The box at the right is a cube with edges that measure 2 feet. The sides of the triangle inside the cube are a diagonal of a face, an edge, and a segment with endpoints at opposite corners of the cube. The triangle is a right triangle with leg lengths 2 and
\( \sqrt{ {2}^{3} } \)
. Write the area of the triangle as the number 2 with a rational exponent.
Answers
Answer:
\(Area = 2 \sqrt{2}\)
Step-by-step explanation:
Given
\(Length_1 = 2\)
\(Length_2 = \sqrt{2^3}\)
Required
Determine the area of the triangle
The given lengths represent the height and base length of the triangle.
So, the area is;
\(Area = \frac{1}{2} * Length_1 * Length_2\)
Substitute values for Length1 and Length2
\(Area = \frac{1}{2} * 2 * \sqrt{2^3}\)
\(Area = \frac{2}{2} * \sqrt{2^3}\)
\(Area = 1* \sqrt{2^3}\)
\(Area = \sqrt{2^3}\)
Express 2^3 as 2 * 2 * 2
\(Area = \sqrt{2*2*2}\)
\(Area = \sqrt{4*2}\)
Split
\(Area = \sqrt{4} *\sqrt{2}\)
\(Area = 2 *\sqrt{2}\)
\(Area = 2 \sqrt{2}\)
Related Questions
I don't know how to evaluate an algebraic expression. How can I evaluate an algebraic expression?
Answers
Answer:
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. if it's 6÷x=3, do 6÷3=2 to get the value of x. 6÷2=3.
PLEASE HELP WILL GIVE BRAINLIST
Answers
Answer:
B
Step-by-step explanation:
∠ 3 and ∠ 8 are alternate angles and are congruent, then
6x + 3 = 4x + 29 ( subtract 4x from both sides )
2x + 3 = 29 ( subtract 3 from both sides )
2x = 26 ( divide both sides by 2 )
x = 13 → B
The poaching model for Species Y is Y′=aY(1−Y)−b where the variable Y represents the population of Species Y and Y=0.092 when t=0. If a=0.4 and b=0.06, what can be said about the population of Species Y in the long run? a) The population will level off near 18% of its carrying capacity. b) The population will level off near 82% of its carrying capacity. c) The population will die off. d) The population will level off near 74% of its carrying capacity.
Answers
The population of Species Y will level off near 74% of its carrying capacity in the long run.
Explanation:
To analyze the long-term behavior of the population, we can examine the equilibrium points of the differential equation. Equilibrium points occur when the population remains constant over time, meaning that the derivative is equal to zero.
Given the differential equation Y' = aY(1 - Y) - b, we set Y' = 0 and solve for Y:
0 = aY(1 - Y) - b
Expanding the equation, we have:
0 = aY - aY^2 - b
Rearranging the terms, we get:
aY^2 - aY + b = 0
This is a quadratic equation in Y. Applying the quadratic formula, we find:
Y = (-(-a) ± √((-a)^2 - 4ab)) / (2a)
= (a ± √(a^2 - 4ab)) / (2a)
= (a ± √(a^2 - 4ab)) / (2a)
Substituting the given values a = 0.4 and b = 0.06, we can calculate the roots:
Y = (0.4 ± √(0.4^2 - 4 * 0.4 * 0.06)) / (2 * 0.4)
= (0.4 ± √(0.16 - 0.096)) / 0.8
= (0.4 ± √0.064) / 0.8
= (0.4 ± 0.253) / 0.8
The two equilibrium points are approximately:
Y ≈ 0.908 and Y ≈ 0.092
Given that Y(0) = 0.092, which corresponds to the initial condition when t = 0, we can conclude that the population of Species Y will approach the equilibrium point Y ≈ 0.908 in the long run.
Therefore, the population will level off near 74% (0.908 * 100) of its carrying capacity, which corresponds to option d).
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SECTION A (20 MARKS) QUESTION 1 (a)Identify the relevant population for the below foci, and suggest the appropriate sampling design to investigate the issues, explaining why they are appropriate. Wherever necessary identify the sampling frame as well. 10 marks A public relations research department wants to investigate the initial reactions of heavy soft- drink users to a new all-natural soft drink'. (b) What type of sampling design is cluster sampling? What are the advantages and disadvantages of cluster sampling? Describe a situation where you would consider the use of cluster sampling. 10 marks
Answers
a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is stratified random sampling. The list of all heavy soft-drink users is the sampling frame.
b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.
The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.
a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.
Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.
Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.
b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.
The advantages of cluster sampling are:
Cluster sampling is an efficient method of sampling large populations. It is much cheaper than other types of sampling methods.Cluster sampling is relatively easy to perform compared to other methods of sampling, such as simple random sampling.Cluster sampling can be used when the population is widely dispersed, and it would be difficult to cover the entire population.The disadvantages of cluster sampling are:
Cluster sampling introduces sampling errors that could lead to biased results.Cluster sampling has a lower level of precision and accuracy compared to other types of sampling methods.Cluster sampling increases the standard error of the estimate, making it difficult to achieve the desired level of statistical significance.A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.
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Today, the waves are crashing onto the beach every 4.5 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.5 seconds. Round to 4 decimal places where possible.
The probability that wave will crash onto the beach exactly 0.6 seconds after the person arrives is P(x = 0.6) =
The probability that the wave will crash onto the beach between 1.5 and 2.3 seconds after the person arrives is P(1.5 < x < 2.3) =
The probability that it will take longer than 1 seconds for the wave to crash onto the beach after the person arrives is P(x > 1) =
Suppose that the person has already been standing at the shoreline for 1 seconds without a wave crashing in. Find the probability that it will take between 1.3 and 2 seconds for the wave to crash onto the shoreline.
94% of the time a person will wait at least how long before the wave crashes in? seconds.
Find the minimum for the upper quartile. seconds.
Answers
(a) The probability that a wave will crash onto the beach exactly 0.6 seconds after the person arrives is: P(X = 0.6) = 0. b) P(1.5 < X < 2.3) = 0.511 c) P(X > 1) = 0.7778.
What is probability density function?A probability density function (PDF) expresses the likelihood at which a continuous random variable will take on a particular value. The integral of f(x) across a range is used to determine the likelihood that a continuous random variable X will fall within that range when the PDF f(x) is specified for that variable. Namely, the likelihood that X falls inside of the range [a,b].
The probability density function of random variable X in the interval [a, b] is given as:
f(x) = 1/(b-a), for a ≤ x ≤ b
and its cumulative distribution function is given by:
F(x) = (x-a)/(b-a), for a ≤ x ≤ b
(a) The probability that a wave will crash onto the beach exactly 0.6 seconds after the person arrives is:
P(X = 0.6) = 0, since the Uniform distribution is a continuous distribution and the probability of a specific value is always zero.
(b) For 1.5 and 2.3 seconds after the person arrives is:
P(1.5 < X < 2.3) = F(2.3) - F(1.5)
= (2.3 - 0)/(4.5 - 0) - (1.5 - 0)/(4.5 - 0)
= 0.5111
c) It will take longer than 1 second:
P(X > 1) = 1 - F(1)
= 1 - (1 - 0)/(4.5 - 0)
= 0.7778
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Catherine has a 6-sided number cube that is numbered from 1 through 6. she plans on rolling the number cube 60 times. about how many times should she expect to roll a number that is greater than 4?
a. 10
b. 15
c. 20
d. 40
Answers
Catherine should expect to roll a number 20 times to get a number that is greater than 4.
The cube has 6 sides numbered 1 to 6
The sample space for a cube having 6 sides numbered 1 to 6 is given by {1,2,3,4,5,6}
Catherine expects to roll a number greater than 4.
The only numbers greater than 4 that are present in sample space are {5,6}
Total number of events= 6
Probability of getting a 5= \(\frac{1}{6}\)
Probability of getting a 6= \(\frac{1}{6}\)
Probability of getting a 5 or 6= \(\frac{1}{6} +\frac{1}{6} = \frac{2}{6} = \frac{1}{3}\)
She rolls the dice 60 times
Outcome= \(\frac{1}{3}\)×60= 20 times
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what is the yield of 5x2?
Answers
The yield of 5x2 is 10
Yield is a term used in mathematics to describe the output or result of a calculation or operation. In this case, we are looking at the yield of 5 multiplied by 2 (5x2).
When we multiply two numbers together, we are finding the yield or product of those numbers. In this case, 5 multiplied by 2 gives us a yield of 10. So, the yield of 5x2 is 10.
It's important to note that yield can be used in different contexts in mathematics, such as in finance to describe the return on an investment or in chemistry to describe the amount of product obtained from a chemical reaction. But in this case, we are simply looking at the yield of a multiplication operation.
In summary, which means that when we multiply 5 and 2 together, we get a result or output of 10.
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Please i need help with the graph below
Answers
Using translations, the relation between functions f(x) and g(x) is given as follows:
g(x) = f(x) + 3.
What are translations on the graph of a function?Translations in the graph of a function involve operations such as multiplication/division or sum/subtraction, either in the domain of the function, involving values of x, or the range, involving values of y, moving the function up, down, left or right.
From the three points of the function on the table given at the bottom of the page, we have that the value of g(x) is 3 more than the value of f(x), hence the relation between functions f(x) and g(x) is given as follows:
g(x) = f(x) + 3.
This can be confirmed from the graph, as function g(x) is a shift up of 3 units of the function f(x).
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which is the solution to the inequality y - 27 - 13
Answers
Answer:
-40
Step-by-step explanation:
y−27−13
=y+−27+−13
Combine Like Terms:
=y+−27+−13
=(y)+(−27+−13)
=y + −40
three sandwiches were given to each adult and two sandwiches were given to each child that went on the field trip. there were 40 people on the bus and a total of 89 sandwiches were given out. how many adults and how many children were on the trip ? (PLEASE HELP)
Answers
Answer:
the number of children on the trip=31
The number of adult=9
Step-by-step explanation:
Let's call the number of adults on the trip "a" and the number of children on the trip "c".
We know that:
a + c = 40 (the total number of people on the trip)
And:
3a + 2c = 89 (the total number of sandwiches given out)
We can use the first equation to solve for one variable in terms of the other:
a = 40 - c
And substitute this into the second equation:
3(40 - c) + 2c = 89
Expanding and simplifying:
120 - 3c + 2c = 89
120 - c = 89
Subtracting 120 from both sides:
-c = -31
So c = 31, the number of children on the trip.
And the number of adults on the trip, a = 40 - c = 40 - 31 = 9.
If h = 8.1 inches and k = 9 inches, what is the approximate measure of angle α?
Answers
Answer:
Answer: C. 26°
Step-by-step explanation:
Right triangle: a triangle in which one of the interior angles measures 90°.
This type of angle can be solved using trigonometrical functions. As the measure of the sides given are h and k, then we will use:
\(cos a=\frac{adyacent}{hypotenuse} \)
In our case, it would be:
\(cos a=\frac{h}{k} \)
Replacing the values:
\(cos a= \frac{8.1}{9} \)
Solving for a:
\(cos^{-1} (cos a)=cos^{-1}(\frac{8.1}{9} )\)
\(a= cos^{-1}(\frac{8.1}{9} )\)
a≈ 25.8 ≈26
Answer: C. 26°
Answer:
The answer is 26
Step-by-step explanation:
I had this question on a test and got it correct
If x and y are linearly​ independent, and if z is in Span {x, y}​, then {x, y, z} is linearly dependent.
a. true
b. false
Answers
The statement is true: If x and y are linearly independent, and if z is in Span {x, y}, then {x, y, z} is linearly dependent.
The statement is true.
Let's first understand the terms used:
Linearly independent:
A set of vectors is linearly independent if none of them can be expressed as a linear combination of the other vectors. In other words, no vector in the set can be written as a sum of scalar multiples of the other vectors.
Span:
The span of a set of vectors is the set of all linear combinations of those vectors.
In this case, Span\({x, y}\) is the set of all vectors that can be formed by adding scalar multiples of x and y.
Now, let's consider the given statement:
If x and y are linearly independent, it means that neither x nor y can be expressed as a linear combination of the other. However, it is given that z is in the Span\({x, y}.\)
This means that z can be expressed as a linear combination of x and y:
\(z = ax + by\), where a and b are scalar constants.
Let's analyze the set\({x, y, z}\). We know that z can be expressed as a linear combination of x and y, as shown above. This implies that the set \({x, y, z}\)is linearly dependent, because one vector (z) can be expressed as a linear combination of the others \((x and y)\).
Thus, the statement is true: If x and y are linearly independent, and if z is in Span\({x, y}\), then\({x, y, z}\) is linearly dependent.
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What function is represented in the table? HELP!!!!
Answers
Answer:
below
Step-by-step explanation:
y = 3 * 2^x plug in the values of x (first column) to get the values in the second column
the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. when graphed, the function gives a line with a slope of . see the figure below. suppose that the height of the candle after hours is centimeters. what was the height of the candle after hours?
Answers
The linear equation that can be used to find the height considering all the information is h2 = h1 + (-0.5)(t2 - t1)
The height of a candle can be modeled by a linear function with a slope of -0.5 cm/hour.
If the height of the candle after t1 hours is h1 centimeters, then the height of the candle after t2 hours is given by h2 = h1 + (-0.5)(t2 - t1).
So, if the height of the candle after t1 hours is h1 centimetres, and after t2 hours is h2 centimeters, we have:
h2 = h1 + (-0.5)(t2 - t1)
We can use the given information to find the value of h1, and then use the equation above to find the value of h2.
However, the information given in the question is not enough to solve for h1 and h2. We need more information such as the height of the candle after a certain number of hours.
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a value of 36 ml is a measure of
Answers
Answer:
Step-by-step explanation:
The correct answer is Volume.
Milliliter: Is a unit of volume for liquids and gases that is equal to a thousandth of a liter. This refers to Volume so Volume is correct!
Kasen has 3 liters of punch. He adds another 1/2 liter of juice to the punch. How many milliliters of punch does he have now?
Answers
The correct answer is 3500 milliliters of punch now.
Kasen has 3 liters of punch. He adds another 1/2 liter of juice to the punch. How many milliliters of punch does he have now?
Kasen has 3 liters of punch. When he adds 1/2 liters of juice to the punch, the total amount of juice in the punch increases to (3 + 1/2) liters.
Therefore, Kasen now has (6/2 + 1/2) liters of punch= 7/2 liters of punch
To convert liters to milliliters, we need to remember that there are 1,000 milliliters in one liter. Therefore, Kasen has (7/2) x 1,000 = 3,500 milliliters of punch now.
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Ramona drew an isosceles triangle. Two
angles of the triangle measured 48° each.
Which equation can be used to find X, the
measure of the third angle?
A 2x + 48 = 180
B 2x ÷ 48 = 360
C x + 2(48) = 180
D x + 2(48) = 360
Answers
The measure of the third angle (represented by x) is 84 degrees.
The answer is option C, x + 2(48) = 180.
To find the measure of the third angle in the isosceles triangle, we can use the fact that the sum of all angles in a triangle is 180 degrees.
Since two angles of the isosceles triangle measure 48 degrees each, we can write:
48 + 48 + x = 180
Simplifying this equation, we get:
96 + x = 180
Subtracting 96 from both sides, we get:
x = 84
Therefore, the measure of the third angle (represented by x) is 84 degrees.
Option C, x + 2(48) = 180, is the correct equation that represents the above reasoning.
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((sqrt(cos(x))*cos(500*x)+sqrt(abs(x))-0.4)*(3-x*x)^0.1
Answers
The given expression is a combination of various mathematical functions, including square root, cosine, absolute value, and power functions. It is a complex expression that cannot be simplified any further.
The function produces a curve that oscillates rapidly and has multiple peaks and valleys. The graph of this function is periodic with a period of 2π. The value of the expression depends on the input value of x. When x is close to zero, the value of the expression is positive. As x moves away from zero, the value of the expression becomes negative until it reaches a minimum point, then it becomes positive again. The behavior of the expression is very sensitive to small changes in the input value of x, making it a challenging function to work with.
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i'm confused with this who knows about this?
Answers
Answer:
its C :)
Step-by-step explanation:
What is the value of −7 + (−12) + 81?
−100
−76
62
86
Answers
Which of the following is the closest to 15%? A. 1/7 B. 1/5 c. 1/4 d 1/3
Answers
Answer:
15%=0.15
1÷7=0.14
1÷5=0.2
1÷4=0.25
1÷3=0.33
Step-by-step explanation:
1/7
Answer:
1/7
Step-by-step explanation:
1/7 × 100 = 14.28%
1/5 × 100 = 20%
1/4 × 100 = 25%
1/3 × 100 = 33.33%
→ We can that 14.28% is the closest to 15% so 1/7 is the answer
The state of Colorado is 3 centimeters long and 4 centimeters wide on a map. A cartographer wants to use a scale factor of 1.5 to enlarge the map. What is the area of the enlarged map?
42 cm2
27 cm2
21 cm2
18 cm2
Answers
Answer:27 cm squared
Step-by-step explanation: we take both numbers(3,4) and multiply them by the scale factor of 1.5 giving you 4.5 and 6, then you find the area of the new colorado by multiplying 4.5 and 6 giving you 27 centimeters squared.
The following is the Ratio-to-Moving average data for Time Series of Three Years Seasons Ratio to moving average Year Q1 2019 2020 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 0.87 1.30 1.50 0.65 0.77 1.36 1.35 0.65 2021 Find the seasonal index (SI) for Q4 (Round your answer to 2 decimal places)
Answers
The value the seasonal index (SI) for Q4 is 0.63.
To find the seasonal index (SI) for Q4, the first step is to calculate the average of the ratio-to-moving average for each quarter.
The formula for calculating seasonal index is as follows:
Seasonal Index = Average of Ratio-to-Moving Average for a Quarter / Average of Ratio-to-Moving Average for all Quarters
To find the seasonal index (SI) for Q4:
1: Calculate the average of the ratio-to-moving average for Q4.Q4 average = (0.65 + 0.65) / 2 = 0.65S
2: Calculate the average of the ratio-to-moving average for all quarters.All quarters average = (0.87 + 1.30 + 1.50 + 0.65 + 0.77 + 1.36 + 1.35 + 0.65) / 8 = 1.03
3: Calculate the seasonal index for Q4.Seasonal Index for Q4 = Q4 Average / All Quarters Average= 0.65 / 1.03 = 0.6311 (rounded to 2 decimal places)
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Use elimination to solve the system x - 5y = 20 and x + 3y = -4 for x
Answers
Answer:
Step-by-step explanation:
Answer:
the x is 5
Step-by-step explanation:
x=5y+20:
x=5y+20
x=(5)(-3)+20
x=5 (simplify boy sides of the equation)
What value of x satisfies the equation below? Explain
how you know
-3x = 15
Answers
————
-3. -3
x= -5
Answer:
x = -5
Step-by-step explanation:
When slave starting a disabled vehicle, which of the following is an important safety consideration?
a. Ensure the battery caps are removed from bothvehicles batteries during the save start
b. Connecting the slave cable to the disables vehicle fisrt may cause damage to the batteries
c. The slaving vehicle engine must be running while connecting the slave cable
Answers
When slave starting a disabled vehicle, the term that serves an important safety consideration is c. The slaving vehicle engine must be running while connecting the slave cable
What is slave starting a vehicle?The dead car is started while the live vehicle's engine is running by inserting a slave cable into the receptacle on each vehicle.
Vehicles with manual transmissions rely heavily on the clutch slave cylinder. When the pedal is depressed, the clutch is disengaged and the transmission is shifted thanks to the slave and clutch master cylinders.
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Johnny is baking muffins. The recipe calls for 1.5 cups of flour for every 1 cup of sugar. Johnny only has
0.5 cups of sugar, how much flour should he add to his recipe?
Answers
Answer:
0.75 cups of flour
Step-by-step explanation:
The recipe
1.5 cups flour - 1 cup sugar
Then
0.5 cups of sugar - ? cups of flour
You divide 1 cup into 2 to get 0.5 cups of sugar, which means the recipe is divided by half to bake the muffins. So,
1.5 divided by 2 gives you 0.75 cups of flour
(If my explanation was wrong, please correct me, Thanks :)
Anthony Harris earns $0.50 per hamper of heirloom tomatoes. One day he picked 43 hampers-worth. What was his total pay that day?
Answers
Answer:
$21.50
Step-by-step explanation:
We want to find Anthony's pay for 43 hampers.
We can multiply his pay per hamper by the number of hampers picked.
pay per hamper * hampers picked
He earns $0.50 for each hamper and he picked 43 hampers. Therefore, we can multiply $0.50 and 43 to find his pay for the day.
$0.50 * 43
$21.5 = $21.50
Anthony's total pay that day is $21.50.
I NEED THIS RN SOMEONE HELP PLS
Draw a line that intersects with a regular pentagon without touching any of its vertices. What is the maximum number of diagonals that this line intersects with?
Hint 1: A polygon is a closed shape with straight sides. For a regular polygon all sides have same length and all angles between neighbouring sides are equal.
Hint 2: A diagonal is a line segment between two vertices that are not connected by a side.
Answers
Answer:sdaf f a
Step-by-step explanation:edsaf dsf
two cyclists, 42 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
Answers
The speed of the faster cyclist is 14\ miles/hr.
What is speed?
It is the average distance coverd in unit time. It is also defined as the rate of change of distance with respect to time.
Since the speed of the first cyclist is double than the second cyclist hence, the first cyclist will cover the double distance than the second cyclist. Consider the first cyclist covers 2s distance and first cyclist covers s distance. The sum of these two distances should be 42 miles. Hence,
\(2s+s=42\\3s=42\\s=14\)
Now, distance coverd by the first cyclist is \(2s=2\times 14\\=28 \ $miles\).
Now, both the cyclists meet after 2 hr hence, time taken by the first cyclist is 2 hr.
\(Speed=\frac{Total\ distance}{Total\ time}\\=28\ miles/2 \ hr\\=14\ miles/hr\)
Hence, the speed of the faster cyclist is 14\ miles/hr.
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