In 1990, the cost of tuition at a large Midwestern university was $94 per credit hour. In 2004, tuition had risen to $290 per credit hour.
Determine a linear function
C
(
x
)
to represent the cost of tuition as a function of
x
, the number of years since 1990.
The linear function c(x) to represent the cost of tuition as a function of "the number of years since 1990" denoted by "x" is [tex][c(x) = 14x+94][/tex].
As per the question statement, the cost of tuition at a large Midwestern university was $94 per credit hour in 1994 while it had risen to $290 per credit hour in 2004.
We are required to determine a linear function c(x) that represents the cost of tuition as a function of "the number of years since 1990", denoted by "x".
To solve this question, we need to know the equation of a line passing through two points (x₁, y₁) and (x₂, y₂) which goes as
[tex](y-y_{1} )=(\frac{y_{2} -y_{1} }{x_{2} -x_{1}})(x-x_{1})[/tex].
Here, if we consider (x = 0) at 1990, c(x) = 94.
And since the standard form of conversion of functions into coordinate points goes as [y = f(x)], i.e., the ordinate is a function of the abscissa, therefore in this case, [y = c(x) = 94].
Thus, we can consider (x₁, y₁) as (0, 94).
Similarly, at 2004, [x = (2004-1990) = 14], and c(x) = 290, i.e.,
We can consider as (x₂, y₂) as (14, 290).
Using the values of (x₁, y₁) and (x₂, y₂), in the above mentioned standard equation of line passing through two points, we get,
[tex](y-94)=\frac{290-94}{14-0} (x-0)\\or, (y-94)=\frac{196}{14}x\\or,(y-94)=14x\\or,y=14x+94[/tex].
Hence, the linear function c(x) that represents the cost of tuition as a function of "the number of years since 1990", denoted by "x" is [tex][c(x) = 14x+94][/tex].
Linear Function: In Mathematics, a function is an operator which when provided with a input, gives a certain output, and when a function can be depicted in form of a linear equation, it is known as a linear function.To learn more about Linear Functions, click on the link below.
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If mpoq =19 mqor=31 and ros = 15 what is mpos
The m∠POS would be - 65° by the angle addition postulate and substitution postulate.
Given, m∠POQ = 19° , m∠QOR = 31° and m∠ROS = 15°
Angle Addition Postulate is the measure of the larger angle is the sum of the measures of the two smaller angles.
Substitution postulate states that a quantity may be substituted for its equality in any expression.
Then substitute the angle measurements into the resulting equation to find, m∠POS:
m∠POQ + m∠QOR = m∠POR (by angle addition)
m∠POR + m∠ROS = m∠POS (by substitution)
m∠POS = m∠POQ + m∠QOR + m∠ROS
= 19° + 31° + 15°
= 65°
Thus, the m∠POS would be - 65° by the angle addition postulate and substitution postulate.
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leta had $45 in her account in may. how much money does she have in her account in august?
Leta has $24 in her account in august;
Amount of money in Leta's Account in may=$ 45
If leta has not spent a penny till august,and not added a penny in her account, then amount of money in leta's account = $45
Money in Leta's account in June = $45 - $17 = $28
Money in Leta's account in July = $28 - $22 = $6
Money in Leta's account in August = $6 + $18 = $24
Amount, sum, sum of money; "he borrowed a considerable sum," "the amount he had in cash was insufficient." Gain is the difference between a company's revenue and operating expenses. The whole amount of income before any deductions is referred to as gross, receipts, or revenue.
The amount of money you have accessible in your checking or savings account is known as your account balance in the world of banking. The net amount remaining in your account after all deposits and credits have been balanced against any charges and debits is your account balance.
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If 3/8 in. on a drawing represents 1 ft, how many inches on the drawing will represent 42 ft?
Answer:
[tex]\frac{63}{4}[/tex]
Step-by-step explanation:
[tex]\frac{42}{1} x \frac{3}{8}[/tex]
Cross out common factors 42 & 8;
[tex]21 * \frac{3}{4}[/tex]
Write as a single factor.
[tex]\frac{21*3}{4}[/tex]
21*3= 63
[tex]\frac{63}{4}[/tex]
Consider the set of all factors of 42 and 48 are greater than 1, with no repeating element. What is the median of the set?
A. 7
B. 12
C. 7.5
D. The set has no median.
The tutor who answered this question said C, but I don't understand how he got that answer. Can you please help?
Answer:
it is C because If you subtract 48 from 42 and then you ad 1 you get 7.5
Evaluate m•s when m=2 and s=5
The value of the expression m • s will be 10 after evaluating it for m = 2 and s = 5.
We are given an expression:
m • s
We need to evaluate the expression for m = 2 and s = 5
So, after substituting the values in the expression, we get that:
m • s
= ( 2 ) • ( 5 )
Multiplying the values, we get that:
= 10
Therefore, the value of the expression m • s will be 10 after evaluating it for m = 2 and s = 5.
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Carl’s grandfather is exactly 5 times older than Carl.
Which three statements must be true?
please help me
Copyright © McGraw Hill
7. The table gives information about how many
times a butterfly flaps its wings in a set
amount of time. Write a description of the
relationship. Include if it is proportional. If it
is, give the constant of proportionality and
the unit rate. If it is not, explain why not.
(Example 5)
Time (sec)
1
Number of Wing Flaps 20
2 3
4
40 60 80
3.1
8. The table s
runner. Use
proportion
Distance
Time (h)
The description in the table is that for every second, there are 20 wing flaps.
How to illustrate the information?It should be noted that the constant of proportionality is a term that used to show the proportional relationship between different values.
In the table, at 1 second, the number was 20 while at 2 seconds, the number of wing flaps is 40.
Therefore, the constant of proportionality will be:
= 20/1
= 20
Therefore, the description in the table is that for every second, there are 20 wing flaps.
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12 pages in 2 days = pages per day Submit
Answer:
6
Step-by-step explanation:
Answer:
6 pages per day
Step-by-step explanation:
Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).
A recent survey by the American Automobile Association showed that a family of two adults and two children on vacation in the United States will pay an average of $247 per day for food and lodging with a standard deviation of $60 per day. If the data are normally distributed, find the percentage of these families who spent:
a. Less than $167 per day. _____
b. Less than $367 per day. _____
c. More than $247 per day. _____
d. More than $350 per day. _____
e. Less than $67 per day. ______
f. Between $200 and $300 per day. _____
g. Between $360 and $400 per day. _____
h. More than the median. ____
i. Less than the mean. _____
Using the normal distribution, the percentages are given as follows:
a) 9.18%.
b) 97.72%.
c) 50%.
d) 4.27%.
e) 0.13%.
f) 59.29%.
g) 2.46%.
h) 50%.
i) 50%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, the mean and the standard deviation are given as follows:
[tex]\mu = 247, \sigma = 60[/tex]
For item a, the proportion is the p-value of Z when Z = 167, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (167 - 247)/60
Z = -1.33.
Z = -1.33 has a p-value of 0.0918.
Hence the percentage is of 9.18%.
For item b, the proportion is the p-value of Z when Z = 367, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (367 - 247)/60
Z = 2.
Z = 2 has a p-value of 0.9772.
Hence the percentage is of 97.72%.
For item c, the proportion is one subtracted by the p-value of Z when X = 247, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (247 - 247)/60
Z = 0
Z = 0 has a p-value of 0.5.
Hence the percentage is of 50%.
For item d, the proportion is one subtracted by the p-value of Z when X = 350, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (350 - 247)/60
Z = 1.72
Z = 1.72 has a p-value of 0.9573.
1 - 0.9573 = 0.0427.
Hence the percentage is of 4.27%.
For item e, the proportion is the p-value of Z when Z = 67, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (67 - 247)/60
Z = -3.
Z = -3 has a p-value of 0.0013.
Hence the percentage is of 0.13%.
For item f, the proportion is the p-value of Z when X = 300 subtracted by the p-value of Z when X = 200, hence:
X = 300:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (300 - 247)/60
Z = 0.88.
Z = 0.88 has a p-value of 0.8106.
X = 200:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (200 - 247)/60
Z = -0.78.
Z = -0.78 has a p-value of 0.2177.
0.8106 - 0.2177 = 0.5929.
Hence the percentage is 59.29%.
For item g, the proportion is the p-value of Z when X = 400 subtracted by the p-value of Z when X = 360, hence:
X = 400:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (400 - 247)/60
Z = 2.55.
Z = 2.55 has a p-value of 0.9946.
X = 360:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (360 - 247)/60
Z = 1.88.
Z = 1.88 has a p-value of 0.97.
0.9946 - 0.97 = 0.0246
Hence the percentage is 2.46%.
For items h and i, the distribution is symmetric, hence median = mean and the percentages are of 50%.
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A worm is at the bottom of a ravine. Every day it climbs up 5 feet, but every night while it is sleeping, it falls back 3 feet. a) How long will it take the worm to crawl up the ravine if it is 20 ft high? b) What if the ravine is 97 feet high?
Answer:
a) 9 days
b) 47 days
Step-by-step explanation:
Given information:
Distance worm climbs each day = 5 ftDistance worm falls back each night = 3 ftPart (a)[tex]\begin{array}{|c|r|c|r|}\cline{1-4} \sf Day & \sf Height\:{(ft) & \sf Night & \sf Height\:(ft) \\\cline{1-4} 1 & 5 & 1 & 5 - 3 = 2\\\cline{1-4} 2 & 2 + 5 = 7 & 2 & 7 - 3 = 4 \\\cline{1-4} 3 & 4 + 5 = 9 & 3 & 9 - 3 = 6 \\\cline{1-4} 4 & 6 + 5 = 11 & 4 & 11 - 3 = 8 \\\cline{1-4} 5 & 8 + 5 = 13 & 5 & 13 - 3 = 10 \\\cline{1-4} 6 & 10 + 5 = 15 & 6 & 15-3=12\\\cline{1-4} 7 & 12 + 5 = 17 & 7 & 17 - 3 = 14 \\\cline{1-4} 8 & 14 + 5 = 19 & 8 & 19-3=16\\\cline{1-4} 9 & 16 + 5 = 21 &&\\\cline{1-4}\end{array}[/tex]
On the first day the worm climbs 5 ft, but slips back 3 ft during the first night.
On the second day the worm climbs a further 5 ft, so is now at 7 ft, but slips back 3 ft during the second night. Therefore, it starts the third day at a height of 4 ft.
The progression continues this way so that the worm starts the 9th day at a height of 16 ft. As it climbs 5 feet during the day, it will reach the height of 20 ft during the 9th day, and so will climb out of the ravine before it sleeps for the night.
Therefore, it will take 9 days for the worm to crawl up a 20 ft ravine.
This can be modeled as an arithmetic sequence:
[tex]y=a+(x-1)d[/tex]
where:
y = height of ravinex = number of daysa = initial height after the first dayd = common difference = 2Therefore:
[tex]\implies y=5+(x-1)2[/tex]
[tex]\implies y=5+2x-2[/tex]
[tex]\implies y=3+2x[/tex]
Part (b)To calculate how long it will take the worm to crawl up the ravine if it is 97 ft high, substitute y = 97 into the equation and solve for x:
[tex]\implies 3+2x=97[/tex]
[tex]\implies 3+2x-3=97-3[/tex]
[tex]\implies2x=94[/tex]
[tex]\implies \dfrac{2x}{2}=\dfrac{94}{2}[/tex]
[tex]\implies x=47[/tex]
Therefore, it will take 47 days for the worm to crawl up a 97 ft ravine.
Cristian made an ankle bracelet using 6 red beads, 10 green beads, 4 purple beads, and 5 yellow beads. He wants to make a necklace that has the same ratio of color beads as the ankle bracelet. If the necklace has 15 yellow beads, how many purple beads will it have?
Answer:
Step-by-step explanation:
20
Sells are 3750000 what is 2.5%
Answer:
93750 is the answer!!!!!
ASHBOARD OURSES TY PATH UNCEMENTS D HELP? 7. Find the area of the circle. Use 3.14 for the value of 7. Round your answer to the nearest tenth. 804 mi O 12866.6 mi² 201 mi O226.9 mi 5.9 mi²'s 8 mi
Based on the radius of the circle and the value of pie, the area of the circle to the nearest tenth is 201 mi²
What is the area of the circle?The area of a circle can be found by the formula:
= Pie x radius x radius
The radius of this circle is 8 mi and pie is 3.14.
The area of the circle is:
= 3.14 x 8 x 8
= 3.14 x 64
= 200.96
= 201 mi²
In conclusion, the area of the circle is 201 mi².
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europa why do you keep deleting my answers and questions im just answering questions honestly and also im just asking honest questions like: who is ´The Brain´ and how does he have so many coins but doesnt ever answer and the such, im just a little curious and ur ruining the fun
Answer:
hahah thats funny
Step-by-step explanation:
X N How many lines of symmetry does the pattern have? b What is the order of rotational symmetry of the pattern?
Answer:
The answer is 5
Step-by-step explanation:
From every side
12. Damian can make 3 free-throw shots in
10 seconds and 18 free-throw shots in
1 minute. What is the constant of
proportionality?
The constant of proportionality is 0.3.
How to calculate the constant?From the information, Damian can make 3 free-throw shots in 10 seconds and 18 free-throw shots in 1 minute.
Therefore, we can choose any of the figures to solve the question since it is constant.
The constant of proportionality will be:
= Number of throes / Time taken
= 3/10
= 0.3
The constant of proportionality is 0.3.
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PLS HELP ASAP
(50 POINTS)
What is the
value of the function when x = -2?
Enter the answer in the box.
Answer: 334.600
Step-by-step explanation:
I should be that, you have to look at the line
Answer:
The right answer would be 1
Step-by-step explanation:
Mum bought some steaks . She put 2/5 of them in the refrigerator and the rest in the freezer . She put 12 in the freezer . How many streaks did she buy
Answer: 20 steaks
Step-by-step explanation: 12x0.6= 20
Find the slope to the line parallel to f(x)=-3x+12
Answer: -3
Step-by-step explanation:
Parallel lines have the same slope.
The slope of f(x)=-3x+12 is -3.
Slope: -3
Answer:
The slope would be -3
Step-by-step explanation:
The number before the x represents the slope. Parallel lines have the same slope.
Jade earned $20 for walking 4 dogs. If the ratio of money earned to dogs walked is constant, how many more dogs will she need to walk to earn a total of $100?
Answer:
Jade would need to walk 16 more dogs to earn $100 total.
Step-by-step explanation:
20 divided by 4 equals 5, so that means Jade is earnings $5 per dog. Just multiply 5 for each dog Jade walks, and you have your answer! If she already walked 4 dogs and made $20, then do 5 times 16 for your answer.
m-4=2m
Help on two step equations
Answer:
m = -4
Step-by-step explanation:
You want the solution to the "two step" equation m -4 = 2m.
Two-step equationA "two-step" linear equation is one that can be solved in two steps. The steps in general are ...
addition of somethingmultiplication by somethingThe "inverse" properties of addition and multiplication are used to identify the quantities added or multiplied.
Forms of a two-step equationThere are two forms a two-step equation might take:
ax +b = c
ax +b = cx
You will notice that one side of the equal sign has a sum of two terms: a term with the variable, and a constant term without the variable. The other side of the equation will have one term, which may be either a constant term or a variable term.
First stepThe idea of the first step is to make sure the variable term ends up on one side of the equal sign, and the constant term ends up on the other side.
The parts of the first step are ...
identify the kind of term on the side of the equation with one termidentify the term of the same kind on the other side of the equal signadd the opposite of that identified term to both sides of the equation.For the given equation ...
m - 4 = 2m
The term by itself is a variable term. The variable term on the other side of the equation is "m". The first step will be to add "-m" to both sides of the equation.
m -4 -m = 2m -m . . . . . . -m added to both sides
-4 = m . . . . . . . . . . . . . simplify
Now, we have a variable term (m) on one side of the equal sign, and a constant term (-4) on the other side. This is the desired result of the first step.
Second stepThe idea of the second step is to make the coefficient of the variable be 1. We do that by multiplying both sides of the equation by the reciprocal (inverse) of the coefficient of the variable.
For the equation ...
ax = b
we multiply by the reciprocal of 'a', which is 1/a.
(ax)(1/a) = b(1/a)
x = b/a . . . . . . . . . . . effectively, we're dividing by 'a'
In the given equation, we have ...
-4 = m
which already has a coefficient of 1 on the variable m. This means we're done, and no additional step is actually needed.
The solution is m = -4.
__
Additional comment
There is another form of 2-step equation you may see occasionally:
a(x +b) = c
Solving this can be done by reversing the order of the steps: first divide by the coefficient of x, then subtract the constant.
x +b = c/a
x = (c/a) -b
If the variable term inside parentheses has a coefficient other than 1, it may be useful to eliminate parentheses using the distributive property, then solve like a regular 2-step equation.
SOMEONE PLEASE HELPPPO
By evaluating the functions we get:
f(3)= -15f(-2) = -1g(4) = 23g(-5) = 77g(a) = 3*a^2 - 3*a - 13How to evaluate a function?Here we have the two functions:
f(x) = -2x - 5
g(x)= 3x^2 - 3x - 13
And we want to evaluate them in some values of x, first let's do the ones for f(x).
We just replace the variable x by the numbers.
f(3)= -2*3 - 5 = -10 - 5 = -15
f(-2) = -2*(-2) - 5 = 4 - 5 = -1
The ones for the function g(x) are:
g(4) = 3*4^2 -3*4 -13 = 23
g(-5) = 3*(-5)^2 - 3*(-5) - 13 = 77
g(a) = 3*a^2 - 3*a - 13
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Find the perimeter of the triangle whose vertices are (−3,−1), (1,−1), and (1,2). Write the exact answer
According to the solving the perimeter of the tringle = 12 cm.
What is the formula for triangle perimeter?Add the lengths of the triangle's sides to find its perimeter. For instance, if a triangle comprises sides a, b, as well as c, the perimeter of the that triangle is P = a + b + c.
What exactly is a 2D shape?2D objects have two dimensions, for example, width and height. A rectangle or even a circle are two-dimensional shapes. Because they have without depth, 2D forms are absolutely flat and can not be physically handled.
According to the given data:Points of the tringles:
A (−3,−1),
B (1,−1),
C (1,2)
we know that the:
Perimeter of the triangle = sum of all the side of the triangle
= AB + BC + CA
So
Length of the AB :
A (−3,−1),
B (1,−1),
AB =√((x2 – x1)² + (y2 – y1)²).
AB = √((1 – (-3))² + (-1 – (-1))²).
AB = √((4) + (0))
= √(16)
= 4
Length of the BC :
B (1,−1),
C (1,2)
BC =√((x2 – x1)² + (y2 – y1)²).
BC =√((1 – 1)² + (2 – (-1))²).
BC =√(0)² + (3)²).
BC = √(9)
= 3
Length of the CA:
A (−3,−1),
C (1,2)
CA =√((x2 – x1)² + (y2 – y1)²).
CA =√((1 – (-3))² + (2 – (-1))²).
CA =√((4))² + (3)²).
CA =√(16 + 9)
CA =√(25)
= 5
The perimeter of the triangle asked = AB + BC + CA
= 4 + 3 + 5
= 12 cm
According to the solving the perimeter of the tringle = 12 cm.
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Joseph Selects a card from a standard deck of 52 cards and then replaces it afterwards he decides to record the total number of red cards that he selects and calculates the proportion of red cards that he has selected so far after each pick he then constructs a graph to visualize his results
The answer to the given question is Option B.
Probability means possibility. A branch of mathematics that deals with the occurrence of random events. Probability is a measure of the likelihood of an event occurring. Many events cannot be predicted with absolute certainty.We can only predict the probability that an event will occur. H. Possibility of using it. Probabilities can range from 0 to 1. 0 means the event is not possible, 1 indicates the specific event. For example, if you toss a coin, you get either heads or tails. There are only two possible outcomes (H, T). But if you toss two coins in the air, three events can occur, such as ), (T, T). Probability of an event occurring P(E) = number of favorable outcomes/total number of outcomes.At no point can we distinguish between diamonds and hearts, as we are only interested in finding red cards. as a result,
The wrong statement is:
For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far.
Therefore, the ultimate answer to the given question is Option B.
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The question is incorrect, The correct question is
Joseph selects a card from a standard deck of 52 cards and then replaces it afterwards. He decides to record the total number of red cards that he selects and calculates the proportion of red cards that he has selected so far after each pick. He then constructs a graph to visualize his results. Which of the following statements is FALSE?
A. The theoretical probability for selecting a red card in each pick is 0.5.
B. For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far.
C. This is an example of the law of large numbers.
D. The relative frequency of selecting a red card changes with the increase in number of selections.
light travels about 186,000 mi / s. The function d(t) = 186,000t gives the distance d(t), in miles, that light travels in t seconds. How far does light travel in 36 s?
The distance that the light travels on 36 seconds is 6696000 miles.
How to calculate the distance?From the information, it was illustrated that light travels about 186,000 mi/s and the function d(t) = 186,000t gives the distance.
Therefore, the distance in 36 seconds will be:
d(t) = 186,000t
= 186000 × 36
= 6696000 miles.
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Jackson has 2,000 baseball cards in his collection Gabe has 1/10 as many baseball cards in his collection as Jackson. how many baseball cards does Gabe have in his collection
Answer:
2200
Step-by-step explanation:
1/10 of 2000 is 200. add it on top of 2000
A vintage car costs $32,000 when purchased. The car increases in value by approximately 7% at the end of each year, x, after it is purchased. Which inequality can be used to find the years the car is worth more than $75,000?
Answer:
[tex]32000( {1.07}^{x} ) > 75000[/tex]
The required inequality represents the worth of the car more than $75,000 is 32000[1.07]ˣ > 75000.
Given that,
A vintage car costs $32,000 when purchased. The car increases in value by approximately 7% at the end of each year, x, after it is purchased.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
According to the question,
The relationship of the cost of the car after x year,
= 32000[1 + 0.07]ˣ
= 32000[1.07]ˣ
Now, this cost should be more than $75000
So,
32000[1.07]ˣ > $75000
Thus, the required inequality represents the worth of the car more than $75,000 is 32000[1.07]ˣ > 75000.
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Two pedestrians simultaneously left two villages 27 km apart and walked toward each other, meeting after 3 hours. The first pedestrian walked at a speed of 4 km per hour. At what speed (in km per h) did the second pedestrian walk?
The speed of the second pedestrian is 5 kilometers per hour.
At what speed did the second pedestrian walk?Let's say that the speed of the second pedestrian is S.
We know that the other pedestrian walks at a speed of 4km/h, and they (together) travel a distance of 27km in 3 hours, then we can write the linear equation:
(4km/h + S)*3h = 27km
It says that both pedestrians work, together, a total of 27km in 3 hours.
Now we can solve that linear equation for S, to do this, we need to isolate S in the left side of the equation.
4km/h + S = 27km/3h = 9 km/h
S = 9km/h - 4km/h = 5km/h
The speed of the second pedestrian is 5 kilometers per hour.
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Which function has an inverse that is a function?