Let's call the grandmother's current age G and the grandson's current age S.
From the first piece of information given, we know that:
G = S + 48
From the second piece of information given, we know that:
G - 14 = 13S
We can use the first equation to substitute for G in the second equation:
(S + 48) - 14 = 13S
S + 34 = 13S
34 = 12S
S = 34/12
S = 2.8 years
So the grandson is 2.8 years old.
Now we can use this information to find the grandmother's age:
G = S + 48
G = 2.8 + 48
G = 50.8 years
So, the grandmother is 50.8 years old and the grandson is 2.8 years old.
what is the angle between the given vector and the positive direction of the x-axis? (round your answer to the nearest degree. i + sqrt (15) j
The angle between the given vector and the positive direction of the x-axis is found by taking the inverse tangent of the vector components. The angle is equal to arctan(i/sqrt(15)) = 90°.
The angle between the given vector and the positive direction of the x-axis is found by taking the inverse tangent of the vector components. The angle is equal to arctan(i/sqrt(15)) = 90°.
90°
The angle between the given vector and the positive direction of the x-axis is found by taking the inverse tangent of the vector components. The angle is equal to arctan(i/sqrt(15)) = 90°.
The angle between the given vector with components i and sqrt(15) j and the positive direction of the x-axis is equal to arctan(i/sqrt(15)) = 90°. To calculate this angle, we take the inverse tangent of the components of the vector, which is equal to 90°. This angle is then rounded to the nearest degree, resulting in an angle of 90° between the two.
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Write the first five terms of the sequence that is represented by the recursive function
f(1) =3
f(n) = f(n-1) = 4, where n is an integer and n > 1.
The first five terms of the arithmetic sequence are given as follows:
3, -1, -5, -9, -13.
How to model the arithmetic sequence?An arithmetic sequence is a sequence for which the difference between consecutive terms is constant, being called common difference d.
The recursive definition is given as follows:
f(n) = f(n - 1) + d.
For this problem, the definition is given as follows:
f(n) = f(n - 1) - 4.
Meaning that the common difference is of 4, and hence each term is obtained subtracting the first term by 4, starting with the first term given by f(1) = 3.
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how to solve 9x-3y=5 & 2x -3y=7 using the elimination method
The solution to the system of equations 9x - 3y = 5 and 2x - 3y = 7 is (-2/7, -53/21)
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Given the equations:
9x - 3y = 5 (1)
2x - 3y = 7 (2)
To solve by elimination method, subtract equation 2 from 1, hence:
7x = -2
Dividing by 2:
x = -2/7
Put x = -2/7 in equation 2:
2(-2/7) - 3y = 7
y = -53/21
The solution is (-2/7, -53/21)
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The local coffee shop ran a summer special. With the purchase of an $8.75 reusable mug, the cost of a coffee would only be $1.95 per cup for every visit through out the entire month. If Bre spent a total of $41.90 in the month of July, how many cups of coffee did she purchase?
PLS HELP
Answer: X = 17
Step-by-step explanation:
8.75 + 1.95x = 41.9
1.95x = 41.9 - 8.75
1.95x = 33.15
x = 33.15/1.95
x = 17
) draw a chord that goes between points a and b. 2) identify how many points along the curve have a tangent line parallel to the chord through . watch for rules about when there are and aren't tangent lines to the curve.
There are no points along the curve that have a tangent line parallel to the chord through A and B.
1) The chord between points A and B is a straight line connecting those two points.
2) There are no points along the curve that have a tangent line parallel to the chord through A and B, since the chord is a straight line and the curve is curved.
1) To draw the chord between points A and B, you must use a straight line to connect those two points.
2) Since the chord is a straight line and the curve is curved, there are no points along the curve that have a tangent line parallel to the chord through A and B.
To draw the chord between points A and B, draw a straight line connecting those two points. However, since the chord is a straight line and the curve is curved, there are no points along the curve that have a tangent line parallel to this chord. This is due to the fact that tangent lines only exist at points where the curve changes direction, and the chord is a straight line, not affected by the curvature of the curve. Therefore, there are no points along the curve that have a tangent line parallel to the chord through A and B.
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One of the legs of a right triangle measures 11 cm and the other measures 14 cm
The measure of hypotenuse of the triangle whose sides are given would be = 17.80cm
How to find the hypotenuse of triangle?The formula used to calculate the hypotenuse of a triangle is the Pythagorean formula= C²= a² + b²
Where c = hypotenuse = ?
a² = 11 cm
b² = 14 cm
Substitute the given values into the formula to find hypotenuse.
c² = 11² + 14²
c² = 121+196
c² = 317
C = √317
C = 17.80cm.
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Complete question:
One of the legs of a right triangle measures 11 cm and the other leg measures 14 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
(a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use μ 20−39 −μ 60 and older.)Interpret the interval. O We cannot draw a conclusion from the given information. O We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval. O We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval. O We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval.
We have a 95% confidence interval around the real average height of younger women being greater than that of older women.
What is meant by real average?You will make the same amount of money if you earn $50,000 this year as you did last year. The purchasing power you previously had will be impacted if inflation changes. The cost of things increases by 2% if inflation does as well. An estimated $54,132 is the annual take-home pay for the average American worker. According to location, education level, and other criteria, salaries might vary widely. Along with net worth and assets, income is a crucial component of your total financial wellness. A reference base period's average hourly wage rate expressed in USD. It demonstrates how much merchandise and services one hour of labour can acquire. Real wage rate is calculated as follows: 100% x (current-year nominal wage rate / current-year CPI).To learn more about real average, refer to:
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Sandy used a virtual coin toss app to show the results of flipping a coin 50 times, 400 times, and 2,000 times. Explain what most likely happened in Sandy's experiment.
A. Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
B. Sandy's experimental probability was closest to the theoretical probability in the experiment with 400 flips.
C. Sandy's experimental probability was closest to the theoretical probability in the experiment with 50 flips.
D. Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The correct option regarding the probabilities for Sandy's is given as follows:
A. Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
How to obtain the probability?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
For the theoretical probability, the outcomes are considering without any experiment, while for an experimental probability the outcomes are taken from previous experiment.
This means that for a large number of trials, these probabilities should be very close, meaning that the correct option is given by option A.
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Its A...............
Step-by-step explanation:
when performing an addition or subtraction calculation, significant figures in the calculated result are dictated by the decimal places of the measured numbers. the calculated result should have choose... the measured number in the calculation with the fewest
The number with the fewest Decimal point will determine the number of significant figures in the calculated result.
The significant figures in the estimated result of an addition or subtraction calculation are determined by the decimal places of the measured values. This is so that the computed result can accurately reflect the precision of the measurement, which is shown by the decimal points in the measured values. Therefore, in the calculation with the fewest decimal places, the calculated result should have the same number of decimal places as the measured value. The result should have two decimal places, for instance, if one number has two decimal places and the other has four. By doing this, it is ensured that the result is not given a higher level of precision than the measured data utilized in the computation warrant.
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please help. solve the inequality
Answer:
x ≤ - 2 ; 0 ≤ x ≤ 7
Step-by-step explanation:
x ≤ - 2
0 ≤ x ≤ 7
Which expression is the least absolute value ?
|-28|
|-1|
|6|
|15|
Answer:
|-28|
Step-by-step explanation:
-28 is the least value in the expression given
There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple? (Give your answer as a fraction in simplest form.)
The probability that the next fruit out of the bag is an apple is P = 4/5
How to find the probability?We want to fnind the probability of randomly selecting an apple from the bag, where we assume that all the fruits have the same probability of being randomly selected.
Remember that the probability is equal as the quotient between the number of apples and the total number of fruit on the bag.
Originally, there are:
4 apples.3 peaches2 plums.The checkout person takes 2 plums and 1 peach, so now there are:
4 apples.1 peach.For a total of 4 + 1 = 5 fruits
Then the probability of randomly grabing an apple is:
P = 4/5
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Some values of functions f, g, h, and k are provided in the table on the right.
Find a possible equation of each function Verify your results with a graphing
calculator table. (HINT Use linear or exponential equations]
The equation of function f is f(x) =?
Without any values of the functions f, g, h, and k, it is not possible to find the equation of each function. The equation of a function can be determined by analyzing the values of the function. Based on the given values, a possible equation can be found and then verified by plotting the points on a graph and seeing if they align with the equation.
It's important to note that the equation can be a linear or exponential equation but it's impossible to determine it without any values.
HELP!!! You go out to dinner and the bill comes to $40.94. How much should you tip if you want the tip to be 15.0% of the bill? Express the dollar amount to the nearest cent
Answer: 6.14for the tip
Step-by-step explanation:
Answer:
$6.14
Step-by-step explanation:
Well, first step is to divide 15.0% by $40.94.
Then you get 6.141
Translate that to money, rounding off, you get:
$6.14!
I hope this helps! Great to be of service to you!
Find the area of the circle, given the square has an area of [tex]144 cm^{2}[/tex]. Leave your answer in terms of π.
A) 24π [tex]cm^{2}[/tex]
B) 144π[tex]cm^{2}[/tex]
C) 36π[tex]cm^{2}[/tex]
The area of this inscribing circle is 36π cm².
What are the dimensions of a square?The area of a square is a product of it's any two sides or a product of diagonals divided by two. If side has a length a then diagonal is a√2.
The perimeter of a square is the sum of the lengths of all the sides.
We know area of a square is side².
Given, The area of this square is 144 cm².
We know 12×12 is 144.
Therefore, The length of the sides of this square is 12 cm.
We know a circle inscribed in a square has a diameter that is equal to the side of a square.
Therefore, The diameter of this circle is 12 and hence radius is 12/2 = 6 cm.
We also know that the area of a circle is πr².
Therefore, The area of this circle is π(6)² cm².
= 36π cm².
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NEED HELP ASAP Select from the drop-down menu to correctly complete the statement.
The product of 7 and 58 is
Choose...
because 58 is less than 1.
Drop downs: greater than 7
less than 7
equal to 7
The product of 7 and ⁵/₈ is less than 7 because ⁵/₈ is less than 1
How to find the product of fractions?We want to find the product of 7 and ⁵/₈.
Now, this will be expressed as;
7 * ⁵/₈.
Now, we are multiplying a whole number by a proper fraction that is less than 1 and as such, it means that the product will be lesser than 7 simply because ⁵/₈ is less than 1.
Thus;
7 * ⁵/₈ = 35/8
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Use the converse of the Pythagorean theorem to determine whether the triangle is
right, obtuse or acute.
9 m
15 m
10 m
The given triangle is obtuse triangle according to the corollary to the converse of the Pythagorean Theorem.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
The triangle's longest side measures 15 units in length.
Compare the sum of the squares on the other two sides to the square that is the length of the longest side.
The square of the longest side is 15², which equals 225.
9² + 10² = 181 square units make up the sum of the squares on the other two sides.
Thus, 181 < 15².
As a result, the triangle is an obtuse triangle according to the corollary to the converse of the Pythagorean Theorem.
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Identify the pattern in the list of numbers. Then use this pattern to find the next number. 5,7,12,19,31,50
The next number in the sequence is 81.
The pattern in the list of numbers is that each number is the sum of the previous two numbers in the sequence. It is a Fibonacci sequence.
The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1.
So, to find the next number, we add the two last numbers of the sequence:
50 + 31 = 81
Therefore, the next number in the sequence is 81.
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can you help me with my math today
Thank you to anyone that can help I am ever so appreciative!!
Answer:
C. Angle Bisector Theorem
x = 5
PO = 34
Step-by-step explanation:
The theorem used is C: Angle bisector theorem
A can be eliminated because there is no midsegment here
B can also be eliminated - no perpendicular bisector
D relates to a median and there is no median here
C is the best choice. You can see in the figure that EO bisects ∠NEP.
Because of this angles ∠NEO and ∠OEP are equal
That makes the triangles congruent since we have one common side and two angles that are equal to each other
Therefore PO = NO
8x - 6 = 6x + 4
8x - 6x = 4 + 6
2x = 10
x = 5
PO = 8(5) - 6 = 40 - 6 = 34
Find the surface area of the soild.
The surface area of the square pyramid shown is 466.56 in²
What is an equation?An equation is an expression showing the relationship between numbers and variables.
The shape shown is a square pyramid with 5 surfaces. The surface area is the sum of each individual area surface. It is given as:
Surface area = base² + 4(1/2 * base * height)
base = 10.8 in, height = 16.2 in, hence:
Surface area = 10.8² + 4(1/2 * 10.8 * 16.2) = 466.56 in²
The surface area of the solid is 466.56 in²
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what is the y-intercept in the following equation y=-4x-5
Answer:
y intercepts : (0, -5)
Step-by-step explanation:
hope it helps<3Answer:
(0,-5)
Step-by-step explanation:
a jet airplane reaches 769. km/h on a certain flight. how long does it take to cover 272 m?Set up the math. But don't do any of it. Just leave your answer as a math expression. Also be sure your answers includes all the correct unit symbols.
The airplane will take 0.0095 seconds to cover 272 meters at a rate of 769 kilometers per hour, which is equivalent to 213.6 meters per second.
(272 m) / (769 km/h) x (1 h/3600 s) = 0.0095 s
1. Convert km/h to m/s: 769 km/h x (1000 m/1 km) x (1 h/3600 s) = 213.6 m/s
2. Divide the distance to travel (272 m) by the rate (213.6 m/s): 272 m / 213.6 m/s = 0.0095 s
The airplane's speed on this certain flight is 769 kilometers per hour. In order to calculate how long it will take to cover a distance of 272 meters, we must first convert the speed to meters per second. 769 kilometers per hour is equivalent to 213.6 meters per second. Once we have the rate, we can divide the distance by the rate, which is 272 meters divided by 213.6 meters per second. This calculation yields a result of 0.0095 seconds. Therefore, the airplane will take 0.0095 seconds to cover 272 meters.
The airplane will take 0.0095 seconds to cover 272 meters at a rate of 769 kilometers per hour, which is equivalent to 213.6 meters per second.
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The GDP in Canada is $1.65 trillion. The rate of
inflation is 2.5%. If the population of Canada is
36,732,000, find the per capita GDP in this country.
per capita GDP = $ [?]
Round to the nearest hundredth.
Enter
PH
The per capita GDP can be calculated by dividing the total GDP by the population.
How is this calculated?$1.65 trillion (GDP) / 36,732,000 (population) = $45,073.58 (per capita GDP)
This means that, on average, each person in Canada has a GDP of $45,073.58. However, it's important to note that this number doesn't necessarily reflect the distribution of wealth within the country. It's just a way of measuring the overall economic output of a country on a per person basis.
Additionally, it's worth noting that this number only takes into account the GDP and population at the time of the calculation. The inflation rate of 2.5% would increase the GDP but not the population so it's not considered in this calculation
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Given the following probabilities for choosing 2 marbles from a bag of 10 marbles, determine if the events are dependent or independent.
P(blue) = 3/10 , P(green) = 1/5 , and P(blue and green) = 3/100
probabilities for choosing 2 marbles from a bag of 10 marbles is Dependent events
Given the following probabilities for choosing 2 marbles from a bag of 10 marbles are:-
P(blue) = 3/10, P(green) = 1/5, P(blue and green) = 3/100
We know the fact that two event are independents if we have following:-
P(X and Y) = P(X) times P(Y)
For this problem, we must have P(blue and green) = P(blue) times P(green).
P(blue and green) = (3/10) * (1/5) = 3/50
But given P(blue and green) = 3/100
Since we have 3/100 ≠ 3/50
Hence, the events are not independent events.
So, they are dependent events.
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ara sells apples at a farmers market she begins the day with 35 1/2 pounds of apples she sells half of the apples in the mornning 4/19 of the apples in the afternoon and 1/4 of the apples in the evening how many pounds of apples dose she have left
Using mathematical operations, Ara's remaining pounds of apples are 1.405 pounds.
What are mathematical operations?The four basic mathematical operations are addition, subtraction, division, and multiplication.
In this situation, we applied the mathematical operations of multiplication, addition, and subtraction to determine the difference (or the quantity of apples left) between the quantity brought to the market and the quantity sold.
The total quantity of apples = 35¹/₂ pounds
The quantity sold in the morning = ¹/₂ of 35¹/₂ pounds = 17.75 pounds
The quantity sold in the afternoon = ⁴/₁₉ of 35¹/₂ pounds = 7.47 pounds
The quantity sold in the evening = ¹/₄ of 35¹/₂ pounds = 8.875 pounds
The total quantity sold = (¹/₂ + ⁴/₁₉ + ¹/₄) = ³⁶/₃₈ of 35¹/₂ pounds = 34.095 pounds
The remaining pounds of apples = 1.405 pounds (35.5 - 34.095)
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the gini coefficients for countries a and b are 0.25 and 0.30, respectively. we can definitely conclude that group of answer choices none of the above the lowest 20 percent family income group receives a greater share of total income in country a than in country b. the lowest 50 percent family income groups in a and b receive 25 percent and 30 percent of total income, respectively. the lowest 20 percent family income group receives a greater share of total income in country b than in country a. the lowest 20 percent family income groups in a and b receive 25 percent and 30 percent of total income, respectively.
The Gini coefficients for countries A and B are 0.25 and 0.30, respectively. This situation is justified by the option E: None of the above.
What is Gini coefficient?
The Gini coefficient, commonly referred to as the Gini index or Gini ratio, is a measure of demographic distribution used in economics to estimate the average income of a population. The most often used method for estimating inequality is the Gini coefficient.
The Italian statistician and sociologist Corrado Gini is honoured as the creator of the Gini Coefficient.
If everyone has the same wealth or income, then a Gini coefficient of 0 implies complete equality, whereas a value of 1 indicates perfect inequality (that is, where one person owns all the wealth in a country).
For most nations, the value actually ranges between 0 and 1. It would be close to 1 in nations with significant levels of inequality.
The options are -
The lowest 20 percent family income groups in A and B receive 25 percent and 30 percent of total income, respectively.
The lowest 50 percent family income groups in A and B receive 25 percent and 30 percent of total income, respectively.
The lowest 20 percent family income group receives a greater share of total income in country A than in country B.
The lowest 20 percent family income group receives a greater share of total income in country B than in country A.
These all are incorrect as for country A, 0.25 Gini coefficient means that the 25% of the country's population has all the wealth and for country B, 0.30 Gini coefficient means that the 30% of the country's population has all the wealth.
Therefore, none of the options justify the answer.
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The Gini coefficients for countries A and B are 0.25 and 0.30, respectively. We can definitely conclude that
a) the lowest 20 percent family income groups in A and B receive 25 percent and 30 percent of total income, respectively.
b) the lowest 50 percent family income groups in A and B receive 25 percent and 30 percent of total income, respectively.
c) the lowest 20 percent family income group receives a greater share of total income in country A than in country B.
d) the lowest 20 percent family income group receives a greater share of total income in country B than in country A.
e) none of the above
find $53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} 1\frac{2}{3} \right)$. express your answer as a mixed number.
The result of [tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} - 1\frac{2}{3} \right)$[/tex] is[tex]$-56\frac{13}{20}$[/tex]
A mixed number is a combination of a whole number and a fraction, like [tex]3\frac{1}{2}[/tex], expressing numbers greater than one whole unit. It can be converted to an improper fraction.
To find the solution of [tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right) \div \left(2\frac{3}{4} - 1\frac{2}{3} \right)$[/tex]
We can first simplify the inner parenthesis
[tex]$53\cdot\left(3\frac{1}{5} - 4\frac{1}{2}\right)=53\cdot(-1\frac{1}{10})=-53\frac{11}{10}$[/tex]
Then simplify the denominator, The denominator is the bottom part of a fraction, which represents the total number of parts in the whole. It is used to indicate the size of the fraction's unit or whole. It is also used to divide the numerator (top part of a fraction) by in order to determine the fraction's value.
[tex]$2\frac{3}{4} - 1\frac{2}{3} = \frac{11}{4} - \frac{5}{3} = \frac{44}{12} - \frac{20}{12} = \frac{24}{12} = 2$[/tex]
Now we can divide -53 and 11/10 by 2
[tex]$-53\frac{11}{10} \div 2 = -53\frac{11}{20} = -\frac{1133}{20} = -56\frac{13}{20}$[/tex]
So, the answer is [tex]$-56\frac{13}{20}$[/tex]
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Kevin hiked up Lamb's Canyon in 3 hr and then ran back down in 2 hr. His speed running downhill was 1.8 mph greater than his speed hiking uphill. How far up the canyon did he hike?
Kevin hiked (blank) mi up the canyon.
Kevin hiked up Lamb's Canyon with the goal of making it to the top.
How far up the canyon did he hike?To solve it, you need to set up two equations - one for hiking and one for running.Let x be the distance Kevin hiked up the canyon.
For hiking: 3 hr = x / h
For running: 2 hr = (x + 1.8) / r
Where h is the speed at which Kevin hiked uphill and r is the speed at which he ran downhill.Solving the two equations for x yields:
x = (3h * r) / (h + r)
To find the distance Kevin hiked up the canyon, you need to plug in the values for h and r.Therefore, Kevin hiked (3h * r) / (h + r) mi up the canyon.
For the distance that Kevin hiked uphill, the equation would look like this:Distance = (x mph) * (3 hr)
For the distance that Kevin ran downhill, the equation would look like this:Distance = (x + 1.8 mph) * (2 hr)
We can combine these two equations by setting them equal to each other and solving for x. We get:(x mph) * (3 hr) = (x + 1.8 mph) * (2 hr)
Solving for x, we get x = 2.4 mph.
Now that we know x, we can plug it back into our original equation for the distance that Kevin hiked uphill. We get:Distance = (2.4 mph) * (3 hr) = 7.2 mi. Therefore, Kevin hiked 7.2 mi up the canyon.To learn more about to find the distance refer to:
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Is 4.259462364423... Rational or irratioL
