Carol is cross-country skiing. The table shows the distance she traveled after various numbers of minutes. What is the rate of change? Distance Carol Traveled while Cross-Country Skiing Minutes Distance Traveled (miles) 2 StartFraction 1 Over 6 Endfraction 3 StartFraction 17 Over 48 EndFraction 4 StartFraction 13 Over 24 EndFraction 5 StartFraction 35 Over 48 EndFraction 6 StartFraction 11 Over 12 EndFraction StartFraction 1 Over 12 EndFraction StartFraction 1 Over 6 Endfraction StartFraction 3 Over 32 EndFraction StartFraction 3 Over 16 EndFraction
Answers
Answer:
3/16 miles/minute
Step-by-step explanation:
A rate of change describes how an output quantity changes relative to the change in the input quantity.
Points given:
Input Output
2 1/6
3 17/48
4 13/24
5 35/48
6 11/12
Here input values describe the time in minutes from 2 to 6 and output values describe the distance in miles from 1/6 to 11/12
Calculating the rate of change using the first two pairs of input-output values
Relative change = change in distance/change in time
(17/48 - 1/6)/(3-2) = (17/48 - 8/48) /1 = 9/48 = 3/16 miles/minute
We will get the same result if we take any other ordered pair of input and output values.
So D is your answer! Hope this helped!
Rate of change is the change in a particular variable, over another variable.
The rate of change is: 3/16 miles per minutes
To calculate the rate of change, we select any two points on the table (see attachment)
[tex](x_1,y_1) = (2,\frac 16)[/tex]
[tex](x_2,y_2) = (3,\frac{17}{48})[/tex]
The rate of change (m) is calculated as follows:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{\frac{17}{48} - \frac{1}{6}}{3-2}[/tex]
[tex]m = \frac{\frac{17}{48} - \frac{1}{6}}{1}[/tex]
[tex]m = \frac{17}{48} - \frac{1}{6}[/tex]
Take LCM
[tex]m = \frac{17- 8}{48}[/tex]
[tex]m = \frac{9}{48}[/tex]
Reduce fraction
[tex]m = \frac{3}{16}[/tex]
Hence, the rate of change is: 3/16 miles per minutes
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Related Questions
Will mark as Brainlist!
the pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 16 minutes. Air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.
y= 1/4x - 16
y = 4x − 16
y=1/4x + 16
y = 4x + 16
Answers
Answer:
y=1/4x + 16
Step-by-step explanation:
Answer:
cccccccccccccccccccccccccccc
C!
BOSE
Consider the quadratic function.
f(p) = p? – Sp-5
What are the values of the coefficients and the constant in the function?
a = -1, b = -8, c = -5
a = 1, b= -5, C = -8
a = 1, b = -8, c = -5
a = -1, b = -5, C = 8
Answers
Answer:
a = 1 ; b = -8 ; c = -5
Step-by-step explanation:
f(p) = p² - 8p -5
a = co-efficient of p² = 1
b = co-efficient of p = -8
c = constant = -5
Attempt 1 of 1
Jamin wants to paint a wall in his bedroom. In order to know how much paint to buy, he first needs to know the
approximate area. There is a window in the middle of the wall, so he'll only need to paint the shaded part shown. How
many square feet is just the window? [Note: The wall and window are both rectangular.)
611
2
18 in.
81
>
362
0742
1.5 ft2
32
O
Type here to search
-
12:36 PM
7/10/2020
is this right??
Answers
Answer:
Step-by-step explanation:
Window is in the shape of rectangle
Area of the rectangular window = length * width
= 18 * 2
= 36 ft²
Answer:
36
Step-by-step explanation:
i got 100%(❁´◡`❁)
A person purchased a $239,127 home 10 years ago by paying 15% down and signing a 30-year mortgage at 10.8% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 20-year mortgage at 6 % compounded monthly. How much interest will refinancing save?
Answers
Answer:
$135,629.37
Step-by-step explanation:
For computing the interest amount first we need to find out the monthly payment, present value, monthly payment and finally the interest amount which is shown below with the help of an attached spreadsheet
The value of the loan could come by
= $239,127 - $239,127 × 15%
= $203,257.95
The amount of interest saved is
= ($1,905 × 20 × 12) - ($1,399.18 × 20 × 12)
= $135,629.37
a miving company's moving rates can be represented by the function f(x)=3x+400, where x is the number of miles for the move. Another moving company's rates can be represented by the function g(x)=5x+200. Which function represents the difference between the moving companies rates , h(x)=f(x)-g(x)?
A) h(x)=-2x+200
B) h(x)=-2x+200
C) h(x)=5x-200
D) h(x)=5x+600
Answers
Answer:
Option a
Step-by-step explanation:
This is a nice simple problem!
Given that the function f( x ) is equivalent to 3x + 400, respectively g( x ) = 5x + 200, all we are being asked to do is find their difference. Substitute the given values as such -
h( x ) = f( x ) - g( x )
⇒ h( x ) = ( 3x + 400 ) - ( 5x + 200 ) - Distribute negative sign, taking out ( )
⇒ h( x ) = 3x + 400 - 5x + 200 - Combine like elements
⇒ h( x ) = - 2x + 200
And there you have it! Our solution should be option a ( h( x ) = - 2x + 200 )
If you would like, there is a graph of the function in the attachment below.
Answer:
It's B on edge!
Using the given points and line, determine the slope of the line. (-3, 0) and (2, 7) slope = - slope = - slope = slope =
Answers
Answer:
slope = [tex]\frac{7}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (2, 7)
m = [tex]\frac{7-0}{2+3}[/tex] = [tex]\frac{7}{5}[/tex]
Answer:
7/5
Step-by-step explanation:
m=y2-y1/x2-x1
7-0=7
2-(-3)=5
7/5
1. fill in the blanks below and write and evaluate an example of a function part1: Ashley earns 17 per hour. define the variables and state which quantity is a function of the other. part 2: using the variables defined in part 1, write a function using notation that represents Ashley's income Part 3: Ashley's hours for the last two weeks were 35 hours and 29 hours. Using the function you wrote in Part II, determine her income for each of the two weeks. Show your work. (4 points) 37 Week 1: Ashley worked 35 hours. She earned __________. Week 2: Ashley worked 29 hours. She earned __________.
Answers
Answer:
See below
Step-by-step explanation:
Part 1 -
x: number of hours worked
y: total income
This is written as → y = f(x)
Part 2 -
y = 15*x
Part 3 -
f (35) = 15 × 35 = $525
f (29) 15 × 29 = $435
Week 1 - Ashley worked 35 hours with a total income of $525.
Week 2 - Ashley worked 29 hours with a total income of $435.
Triangle STV has vertices S (-3, -2) , T (-4, 3) and V (-2, 3). If (x, y) arrow (x+2, y-3), what are the vertices of its image?
Answers
Answer:
see below
Step-by-step explanation:
The mapping tells you how to find the vertices of the image:
(x, y) ⇒ (x +2, y -3)
S(-3,-2) ⇒ S'(-3 +2, -2 -3) = S'(-1, -5) . . . . . matches choice D
T(-4, 3) ⇒ T'(-4 +2, 3 -3) = T'(-2, 0)
V(-2, 3) ⇒ V'(-2 +2, 3 -3) = V'(0, 0)
Answer:
D
Step-by-step explanation:
HELPPPP NOW Lisa paid $35.00 to join an online music service. If she purchases 18 songs each month at a cost of $0.75 per song, what will be the total amount she has spent after 4 months?
Answers
Answer:
$54 for 4 months $89 in total
Step-by-step explanation:
Lisa paid $35 at first
then she paid 0.75 per song which is 0.75 *18 = $13.5
Then just multiply 13.5 by 4 b/c of 4 months
The total amount Liza has spent after 4 months is $89.
What is an equation?Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.
Given that, Lisa paid $35.00 to join an online music service, she purchases 18 songs each month at a cost of $0.75 per song,
we need to find the total amount she paid after 4 months,
So, the cost of 18 songs = 0.75 x 18 = $13.5
The cost of 18 songs in 4 months = $54
Now, the total amount she paid = $54 + $35 = $89
Hence, the total amount Liza has spent after 4 months is $89.
Learn more about equations, click;
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Find the perimeter Jose wants to put a fence around his rectangular garden. His garden measures 33 feet by 39 feet. How much fencing material does Jose need to enclose the garden? Question 2 options: a) 257.4 feet b) 1287 feet c) 144 feet d) 72 feet
Answers
Answer:
144
Step-by-step explanation:
2(39+33)
2(72)
144
=144
can somewon help me plz
Answers
Answer: s=36
Step-by-step explanation:
To solve for s, we can use our algebraic properties to solve.
[tex]\frac{1}{3}s+14=26[/tex] [subtract both sides by 14]
[tex]\frac{1}{3}s=12[/tex] [multiply both sides by 3]
[tex]s=36[/tex]
Answer:
The answer is s=36
Step-by-step explanation:
Marcus is saving up his money to buy a television that costs $395.50. Right now he has $85.00, and can save $29.00 each week. How many weeks will it take for Marcus to have enough money to buy the television?
Answers
Answer:
11 weeks
Step-by-step explanation:
He has 85 and can save 29 each week. This must be greater than the cost of the tv
85 + 29 w > 395.50
Subtract 85 from each side
85 -85 + 29 w > 395.50-85
29w >310.50
Divide by 29
29w/29 > 310.5/29
w >10.70689655
The number of weeks must be greater than 10.7 so rounding up
He must save for at least 11 weeks
Two random samples were taken to determine how often people in a community listen to the local radio station each month. The first sample surveyed 15 people as they exited the bank on Main Street. The first sample found that the mean number of hours they listened to the radio each month was 20. The second sample surveyed every sixth person as they exited the only local grocery store until 100 people were surveyed. The second sample found that the mean number of hours they listened to the radio each month was 12. Which statements are true? Check all that apply. The second sample is random. The second sample is likely to be more representative of the population. The first sample is likely to be more representative of the population. The second sample will give a better representation because is it larger. The first sample will give a better representation because it is smaller. Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month.
Answers
Answer:
The answers to this question are 1,2,4,6. Hope this helps you
Step-by-step explanation:
Statements A, B, E, and F are true. The second sample was taken at random using a fair sampling technique.
What is the probability?Probability is synonymous with possibility. It is concerned with the occurrence of a random event.
Probability can only have a value between 0 and 1. Its simple notion is that something is very likely to occur. It is the proportion of favorable events to the total number of events.
The correct statement is as follows;
A) The second sample is random.
B) The second sample is likely to be more representative of the population.
D) The second sample will give a better representation because is it larger.
F) Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month.
The second sample was taken at random using a fair sampling technique.
Because the research using the larger data size is accepted rather than that of the smaller data, community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours.
A research's sample size is a crucial consideration. Additionally, the second sample is probably a better indicator of the broader population.
Hence statements A, B, E, and F are true.
To learn more about probability, refer to the link: https://brainly.com/question/795909.
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You are a young entrepreneur who ventures into selling milk tea. On the soft opening day, you sold all 50 glasses of classic and flavored milk tea, and bought in P4700. You need to determine how many glasses of classic milk tea and how many glasses of flavored milk tea were sold on that day if a glass of classic milk tea costs P100 and a glass of flavored milk tea is P80.
Answers
Answer:
35 glasses of classic milk tea
15 glasses of flavored milk tea
Step-by-step explanation:
You sold 50 glasses of classic and flavored milk tea.
c + f = 50
You made 4700 when classic tea costs 100 and flavored tea costs 80.
100c + 80f = 4700
Use this system of equation to solve. Use substitution. Rearrange the first equation so that it is equal to c. Then, plug the c-value into the second equation.
c + f = 50
c = 50 - f
100c + 80f = 4700
100(50 - f) + 80f = 4700
5000 - 100f + 80f = 4700
5000 - 20f = 4700
-20f = -300
f = 15
Plug the f-value into one of the equations and solve for c.
c + f = 50
c + 15 = 50
c = 35
35 glasses of classic milk tea and 15 glasses of flavored milk tea were sold.
Plz help me I don't know how to do this!!!!
Answers
Answer:
x = 25
Step-by-step explanation:
Since it is an equilateral triangle it means that all the sides are 50. Each side is equal so, if you divide 150 by 3 you get 50. (and since perimeter is the adding of each side)
Now you want to try to figure out what the altitude is of the triangle so you divide it in half. Making the bottom side length now 25 because half of 50 is 25. You now have to use Pythagoreans theorem to figure out the altitude:
c^2 - a^2 = b^2
50^2 - 25^2 = b^2
2500 - 625 = b^2
1875 = b^2
√1875 = b
43.30127019
now you put that into the expression: x√3:
x√3 = 43.30127019
x = (43.30127019) ÷ (√3)
x = 25
Hope this helped!
14. Which graph shows the solution to the following system?
1
-x-2
y -
4
7
y = -x + 4
Answers
Answer:
Option (B)
Step-by-step explanation:
Equations of the lines shown in the graph are,
[tex]y=\frac{1}{4}x-2[/tex] and [tex]y=\frac{7}{4}x+4[/tex]
For equation (1),
[tex]y=\frac{1}{4}x-2[/tex]
Slope of the line = [tex]\frac{1}{4}[/tex]
And y-intercept of the line = -2
For equation (2),
[tex]y=\frac{7}{4}x+4[/tex]
Slope of this line = [tex]\frac{7}{4}[/tex]
And y-intercept of the line = 4
From the given graphs in the options,
Graph (B) shows the lines which show the y-intercepts as y = 4 and y = -2
Therefore, Option (B) will be the answer.
A ball has a volume of 4 cubic inches (in3). Use the fact that 1 inch is equal to 2.54 cm to convert this volume to cubic centimeters (cm3).
Answers
Answer:
V = 65.548 cm³
Step-by-step explanation:
We have,
Volume of a ball is 4 cubic inches or [tex]4\ \text{inch}^3[/tex].
We know that, 1 inch = 2.54 cm
It is required to convert this volume to cubic centimetre or [tex]\text{cm}^3[/tex].
[tex]4\ \text{inch}^3=4\ \text{inch}^3\times (\dfrac{2.54\ \text{cm}}{1\ \text{inch}})^3\\\\V=65.548\ \text{cm}^3[/tex]
So, the volume of the ball is 65.548 cm³.
A pole that is 2.6 m tall casts a shadow that is 1.38 m long. At the same time, a nearby tower casts a shadow that is 49.25 m long. How tall is the tower? Round
your answer to the nearest meter.
Answers
Answer:
92.7
Step-by-step explanation:
1.38 ÷ 2.6 = .53076923
this means ↑that number is what percent shadows covers
49.25 ÷ .53076923 = 92.7 (roughly)
Find the missing segment
Answers
Answer:
? = 9.
Step-by-step explanation:
According to the AA Theorem, the two triangles are similar.
[tex]\frac{30}{30 + 5} =\frac{54}{? + 54}[/tex]
30 (? + 54) = 54 * 35
30? + 1620 = 1890
3? + 162 = 189
3? = 27
? = 9
Hope this helps!
pls help me with number 10
Answers
Answer:
D
Step-by-step explanation:
Δ KLM is equilateral ( 3 congruent angles ), thus 3 sides are congruent
KM = LM = 5
Δ MJK is isosceles ( base angles are congruent ), thus
MJ = KM = 5 , substitute value
x + 1 = 5 ( subtract 1 from both sides )
x = 4 → D
x=4
Step-by-step explanation:
all sides are 5 on the bottom triangle and the top triangle has 2 sides that are equal and one equals 5. there for it becomes x +1=5. 4
To graph f(x) = 2x ^2+ 1, what would
you do to the graph of f(x) = x??
Answers
Answer:
Well you make a parabola 2 times more narrow.
move it up 1
Calculate the area and the perimeter of the figure
Answers
Answer:
Area: 5 cm squared
Perimeter: 12 cm
Step-by-step explanation:
The area is Length times Width, and there is 5 different sqaures in the figure.Each sqaure has an area of 1 by 1, which is 1. 1 times 5 is 5. So the area is 5. You can get the perimeter by adding all the side lengths together, 2+3+2+1+1+1+1+1=12. The perimeter is 12. Hope this helps.
-402 + br – 11 = 0
Determine a possible value of b so that the quadratic has two complex solutions.
1)
12
2)
-14
3)
-16
4)
14
Answers
Answer:
2
Step-by-step explanation:
58.30
The slope of the graph of the equation y2x-2 is 2. What is the y-intercept?
y-intercept =
Mark this and retum
Save and Exit
Next
Submit
Answers
Answer:
the slope is 2 and the y intercept is -2
Step-by-step explanation:
y=2x-2
This is in the form y = mx+b where m is the slope and b is the y intercept
the slope is 2 and the y intercept is -2
Somebody please help me!!!
Answers
Answer:
512.
according to the instructions you are told to drag and carry the numbers in the box below to the correct destination in the sequence until the ninth value.
If its not correct drag to the trashcan to delete
Step-by-step explanation:
2, -4, 8, -16, 32, -64, 128, -256,512
that's the sequence to be filled in
What are the domain and the range of this function?
Answers
Answer:
domain: -5≤x<1
range: -4≤y<7
Step-by-step explanation:
The domain of the line segment will be [-5, 1) and the range of the line segment will be [-4, 7).
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
A line segment in mathematics has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a path that joins two places.
The domain means all the possible values of x and the range means all the possible values of y.
From the graph, the domain of the line segment will be [-5, 1) and the range of the line segment will be [-4, 7).
More about the linear equation link is given below.
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Plz help me 2/3(6-9x)+15
Answers
Answer:
19-6x
Step-by-step explanation:
2/3(6-9x)+15
=4-6x+15
=19-6x
Answer:
19-6xSolution,
[tex] \frac{2}{3} (6 - 9x) + 15 \\ = \frac{2}{3} \times 6 - \frac{2}{3} \times 9x + 15 \\ = 4 - 6x + 15 \\ = 4 + 15 - 6x \\ = 19 - 6x[/tex]
Hope this helps...
Good luck on your assignment..
What type of function is represented in the table? exponential linear quadratic logarithmic
Answers
Answer:
quadratic
Step-by-step explanation:
Linear function is represented by the data given on the table.
What is linear equation?" Linear equation is an algebraic expression in which highest exponent of the given variables is one. It represent a straight line."
General form of linear equation
y = ax + b
According to the data given in the table,
When x = 0 , y = -3 ,
Substitute the given values of x and y in general form of linear equation
- 3 = a × 0 + b
⇒ - 3 = b ____(1)
When x = 1 , y = 5
5 = a × 1 + b
5 = a + b ____(2)
Substitute the value of b in (2) we get,
5 = a + ( -3)
⇒ a = 8
Substitute the value of 'a' and 'b' in general form of linear equation and check whether it is true for other values of x and y.
y = 8x - 3
check for the x = 2
y = 8(2) -3
⇒ y = 13
Yes , it is correct.
When x =3
y = 8 (3) - 3
⇒ y = 21
It is correct.
Hence, we conclude that Linear function is represented by the data given on the table.
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Solve this quadratic equation by completing the square.
x2 + 8x= 10
A. X=-8 + V10
B. x= -4 26
O C. X= -8 + V26
D. X=-4 + V10
SUBMI
DO
Answers
Answer:
B
Step-by-step explanation:
The population of Peru is 10904 the population of Franklin is 25248. The population of Franklin is percent more than the population of Peru
Answers
Answer:
132%
Step-by-step explanation:
The population of Peru = 10904
The population of Franklin = 25248.
Difference = 25248-10904=14,344
Expressing as a percentage of the population of Peru
[tex]\dfrac{14344}{10904} X 100[/tex]
=132%
Therefore, the population of Franklin is 132% more than the population of Peru.