There are 84 different combinations of 3 books that can be selected from a stack of 9 books. Each combination can be arranged in 6 different ways, resulting in a total of 504 ways.
The number of ways to select 3 books from a stack of 9 books and arrange them in the empty space on the bookshelf can be calculated using the combination formula and the permutation formula.
First, we need to calculate the number of combinations of 3 books that can be selected from the stack of 9 books:
C(9,3) = 9! / (3! * (9-3)!) = 84
This means there are 84 different combinations of 3 books that can be selected from the stack.
Next, we need to calculate the number of ways that each combination of 3 books can be arranged in the empty space on the bookshelf. Since we have 3 spaces on the bookshelf, we can use the permutation formula to calculate the number of ways that 3 books can be arranged in 3 spaces:
P(3,3) = 3! = 6
This means that there are 6 different ways that each combination of 3 books can be arranged on the bookshelf.
To calculate the total number of ways to select 3 books from the stack and arrange them on the bookshelf, we can multiply the number of combinations by the number of permutations:
Total number of ways = C(9,3) * P(3,3) = 84 * 6 = 504
Therefore, there are 504 different ways to select 3 books from the stack and arrange them on the bookshelf.
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How to turn 0. 1212121212 into a simplified fraction
Answer:
4/33
Step-by-step explanation:
You want to write 0.1212...(repeating) as a simplified fraction.
Repeating decimalA repeating decimal beginning at the decimal point can be made into a fraction by expressing the repeating digits over an equal number of 9s.
Here, there are 2 repeating digits, so the basic fraction is ...
12/99
This can be reduced by removing a factor of 3 from numerator and denominator:
[tex]0.\overline{12}=\dfrac{12}{99}=\boxed{\dfrac{4}{33}}[/tex]
__
Additional comment
Formally, you can multiply any repeating decimal by 10 to the power of the number of repeating digits, then subtract the original number. This gives the numerator of the fraction. The denominator is that power of 10 less 1.
0.1212... = (12.1212... - 0.1212...)/(10^2 -1) = 12/99
Doing this multiplication and subtraction also works for numbers where the repeating digits don't start at the decimal point. Finding a common factor with 99...9 may not be easy.
You can also approach this by writing the number as a continued fraction. The basic form is ...
[tex]x=a+\cfrac{1}{b+\cfrac{1}{c+\cdots}}[/tex]
where 'a' is the integer part of the original number, and b, c, and so on are the integer parts of the inverse of the remaining fractional part. The attachment shows how this works for the fraction in the problem statement.
A calculator cannot actually represent a repeating decimal exactly, so error creeps in and may eventually become significant.
How many Hamiltonian circuits exists in a complete graph with 11 vertices?
10!
12!
11!
9!
An [tex]11[/tex]-vertex full graph has around [tex]19,958,931,200[/tex] Hamiltonian circuits in a complete graph.
Describe the Hamiltonian circuit with an example.At one vertex, the Hamiltonian route begins, and at another, it finishes. Yet, when following a Hamiltonian route, every vertex is encountered. At the same vertex, the Hamiltonian circuit begins and terminates. For instance, if a Hamiltonian circuit's path began at vertex 1, the loop will also conclude at that vertex.
The Hamiltonian circuit: what is it?Single circuit is the sole trip a Hamiltonian circuit makes to each vertex. It must begin and terminate at same vertex since it is a circuit. A Hamiltonian route does not start and end in a single location, but it does visit each vertex just once with no repetitions.
We have to divide by [tex]2(n-2)[/tex]
[tex]11!/(2(11-2)!) = 11!/2,520[/tex] Hamiltonian circuits we get:
[tex]11!/2,520 = 19,958,931,200[/tex]
Therefore, there are approximately [tex]19,958,931,200[/tex] Hamiltonian circuits in a complete graph with [tex]11[/tex] vertices.
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if y varies directly as x, and y=7 when x=3, find when x=7
Direct variation means the ratio of y to x is constant.
y1/x1 = y2/x2 ⇒
y2 = (x2/x1) y1
Plug in
x1 = 3
y1 = 7
x2 = 7
and get y2.
divide the circumference of a pumpkin by its diameter and what do you get?
Dividing the circumference of a pumpkin by its diameter gives a value approximately equal to pi (π)
When you divide the circumference of a pumpkin by its diameter, you get a value that is approximately equal to the mathematical constant pi (π), which is approximately 3.14159.
This is because pi represents the ratio of the circumference of a circle to its diameter, and a pumpkin is roughly spherical in shape. So, no matter how big or small the pumpkin is, if you measure its circumference and diameter and divide them, the result will be very close to pi.
Mathematically, this can be represented by the formula
pi ≈ circumference / diameter
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Two thirds of a number X subtracted from four times the sum of y and 5
Answer: 4y - (2/3)x + 20
Step-by-step explanation:
Write out problem: 4(y+5) - (2/3)x
Expand: 4y + 20 - (2/3)x
Reorder: 4y - (2/3)x + 20
What is 3(25+19) + 4(3)
The value of the expression given is 144
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression 3(25+19) + 4(3) we need to simplify,
Using PEMDAS,
3(25+19) + 4(3)
= 75+57 + 12
= 132+12
= 144
Hence, the value of the expression given is 144
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Which expression was factored completely using the GCF, if the original expression was
16x² + 8x?
4(4x²+2x)
4x(4x+2)
8(2x²+x)
8x(2x+1)
Answer:
It's D
Step-by-step explanation:
[tex]1. \: gcf = 8x \\ 2. \: 8x( \frac{16x {}^{2} }{8x} + \frac{8x}{8x} ) \\ 3. \: 8x(2x + 1)[/tex]
Ex. 1: Last year, the price of a lawnmower was $358.99. The same model sells
for $329.99 this year. What is the percent change in the price of the
over the 2 years? Round your answer to the nearest tenth.
lawnmower
The percent change in the price of the lawnmower over the 2 years is -8.1%.
Calculating the percentage changeTo find the percent change in the price of the lawnmower over the 2 years, we can use the formula:
percent change = (new value - old value) / old value * 100%
Plugging in the values given in the problem, we get:
percent change = (329.99 - 358.99) / 358.99 * 100%
percent change = -8.1%
Therefore, the percent change in the price of the lawnmower over the 2 years is -8.1%. Note that the negative sign indicates a decrease in price.
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how can the idea of a sinusoidal function be used to help us model real-world things, or to help us solve real-world problems?
Sinusoidal functions can model natural phenomena and periodic patterns in data, aiding in better understanding and more accurate predictions, while also solving real-world problems.
The idea of a sinusoidal function can be used to model real-world phenomena or solve real-world problems. Many natural phenomena can be modeled using sinusoidal functions, including tides, sound waves, and electromagnetic waves.
In addition, sinusoidal functions can be used to model periodic patterns in data, such as seasonal trends or cyclical patterns in financial data. By using sinusoidal functions to model these phenomena, we can gain a better understanding of their behavior and make more accurate predictions about their future behavior.
Sinusoidal functions can also be used to solve real-world problems, such as calculating the amplitude, frequency, or period of a wave or predicting the behavior of a system that exhibits periodic patterns.
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An athlete runs 1/3 of a mile every 1/20 hour. At this rate, how far does the athlete run per hour?
Answer: 20/3 mph or 6.667 mph.
Step-by-step explanation:
Since the athlete runs 1/3 of a mile per 1/20 of an hour, to find how much they run in an hour, you multiply both values by 20 to get: the athlete runs 20/3 miles per 20/20 of an hour, or 20/3 miles per hour.
Complete the table below using what you know about trigonometric ratios for right triangles.
Write your ratios as fractions. A message will appear when you are correct.
(a) The ratio of sin A as a fraction is 63/65, cos A is 16/65 and the tan of angle A is 63/16.
(b) The ratio of sin B as a fraction is 16/65, cos B is 63/65 and the tan of angle B is 16/63.
What is the missing part of the right triangle?The missing parts of the right triangle is calculated using the trigonometry principle as shown below.
For angle A:
opposite side = 63
adjacent side = 16
hypothenuse side = 65
sin A = opp/hypo = 63 / 65
cos A = adj/hypo = 16 / 65
tan A = opp/adja = 63/16
For angle B:
opposite side = 16
adjacent side = 63
hypothenuse side = 65
sin B = opp/hypo = 16 / 65
cos B = adj/hypo = 63 / 65
tan A = opp/adja = 16/63
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Two polygons are similar. The perimeter of the larger polygon is 120 yards and the ratio of the corresponding side lengths is $\frac{1}{6}$. Find the perimeter of the other polygon
The perimeter of the smaller polygon is 20 yards.
Two polygons are similar.
The perimeter of the larger polygon is 120 yards and the ratio of the corresponding side lengths is 1/6.
Find the perimeter of the other polygon.
In similar polygons, the ratio of the corresponding side lengths is equal to the ratio of their perimeters.
Since the larger polygon has a perimeter of 120 yards and the ratio of the corresponding side lengths is 1/6,
the smaller polygon must have a perimeter that is 1/6 of the larger polygon's perimeter.
That is, Perimeter of smaller polygon = [tex]\frac {1}{6}[/tex]
The perimeter of larger polygon= [tex]\frac{1}{6} \times120\][/tex]
Multiplying 1/6 by 120 yields
[tex]\frac{120}{6}[/tex] =20
So the perimeter of the smaller polygon is 20 yards.
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8,000 ounces on the model is equal to how many ounces on the actual bridge
Answer:
Step-by-step explanation:
I'ts 128,000 there is 16 oz in a pound we multiply 8,000 by 16 times 8,000 is 128,0003 customers entered a store over the course of 12 minutes. Fill out a table of
equivalent ratios and plot the points on the coordinate axes provided.
Answer: the last box for minutes is 16
And the first box for customers is 1
Step-by-step explanation:
Answer:
See below.
Step-by-step explanation:
1st Box(First row)
We can set up a proportion to solve for the number of customers that would enter the store in 4 minutes:
3 customers is to 12 minutes as x customers is to 4 minutes
This can be written as:
3/12 = x/4
To solve for x, we can cross-multiply and simplify:
3/12 = x/4
3(4) = 12x
12 = 12x
x = 1
Therefore, we can expect 1 customer to enter the store in 4 minutes.
2nd Box(3rd Row)We can use the given ratios to find the time for 10 customers.
From the table, we can see that:
3 customers take 12 minutes.
1 customer takes 4 minutes (divide both sides of the ratio by 3).
So, 10 customers will take:
10 customers × 4 minutes per customer = 40 minutes.
Therefore, for 10 customers, the time is 40 minutes.
if you are a 54 % free-throw shooter and the random variable y denotes the total number of shots in order to make one free-throw, then:
The expected number of shots required to make one free-throw is approximately 1.85.
To calculate the expected value of Y, denoted by E[Y], we need to consider the probability distribution of Y.
The probability distribution of Y is a geometric distribution, since we are counting the number of trials required until the first success (i.e., making a free-throw). The probability of success on each trial is p = 0.54, since you have a 54% chance of making each free-throw. The probability of failure (missing the free-throw) on each trial is q = 1 - p = 0.46.
The probability mass function (PMF) of a geometric distribution is given by:
P(Y = k) = q^(k-1) * p
where k is the number of trials required to achieve the first success.
In this case, we want to find the expected value of Y, which is defined as:
E[Y] = Σ(k=1 to ∞) k * P(Y = k)
We can simplify this expression using the PMF of the geometric distribution:
E[Y] = Σ(k=1 to ∞) k * q^(k-1) * p
This sum can be evaluated using the formula for the sum of an infinite geometric series:
E[Y] = 1/p
Substituting in the value of p = 0.54, we get:
E[Y] = 1/0.54 ≈ 1.85
This means that on average, you need to take about 2 shots to make one free-throw if you have a 54% free-throw shooting percentage.
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Complete question is:
If you are a 54 % free-throw shooter and the random variable y denotes the total number of shots in order to make one free-throw, then:
Calculate E[Y]
what is 3x^4-73x^2-50 factored
Answer:
(3x - 10)(x - 5)
Step-by-step explanation:
That expression is equal to (3x^4 -73x^2 - 50). This factored expression can be written as (3x^2 -17x - 17) * (x+2.5) and can be factored using the FOIL method. (FOIL) - First, Outer, Inner, Last. This method ensures that you include all of the terms with the same variables. The FOIL method is very easy and helpful for factoring complex equations and is something that is good to be familiar with for future study if you are looking to delve deeper into math!
The expression (3x^4 - 73x^2 - 50) factored is an example of a quadratic equation and the expression can be factored into (3x - 10)(x - 5). I think this is a good exercise because it shows how quadratic equations can be factored and the process involved, so students can apply the principles learned to other situations and problems they may encounter later on. It's important to understand how to factor quadratics since they often show up in real-world situations such as physics or statistics, so it's a great thing to have these skills locked in.
To get ready for a pep rally, Mrs. McGee's class is making banners. They have a 3-foot piece of poster board and cut it into pieces that are 1 4 of a foot long. How many banners do they make?
Mrs. McGee's class can make 12 banners from the 3-foot piece of poster board.
The total length of the poster board is 3 feet, which is equivalent to 3 x 12 = 36 inches.
Each piece of poster board is 1/4 of a foot long, which is equivalent to 3 inches (since 1 foot is equal to 12 inches).
To find out how many banners can be made from the poster board, we need to divide the total length of the poster board by the length of each banner:
Number of banners = Total length of poster board / Length of each banner
Number of banners = 36 inches / 3 inches
Number of banners = 12 banners
Therefore, Mrs. McGee's class can make 12 banners from the 3-foot piece of poster board.
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Help explain solve……
Answer:
About 92.1 °
Step-by-step explanation:
[tex]cos(U)=(58.8^{2} +38.4^{2} -71.4^{2} )/2(58.8)(38.4)\\[/tex]
[tex]cos(U)= (3457.44+1474.56-5097.96)/4515.84[/tex]
[tex]cos(U)= (-165.96)/4515.84[/tex]
[tex]cos(U)= -0.03675063775[/tex]
[tex]U= cos^{-1} (-0.03675)[/tex]
[tex]U=92.1[/tex]
Answer:
cosA=b^2+c^2-a^2/2xbxc
58.8^2+38.4^2-71.4^2/2x58.8x38.4=-461/12544
cos^-1 (because finding angle)
cos^1(-461/12544)=92.10613071
Triangle LMN is drawn with vertices at L(−3, −2), M(1, −4), N(−3, −4). Determine the image vertices of L′M′N′ if the preimage is rotated 90° clockwise.
L′(−3, −2), M′(1, −4), N′(−3, −4)
L′(−2, 3), M′(−4, −1), N′(−4, 3)
L′(3, 2), M′(−1, 4), N′(3, 4)
L′(2, 3), M′(4, −1), N′(4, 3)
QUICK HELP 30 POINTS
The image vertices of L′M′N′ are (-2, 3), (-4, -1), and (-4, 3).
What is preimage?
The set of all domain elements for a given function that map to a certain subset of the codomain; (formally) given a function X Y and a subset B Y, the set 1(B) = x X: x B.
Here, we have
Given: Triangle LMN is drawn with vertices at L(−3, −2), M(1, −4), N(−3, −4).
We have to determine the image vertices of L′M′N′ if the preimage is rotated 90° clockwise.
The rule for rotating a point (x, y) 90° clockwise is:
(x,y) ⇒ (y, -x)
The vertices of triangle LMN will be mapped to:
L(-3,-2) ⇒L' (-2, 3)
M(1,-4) ⇒ M'(-4, -1)
N(-3,-4) ⇒ N'(-4, 3)
Hence, the image vertices of L′M′N′ are (-2, 3), (-4, -1), and (-4, 3).
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helppppp!! For #19-20, solve for x. Simplify all radicals.
Which of the following sets of numbers could not represent the three sides of a triangle?
1. 11,25,35 2. 15,24,39
3. 9,20,26 4. 9,13,21
Reason:
a+b = 15+24 = 39 is NOT larger than c = 39
Since a+b > c is false, a triangle is NOT possible.
The sum of any two sides must exceed the third side for a triangle to be possible. For more information, check out the triangle inequality theorem.
a local bakery sells the freshest bread in town. in fact, 65% of customers who come into this store buy bread. what is the probability that at least 3 customers out of the first 6 will buy bread?
The probability that at least 3 customers out of the first 6 will buy bread is 88.3% that is option B.
The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the potential outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.
The formula used is :
P(X=x) = [tex]C_n.x.p^x.(1-p)^n^-^x[/tex]
The parameters are:
x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.
In this problem:
65% of customers who come into this store buy bread, hence p = 0.65.
A sample of 6 customers is taken, hence n = 6.
The probability that at least 3 customers out of the first 6 will buy bread is given by:
P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)
In which
P(X=x) = [tex]C_n.x.p^x.(1-p)^n^-^x[/tex]
P(X = 3) = C₆,₃(0.65)³ x (0.35)³ = 0.2355
P(X = 4) = C₆,₄(0.65)⁴ x (0.35)² = 0.328
P(X = 5) = C₆,₅(0.65)⁵ x (0.35)¹ = 0.2437
P(X = 6) = C₆,₆(0.65)⁶ x (0.35)⁰ = 0.0754
Then,
P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)
= 0.2355 + 0.328 + 0.2437 + 0.0754 = 0.8826
The probability that at least 3 customers out of the first 6 will buy bread is 0.8826 ≈ 88.3%.
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Complete question;
A local bakery sells the freshest bread in town. In fact, 65% of customers who come into this store buy bread. What is the probability that at least 3 customers out of the first 6 will buy bread?
23.5%
88.3%
11.7%
76.5%
6,7,7,8,9,10,10,10,10,13,13,14,14,15,15 box and whisker plot
The box and whisker plot can be created by :
Minimum value - 6
Maximum Value - 15
Median - 10
Quartiles - Q1 - 7.5, Q2 - 10, Q3 - 13.5
To create a box and whisker plot for the given data set {6,7,7,8,9,10,10,10,10,13,13,14,14,15,15}, we need to first find the minimum value, maximum value, median, and quartiles.
Minimum value: 6
Maximum value: 15
Median: To find the median, we need to first arrange the data set in ascending order:
6,7,7,8,9,10,10,10,10,13,13,14,14,15,15
The median is the middle value in the data set, which is 10.
Quartiles: To find the quartiles, we need to divide the data set into four equal parts.
First quartile (Q1): The first quartile is the median of the lower half of the data set. In our case, the lower half of the data set is:
6,7,7,8,9,10
The median of this set is (7+8)/2 = 7.5.
Second quartile (Q2): The second quartile is the median of the entire data set, which we already found to be 10.
Third quartile (Q3): The third quartile is the median of the upper half of the data set. In our case, the upper half of the data set is:
10,10,10,10,13,13,14,14,15,15
The median of this set is (13+14)/2 = 13.5.
Now, we can use the above information to create the box and whisker plot.
The horizontal line inside the box represents the median (10). The bottom of the box represents the first quartile (7.5), and the top of the box represents the third quartile (13.5). The whiskers extend from the box to the minimum value (6) and maximum value (15).
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a jar contains 4 red, 5 white and 6 blue marbles. 3 marbles are selected at random. find the probability that you get one marble of each color using counting.
The probability of getting one marble of each color will be 0.044.
What is probability?The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place. A random event's recurrence is the subject of this area of mathematics. The range of the number is 0 to 1. The degree to which something is likely to happen is essentially what probability means. You will discover the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
In this question,
Total number of balls=4+5+6=15
probability of red ball= 4/15
probability of white ball = 5/14 (Since the number of balls are decreasing
probability of blue ball= 6/13
probability of getting one marble of each color= 4/15×5/14×6/13
= 0.044
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for a recent year, the monthly snowfall (in inches) for chicago, illinois, for november, december, january, and february was 2, 8.4, 11.2, and 7.9, respectively. how much snow would be necessary in march for chicago to exceed its monthly average snowfall of 7.28 in. for these five months?
6.9 inches of snow would be necessary for march for Chicago to exceed its monthly average snowfall of 7.28 in. for these five months.
The given data is as follows:
Snowfall months and their fallen depth is:
November = 2
December = 8.4
January = 11.2
February = 7.9
First, we need to first find out the total snowfall for the five months of November, December, January, February, and March.
Total snowfall = 2 + 8.4 + 11.2 + 7.9 + March
The average snowfall = 7.28 iches.
7.28 inches/month x 5 months = 36.4 inches
2 + 8.4 + 11.2 + 7.9 + March = 36.4
29.5 + March = 36.4
March = 36.4 - 29.5
March = 6.9 inches.
Therefore, we can conclude that more than 6.9 inches of snow would be necessary for march for Chicago to exceed its monthly average snowfall of 7.28 in. for these five months.
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The sum of Joy's age and her brother's age is $24$ . Her brother's age is $3$ years older than twice Joy's age.
What is the difference, in years, between Joy's age and her brother's age?
Answer:
please give question properly
Describe a series of transformations that moves the blue figure to the red figure. If there is a : Translation - show number and direction Reflection - give axis of reflection
Rotation - give direction (clockwise or counterclockwise) and degree amount
Translation: The blue figure can be moved to the red figure by a translation of three units to the right and one unit down.
Reflection: The blue figure can be moved to the red figure by a reflection over the x-axis.
Rotation: The blue figure can also be moved to the red figure by a rotation of 90 degrees counterclockwise.
What is transformation?Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.
To demonstrate this transformation, imagine the blue figure being shifted three units to the right and one unit down, such that it is now completely overlapping the red figure.
This transformation can be visualized by imagining the figure being flipped along the x-axis, so that the right side of the figure is now on the left side and vice versa.
To demonstrate this transformation, imagine the blue figure being spun 90 degrees counterclockwise, so that the top of the figure is now on the left side and the bottom is on the right side. This rotation will align the figure with the red figure.
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Question A store gives away gift bags during a sale. Of these gift bags, 50% are green, 20% are yellow, and 30% are blue. The average number of items in each green bag is 8. The average number of items in each yellow bag is 5. The average number of items in each blue bag is 8. What is the average number of items in all the gift bags? Enter your answer as a decimal in the box.
The average number of items in all the gift bags is 7.4.
What is average?Average, also known as mean, is a numerical value that represents the central or typical value in a set of numbers. It is calculated by adding up all the numbers in a set and dividing the sum by the total number of values in the set. The average is a useful tool for summarizing a large amount of data into a single value that can be easily understood and compared to other values.
In the given question,
We can use the weighted average formula to find the average number of items in all the gift bags:
Average number of items = (proportion of green bags x average items in green bags) + (proportion of yellow bags x average items in yellow bags) + (proportion of blue bags x average items in blue bags)
Proportion of green bags = 50% = 0.5
Proportion of yellow bags = 20% = 0.2
Proportion of blue bags = 30% = 0.3
Average items in green bags = 8
Average items in yellow bags = 5
Average items in blue bags = 8
Substituting the values into the formula, we get:
Average number of items = (0.5 x 8) + (0.2 x 5) + (0.3 x 8)
Average number of items = 4 + 1 + 2.4
Average number of items = 7.4
Therefore, the average number of items in all the gift bags is 7.4
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A rectangle is shown. The length of the rectangle is labeled 5 inches. The width of the rectangle is labeled 8 inches.
A photographer wants to use a scale factor of 2.5 to enlarge a picture. What will the area of the picture be after it is enlarged? (5 points)
40 in2
250 in2
100 in2
81.9 in2
ASAP FAST ANSWER NO TIMEEEEE
Answer:
C
Step-by-step explanation:
A (- 6, - 8 ) and C (9, - 8 )
since the y- coordinates of both points are equal, both - 8
then AC is a horizontal line
the distance AC can be calculated by calculating the absolute value of the x- coordinates, that is
AC = | 9 - (- 6) | = | 9 + 6 | = | 15 | = 15 units
or
AC = | - 6 - 9 | = | - 15 | = | 15 | = 15 units
given 1 unit = [tex]\frac{1}{2}[/tex] mile , then
AC = 15 units = 15 × [tex]\frac{1}{2}[/tex] = 7.5 miles