MATHPHYS HELP
1. Felicia wants to know the gas milgage of her new car. She starts recording how much gasoline
she puts into the car, and how many miles she travels before the warning light comes on and
she need to add more gas. A table of her data is shown below.
Gas (gallons)
1 4 8 10
Miles
19 84 160 203 218
a. Consider miles M as a function of gallon and use data points to find a linear function
to model the data.
b. Consider gallons G as a function of miles M and use data points to find a linear function
to model the data.
C. How do the functions of (a) and (b) compare? Are they both useful models?
d. What could be some reasons why the points do not fit perfectly with your equation?
Answers
Step-by-step explanation:
(a) If M is a function of G (M is the y-axis and G is the x-axis), then the linear function is approximately:
M = 20G
(b) If G is a function of M (G is the y-axis and M is the x-axis), then the linear function is approximately:
G = M / 20
(c) The two functions are inverse of each other. The first function tells us how many miles she can drive with a certain number of gallons. The second function tells us how many gallons she needs to drive a certain number of miles.
(d) There are multiple things that affect fuel mileage. These include:
Speed - idling at a red light or driving at high speeds will lower your mileage.
Weather - high winds will lower your mileage.
Weight - adding weight (even the weight of the gas itself) will lower your mileage.
Tires - low pressure in the tires will lower your mileage.
The given table is an illustration of a linear scatter plot, where:
[tex]M = 19.9G -0.9[/tex].[tex]G = \frac{10}{199}M + \frac{9}{199}[/tex].M and G are both inverse functions(a) M as a function of G
From the table, we have the following points:
[tex](G_1,M_1) = (1,19)[/tex]
[tex](G_2,M_2) = (11,218)[/tex]
Calculate the slope (m)
[tex]m = \frac{M_2 - M_1}{G_2 - G_1}[/tex]
[tex]m = \frac{218-19}{11-1}[/tex]
[tex]m = \frac{199}{10}[/tex]
[tex]m = 19.9[/tex]
The equation is then calculated using the following linear equation formula:
[tex]M = m(G - G_1) + M_1[/tex]
[tex]M = 19.9(G - 1) + 19[/tex]
[tex]M = 19.9G - 19.9 + 19[/tex]
[tex]M = 19.9G -0.9[/tex]
(b) G as a function of M
From the table, we have the following points:
[tex](M_1,G_1) = (19,1)[/tex]
[tex](M_2,G_2) = (218,11)[/tex]
Calculate the slope (m)
[tex]m = \frac{G_2 - G_1}{M_2 - M_1}[/tex]
[tex]m = \frac{11-1}{218-19}[/tex]
[tex]m = \frac{10}{199}[/tex]
The equation is then calculated as follows:
[tex]G = m(M - M_1) + G_1[/tex]
[tex]G = \frac{1}{19.9}(M - 19) + 1[/tex]
[tex]G = \frac{1}{19.9}M - \frac{19}{19.9} + 1[/tex]
[tex]G = \frac{1}{19.9}M - \frac{19-19.9}{19.9}[/tex]
[tex]G = \frac{1}{19.9}M - \frac{-0.9}{19.9}[/tex]
[tex]G = \frac{1}{19.9}M + \frac{0.9}{19.9}[/tex]
[tex]G = \frac{10}{199}M + \frac{9}{199}[/tex]
(c) How (a) and (b) compares
Functions (a) and (b) are both inverse functions of one another;
Because they both represent inverse functions, both are useful models
(d) Reasons points do not fit in the equation
Some reasons why the points do not fit are:
Short tripsVehicle break downSpeedHeavy breaksWhen any of these happens, the mileage will be affected because she won't be able to capture the accurate data by the time she continues her trip.
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Related Questions
21 is 3% of what number?
Answers
Answer:
the answer is 700
Step-by-step explanation:
it's 700 because 100% of 700 is 700,therefore 3 percent of 700 equals 21
there's another one can you help me with it
Answers
Answer:
56cm
Step-by-step explanation:
5488 is the area of the rectangle.
we know that length x width = area
so to find the with we do area/length
so, 5488/98 =56
Answer: 56 cm
Step-by-step explanation:
Area (A) = Length (L) × width (w)
Given: A = 5488 cm², w = 98 cm
A = L × w
5488 = L × 98
56 = L Divided 98 from both sides
On a Ferris wheel, Sarah observes that it takes 45 seconds for her chair to complete a full revolution. Her chair is 30 feet from the axle of the Ferris wheel.
To the nearest hundredth, Sarah’s angular velocity is ____ radians per minute
Answers
Answer:
8.38 radians
Step-by-step explanation:
correct on edge 2021
The angular velocity of the Ferris wheel is 8.38 radians/minute.
What is angular velocity?"The angular velocity is the time rate at which an object rotates or revolves about an axis."
It takes 45 seconds for her chair to complete a full revolution.
Therefore, in terms of revolution per minute, the speed is
= 60/45 revolutions/minute
= 4/3 revolutions/minute.
We know, 1 revolutions = 2π radian
Therefore, 4/3 revolutions/minute
= (4/3) × 2π radians/minute
= 8.38 radians/minute
Hence, the angular velocity is 8.38 radians/minute.
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Jason has $2.25 worth of dimes and quarters. He has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Jason has.
Answers
Use the distributive property to write an equivalent expression.
2(v – 4w + 6)
Answers
Answer:
2v - 8w + 12
Step-by-step explanation:
You need to multiply each term inside the parentheses by the 2 that's in front
2v - 2(4w) + 2(6)
= 2v - 8w + 12
Answer:
2v - 8w + 12:
2x - 1y = -9
y = -5 - 5x
please explain the answer and not just tell me the answer?
Answers
Explanation: your first step would be substitute the equation (y=-5x-5 in for the y in the other equation 2x-1y=-9 making it 2x-1(-5x-5)=-9 then do the distributive property to get 2x+5x+5=-9 then combine like terms and get 7x+5=-9 then you subtract 5 from -9 and get -14 then you get 7x=-14 then get a final answer of x=-2. Then plug in x=-2 to your first equation y=-5(-2)-5 and then you get 10 -5 and get y=5
Heather was assigned the task of making labels for all of the drawers in the file cabinets in her office. There were 12 file cabinets. Three cabinets have 4 drawers; all the other cabinets have 5 drawers. How many labels will Heather need to make?
Answers
Answer:
52 Labels
8 cabinets with 5 drawers 8x5=40
3 cabinets with 4 drawers 3x4=12
40+12=52
Answer:
Heather will need to make 57 labels to complete the task.
Step-by-step explanation:
There are 12 file cabinets.
Three of them have 4 drawers.
Heather will need to make 3*4=12 labels for these cabinets
The rest of the cabinets (12-3=9) have 5 drawers.
Heather will need to make 9*5=45 labels for these cabinets
The total of labels needed is 12+45=57.
Heather will need to make 57 labels to complete the task.
If point (a,b) lies on the graph y=f(x), the graph of f^-1 (x) must contain point:
Answers
Given:
Point (a,b) lies on the graph [tex]y=f(x)[/tex].
To find:
The point which is must be lies on the graph of [tex]y=f^{-1}(x)[/tex].
Solution:
According to the definition of an inverse function, if a function is defined as
[tex]f=\{(x,y):x\in R,y\in R\}[/tex]
then, its inverse is defined as
[tex]f^{-1}=\{(y,x):x\in R,y\in R\}[/tex]
It means, we have to interchange x and y-coordinate of the points which lies on the function f to get f⁻¹.
We have a point (a,b) lies on the graph [tex]y=f(x)[/tex]. So, (b,a) must be lies on the graph of [tex]y=f^{-1}(x)[/tex].
Therefore, the correct option is (1).
By the definition of inverse function,the point (a,b) lies on the graph [tex]\bold{y= f(x).}[/tex] So, (b,a) must be lies on the graph of [tex]\bold{y=f^{-1} (x)}[/tex].
Given:
Point (a,b) lies on the graph y= f(x).
Find:
The graph of [tex]\bold{y=f^{-1} (x)}[/tex] must contain that point.
As per the definition of inverse function, if two one-to-one functions f(x) and g(x). If (f∘g)(x)=x and (g∘f)(x)=x. Then, we say that f(x) and g(x) are inverses of each other.
[tex]\bold{f=\{ (x,y):x\epsilon R,y\epsilon R\}}[/tex]
Then, its inverse is defined as
[tex]\bold{f^{-1} =\{ (y,x):x\epsilon R,y\epsilon R\}}[/tex]
Therefore, we have to interchange x and y-coordinate of the points which lies on the function f to get f⁻¹.
Thus, the point (a,b) lies on the graph [tex]y= f(x).[/tex] So, (b,a) must be lies on the graph of [tex]y=f^{-1} (x)[/tex].
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The sum of two consecutive integers is no more than 55. Find the largest integer.
Answers
Consecutive Integers follow a sequence where each number is one more than the previous number.
The largest consecutive integer is 28, The smallest consecutive integer is 27.
Tom is 4 more than twice andrews age. Sara is 8 less than 5 times ANdrews age. If tom and sara are twins how old is andrew
Answers
Answer:
there
Step-by-step explanation:
T = 4 + 2A
S = 5A - 8
T = S
Since T and S are equal, set them against each other
2A + 4 = 5A - 8
Subtract 2A from each side, and add 8 to each side
12 = 3A
Divide each side by 3
A = 4
If Andrew is 4, then Tom is twice that plus 4, or 12. Sarah is 5 times 4 less 8, or 12.
WHAT IS THR PRICE FOR 18 TICKETS THIS IS RATIOS BTW
Answers
Answer:
$10.80
Step-by-step explanation:
You should Divide 3 / 5 and get 0.6. 0.6 is the price of only 1 ticket. So you can do 18 x 0.6 and get 10.80.
Answer
Step-by-step explanation: i believe its 35
Mrs. Averitt pipes an average of 62 words per minute how many words does it take her to type 3596 words
Answers
Answer:
58
Step-by-step explanation:
Divide 3596/63
Answer:
58 minutes
Step-by-step explanation:
66=1
3596=?
66×1=66
3596÷66=58
?=58
Given the function f defined by the formula f(x)=2x+1 find the following:
(a) f(4)
(b) f(-5)
(c) f(0)
(a) f(a)
Answers
Answer:
BELOWStep-by-step explanation:
[tex]f(x)=2x+1[/tex]
Substitute values into given equation :
[tex]f(4) = ?\\\\f(4) = 2(4)+1\\\\f(4) = 8+1\\\\f(4)=9[/tex]
(b).
[tex]f(-5) =2(-5)+1\\\\f(-5) = -10+1\\\\f(-5) = -9[/tex]
(c) .
[tex]f(0) =2(0)+1\\\\ f(0) = 0+1\\\\ f(0) =1[/tex]
(d) .
[tex]f(a) =2(a)+1\\\\ f(a) = 2a+1[/tex]
5*6+11=what I know the answer but people need points
Answers
Answer:
5.6+11
Step-by-step explanation:
5(6)+11=30+11
41
after how many seconds is needed for a thrown ball to reach a 14-m distance if it's distance is given by the relation d=10+40t-5t? (t=time in seconds)
Answers
Answer:
Time, t = 0.1143 seconds.
Step-by-step explanation:
Given that distance, d = 14m
From the equation;
d = 10 + 40t - 5t
d = 10 + 35t
Substituting the value of distance;
14 = 10 + 35t
35t = 14 - 10
35t = 4
t = 4/35
t = 0.1143 seconds.
The time needed for the ball to reach the 14-m distance is 0.1143 seconds.
The thrown ball will reach a 14-m distance after 0.114 seconds.
The relation given is:
d = 10+40t-5t
where, d = 14
In this case, we've to put the value of d into the relation and this will be:
d = 10+40t-5t
14 = 10 + 40t - 5t
Collect like terms
40t - 5t = 14 - 10
35t = 4
Divide both side by 35
35t/35 = 4/35
t = 0.114 seconds.
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The activity in Jamal's savings account for the month of December is show
Jamal's Savings Account
Starting Balance
$232
Deposit
$57
Deposit
$16
Withdrawal
$28
Withdrawal
-$42
Deposit
$105
Withdrawal
-$54
What was Jamal's account balance at the end of the month?
$534
$410
$286
-$54
Answers
Answer:
286
Step-by-step explanation:
Answer:
$534
Step-by-step explanation:
I did my diagnostics on performance matters, and i checked my score and i got a 83%. The answer is $534
Mr. Gaines is catering his company picnic. He will pay $18.45 for 3 people to eat the barbecue lunch. At this rate, how many people can Mr. Gaines afford to feed on a budget of $1850.00? (Will give brainliest)
Answers
Answer: 300
Step-by-step explanation:
From the question, we are informed that Mr Gaines is catering his company picnic and that he will pay $18.45 for 3 people to eat the barbecue lunch. This means each person spends:
= $18.45/3
= $6.15
With a budget of $1850.00, the number of people that he'll be able to feed will be:
= $1850/$6.15
= $300 people
can you help me on this
Answers
Answer:
1mi =1.61 km
Step-by-step explanation:
the second from the top
I need this 6 questions by tomorrow
Answers
Answer:
The answwer for question 6 is -3x+10xw
Step-by-step explanation:
When given a question like this, you have to separate the variables by adding the one with the same variable together. If you add 5x and -8x you will get -3x and if you add 7w with -7w, you'll get 0w which isn't needed in the equation. 20xw would be alone.
64 ounces of spaghetti sauce for $4.60 OR 48 ounces of sauce for $3.79
Answers
64 Ounces Of spaghetti sauce for 4.60= around 7 cents per Ounce
48 ounces of Sauce for 3.79 = around 8 cents per ounce
Mathmatically speaking, i would choose the 64 ounce
i need help , can someone please help me
Answers
Answer: 90
cuz if you use the ruler thing it gives you 90 trust me
find the measure of the missing angle
a=
Answers
Answer:
68*
Step-by-step explanation:
A right angle is 90* so you subtract 22 from 90 and get 68
Answer:
Step-by-step explanation:
24
how do you solve this and i have other questions like this one i really need to know how to do it
Answers
Answer:
25
Step-by-step explanation:
it's because 5 is squared so 5x5 is 25 and x squared
I WILL BE MARKING BRAINLIEST AND GIVING 40 POINTS IF CORRECT!!!
Jasmine drives every morning to her office that is 12 miles from her home.
Suppose Jasmine drives from home to the office in 20 minutes. Use this information and part (b) to write an equation. Part (b) said that it takes her (12÷s) hours to make it or (12÷s)·60 minutes. Thank you for your time.
Answers
Answer:
you should plug in 20 for x
(12/20) × 60 = 36
Answer:
12/s*20 maybe
Step-by-step explanation:
find the y-intercept of the graph of 2x-5y=10
Answers
Answer:
y-intercept: ( 0 , − 2 )
Step-by-step explanation:
To find the y-intercept, substitute in 0 for x and solve for y
Answer:
(0,-2)
Step-by-step explanation:
Start with:
[tex]2x-5y=10[/tex]
We are going to want this equation in slope-intercept form.
[tex]y=mx+b[/tex]
[tex]mx=slope[/tex]
[tex]b=y-intercept[/tex]
To get the equation in slope intercept from, start by subtracting [tex]2x[/tex] from both sides of the equation:
[tex]-5y=-2x+10[/tex]
Now, divide both sides of the equation by [tex]-5[/tex]:
[tex]y=-\frac{2}{5}x -2[/tex]
[tex]b=-2[/tex]
[tex](0,-2)[/tex]
330 divided by 9.17 and simplify plz
Answers
Answer: 36
Step-by-step explanation:
Multiply and round up from 35.9 to 36
What is 713.49 written in standard form as powers
Answers
Answer:
one hundred seven thirteen and forty nine hundreds standard form
Step-by-step explanation:
Standard form is a way of writing down very large or very small numbers easily. 103 = 1000, so 4 × 103 = 4000 . So 4000 can be written as 4 × 10³ . This idea can be used to write even larger numbers down easily in standard form.
please and thank you
Answers
Answer:
1.25x + 7 = 43.25
Answer: Equation: (43.25 - 7) / 1.25 Answer: 29
Step-by-step explanation:
In slope-intercept form, write the equation of the line that is perpendicular to y: 5x -3 and passes
through (5,-2).
Answers
Answer:
5x+10
Step-by-step explanation:
5x-3+5,-2
-3+-2+5=10
leave the 5x the same
Answer: 5x+10
last one all me points left please help
Answers
Answer:
it dosen't show the picture
Step-by-step explanation:
do you mind putting the questions down