The number of non-similar 1000-pointed stars is
[tex]$\frac{1000-600-2}{2}= \boxed{199}.$[/tex]
If we join the adjacent vertices of the regular [tex]$n$[/tex]-star, we get a regular [tex]$n$[/tex][tex]-gon[/tex]. We number the vertices of this [tex]$n$[/tex][tex]-gon[/tex] in a counter clockwise direction: [tex]$0, 1, 2, 3, \ldots, n-1.$[/tex]
A regular [tex]$n$[/tex]-star will be formed if we choose a vertex number m where [tex]$0 \le m \le n-1$[/tex], and then form the line segments by joining the following pairs of vertex numbers:[tex]$(0 \mod{n}, m \mod{n}),$ $(m \mod{n}, 2m \mod{n}),$ $(2m \mod{n}, 3m \mod{n}),$ $\dots,$ $((n-2)m \mod{n}, (n-1)m \mod{n}),$ $((n-1)m \mod{n}, 0 \mod{n}).$[/tex]
If [tex]$\gcd(m,n) > 1$[/tex], then the star degenerates into a regular [tex]$\frac{n}{\gcd(m,n)}$-gon[/tex] or a (2-vertex) line segment if [tex]$\frac{n}{\gcd(m,n)}= 2$[/tex]. Therefore, we need to find all $m$ such that [tex]$\gcd(m,n) = 1$.[/tex]
Note that [tex]$n = 1000 = 2^{3}5^{3}.$[/tex]
[tex]Let $S = \{1,2,3,\ldots, 1000\}$, and $A_{i}= \{i \in S \mid i\, \textrm{ divides }\,1000\}$. The number of $m$'s that are not relatively prime to $1000$ is: $\mid A_{2}\cup A_{5}\mid = \mid A_{2}\mid+\mid A_{5}\mid-\mid A_{2}\cap A_{5}\mid$ $= \left\lfloor \frac{1000}{2}\right\rfloor+\left\lfloor \frac{1000}{5}\right\rfloor-\left\lfloor \frac{1000}{2 \cdot 5}\right\rfloor$ $= 500+200-100 = 600.$[/tex]
[tex]Vertex numbers $1$ and $n-1=999$ must be excluded as values for $m$ since otherwise a regular n-gon, instead of an n-star, is formed.[/tex]
The cases of a 1st line segment of (0, m) and (0, n-m) give the same star. Therefore we should halve the count to get non-similar stars.
Therefore, the number of non-similar 1000-pointed stars is
[tex]$\frac{1000-600-2}{2}= \boxed{199}.$[/tex]
[tex]Note that in general, the number of $n$-pointed stars is given by $\frac{\phi(n)}{2} - 1$ (dividing by $2$ to remove the reflectional symmetry, subtracting $1$ to get rid of the $1$-step case), where $\phi(n)$ is the Euler's totient function.[/tex] [tex]It is well-known that $\phi(n) = n\left(1-\frac{1}{p_1}\right)\left(1-\frac{1}{p_2}\right)\cdots \left(1-\frac{1}{p_n}\right)$, where $p_1,\,p_2,\ldots,\,p_n$ are the distinct prime factors of $n$.[/tex] [tex]Thus $\phi(1000) = 1000\left(1 - \frac 12\right)\left(1 - \frac 15\right) = 400$, and the answer is $\frac{400}{2} - 1 = 199$.[/tex]
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while traveling to europe, phelan exchanged 250 us dollars for euros. he spent 150 euros on his trip. after returning to the united states he converts his money back to us dollars. how much of the original 250 us dollars does phelan now have? round to the nearest cent. 1 european euro
Phelan now has 81.48 x 1.08 = 87.79 US dollars, which is 87.79 dollars of the original 250 dollars.
First, we need to find out how many euros Phelan has left after spending 150 euros on his trip.
We are taking the exchange rate of 1 euro = 1.08 USD
He started with 250 US dollars, which he exchanged for 250 / 1.08 = 231.48 euros.
After spending 150 euros, he has 231.48 - 150 = 81.48 euros left.
To convert the euros back to US dollars, we need to multiply the number of euros by the exchange rate (1 US dollar = 1.08 euros)
So, Phelan now has 81.48 x 1.08 = 87.79 US dollars, which is 87.79 dollars of the original 250 dollars.
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How many minutes are in 3.5 days?
Answer:
5,040 minutes
Step-by-step explanation:
[tex]\frac{3.5 days}{1}[/tex] x [tex]\frac{24 hours}{1 day}[/tex] x [tex]\frac{60min}{1hour}[/tex]
[tex]\frac{3.5days x 24 hours x 60 minutes}{1day x 1 hour}[/tex] Cross cancels the words days and hours
[tex]\frac{3.5 x 24 x60min}{1x1}[/tex]
[tex]\frac{5040minutes}{1}[/tex] = 5040 minutes
is 7/11 a rational number that is not an integer?
Answer:
yes a rational number
Step-by-step explanation:
a rational number has the form
[tex]\frac{a}{b}[/tex] with a and b integers
[tex]\frac{7}{11}[/tex] is in this form and is therefore a rational number
The total area of the two triangles is _____ square inches.Numerical Answers Expected!Answer for Blank 1:
The total area of the two triangles is 28 square inches.
Step 1: Calculate the area of the first triangle.
The first triangle is a right triangle with a base of 4 inches and a height of 3 inches.
Area of a triangle = (1/2) * Base * Height
Area of the first triangle = (1/2) * 4 * 3 = 6 square inches.
Step 2: Calculate the area of the second triangle.
The second triangle is an isosceles triangle with a base of 4 inches and a height of 4 inches.
Area of a triangle = (1/2) * Base * Height
Area of the second triangle = (1/2) * 4 * 4 = 8 square inches.
Step 3: Add the areas of the two triangles.
Total area = 6 + 8 = 14 square inches.
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Aiden measured a line to be 4.1 inches long. If the actual length of the line is 5.3 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer:
22.6%.
Step-by-step explanation:
To calculate the percent error of a measurement, you can use the following formula:
Percent Error = (|measured value - actual value| / actual value) x 100%
Plugging in the values from the problem:
Percent Error = (|4.1 inches - 5.3 inches| / 5.3 inches) x 100% = (1.2 inches / 5.3 inches) x 100% = 0.226 x 100% = 22.6%
To the nearest tenth of a percent, the percent error is 22.6%.
How do you know if two ratios are proportional?
Answer: Ratios are proportional if they represent the same relationship.
Step-by-step explanation:
One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.
At a research facility that designs rocket engines, researchers know that some engines fail to ignite as a result of fuel system error. From a random sample of 40 engines of one design, 14 failed to ignite as a result of fuel system error. From a random sample of 30 engines of a second design, 9 failed to ignite as a result of fuel system error. The researchers want to estimate the difference in the proportion of engine failures for the two designs. Which of the following is the most appropriate method to create the estimate
It is solved using the concept of z-table. Correct option is: (E)
What is z-table?The difference from the mean is expressed as a z-score in standard deviation units. It is not clear either one agree or disagree with the null hypothesis. The likelihood that a point as severe as their statistic would be seen that under null hypothesis is known as the p-value.
A z-table, sometimes referred to as the standard normal table, gives the area beneath the curve to the left of a z-score. This region indicates the likelihood that z-values will fall inside a particular area of the standard normal distribution.
Here, we have to calculate the confidence interval for determine the population interval.
Now, P₁ - P₂, this is the difference between the two population proportion.
thus, option (E) is the correct answer.
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The complete question is as follows:
What is the equation of the line that is perpendicular to and has the same y-intercept as the given line?A. y = x + 1B. y = x + 5C. y = 5x + 1D.y = 5x + 5
The right option is Option C: y = 5x + 1
The given line passes through the points (5,0) and (0,1).
The slope of the line is found by:
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
This implies that,
[tex]m = \frac{1-0}{0-5} \\m = \frac{-1}{5}[/tex]
The product of the slope of the two perpendicular lines should be negative one.
Thus,
[tex]m_{1} * m_{2} = -1[/tex]
This implies that,
[tex]\frac{-1}{5} * m_{2} = -1[/tex]
Giving us, m2 = 5
We can use the slope intercept formula,
y = mx + b
where b = 1 is the y-value of the y-intercept.
The equation thus becomes,
y = 5x + 1
Therefore, the right option is Option C: y = 5x + 1
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-2x - 3y = 8
5x + y = 6
Step-by-step explanation:
what is the question ?
solve for x and y ?
multiply the second equation by 3 and add that result to the first equation. then solve for x. then pick any original equation and solve for y.
-2x - 3y = 8
15x + 3y = 18
-----------------------
13x 0 = 26
x = 26/13 = 2
5×2 + y = 6
10 + y = 6
y = -4
please help i don't know this.
Answer:
it is you just find the total of the 29 mgs
Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
y^2 + 5y - 750 = 0
y(y + 5) = 750
750 - y(y - 5) = 0
Step-by-step explanation:
Créate a model to represent (a+b)
To create a model to represent (a+b), you could use a mathematical equation such as y = a + b.
What is the model about?Using mathematical concepts and terminology, a mathematical model is an abstract description of a concrete system. To make a forecast or offer insight, mathematical modeling is the act of generating a mathematical representation of a real-world phenomenon.
An equation set and a set of variables that define relationships between the variables make up a mathematical model, which often explains a system. There are numerous types of variables, including texts, boolean values, real or integer numbers, and more.
In this case, the equation y = a + b can be used. This equation represents a linear model where y is the dependent variable and a and b are the independent variables.
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Can a right triangle with side 6 cm 10 cm and 8cm be formed give reason?
Yes , a right triangle with the given sides 6 cm 10 cm and 8cm can be formed because the sides satisfies the Pythagoras Theorem .
According to Pythagoras Theorem , the square of the hypotnuse of triangle is equal to the square of the other two sides of triangle ;
The sides of the triangle are given as : 6cm ,10cm and 8cm ;
which means that ,
the hypotnuse is = 10 cm ;
According to Pythagoras Theorem ;
⇒ [tex]10^{2} =8^{2} +6^{2}[/tex] ;
⇒ [tex]100 = 64 + 36[/tex] ;
⇒ [tex]100= 100[/tex] ;
the side satisfies the condition to form the right triangle .
Therefore , the given sides forms a Right Triangle .
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What should be the measure of ZDAB be
so that AD || BC?
47°
A
43°
90°
B
D
Answer: [tex]90^{\circ}[/tex]
Step-by-step explanation:
By the converse of the alternate interior angles theorem, we need [tex]\angle CBA \cong \angle BAD[/tex].
An aquarium holds 8. 6 cubic feet of water. The aquarium is filled up further to hold 9. 2 cubic feet of water. What is the percent of change for the volume of water inside the aquarium?
The per cent of change for the volume of water inside the aquarium is 93.5.
An aquarium carries 8.6 cubic feet of water.
The aquarium is loaded up further to hold 9.2 cubic feet of water.
We have to find the per cent of change for the volume of water inside the aquarium.
A ratio or value that may be stated as a fraction of 100 is a percentage. If we calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
The per cent of change for the volume of water inside the aquarium = Water holds by aquarium/Further filled water × 100
The per cent of change for the volume of water inside the aquarium = (8.6/9.2) × 100
The per cent of change for the volume of water inside the aquarium = 93.5%.
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Select the correct answer. Y Probability 10 0. 10 20 0. 25 30 0. 05 40 0. 30 50 0. 20 60 0. 10 The probability distribution of y, a discrete random variable, is given in the table. What is the expected value of y? A. 25. 0 B. 26. 5 C. 35. 0 D. 35. 5
The expected value of y is (D.) 35.5.
The expected value of a discrete random variable is found by multiplying each value of the variable by its corresponding probability and then summing these products. In this case, the probability distribution of y is given in the table.
To find the expected value of y, we need to calculate the sum of the products of each value of y and its corresponding probability.
y * probability = y * P(y)
The expected value of y is E(y) = 100.10 + 200.25 + 300.05 + 400.30 + 500.20 + 600.10
= 2 + 5 + 1.5 + 12 + 10 + 6 = 37.
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(a−2b)3 when a=−3 and b=−12
help plsss
(the three is an exponent)
Answer:
9261
Step-by-step explanation:
[tex](-3-2(-12))^3=(-3+24)^3=21^3=441(21)=9261[/tex]
What is an example of one solution?
A food pantry is a solution to food insecurity, where people can donate non-perishable food items for those in need.
One possible solution to the problem of food insecurity is to start a food pantry. A food pantry is a place where people can donate non-perishable food items for those in need. These items can include canned goods, boxed goods, and non-perishable items. People can then come to the pantry and take what they need. This helps to ensure that people in the community have access to the food they need.
A food pantry is a solution to food insecurity, where people can donate non-perishable food items for those in need. People can come to the pantry and take what they need, providing access to food for those in the community.
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n the diagram, four circles of radius 1 with centres $P$, $Q$, $R$, and $S$ are tangent to one another and to the sides of $\triangle ABC$, as shown. The radius of the circle with center $R$ is decreased so that the circle with center $R$ remains tangent to $BC$, the circle with center $R$ remains tangent to the other three circles, and the circle with center $P$ becomes tangent to the other three circles. The radii and tangencies of the other three circles stay the same. This changes the size and shape of $\triangle ABC$. $r$ is the new radius of the circle with center $R$. $r$ is of the form $\frac{a \sqrt{b}}{c}$. Find $a b c$.
On solving the provided question we can say that so the value of triangle - y + Z = 1+ r = > 1 -r +
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
Here,
in triangle
by construction = y0 = r - 1
Pythagoras = x² + y²
=> (1+r)² = x
=> x = √(1+r)² - (1-r)²
Pythagoras = x² + z² = 2²
=> z =√4-4r
so the value of triangle -
=> y + Z = 1+ r
=> 1 -r + 2√1 -r1 =
=> r = -1 + √5/2
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The complete question is "In the diagram, four circles of radius 1 with centres P, Q, R, and S are tangent to one another and to the sides of triangle ABC, as shown."
For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits. A recent Mercer survey showed that of U.S. employers were likely to require higher employee contributions for health care coverage in 2009. Suppose the survey was based on a sample of companies.
Therefore, 0.4854 to 0.5546 is the 95% confidence range for the percentage of businesses that are anticipated to need greater employee payments for health insurance coverage in 2009.
A. Computation the margin of error
First step is to calculate the Confidence level using this formula
Confidence level= 1 -α
Where,
α=0.95
Let's enter the formula.
Level of confidence = 1-0.95
Level of confidence = 0.05
The following step is to use this formula to get Z.
Zα/2
Let's enter the formula.
Z= 0.05/2
Z=0.025
Finding the Z score of Z=0.025 is the third stage.
Zα/2=1.96
Let's now use this approach to calculating the margin of error.
Margin of error=Zα/2√p(1-p)/n
Where,
Zα/2=1.96
p=0.52
n=800
Let plug in the formula
Margin of error=1.96√0.52(1-0.52)/800
Margin of error=1.96√0.52(0.48)/800
Margin of error=1.96√0.2496/800
Margin of error=1.96√0.000312
Margin of error=0.0346
Therefore Margin of error will be 0.0346
B. Calculating the proportion of businesses anticipated to demand greater employee payments for health insurance coverage in 2009 with a 95% confidence interval
computation for the confidence interval's outer limits
p- Zα/2√p(1-p)/n
Where,
Zα/2=1.96
p=0.52
n=800
Let plug in the formula
Confidence interval=0.52-1.96√0.52(1-0.52)/800
Confidence interval=0.52-1.96√0.52(0.48)/800
Confidence interval=0.52-1.96√0.2496/800
Confidence interval=-0.52-1.96√0.000312
Confidence interval=0.4854
Computation for the boundaries of confidence interval
Using this formula
p+ Zα/2√p(1-p)/n
Where,
Zα/2=1.96
p=0.52
n=800
Let plug in the formula
Confidence interval=0.52+1.96√0.52(1-0.52)/800
Confidence interval=0.52+1.96√0.52(0.48)/800
Confidence interval=0.52+1.96√0.2496/800
Confidence interval=-0.52+1.96√0.000312
Confidence interval=0.5546
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What's the percentage of 6 by 5 ?
Answer:
0.3
Step-by-step explanation:
Were you asking for 5% of 6? Because then you would just multiply 6 by 0.05 (because percents are always out of 100%, so converted to decimal it is out of 1) and then get 0.3
Answer: The percentage of 6 by 5 (i.e. 6:5) is 120
Step-by-step explanation:
Given: 6 by 5 i.e. 6/5
Solution: (value/ total value)* 100
hence, (6/5)*100
=1.2*100
=120.
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B C= 16 c m, and is the diameter of the circle,A B CDis a rectangle, a section A B is 12 taller thanB C.
Determine the areaSfor the given figure!
In the calculations, it is assumed thatπ≈ 3!
Area of a semicircle S1 =
Area of the figure S =
We should be aware that if a circle encircles a rectangle, its diameter is equal to the diagonal of the rectangle, where 2r is the reciprocal of the diagonal. AB = 8cm ; BC = 6.5 cm.
Determine the area ?We should be aware that if a circle encircles a rectangle, its diameter is equal to the diagonal of the rectangle, where 2r is the reciprocal of the diagonal.
The formula for calculating the area of a circle is [pi r 2], which we should keep in mind. With respect to a rectangle, there is only one such circle.The Pythagorean theorem states that the diagonal of a rectangle with sides lengths a and b is equal to a2 + b2.
The radius is simply a2+b22 since the diagonal has a diameter.Keep this response on hand.
BC = x- 1.5
x * (x-1.5) = 52
x^2 - 1.5x - 52 = 0
Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25
We are searching only positive value
(1.5 + 14.5)/2 = 16 / 2 = 8 cm
AB = 8 cm
BC = 8 - 1.5 = 6.5 cm
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Help with geometry similar triangles
The value of x in the similar triangles is 40.
What are similar triangles?Those triangles that looks the same but different in sizes.
And in the similar triangle,
the corresponding sides in proportion to each other and corresponding angles are equal to each other.
Given:
Triangles are similar.
That means,
the corresponding sides are in the proportion to each other.
That means,
(x + 8)/x = 12/10
10x + 80 = 12x
2x = 80
x = 40
Therefore, the value of x is 40.
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Joaquin is getting a new locker at school and the first thing he must do is decide on a new combination. The three number locker combination can be selected from the numbers 0 through 21.How many different locker combinations can Joaquin choose if none of the numbers can be repeated?With your understanding of permutations, combinations, and factorials, decide if the name "combination lock" is appropriate.How many mathematical combinations are possible?:How many choices would there be if you could repeat a number, but not use the same number twice in a row?
Joaquin would have 9, 612 different locker combinations if he could repeat a number, but not use the same number twice in a row.
What is the combination?
In simple words, combination involves the selection of objects or things out of a larger group where order doesn't matter. The formula for combination helps to find the number of possible combinations that can be obtained by taking a subset of items from a larger set.
If none of the numbers can be repeated, Joaquin can choose from a total of 22 numbers (0 through 21), and he needs to select three of them for his locker combination. This is a classic example of a combination problem, as the order in which he chooses the numbers does not matter. The number of ways to choose three numbers from a set of 22 without repetition is given by the formula for combinations:
C(22,3) = 22! / (3!(22-3)!) = 222120/(321) = 2310
So, Joaquin can choose from 2310 different locker combinations if none of the numbers can be repeated.
The name "combination lock" is appropriate because it refers to the process of combining numbers in a specific order to open the lock. In this case, the order of the numbers selected does not matter.
If Joaquin could repeat a number, but not use the same number twice in a row, the number of mathematical combinations are possible is given by the formula for permutations:
A(22,3) = 222120 = 9, 612
Hence, Joaquin would have 9, 612 different locker combinations if he could repeat a number, but not use the same number twice in a row.
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You work as the IT administrator for a small startup company. Lily's computer has two internal hard drives and runs Windows 10. She is concerned that she may accidently delete a file or that her primary hard disk may fail at some future time. She has come to you for suggestions about how to protect her files. Due to the size and revenue of this startup company, resources are somewhat limited.
On solving the provided question, we can say that Due to the size and revenue of this startup company, resources are somewhat limited.
What is size?In mathematics, "Size is an abstraction from the comparison and measurement of long and short items." Comparing or measuring objects allows us to determine their sizes. The amount's size will be decided by this. B. Mass or length with relation to measurement units. The total area of space occupied by a person or object; the size of someone or something. [Count] Box is 5 inches tall, 6 inches broad, and 12 inches long. The mistake was roughly the size of a dime. The size of twins is the same.
People make mistakes, but there is a potential that she can unintentionally destroy a personal file if she is removing something.
Due to the size and revenue of this startup company, resources are somewhat limited.
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a survey company that wants to know the views of the average person sends an agent to a shopping mall to interview anyone who is available. the people who are interviewed constitute a
The people who are interviewed constitute a convenience sample.
If the survey company is interviewing anyone who is available in the shopping mall without using any systematic method for selecting the participants, it would be considered a convenience sample.
In a convenience sample, the sample is selected based on ease of access to the participants, and it may not be representative of the entire population. This type of sampling can lead to bias in the sample, as the views of people who happen to be available in the mall at the time may not be representative of the views of the entire population.
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students majoring in psychology surveyed 200 of their fellow students about their dreams. the results of the survey are shown in the venn diagram. let b be the event that the participant dreams in black and white and let c be the event that the participant dreams in color. a venn diagram titled student dreams. one circle is labeled b, 4, the other circle is labeled c, 10, the shared area is labeled 12, and the outside area is labeled 174. what is the probability that a randomly selected participant dreams in black and white or color? 0.06 0.07 0.13 0.26
The probability that a randomly selected participant dreams in black and white or color is 0.01
The probability that a randomly selected participant dreams in black and white or color is the sum of the probabilities of the individual events (dreaming in black and white or dreaming in color) and the probability of the intersection of the two events (dreaming in both black and white and color).
The probability of dreaming in black and white is the number of participants who dream in black and white divided by the total number of participants surveyed:
P(b) = 4/200
The probability of dreaming in color is the number of participants who dream in color divided by the total number of participants surveyed:
P(c) = 10/200
The probability of dreaming in both black and white and color is the number of participants who dream in both black and white and color divided by the total number of participants surveyed:
P(b ∩ c) = 12/200
The probability of dreaming in black and white or color is the sum of the individual probabilities and the intersection probability:
P(b ∪ c) = P(b) + P(c) - P(b ∩ c) = 4/200 + 10/200 - 12/200 = 2/200 = 1/100
The probability that a randomly selected participant dreams in black and white or color is 1/100.
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A taxi charges a base fee of $3. 00 and $0. 15 for every mile of the ride. What would be the cost of a 3. 4 mile ride?
Someone please help me on this…
The cost of a 3.4 mile ride when a taxi charges a base fee of $3.00 and $0.15 for every mile of the ride is $3.51.
Therefore the answer is $3.51
The cost of a 3.4 mile ride can be calculated by multiplying the distance of the ride by the cost per mile and adding the base fee. Here base fee is the fixed charge and $0.15 is the variable charge that depend on distance covered.
To calculate the cost of the ride:
= (3.4 miles * $0.15 per mile) + $3.00 base fee
= $0.51 + $3.00
= $3.51
So, a 3.4 mile ride would cost $3.51.
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99.99, 99.09, 99.091 leash to greatest
Car rental company A charges a set fee of $75 for the week plus an additional $0.07 per mile driven. Car rental company B shares a set fee of $100 for the week plus an additional $0.03 per mile driven. When would the two car companies cost you the same amount of money?
Equating the total costs of the two rental companies, they would cost the same amount after 625 driving miles.
What is an equation?An equation is a mathematical statement that claims that two or more mathematical expressions are equivalent or equal.
Equations use the equation symbol (=) to depict the equality of the expressions.
Company A Company B
Fixed rental charge $75 $100
Rental charge per mile $0.07 $0.03
Let the number of miles driven = m
Equations:Total cost of Company A's rental = 75 + 0.07m
Total cost of Company B's rental = 100 + 0.03m
For the cost to be the same, 75 + 0.07m = 100 + 0.03m.
Solving for m:
75 + 0.07m = 100 + 0.03m
0.07m - 0.03m = 100 - 75
0.04m = 25
m = 625
Thus, for the two car companies' rental cost to be the same amount, one would rent a car for 625 miles.
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