a) (f ∘ g)(4) = 2
b) (g ∘ f)(4) = √2 + 5
c) (h ∘ g ∘ g)(-5) = 2 - 1/ (√(2√5) + 5)
d) (g ∘ f)(x) = √(x + 5) + 5.
e) (f ∘ g)(x) = √(√x + 5) + 5
f) (h ∘ f)(x) = 2 - 1/ (√x + 5)
What is Function?
A function is an expression or relationship that involves one or more variables. It has several inputs and outputs.
a) (f ∘ g)(4) means plugging in the value of 4 into g(x) and then plugging the result into f(x). So we have:
g(4) = √4 + 5 = √9 = 3
f(g(4)) = f(3) = √3 + 5 = 2
Therefore, (f ∘ g)(4) = 2.
b) b) (g ∘ f)(4) means plugging in the value of 4 into f(x) and then plugging the result into g(x). So we have:
f(4) = √4 = 2
g(f(4)) = g(2) = √2 + 5
Therefore, (g ∘ f)(4) = √2 + 5.
c) (h ∘ g ∘ g)(-5) means plugging in the value of -5 into g(x) twice, and then plugging the result into h(x). So we have:
g(-5) = √(-5) + 5 = √(20) = 2√5
g(g(-5)) = g(2√5) = √(2√5) + 5
h(g(g(-5))) = h(√(2√5) + 5) = 2 - 1/ (√(2√5) + 5)
Therefore, (h ∘ g ∘ g)(-5) = 2 - 1/ (√(2√5) + 5).
d) (g ∘ f)(x) means plugging in the function f(x) into g(x), which gives:
g(f(x)) = √(x + 5) + 5
Therefore, (g ∘ f)(x) = √(x + 5) + 5.
e) (f ∘ g)(x) means plugging in the function g(x) into f(x), which gives:
f(g(x)) = √(√x + 5) + 5
Therefore, (f ∘ g)(x) = √(√x + 5) + 5.
f) (h ∘ f)(x) means plugging in the function f(x) into h(x), which gives:
h(f(x)) = 2 - 1/ (√x + 5)
Therefore, (h ∘ f)(x) = 2 - 1/ (√x + 5).
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amit took part in an cycle race .he started at 1:25 pm and reached the finishing line at 1:50 . what was the duration of the race ?
amit took a part in cycle race .he started at 1:25 and he reached finishing lline at 1:50 pm what was the duration of the race .
Answer:
25 minutes
Step-by-step explanation:
The time difference between 1:25 and 1:50 is 25 min
given that the electricity for home use is 5 cents per kilowatt-hour (kwh), how much would it cost to operate 5 fluorescent 40w light bulbs for the months of april and may if they are on for 3 hours/day?
The total cost to operate 5 fluorescent 40w light bulbs for the months of April and May if they are on for 3 hours/day is given as follows:
$1,830.
How to obtain the total cost?The total cost is obtained applying the proportions in the context of the problem.
The number of kilowatt hours is given as follows:
200 kw in total per day, as 5 bulbs of 40 kw -> 40 x 5 = 200 kw.Bulbs are on for 30 + 31 = 61 days.Each day, the bulbs are on for 3 hours.Hence:
200 x 61 x 3 = 36,600 kwh.
The cost is of $0.05 per kwh, hence the total cost is given as follows:
0.05 x 36600 = $1,830.
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I need explanations under similar shapes
The two major properties of similar shapes include the following:
They must have the same shape.They can have different sizes.What are the properties of similar geometric shapes?In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied because it would either enlarge (increase) or reduce (decrease) them.
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From the tree diagram find the following.
(a) P(An E)
0
(b) P(A)
(c) P(A|E)
X
0.1
0.9
A A
0.3
0.3
0.4
0.4
0.4
0.2
Answer:
(a) P(A ∩ E) = 0.03
(b) P(A) = 0.39
(c) P(A | E) = 0.1
Step-by-step explanation:
The first level of the tree gives the following probabilities
P(E) = 0.1
P(E') = 1 - P(E) = 0.9
The second level gives conditional probabilities
P(A|E) = 0.3 this is the top most branch from the root
P(A ∩ E) = P(A|E) P(E) = 0.3 x 0.1 = 0.03 Answer(a)
To find P(A) we find all routes that will end in A, compute each probability and add up the individual probabilities
For event E happening, P(A ∩ E) = 0.03 which is computed in A
However A can also happen when the complement event E' happens
P(A ∩ E') = P(A | E') P(E') = 0.4 x 0.9 = 0.36
Add these two together to get 0.03 + 0.36 = 0.39 Answer (b)
P(A|E) is nothing but the probability value when we follow the E branch first followed by the A branch
This is 0.1 answer (c)
The t-value changes depending on the number of data points collected.
a. True
b. False
The statement that " t-value changes depending on the number of data points collected" is (b) False because t-value is a statistic that is used in hypothesis testing to determine the difference between 2 sample means is significant or not.
The t-value does depend on the sample size (number of data points) as well as the sample mean and standard deviation, but it does not change "depending on" the number of data points in the sense that the same data set will always produce the same t-value for a given statistical test.
So , it is important to note that the t-value is a fixed value for a given set of data, regardless of the number of data points collected.
Therefore, if the same data set is used to perform a t-test multiple times, the resulting t-value will always be the same.
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What is the surface area of the net shown below?
▸
8 ft
3 ft
3 ft
3 ft
The surface area of the net is 108 squate feet
How to determine th surface area of the netThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
A net that has the following shapes
Rectangle: 8ft by 12 ftTwo triangles: 3ft by 4ftThe area of the net is the sum of the individual areas
So, we have
Area = 8 * 12 + 2 * 0.5 * 3 * 4
Evaluate
Area = 108
Hence, teh area is 108 squate feet
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What is the GCF of 4454 and 121j²k?
O 4j³k²
O 4j²k4
O 11j³k²
O 11j²4
The required, there is no highest common factor between 4454 and 121j²k. None of the options are correct.
What is the greatest common factor?The highest common factor (HCF) of two or more numbers is the largest number that divides all of the numbers exactly.
Here,
To find the greatest common factor (GCF) of 4454 and 121j²k, we need to factor both numbers into their prime factors and then identify the common factors.
Since 4454 is an even number and 121 is an odd number so there is no prime highest common factor between the given number.
Thus, none of the options are correct.
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Neeeeeed hellppppppppll
To draw a centroid for ΔABC, follow the steps below.
Draw the triangle ABC with the line segment CD bisecting it. Line segment CD is called a median and it connects the midpoint of side AB to the opposite vertex, C.Using a protractor, measure the distance between B and C, place the protractor on C and make an arc on both sides of the triangle. Place the protractor on B and repeat the same step. place your ruler such that the ruler is actactly in between the twin arcs on both sides of the triangle, mark the point where the ruler crosses the line segment BC.Call this point long BC point x.repeat this for LIne segment AC.Call the point on line AC y.Draw another line segment from point B to the midpoint of side BC, that is point x and repeat same for point y.The intersection point of line segments CD and XY is the centroid of the ΔABC. Label this point as G.
See the sample attached. Note that this is not constructed to scale.
What is a Centroid?The centroid is the point where the three medians of a triangle intersect.
A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. In this case, line segment CD is one of the medians of triangle ABC because it connects the midpoint of AB (which is also the midpoint of CD) to vertex C. The other two medians connect the midpoints of the other two sides to their opposite vertices.
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describe to use or importance of points , lines , and planes in daily life
Points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.
What are points, lines, and planes?
Point: A point is a basic geometric object that represents a specific location in space.
Line: A line is a straight path that extends infinitely in both directions. It is made up of an infinite number of points that are all collinear, or lie on the same straight path.
Plane: A plane is a two-dimensional flat surface that extends infinitely in all directions.
Navigation: Points and lines are essential for navigation, both on land and in the air. For example, on a map, points represent specific locations, while lines represent roads, highways, and other paths that can be taken to get from one point to another.
Architecture and Design: Points, lines, and planes are critical for architecture and design. Architects use points to specify the locations of walls, columns, and other structural elements, while lines are used to create the edges of rooms and buildings. Planes are used to define the surfaces of walls, floors, and ceilings.
Art: Artists often use points, lines, and planes to create visual effects in their work. Points can be used to create texture, while lines can be used to create movement and depth. Planes can be used to create shapes and form.
Engineering: Points, lines, and planes are fundamental to engineering, which involves the design and construction of structures and machines. Engineers use points to specify the locations of components, while lines are used to create the edges of parts. Planes are used to define the surfaces of structures, such as the wings of an airplane.
Hence, points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.
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2 2 2 2 = 9 use subtraction addition multiplication addition or parentheses to make the equation true
The numbers 2 2 2 2 can be arranged to make the equation true as follows
(2 + 2/2)² How to arrange the numbers to make the equation trueThe numbers arranged by applying the rule which had acronym of PEMDAS
the full meaning include
P - parenthesis
E - exponents
M - multiplication
D - division
A - addition
S - subtraction
applying the sequence the problem is solved as follows
= (2 + 2/2)²
solving the parenthesis first we solve the problem inside the parenthesis. Inside the parenthesis we start with division
= (2 + 2/2)²
= (2 + 1)²
Then addition
= (3)²
having completed the parenthesis, we solve for the exponents
= 9
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A moderately active 40-pound dog needs an average of 1,215 calories per day. Taryn's dog participated in a dog race this morning, so it will need more than the average calories. Taryn's dog has already eaten 729 calories, and she feeds her dog 243 calories per meal.
243x + 729 > 1,215
How many more meals does Taryn need to feed her dog today? A.
x > 3
B.
x > 243
C.
x > 729
D.
x > 2
help please its due today
The amount of extra meals that Taryn needs to feed her dog today is given by the inequality expression; x > 2
How to solve Inequality word problems?The parameters given in the question are;
Weight of dog = 40 pounds
Average amount of calories required per day = 1215 calories
Amount of calories already eaten = 729 calories
Amount of calories fed per meal = 243 calories
The inequality that represents the given word problem is;
243x + 729 > 1215
Subtract 729 from both sides to get;
243x > 486
divide both sides by 243 to get;
x > 2
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Find the value of x
Answer:
x = 20
Step-by-step explanation:
since the 3 sides of the triangle are congruent then it is equilateral with 3 congruent angles, each of 60° , then
3x = 60 ( divide both sides by 3 )
x = 20
Answer:
20
Step-by-step explanation:
We know that sum of corner of a triangle is 180° and if the triangle is equilateral, the corners are same
180:3=3x
60=3x
x=20
Help with geometry pls?
The following are the area of the sectors:
6a). π square inches
6b). 24π square centimeters
7a). 9 square centimeters
7b). 16.7 square inches
How to evaluate for the area of the sectors.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
For question 6:
a). (40/360) × π × 3 in × 3 in = π in²
b). (135/360) × π × 8 cm × 8 cm = 24π cm²
For question 7:
a). (90/360) × π × 6 cm × 6 cm = 9 cm²
b). (60/360) × π × 10 in × 10 in = 16.7π in²
Therefore, the following are the area of the sectors:
6a). π square inches
6b). 24π square centimeters
7a). 9 square centimeters
7b). 16.7 square inches
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A square pyramid is shown. What is the surface area?
A square based pyramid, with bases labeled 3.5 centimeters and side length of triangle labeled 7 centimeters.
(4 points)
19.25 cm2
30.625 cm2
49.625 cm2
61.25 cm2
Answer:
61.25
Step-by-step explanation:
brainlest pls and I hope this helped u :)
32 children voted for thier favorite ice cream chocolate 3/8 so how may children voted for chocolate explanation
Multiplying the total number of children by the fraction that like chocolate yields [tex]32(3/8)=12[/tex]
Briana ha $3 in her piggy bank. She has all quarters and dimes. Write and equation in STANDARD FORM to represent this scenario. Use X and Y as your variables (Ax+By=C)
The equation in standard form representing the scenario where Briana has $3 in her piggy bank and has all quarters and dimes, using x for the number of quarters and y for the number of dimes, is [tex]25x + 10y = 300[/tex].
Let x be the number of quarters and y be the number of dimes Briana has in her piggy bank.
The value of each quarter is 25 cents or 0.25 dollars, and the value of each dime is 10 cents or 0.10 dollars. Therefore, the total value of the coins in Briana's piggy bank can be expressed as:
[tex]0.25x + 0.10y[/tex]
Since Briana has $3 in her piggy bank, we can set up the following equation:
[tex]0.25x + 0.10y = 3.00[/tex]
To write this equation in standard form ([tex]Ax + By = C[/tex]), we need to clear the decimals by multiplying both sides of the equation by 100:
[tex]25x + 10y = 300[/tex]
Therefore, the equation in standard form that represents this scenario is:
[tex]25x + 10y = 300[/tex]
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shawna knows that a correlation between calories of sweeteners consumed and mortality rates among women does not, in itself, mean that drinking more soft drinks will lead to a higher chance of her dying. which of the following would not be a lurking variable in the above scenario? a.) shawna's weight b.) the time of day shawna exercises c.) the number of soft drink brands available for purchase d.) the amount of caffeine available in soft drinks
Answer: Musical preferences
A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely your musical preferences affect mortality or how much sweetener you consume.
The number of soft drink brands available for purchase is not a lurking variable in this scenario. Correct option is C.
The statement is asking which of the given variables is not a lurking variable in the scenario where Shawna is considering the correlation between the calories of sweeteners consumed and the mortality rates among women, and is trying to determine whether drinking more soft drinks will lead to a higher chance of her dying.
A lurking variable is a variable that is not included in the analysis, but has an effect on the relationship between the variables being studied. In this case, the variables being studied are the calories of sweeteners consumed and the mortality rates among women, and the effect of drinking more soft drinks on the chances of dying.
Out of the given variables, the number of soft drink brands available for purchase would not be a lurking variable, as it does not have an effect on the relationship being studied.
Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could all potentially have an effect on the relationship being studied, either as confounding variables or moderators.
For example, Shawna's weight could be a confounding variable, as it is associated with both sweetener consumption and mortality rates. The time of day she exercises could be a moderator, as exercise may affect the metabolism of sweeteners and caffeine, which could in turn affect mortality rates.
The amount of caffeine available in soft drinks could be a confounding variable, as caffeine consumption is associated with both sweetener consumption and mortality rates.
In summary, the number of soft drink brands available for purchase is not a lurking variable in this scenario, while Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could potentially be confounding variables or moderators that need to be accounted for in the analysis.
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Please help I don't understand.
The surface area of the sphere is 113.2 ft².
Surface area of the Sphere:The area that a sphere's outer surface covers in three dimensions is known as the surface area of the Sphere. A sphere is a three-dimensional solid that resembles a circle in shape and is round.
The formula for a sphere's total surface area is given by
Surface area = 4 π r² square unitsHere we have
The formula for the radius of a sphere r = 1/2 [√S/π]
Diameter of the Moeraki boulder radius = 3 feet
=> 3 feet = 1/2 [√S/π]
=> 6 = [√S/π]
Squaring on both sides
=> 36 = [√S/π]²
=> S/π = 36
=> S = 36π
=> S = 113.2
Therefore,
The surface area of the sphere is 113.2 ft².
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3. In the figure below, what is m/2 if m26 = 120°?
A.
60°
B. 90⁰
32
41
5 6
87
C. 120°
D. 150°
The value of m <2 is C. 120°
What is a Corresponding Angle?In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.
In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.
Therefore,
m<2 = m<6
This is because they are corresponding angles
With this in mind, m<6 = 120°
Therefore, m<2 = 120°
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Bunolo ran a 10km race her average speed was 6km per hour how long did it take her in minutes to complete the race
It took Bunolo 100 minutes (or 1 hour and 40 minutes) to complete the 10 km race at an average speed of 6 km/h.
To find out how long it took Bunolo to complete a 10 km race with an average speed of 6 km/h, we can use the formula:
time = distance / speed
where "distance" is the distance of the race and "speed" is the average speed at which Bunolo ran. We can convert the speed to km/minute to get the time in minutes.
To do this, we can divide the speed in km/hour by 60 (the number of minutes in an hour) to get the speed in km/minute:
6 km/hour ÷ 60 minutes/hour = 0.1 km/minute
Now, we can substitute the distance and speed values into the formula to get the time in minutes:
time = 10 km / 0.1 km/minute = 100 minutes
Therefore, To complete the 10 km race with the average speed of 6 km/h, it took Bunolo 100 minutes.
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Johnson's Farm charges a fee of $26 to enter their orchard, then charges $6 for every pound of cherries you pick. Mood's Farm does not charge customers an entry fee, but cherries picked cost $8 a pound. How many pounds of cherries would you need to pick in order to pay the same amount at each farm?
There are 11/3 pounds of cherries at Johnson's Farm in order to pay the same amount as picking 6 pounds of cherries at Mood's Farm.
In general, the unitary method is a useful tool for solving problems like this where we need to compare the cost of two different scenarios. We can set up equations based on the rates or costs involved, and then use algebra to solve for the unknown variables.
To begin, let's use a unitary method to find the total cost of picking cherries at Johnson's Farm. We know the entry fee is $26, so we can start with that. Then, for each pound of cherries picked, the cost is $6. So, if we let x be the number of pounds of cherries picked, the total cost at Johnson's Farm would be:
Total Cost = $26 + $6x
Now, let's use a unitary method to find the total cost of picking cherries at Mood's Farm. We know that there is no entry fee, so we can start with just the per-pound cost of $8. If we let y be the number of pounds of cherries picked, the total cost at Mood's Farm would be:
Total Cost = $8y
To find how many pounds of cherries you would need to pick at each farm in order to pay the same amount, we need to set these two total costs equal to each other and solve for x:
$26 + $6x = $8y
$6x = $8y - $26
x = (8/6)y - 13/3
x = (4/3)y - 13/3
So, if you picked 6 pounds of cherries at Mood's Farm (y = 6), the equivalent cost at Johnson's Farm would be:
x = (4/3)(6) - 13/3
x = 8 - 13/3
x = 11/3
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A student has completed 3 tests in biology class. How many points above her present test average must she
score on the fourth test in order to raise her test average 4 points?
OA. 7
OB. 9
OC. 12
O D. 16
OE. 20
The student must she score on the fourth test in order to raise her test average 4 points is 4 points.
What is average?An average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Given that, a student has completed 3 tests in biology class, we need to find that how many points above her present test average must she score on the fourth test in order to raise her test average 4 points,
Let the required point be x,
According to question,
x+4×3 / (3+1) = 4
x+12 = 16
x = 4
Hence, the student must she score on the fourth test in order to raise her test average 4 points is 4 points.
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which function represents an exponential decay function with a y-intercept of -3?
a. f(x) = (0.5)^x - 4
b. f(x) = (0.5)^x - 3
c. f(x) = 2^x - 4
d. f(x) = 2^x - 3
Answer:
A
Step-by-step explanation:
The line has a negative slope, with a y-intercept of (0,-3), and an x-intercept of (-2,0)
A roller coaster with a potential energy of 235,200 J sits at the top of a 30 m high hill. What is the mass of the roller coaster? (Formula: PE = mgh)
How do i get 800?
The mass of the roller coaster is 800.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
PE = 235,200
Height = h = 30 m
Now,
PE = mhg
We use g = 9.8
So,
Substituting the values.
235,200 = m x 30 x 9.8
m = 235200 / (9.8 x 30)
m = 235200 / 294
m = 800
Thus,
The mass of the roller coaster is 800.
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What is the slope of a line that contains the points (14,-42) (-48,24)
Enter the correct answer as m=
PLEASE SHOW WORK
The slope on the line containing the points (14,-42) is 1.06, as stated in the preceding sentence (-48,24).
How is slope determined?The % slope is calculated by multiplying the distance between two locations by the differences in elevation above them. The difference in height between two places is referred to as "rise." The distance between it sites is known as the run. Therefore, the formula for percent slope is (rise / run) x 100.
The slope's formula is as follows:
m = (y₂-y₁)/x₂-x₁)
In the formula, replace the point values as follows:
m = (24-(-42))/(-48-14)
Make the fraction simpler:
m = (24-(-42))/(-48-14)
m = 66/-62
m = 1.06
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Express 0.10670.10670, point, 1067 as a fraction.
Answer: 1067/10000 is a fraction in simplest form. where, 0.1067 is a decimal, 10.67% is a percentage.
Step-by-step explanation:
Last year, Becky's dog weighed 55 pounds. One year later, she had gained p pounds. Which expression gives her weight one year later?'
Answer: 55+p
Step-by-step explanation: Since p is in unlike terms as 55, you can just write that as is an the expression to represent the dog's weight.
what number when divided by 15 20 30 the remainder is always 8
The number when divided by 15, 20, and 30 and the remainder is always 8 will be 68.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The number which is divisible by 15, 20, or 30 will be given as,
LCM of the numbers 15, 20, and 30 will be given as,
2 | 15, 20, 30
2 | 15, 10, 15
3 | 15, 5, 15
5 | 5, 1, 5
1, 1, 1
LCM = 2 x 2 x 3 x 5
LCM = 60
The number whose remainder is always 8 is given as,
⇒ 60 + 8
⇒ 68
The number when divided by 15, 20, and 30 and the remainder is always 8 will be 68.
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The radius of a circle is 5 m. Find its circumference in terms of pie
next, place point a on the graph to demonstrate how many trips kathy will take if the price is $230 per round-trip ticket. c. if the price of a round-trip ticket is $230, how many trips should kathy take?
Kathy should take 4 trips if the price of a round-trip ticket is 230.
Point A on the graph would be placed at (230, 4). This demonstrates that Kathy should take 4 trips if the price of a round-trip ticket is 230. This can be calculated as follows:
Kathy has a budget of 1,000. Therefore, she can afford 4 round-trip tickets at the price of 230 each. This can be calculated by dividing 1000 by 230, which gives 4. Therefore, Kathy should take 4 trips if the price of a round-trip ticket is 230.
It is important to note that Kathy should also consider other factors such as the cost of other expenses, such as accommodation and food, when deciding how many trips to take. Additionally, Kathy may also want to consider whether the benefits of taking more trips are worth the additional cost.
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