Amy and Laura recorded the average gas mileage (MPG) of their vehicles each week for four weeks. What can be concluded about the relationships shown in the graph and table?
Amy and Laura recorded the same gas mileage each week.
Both Amy and Laura increased their gas mileage in the first two weeks.
Amy had greater gas mileage than Laura.
Laura had a constant gas mileage in the first four weeks of data.
Who runs fastest?
When do Andy and Berta cross paths?
Who is closest to the 1.5 mile mark after 6 minutes?
Answers
Both Amy and Laura increased their gas mileage in the first two weeks.
Option B is the correct answer.
The missing graph is attached with the answer.
What is a Graph ?A graph is a statistical way of showing data , it is used to show relation between the points.
A graph is useful in understanding the nature of a function.
From the data given in the question
The statements that can be concluded is , Option B
Both Amy and Laura increased their gas mileage in the first two weeks.
To know more about Graph
https://brainly.com/question/16608196
#SPJ1
Related Questions
round 0.3391 to the nearest thousandth
Answers
Answer:
0.339
Step-by-step explanation:
Hope it helped!
Hii!
___________________________________________________________
Answer: 0.339
Explanation:
Rounding Rules
There are two rounding rules that will help us whenever we need to round a number! These are the rules.
If the number that you need to round is followed by a digit that is less than 5, you round down.If the number that you need to round is followed by a digit that is either greater than or equal to 5, you round up.---
Now that we know the rules, let's get down to solving our problem! ^^
The nearest thousandth is 3 decimal places.
_._ _ _ <==== Nearest thousandth
The third number after the decimal point is 9. After it is a digit that is less than 5. According to the rounding rules, we should round down.
[tex]\boldsymbol{0.3391=== > 0.339}[/tex]
--
Hope that this helped! Best wishes.
--
4+0.4+0.0024 in Standard Form
Answers
Answer:
In standard form thats 4.4024
In standard form, 4+0.4+0.0024 can be written as 4.4024
Concept: Any number we can write as a decimal number, between 1.0 and 10.0, multiplied by 10, is said to be in the normal range. 1.23 × 108;
If you look closely, 1.23 is a decimal number between 1.0 and 10.0 so we have a standard form 123,000,000 as 1.23 × 108.
Given: 4+0.4+0.0024
In this case,4 is the integral value and 0.4 is at the first decimal place followed by 0.0024 at the third and 4th decimal place so combining them all together and writing them in standard form we get,4.4024
For more information on the standard form, visit https://brainly.com/question/19169731
#SPJ10
Two buses leave a station at the same time and travel in opposite directions. One bus travels12m/hrslower than the other. If the two buses are 765 miles apart after 6 hours, what is the rate of each bus?
Answers
distance = speed * time
the first bus speed = x
second bus = x - 12
the sum of distance = 765 miles
first distance = 6x
second distance = 6 (x -12)
6x + 6(x-12) = 765
x + x -12 = 127.5
2x = 139.5
x = 69.75 mi/h which is the faster bus
the second bus speed = 57.75 mi/h
(1 point)Let S be the part of the plane 2x+2y+z= 1 which lies in the first octant, oriented upward. Find the flux of the vector field
F = 2i+2j + 2k across the surface S.
Answers
The flux is 9.
What is Flux?Flux is the presence of a force field in a specified physical medium, or the flow of energy through a surface.
Given:
2x+2y+z= 1
F = 2i+2j + 2k
Now,
r = xi + yj + z( 1-2x-2y) K
dr/dx= i - 2k
dr/dy = j-2k
dr/dx* dr/dy
= ( i - 2k) * (j-2k)
= 2i + 2j + k
F(x)= 2i+2j + 2k
F(x). da = 4 +4 +2 = 10 dxdy
Hence, flux
= [tex]\int\limits^1_0 {\int\limits^{1-2y}_0 {10 } \, dx dy } \,[/tex]
= [tex]\int\limits^1_0[/tex] 10(1-2y) dx
= [tex]\int\limits^1_0[/tex] 10-2y
= 10(1) - (1)²
=9
Learn more about flux here:
https://brainly.com/question/14527109
#SPJ1
The plane has intercepts (1/2, 0, 0), (0, 1/2, 0), and (0, 0, 1). Parameterize [tex]S[/tex] by the vector function
[tex]\vec s(u,v) = \dfrac{(1-u)(1-v)}2 \, \vec\imath + \dfrac{u(1-v)}2 \, \vec\jmath + v \,\vec k[/tex]
with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. (More explicitly, we have the parameterization
[tex]\vec s(u,v) = (1-v)((1-u) p_1 + u p_2) + v p_3[/tex]
where [tex]p_i[/tex] denote the given points.)
The normal vector to [tex]S[/tex] is
[tex]\vec n = \dfrac{\partial\vec s}{\partial u} \times \dfrac{\partial\vec s}{\partial v} = \dfrac{1-v}2\,\vec\imath + \dfrac{1-v}2\,\vec\jmath + \dfrac{1-v}4\,\vec k[/tex]
Then the flux of [tex]\vec F = 2\,\vec\imath+2\,\vec\jmath+2\,\vec k[/tex] across [tex]S[/tex] is given by the surface integral,
[tex]\displaystyle \iint_S \vec F \cdot d\vec\sigma = \iint_S \vec F \cdot \vec n \, dA[/tex]
[tex]\displaystyle = \int_0^1 \int_0^1 \left(2\,\vec\imath+2\,\vec\jmath+2\,\vec k) \cdot \left(\frac{1-v}2\,\vec\imath + \frac{1-v}2\,\vec\jmath + \frac{1-v}4\,\vec k\right) \, du \, dv[/tex]
[tex]\displaystyle = \frac52 \int_0^1 \int_0^1 (1-v) \, du \, dv[/tex]
[tex]\displaystyle = \frac52 \int_0^1 (1-v) \, dv = \boxed{\frac54}[/tex]
The function G is defined by g (X) =X^2+2
Find g(4n)
Answers
Answer:
the answer is 4gn Puig IT in
what is the domain of the ordered pair shown in the graph?
Answers
Answer:
D.
Step-by-step explanation:
It is the only one that contains all the x-values of the points. (Domain is the set of x-values).
Need help with number 2 please!!!
Answers
Answer:
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
Step-by-step explanation:
The graph of function f(x) is the parent function.
(Parent functions are the simplest form of a given family of functions).
The graph of g(x) is related to the graph of f(x) by a series of transformations. To determine the series of transformations, work out the steps of how to go from f(x) to g(x).
Transformations
For a > 0
[tex]\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of }\:a \\& \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\& \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a \end{aligned}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
Parent function:
[tex]f(x)=x^3[/tex]
Step 1
Multiply the parent function by 6:
[tex]\implies 6f(x)=6x^3[/tex]
Therefore, this is a vertical stretch by a factor of 6.
Step 2
Now make the function negative:
[tex]\implies -6f(x)=-6x^3[/tex]
Therefore, this is a reflection in the x-axis.
Step 3
Finally, add 2 to the function:
[tex]\implies -6f(x)+2=-6x^3+2[/tex]
Therefore, the function has been translated 2 units up.
Conclusion
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
Learn more about graph transformations here:
https://brainly.com/question/27845947
Write and solve an inequality that means a number plus six is less than or equal to twenty-four.
Answers
Answer:
Inequality: x + 6 ≤ 24
Solution: x ≤ 18
Step-by-step explanation:
Plus: "+" → to add something to something else
Less than or equal to: "≤" → the expression on the left side of the inequality sign is smaller than the expression on the right side of the sign.
Let x be the unknown number.
A number plus 6 is less than or equal to twenty-four:
x + 6 ≤ 24
To solve the found inequality, subtract 6 from both sides:
⇒ x + 6 - 6 ≤ 24 - 6
⇒ x ≤ 18
Therefore, the solution to the inequality is x ≤ 18. The unknown number x can be any real number equal to or less than 18.
No be n
n+6≤24Solve
n≤24-6n≤18Solution set
(-oo,18]
Match each fraction to a reasonable estimate.
(-6/11)
(-7/9)
(-3/13)
(-1/4)
(-3/4)
(-1/2)
Which one goes with each?
Answers
Answer:
-6/11 goes with -1/2
-7/9 goes with -3/4
-3/13 goes with -1/4
Step-by-step explanation:
6/11 is close to 6/12 which is the same as 1/2, so -6/11 goes with -1/2
7/9 is close to 6.75/9 which is 3/4, so -7/9 is close to -3/4
3/13 is close to 3/12 which is the same as 1/4, so -3/13 goes with -1/4
Based on local population projections for 2010, school district 31 will lose 5 teaching positions, district 222 will lose 5 teachers, and district 225 will lose 2. Write a
signed number that represents the total number of teachers that these three school districts are projected to lose.
What is the signed number that represents the total number of positions that these three districts are projected to lose?
Answers
Answer:
2+3+4 = 9
Add the three numbers of the three school districts that project to lose.
evaluate question 3 only
Answers
Step-by-step explanation:
(4²-x²)³/²
or,(4+X) (4-X)
Substitute [tex]x = 4 \sin(y)[/tex], so that [tex]dx = 4\cos(y)\,dy[/tex]. Part of the integrand reduces to
[tex]16 - x^2 = 16 - (4\sin(y))^2 = 16 - 16 \sin^2(y) = 16 (1 - \sin^2(y)) = 16 \cos^2(y)[/tex]
Note that we want this substitution to be reversible, so we tacitly assume [tex]-\frac\pi2\le y\le \frac\pi2[/tex]. Then [tex]\cos(y)\ge0[/tex], and
[tex](16-x^2)^{3/2} = 16^{3/2} \left(\cos^2(y)\right)^{3/2} = 64 |\cos(y)|^3 = 64 \cos^3(y)[/tex]
(since [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex])
So, the integral we want transforms to
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 64 \int \cos^3(y) \times 4\cos(y) \, dy = 256 \int \cos^4(y) \, dy[/tex]
Expand the integrand using the identity
[tex]\cos^2(x) = \dfrac{1+\cos(2x)}2[/tex]
to write
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 256 \int \left(\frac{1 + \cos(2y)}2\right)^2 \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \cos^2(2y)) \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \frac{1 + \cos(4y)}2\right) \, dy \\\\ = 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy[/tex]
Now integrate to get
[tex]\displaystyle 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy = 32 \left(3y + 2 \sin(2y) + \frac14 \sin(4y)\right) + C \\\\ = 96 y + 64 \sin(2y) + 8 \sin(4y) + C[/tex]
Recall the double angle identity,
[tex]\sin(2y) = 2 \sin(y) \cos(y)[/tex]
[tex]\implies \sin(4y) = 2 \sin(2y) \cos(2y) = 4 \sin(y) \cos(y) (\cos^2(y) - \sin^2(y))[/tex]
By the Pythagorean identity,
[tex]\cos(y) = \sqrt{1 - \sin^2(y)} = \sqrt{1 - \dfrac{x^2}{16}} = \dfrac{\sqrt{16-x^2}}4[/tex]
Finally, put the result back in terms of [tex]x[/tex].
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 128 \frac x4 \frac{\sqrt{16-x^2}}4 + 32 \frac x4 \frac{\sqrt{16-x^2}}4 \left(\frac{16-x^2}{16} - \frac{x^2}{16}\right) + C \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 8 x \sqrt{16 - x^2} + \frac14 x \sqrt{16 - x^2} (8 - x^2) + C \\\\ = \boxed{96 \sin^{-1}\left(\frac x4\right) + \frac14 x \sqrt{16 - x^2} \left(40 - x^2\right) + C}[/tex]
Select the correct answer from each drop-down menu. Consider this system of equations: (equation A) (equation B) The solution for the system of equations is .
Answers
The solution for the system of equations is: (99/13, 150/13)
Given the two expression 2/3x+3/5y=12 and 5/2y-3x=6
We have to find solution of two given expression.
To find the value of x, we have to eliminate y by making y the subject of formula in any of the equations.
Multiply equation A by 5/3 t.o get,
5/3(2/3x) + 5/3(3/5y) = 5/3(12)
10/9x + y = 20
y = 20 - 10/9x
substituting for y into equation b, we have:
5/2(20 - 10/9x) - 3x = 6
50 - 25/9x - 3x = 6
52/9x = 44
52x = 396
The expression that gives the value of x is: 52x = 396
Hence, x = 396/52 = 99/13
y = 20 - 10/9(99/13) = 20 - 110/13 = 150/13
Hence The solution for the system of equations is: (99/13, 150/13)
Learn more about system of equations here:
https://brainly.com/question/13729904
#SPJ10
Fireside Shop offers chimney caps for $120 less trade discounts of 25/10. The same chimney cap is being offered at Builder's Supply for $111 less trade discounts of 25/5. What is the price difference between the two companies?
Answers
The difference in price between the two companies is $81-$79.56 = $1.44
Fire side Shop
Price of Chimney cap =$120
First Discount = 25% of(120)=$30
Price after 1st Discount = $120-$30=$90
Second Discount = 10% of 90=$9
Price after 2nd Discount = $90-$9=$81
Builders' Supply
Price of Chimney Cap= $111
First Discount= 25% of 111 = $27.75
Price after 1st Discount = $111 - $27.75 = $83.75
Second Discount = 5% of $83.75 = $ 4.1875
Price after 2nd Discount = $83.75 - $4.1875 = $79.5625 ≈ $79.56
Therefore,
a) Builders supply offers the lower price.
b) Difference in price = $81-$79.56 = $1.44
Learn more about discounts here-
brainly.com/question/3541148
#SPJ10
The value of x for the function f(x) = 100+ 0.3x is 210, when
f(x) = 121. True Or False
Answers
Answer:
false
Step-by-step explanation:
the answer is x=70
How many solutions exist for the given equation?
3(x - 2) = 22 -x
Answers
3x - 6 = 22 - x
3x + x = 22 + 6
4x = 28
X = 7
Answer:
One solution
Step-by-step explanation:
The equation can be rewrite as 3x - 6 = 22 - x
so we try to get all the x on one side so we add x and 6 to both sides so we get 4x = 28 then we divide by 4 both side and get x=7
Mountain Climbing Gym has a gym registration fee of $30 and then charges $55 per month for all access climbing.
Susie wanted to model what she has spent in total on the climbing gym at any given month in the future.
Fill in the blanks for the equation if C = total Cost and m = number of months.
Answers
Answer:
C=55m + 30
Step-by-step explanation:
You would multiply 55 by the number of months so you'd get 55m, and since 30 is a one time fee you would just add 30 to your monthly payment.
Using the diagram, if angle 3 + angle 4 is a straight line then what is the total
measure?
Answers
Answer: 180 degrees
Step-by-step explanation:
Angles on a line add to 180 degrees since they form a straight angle.
Find the midpoint of the line segment whose endpoints are given. (9,3), (10,- 10)
Answers
Answer:
Step-by-step explanation:
(xm , ym ) = x1 + x2 / 2 and y1 + y2 / 2
= 9 +3 / 2 = 10 -10 / 2
= 12/2 = 0/2
= 6 = 0
So midpoints are (6 , 0)
Answer:
midpoint = [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]
Step-by-step explanation:
To find the midpoint of a line segment, you have to find the average of the x and y-values of the end-points, i.e., add the x-coordinate values and divide the answer by 2, and do the same for the y-coordinate values.
• midpoint = [tex](\frac{x_{2} + x_1}{2}, \frac{y_2 + y_1}{2} )[/tex]
= [tex](\frac{9 + 10}{2}, \frac{3 + (-10)}{2} )[/tex]
= [tex](\frac{19}{2}, \frac{-7}{2} )[/tex]
= [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]
When we're solving minimum or maximum problems, are we h or the constant k? looking for the constant
Answers
In solving minimum and maximum problems, result we are looking for would be the constant, k.
What is being solved for in minimum and maximum problems?When looking for the minimum functional value, we are looking for the constant, k because it can be thought of as the absolute minimum value.
An open parabola would then have k as the maximum functional value which means that the constant k is the value being sought.
Find out more on maximum and minimum functional values at https://brainly.com/question/19921479.
#SPJ1
Which graph represents the function f(x)=−3x−2?
Answers
Answer:
Step-by-step explanation:
julie ran a race 2 minutes faster than teri did. if teri ran the race in 28 minutes, what equation would be used to find the number of minutes teri took to run the race
Answers
Th equation that can be used to find the umber of minutes Teri ran is m + 2 = 28 minutes.
How many minutes did it take Teri to run the race?Addition is a mathematical operation that is used to determine the sum of two or more numbers.
The total minutes run by Julie = minutes ran by Teri + 2
28 = m + 2
Please find attached the complete question. To learn more about addition, please check: https://brainly.com/question/19628082
#SPJ1
Steve bought a new car for $22,000 but paid 93% of the list price. How much was the list price
Answers
Answer:
approximately $23,655.91 (rounded to the nearest hundredths place)
Step-by-step explanation:
[tex]22,000=0.93x\\x=23,655.91[/tex]
Answer:
Step-by-step explanation:
let the list price=x
93% of x=22,000
x=22,000 ×100/93
≈23,655.91 $
Solve for x in the inequality |2x + 5| ≤ 11. (If this is an "and" inequality, give your answer as a single compound inequality. If this is an "or" inequality, separate your answers using a comma.) Solve for x in the inequality | 2x + 5 | ≤ 11. ( If this is an " and " inequality , give your answer as a single compound inequality . If this is an " or " inequality , separate your answers using a comma . )
Answers
|2x + 5| ≤ 11
x = 3
2(3) + 5
6 + 5
11 ≤ 11
The solution for the x in the inequality |2x + 5| ≤ 11 is {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3}
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
|2x + 5| ≤ 11
To find the solution for the x, solve the inequality,
|2x + 5| ≤ 11
-11 ≤ 2x + 5 ≤ 11
Subtract 5 from whole the expression,
-11 - 5 ≤ 2x + 5 - 5 ≤ 11 - 5
-16 ≤ 2x ≤ 6
-8 ≤ x ≤ 3
The value of x for the given inequality varies from -8 to 3.
To know more about Inequality on:
https://brainly.com/question/20383699
#SPJ2
the probability that Luis will pass his test is 0.82. find the probability that he will fail his statistic test
Answers
The probability of failure for Luis will be 0.18.
What is probability?
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability of passing is = 0.82
We know that the maximum probability of happening any event is 1 or 100 per cent if the probability of passing of the person is 0.82 then the probability of failure will be calculated as:-
Probability of failing = 1 - probability of passing
Probability of failing = 1 - 0.82
Probability of failing = 0.18
Therefore the probability of failure for Luis will be 0.18.
To know more about probability follow
https://brainly.com/question/24756209
#SPJ1
graph x=4y , x+y=7.0
Answers
Answer:
First find the x and y intercepts. Recall that intercepts intersect the x and y axis of a graph, therefore either the x or y value of a coordinate point must be 0 in order for it to be an intercept.
After you find the intercept, plot the them on the cartesian coordinate system and draw a straight line (it’s a linear equation) going through the two intercepts.
Side note: Not sure how credentials work on Quora yet. I meant to say I am a student
The equation of the lines can be plotted on the graph after calculating the coordinates on each line.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have two linear equation:
x = 4y
x + y = 7.0
To plot the linear equation first we will find the few coordinates to plot on the coordinate plane.
For the equation of line:
x = 4y
x 0 1 2 3 -1 -2 -3
y 0 4 8 12 -4 -8 -12
For the equation of line:
x + y = 7.0
x 0 1 2 3 -1 -2 -3
y 7 6 5 4 8 9 10
Thus, the equation of the lines can be plotted on the graph after calculating the coordinates on each line.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ1
help! asap! algebra 2
Answers
We can subtract the function that represents the cost in 2000 from the function that represents the cost in 1990.
Doing this gives us [tex](-20t^{2}+1000)-(-10t^{2}+1500)=\boxed{-10t^{2}-500}[/tex]
When treated with an antibiotic, 92% of all the dolphins are cured of an ear infection. If 7 dolphins are treated, find the probability that exactly 4 are cured.
The probability is
(Round your answer to 4 decimal places.)
Answers
The probability that exactly 4 are cured from 7 dolphins is 0.0128
What is Probability ?Probability is the likeliness of an event to occur and it has a range of 0 to 1, where 0 means unlikely and 1 indicates certainty of the event to happen.
It is given that the 92% of all the dolphins are cured of an ear infection ,When treated with an antibiotic
If there are total dolphins given as 7
On the basis of given data
The dolphin that cannot be cured is given by
1 - p = 1 - (92/100) = 0.08 = 8/100
q = (8/100)
n= 7
r = 4
Therefore by Binomial Distribution
[tex]P = ^nC_r p^r q^{n-r}[/tex]
Putting the values
[tex]P = ^7C_4 (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]
[tex]P = \dfrac{7!}{4! \;3!} (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]
P = 0.0128
Therefore the probability is 0.0128.
To know more about Probability
https://brainly.com/question/11234923
#SPJ1
Find the perimeter of the following shape, given its curves are made from parts of circles.
Give your answers in terms of .
4cm
4cm
4cm
The diagram is not drawn to scale.
Answers
Find the inverse of the function.
y=x+9
Answers
Answer: [tex]y=x-9[/tex]
Step-by-step explanation:
To find the inverse of a function you must first swap the places of x and y
[tex]x=y+9[/tex]
Now solve for y
Step 1: Flip the equation.
[tex]y+9=x[/tex]
Step 2: Subtract 9 from both sides.
[tex]y+9-9=x-9\\y=x-9[/tex]
Can someone help me? I’ll give brainliest to whoever gets it right first
Answers
Answer:
the measure of line AD is 8
Step-by-step explanation:
lines AD and BC are equal, due to the markings on the lines
this means that if line BC is 8, than line AD is also 8
