So Rolle's Theorem has been applied here

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Answer:

(# - 5) x 2

or

(# - 5) 2

I think it should look Iike this but I might be wrong.

Answer:

So we must determine the distance between our two given points and that can be found using the distance formula \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\).

Plugging the values into the equation and solve

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(d=\sqrt{(-9-5)^2+(-2-6)^2}\)

\(d=\sqrt{(-14)^2+(-8)^2}\)

\(d=\sqrt{196+64}\)

\(d=\sqrt{260}\)

\(d=16.125\ units\)

Therefore, our final answer is that the distance is 16.125 units

Hope this helps!  Let me know if you have any questions

The measurement of side AC in the given right triangle is 10.12 units.

A triangle having at least one angle measuring 90° is called a right triangle.

Given that, a triangle ABC, right-angled at A,

AB = 15 and BC = 18.1, we need to find AC,

Please refer to the figure attached,

Using Pythagoras theorem,

BC² = AB² + AC²

AC² = BC² - AB²

AC² = (18.1)² - 15²

AC² = 327.61 - 225

AC² = 102.61

AC = 10.12

Hence, the value of AC = 10.12

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Mia's initial deposit of $3,800 will grow to approximately $4,057 after one year with a 6.5% annual interest rate compounded annually.

With an initial deposit of $3,800, Mia's savings account will grow over time due to the annual compound interest. Compound interest refers to the interest that is calculated on both the initial deposit and any accumulated interest from previous periods.

The formula to calculate the future value of the deposit with compound interest is given by the equation:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment/amount

P = the principal amount (initial deposit)

r = annual interest rate (in decimal form)

n = number of times interest is compounded per year

t = number of years

In this case, Mia's deposit of $3,800 will earn interest at a rate of 6.5% per year, compounded annually. Assuming she does not make any additional deposits, the future value of her investment can be calculated using the formula. The number of times interest is compounded per year is 1 since it is compounded annually.

Using the formula, the future value can be calculated as:

A = 3800(1 + 0.065/1)^(1*1)

= 3800(1 + 0.065)

= 3800(1.065)

= $4,057

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Answer: 0 bottles of Brand X and 10 bottles of Brand Y

(please let me know if I read the question wrong and I will do my best to fix it)

Step-by-step explanation:

This problem can be solved using linear programming. Let x be the number of Brand X bottles and y be the number of Brand Y bottles. The objective is to minimize the cost, given by:

Cost = 25x + 15y

Subject to the following constraints, which represent the minimum nutrient requirements:

3x + 9y ≥ 30 (Nutrient A)

3x + 2y ≥ 16 (Nutrient B)

7x + 2y ≥ 24 (Nutrient C)

x ≥ 0, y ≥ 0 (Non-negativity constraint)

We can solve this system of inequalities graphically by finding the feasible region and the corner points.

Nutrient A constraint (3x + 9y ≥ 30):

Divide the inequality by 3:

x + 3y ≥ 10

Nutrient B constraint (3x + 2y ≥ 16):

Divide the inequality by 2:

1.5x + y ≥ 8

y ≥ 8 - 1.5x

Nutrient C constraint (7x + 2y ≥ 24):

Divide the inequality by 2:

3.5x + y ≥ 12

y ≥ 12 - 3.5x

Now we will graph the inequalities on the xy-plane:

y ≥ 10 - x/3

y ≥ 8 - 1.5x

y ≥ 12 - 3.5x

The feasible region is the area where all three inequalities are satisfied. It's a triangular region with corner points A(0,10), B(4,4), and C(8/3, 2).

Now we need to find the cost at each corner point:

Cost A (0, 10) = 25(0) + 15(10) = $150

Cost B (4, 4) = 25(4) + 15(4) = $160

Cost C (8/3, 2) = 25(8/3) + 15(2) ≈ $153.33

The minimum cost is $150, which occurs when 0 bottles of Brand X and 10 bottles of Brand Y are used. So, the public aquarium should add 0 bottles of Brand X and 10 bottles of Brand Y to satisfy the needs of the reef tank at the minimum possible cost.

To support conclusions made in proving statements by deductive reasoning, you can use previously proved theorems, definitions, hypotheses, postulates, and logical principles. These tools help establish a logical progression of deductions and ensure the validity of the conclusions reached.

To support conclusions made in proving statements by deductive reasoning, the following types of statements can be used:

1. Previously proved theorems: These are statements that have been proven to be true using deductive reasoning in previous mathematical proofs. By referencing these theorems, you can use their conclusions as a basis for further deductions. For example, if you have proved that "If two angles are congruent, then their measures are equal," you can use this theorem to support a conclusion in a new proof that involves congruent angles.

2. Definitions: Definitions provide the meanings of mathematical terms. They establish the properties and characteristics of objects or concepts. By using definitions, you can make deductions based on the properties and relationships described. For example, if you define a rectangle as a quadrilateral with four right angles, you can use this definition to support the conclusion that a given shape is a rectangle if it has four right angles.

3. Hypotheses: These are assumptions or statements that are accepted as true for the purpose of a proof. Hypotheses can be used to support conclusions by assuming their validity and then deducing further statements. For example, if the hypothesis is "If a triangle has two congruent sides, then it is an isosceles triangle," you can use this hypothesis to support the conclusion that a given triangle is isosceles if it has two congruent sides.

4. Postulates: Postulates, also known as axioms, are basic assumptions or statements that are accepted without proof. They serve as the foundation for deductive reasoning. By using postulates, you can establish the initial statements from which you derive further conclusions. For example, if you have a postulate stating that "Two points determine a unique line," you can use this postulate to support the conclusion that a line passing through two given points is unique.

5. Logic: Logic is the reasoning process used in making deductions. It involves using logical principles such as the laws of logic (e.g., law of detachment, law of contrapositive) and logical inference rules (e.g., modus ponens, modus tollens) to draw valid conclusions from given statements. By applying logical principles correctly, you can support conclusions made in proving statements by deductive reasoning.

In summary, to support conclusions made in proving statements by deductive reasoning, you can use previously proved theorems, definitions, hypotheses, postulates, and logical principles. These tools help establish a logical progression of deductions and ensure the validity of the conclusions reached.

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The Hungarian algorithm, we can find the optimal assignment that minimizes the overall cost, ensuring all jobs are completed and each worker is assigned to a job.

The transportation model for the allocation problem with r workers and o jobs, we can use the transportation problem framework. We can represent the problem as a cost matrix C, where C[i][j] represents the cost of worker i doing job j.

The objective is to minimize the total cost, considering that each worker must be assigned to exactly one job and each job must be done by exactly one worker.

By applying the transportation problem algorithms, such as the minimum-cost network flow or the Hungarian algorithm, we can find the optimal assignment that minimizes the overall cost, ensuring all jobs are completed and each worker is assigned to a job.

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When a sample has the same characteristics as the target population, the sample is said to be a representative sample.

When a sample has the same characteristics as the target population, the sample is said to be a representative sample.

Let's take a look at this definition in more detail below:

A representative sample is a sample that adequately represents the population, which is selected randomly, so that each member of the population has an equal chance of being included. A representative sample should have the same characteristics of the population it represents.

To get a representative sample, researchers must select participants randomly. A representative sample has the same distribution of variables as the population in which it was derived. It is generally believed that a representative sample is necessary for generalizing the results to the population

Therefore, the results obtained from a representative sample can be generalized to the larger population.In a nutshell, a representative sample is a sample that represents the population from which it was selected. It should have similar characteristics to the population from which it was drawn.

A representative sample is a necessary prerequisite for generalizing the results to the larger population. It ensures the accuracy of the study and the validity of the results obtained. The sample size should be large enough to provide adequate statistical power and enable the results to be generalized to the population.

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Answer:

h(-8) = -8

Step-by-step explanation:

Plug -8 in for x:

h(x) = \(\frac{-8^{2}+3(-8) }{4(-8)+27} = \frac{64-24}{-32+27} = \frac{40}{-5} = -8\)

Answer:

5 days.

Step-by-step explanation:

Jasmine has two options:

Rent skis at the resort for $30 per day.

Then if she rents the skis for N days, the cost will be:

C(N) = N*$30

Buy skis for $150

Now we can ignore the lift pass because she will pay that in both cases.

Now we want to find the number of days N such that the cost of renting is the same as the cost of buying.

Then we need to solve:

C(N) = $150

N*$30 = $150

N = $150/$30 = 5

So if you rent the skis for 5 days, you will pay the same as if you bought the skis.

Answer:

See below in bold.

Step-by-step explanation:

1. x^2 - 13x - 30

We need 2 numbers whose product is -30 and whose sum = -13.

They are  -15 and + 2:

Answer is (x - 15)(x + 2).

2.   2x^2 + 4x - 126

First we can take 2 out to give:

2(x^2 + 2x - 63)

Now we need 2 numbers whose product is - 63 and sum = +2.

These are +9 and - 7 so

Answer is  2(x - 7)(x + 9).

3. -30x^3 + 3x^2 + 9x

First we can take out -3x to give

-3x(10x^2 - x - 3)

Now we want  2 numbers whose product is 10*-3  = -30 and whose sum is -1. They are  -6 and +5 so we write the above as:

-3x(10x^2 + 5x - 6x - 3)

Now we factor the parentheses by grouping:

= -3x( 5x(2x + 1) - 3(2x + 1)

= -3x(2x + 1)(5x - 3)  Answer.

The answer to the second part is 12x^2 - 13x - 21.

Part 3

1, 18.

2. 6.

3. = 5(2(-3)^2 - 3*3*4 + 4^2) - 3)) - 2(-3)(-3 + 7(4) - 1) - 3*4^2

=  5*(67) - 2(72) - 48

= 143.

4.  (11m^2 - 7) - (6m^2 + 3m - 11) + (3m^2 - m - 9)

= 11m^2 - 7 - 6m^2 - 3m + 11 + 3m^2 - m - 9

=  8m^2 - 4m - 5

A = 8, B = 4 and C = 5.

Expression as a fraction of 0.7 cm³ for 117 mm³ is given by the fraction 0.117 / 0.7.

To write 117 mm³ as a fraction of 0.7 cm³,

we need to convert the units so they match.

Since there are 10 millimeters in a centimeter

1 cm = 10 mm

This implies,

1 cm³ = (10 mm)³

         = 1000 mm³

Now we can express 117 mm³ as a fraction of 0.7 cm³:

117 mm³ / 0.7 cm³

To convert mm³ to cm³, we divide by 1000,

117 mm³ / 1000 = 0.117 cm³

Now we can express it as a fraction,

0.117 cm³ / 0.7 cm³

Simplifying the fraction, we divide the numerator and the denominator by 0.117,

= (0.117 cm³ / 0.117 cm³) / (0.7 cm³ / 0.117 cm³)

= 1 / (0.7 / 0.117)

To divide by a fraction, we multiply by its reciprocal:

= 1 × (0.117 / 0.7)

= 0.117 / 0.7

Therefore, 117 mm³ is equal to the fraction 0.117 / 0.7 when expressed as a fraction of 0.7 cm³.

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