Which table shows a proportional relationship between miles traveled and gas used?
Answers
cross multiply to see if it is a true proportion
(15)(135) = (270)(7.5)
2025 = 2025 (correct...so this is a true proportion)
answer is : bottom right one
Answer:
last fourth table given in the figure shows the proportional relationship .
Step-by-step explanation:
Definition of proportional relationship
The relationship in which two quantities are varies proportional to each other .
[tex]a = kb[/tex]
Where k is called the proportional constant .
Let us assume that the number of miles travelled be y .
let us assume that the gas used be x .
[tex]y\propto x[/tex]
y = ca
Where c is the proportional constant .
In first table
Miles travelled = 27.3 mi
Gas used =1.5 gal
Putting in the formula
y = ca
27.3 = 1.5c
[tex]\frac{27.3}{1.5}=c[/tex]
c = 18.2
Miles travelled = 49.16 mi
Gas used = 3.8 gal
Putting in the formula
y = ca
49.16 = 3.8c
[tex]\frac{49.16}{3.8}=c[/tex]
c = 12.94 (Approx)
Thus the miles travelled is not vary with the gas used .
Therefore table not shows the proportional relationship .
Second Part
Miles travelled = 135 mi
Gas used = 7.4 gal
Putting in the formula
y = ca
135 = 7.4c
[tex]\frac{135}{7.4}=c[/tex]
c = 18.2
Miles travelled = 135.5 mi
Gas used = 7.9 gal
Putting in the formula
y = ca
135.5 = 7.9c
[tex]\frac{135.5}{7.9}=c[/tex]
c = 17.2 (Approx)
Thus the miles travelled is not vary with the gas used .
Therefore table not shows the proportional relationship .
Third table
Miles travelled = 120 mi
Gas used = 6.2 gal
Putting in the formula
y = ca
120 = 6.2c
[tex]\frac{120}{6.2}=c[/tex]
c = 19.4 (Approx)
Miles travelled = 180 mi
Gas used = 12.2 gal
Putting in the formula
y = ca
180 = 12.2c
[tex]\frac{180}{12.2}=c[/tex]
c = 14.8 (Approx)
Thus the miles travelled is not vary with the gas used .
Therefore table not shows the proportional relationship .
Fourth table
Miles travelled = 270 mi
Gas used = 15gal
Putting in the formula
y = ca
270 = 15c
[tex]\frac{270}{15}=c[/tex]
c = 18
Miles travelled = 135 mi
Gas used = 7.5 gal
Putting in the formula
y = ca
135= 7.5c
[tex]\frac{135}{7.5}=c[/tex]
c = 18
Thus the miles travelled is vary with the gas used .
Therefore table shows the proportional relationship .
The last fourth table given in the figure shows the proportional relationship .
Related Questions
Write the decimal 5.16 as a percent
Answers
I hope this helps:)) !!
seven subtracted from 4 times a number (x) is more than 13
Answers
4n>20 divide both sides by 4
n>5
In this equation, you will use subtraction, multiplication, and addition.
during a baseball game, a player's ball hit into the outfield is modeled by the equation h=-16t^2 + 65t. A bird flying across the field follows the path modeled by the equation h=8t+20. let t be the time since the ball is hit and h be the height. what do the intersection points of the equations represent?
Answers
8t+20=-16t^2+65t
16t^2-57t+20=0, using the quadratic equation for expediency:
t=(57±√4529)/32 and since we know t>0
t≈3.88 seconds (at a approximate height of 51 feet)
Answer:
Intersection points are
(0.39,0) and (3.16,0)
Step-by-step explanation:
The equation of the outfield is [tex]h=-16t^2 + 65t[/tex]
The path equation is [tex]h=8t+20[/tex]
To find intersection of two equations , we make them equal and solve for t
[tex]-16t^2+65t= 8t+20[/tex]
Subtract 8t from both sides
[tex]-16t^2+57t=20[/tex]
Subtract 20 on both sides
[tex]-16t^2+57t-20=0[/tex]
Divide whole equation by -1
[tex]16t^2-57t+20=0[/tex]
Apply quadratic formula to solve for t
[tex]t=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a= 16, b=-57 and c=20
[tex]t=\frac{57+-\sqrt{(-57)^2-4(16)(20)}}{2(16)}[/tex]
[tex]t=\frac{57+-\sqrt{1969}}{32}[/tex]
[tex]t=\frac{57+\sqrt{1969}}{32}=3.16[/tex]
[tex]t=\frac{57-\sqrt{1969}}{32}=0.39[/tex]
Please I need help with number 9 !!!! For brainlest answer and thanks !!!!!
Answers
Isolate s by subtracting 2.8 from both sides. What you do to one side, you must do to another in an equation.
s+2.8-2.8= 6.59-2.8
s= 3.79
Final answer: B
which whole number is closest to √149
Answers
part 2
Fred bakes 10 dozen cookies for the bake sale. He makes the following types of cookies:
. 1/2 chocolate chip
. 1/4 peanut butter
. 1/8 sugar cookies
. 1/8 oatmeal raisin cookies
4. How many of each type of cookie did Fred make? Show your work.
Chocolate chip_________
Peanut Butter _______
Sugar cookies ________
Oatmeal raisin_______
5. Unfortunately, Fred had some trouble in the kitchen and 3/5 of the peanut butter cookies were burned.
a. How many peanut butter cookies does Fred have left to sell? _____
b. Explain how you know this is correct.
Answers
12*10= 120 cookies
chocolate chip is 1/2
1/2 of 120 is 60
60 chocolate chip cookies
Peanut Butter is 1/4 (or half of 1/2)
1/2=60 so that means 1/4=30
30 PB cookies
Sugar and oatmeal raisin are both 1/8 (half of 1/4)
1/4= 30 so that means 1/8=15
15 Sugar Cookies
15 Oatmeal Raisin
3/5 of PB were burned
Original PB was 30
3/5 of 30 is 18
18 cookies were burnt
30-18=12 (which were salvaged)
12 PB cookies remain
Hope this helps
what is the slope of (4,3.5),(-4,3.5)
Answers
** if ur x values would have been the same, instead of ur y values, then u would have had a vertical line with an undefined slope.
a string was 4m long. she gave 1/4m of it to her sister and 3/4m to her friends. how much string had she given away?
Answers
____________________________
Explanation:
____________________________
Add up the amounts she had given away:
3/4 m + 1/4 m = 4/4 m = 1 m.
____________________________
The answer is: " 1 m " .
____________________________
what is the product of any integer and -1
Answers
Remember:
Multiply and divide
Then look at the signs
Different signs are negative
Same signs are just fine (positive)
For example: -5 x 5 = -25 -5 x -5 = 25
Different signs Same signs (positive & positive)
So in your specific case, the product of any integer and -1 depends. If the integer is positive, than the final product would be the integer in it's negative form. If the integer is negative, than the final product would be the integer in it's positive form.
I hope this makes sense to you!
how do u write the product of 10 and the difference of a number X and 14 is 90
Answers
[tex]10(x-14)=90[/tex]
Identify all sets to which the number 3.1214122144 . . . belongs. Choose from irrational,rational,whole,and integer
Answers
hope this helps:)
please mark thanks and brainleist:)
Which of the following is equivalent to the complex number
[tex]i ^{34}[/tex]
:
Answers
A square patio has an area of 200 square feet how long is each side of the patio to the nearest 10th
Answers
200= x^2
Root both sides
x= root 200
x= approx. 14.1
Final answer: 14.1 ft
what polynomial could you add to 3x^4 - 9x^3 + 5x^2 - x + 7 to get a sum of 3+4x^4 + 3x-x^3 + 3x^2
Answers
8;7 ratio is boys out of 195 campers
Answers
PLEASE HELP {It costs 5,700 every one sixth of an hour to build a hotel how many cents does building a hotel cost per second?}
Answers
That means it costs 5,700 every 10 minutes.
Costs 5,700 = 10 minutes
Dive 10 on both sides.
Costs 570 = 1 minute
Lets convert the minute into seconds.
Costs 570 = 60 seconds
Divide both sides by 60.
Costs 9.5 cents = 1 second
Round it off since you can't pay 9.5 cents.
Costs 10 cents = 1 second
This means that every second they pay 10 cents for the hotel. :D
What two-dimensional cross-sections could we create by slicing a sphere?
Answers
Choose the correct simplification of (3xy6)2(y3)3
A.9x2y21
B.6x2y21
C.9x2y14
D.6x2y14
Answers
Answer: A. [tex]9x^2y^{21}[/tex]
Step-by-step explanation:
The given expression : [tex](3xy^6)^2(y^3)^3[/tex]
Using laws of exponents :
[tex]a^m*a^n=a^{m+n}\\\\(a^m)^n=a^{mn}[/tex]
To simplify the given expression :
[tex](3xy^6)^2(y^3)^3\\\\=(3)^2(x)^2(y^6)^2(y^{3\times3})\\\\=9x^2y^{12}\times y^9\\\\=9x^2y^{12+9}\\\\=9x^2y^{21}[/tex]
Therefore, [tex](3xy^6)^2(y^3)^3=9x^2y^{21}[/tex]
because the angles in a rectangle are 90 degrees it is not a parallelogram true or false? please explain why
Answers
But a rectangle is a shape where opposites sides are parallel *and* all the corners are 90 degree angles. So you can't say that all parallelograms would be rectangles. Some parallelograms would be rectangles, but not all.
Rectangles are a subset of the shapes called parallelograms. But parallelograms are *not* a subset of the shapes called rectangles.
It's similar to saying all cars are vehicles. But you can't say that all vehicles are cars.
Darren and Latisha are decorating cupcakes for a bake sale. They need to decorate 100 cupcakes. Each of them has decorated 40% of the cupcakes. What percentage of cupcakes do they have left to decorate?
Answers
They only need to decorate 20% of the cupcakes left.
Answer:
Now they have left to decorate 20% cupcakes.
Step-by-step explanation:
Darren and Latisha are decorating cupcakes for a bake sale.
They need to decorate 100 cupcakes.
Each of them has decorated 40% of the cupcakes = 40% + 40% = 80%
Both of them has decorated 80% of the cupcakes.
80% of 100 cupcakes = 80 cupcakes
Now they have left to decorate 100 - 80 = 20
Now they have left to decorate 20% cupcakes.
The diameter of a beach ball is 10 inches. How many cubic inches of air can the beach ball hold? Use 3.14. Round to the nearest tenth of a cubic inch.
Answers
So, it looks like we got the volume of a sphere. We know that the formula for it when we got the diameter is, [tex]V=\frac{\pi d^3}{6}[/tex]
We are going to use 3.14 for [tex] \pi [/tex]
[tex]V=\frac{3.14* d^3}{6}[/tex]
Let's plug in the values,
[tex]V=\frac{3.14*10^3}{6}[/tex]
Simplify,
[tex]V=\frac{500*3.14 }{3}[/tex]
Our volume of the beach ball is,
V ≈ 523.333333333
Round to the nearest tenth.
V ≈ 523.3 in³
Thanks!
-TetraFish
For normally distributed data, what proportion of observations have z-scores satisfying the following conditions:
0.62 < z < 2.92
Answers
P(z<=0.62) = 0.7324
P(z<=2.92) = 0.9983
Therefore
P(0.62 < z <2.92) = 0.9983 - 0.7324 = 0.2659
The required proportion is 0.2659 or 26.6%
Answer: 0.266 or 26.6%
write an equation to represent the relation. Then solve the equation. A number decreased by 30 is the same as 14 minus 3 times the number
Answers
x-30 =14-3x
subtract 1 x from each side
-30 =14-2x
subtract 14 from each side
-44 = 2x
x=-44/2 = -22
x=-22
check:-22-30 = -52
14-3(-22) = 14-66 =-52
both equations equal
X = -22
convert 2.998m/s to km/h and to miles per hour
Answers
1 meter per second = 3.6 km per hour
2.998 x 3.6 = 10.7928 km per hour
1 KM per hour = 0.621371 mph
10.7928 x 0.621371 = 6.706
6.706 miles per hour
round answer as needed
Barrie had stamps he gave 1/8 of them to tom if he gave 15 stamps to tom how many stamps did Barrie have at first
Answers
120X(1/8)=15
A gardener uses a tray of 6 conical pots to plant seeds. Each conical pot has a radius of 3 centimeters and a depth of 8 centimeters. About how many cubic centimeters of soil are needed to plant the full tray? Round to the nearest cubic centimeter.
Answers
By definition, the volume of a cone is given by:
[tex] V = (\frac{1}{3}) * (\pi) * (r ^ 2) * (h)
[/tex]
Where,
r: radius of the circular base
h: height of the cone
Since we have 6 conical pots, then the total volume is:
[tex]Vt=6V[/tex]
[tex] Vt = 6 * (\frac{1}{3}) * (\pi) * (r ^ 2) * (h)
[/tex]
Substituting values we have:
[tex] Vt = 6 * (\frac{1}{3}) * (3.14) * (3 ^ 2) * (8)
Vt = 452.16 cm ^ 3
[/tex]
Rounding to the nearest cubic centimeter:
[tex] Vt = 452 cm ^ 3
[/tex]
Answer:
are needed 452 cm^3 of soil to plant the full tray
The cubic centimeters of soil are needed to plant the full tray is approximately 452cubic in
Volume of a coneThe formula for calculating the volume of a cone is expressed as:
V = 1/3πr²h
r is the radius = 3cm
h is the height = 8cm
Substitute
V = 1/3 * 3.14 * 3^2 * 8
V = 75.36 cubic cm
Since the gardener uses a tray of 6 conical pots to plant seeds, the total volume will be expressed as:
T = 6(75.36)
T = 452cubic in
Hence the cubic centimeters of soil are needed to plant the full tray is approximately 452cubic in
Learn more on volume of cone here: https://brainly.com/question/1082469
Which number sentences show how to solve the problem?
A pair of socks costs $5.00. A package of 3 pairs costs $12.00. How much would you save if you buy 2 packages instead of 6 individual pairs?
Choose all answers that are correct.
A.
6 × 5 = 30, 2 ×12 = 24, and 30 – 24 = 6
B.
12 – 5 = 7, 7 x 2 = 14, and 14 – 6 = 8
C.
12 ÷ 3 = 4, 5 – 4 = 1, and 1 × 6 = 6
D.
12 ÷ 3 = 4, 4 × 5 = 20, and 20 – 12 = 8
Answers
Answer:
a is the answer
Step-by-step explanation:
first you divded 12.00
Lucy has to run two errands. She starts from home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. Then, from the gas station, she travels 5 miles to return home. The entire trip forms a triangle.
What was the smallest angle made in her trip?
It is at the gas station.
It is at Lucy’s home.
It is at the post office.
It depends on the direction Lucy is traveling.
Answers
Lucy starts from home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. As it is known south and east directions form right angle. Since the entire trip forms a triangle, this triangle is right with right angle at post office.
Call the vertices of this triangle P - post office, G - gas station, H - home. Then HP and PG are legs of this triangle and GH is hypotenuse.
From the given data:
HP=3;PG=4;GH=5;∠P=90°.The smallest angle is opposite to the smallest side. The smallest side is leg HP, so the smallest angle is G that is the angle at gas station.
Answer: correct choice is A.
In this exercise we have to mark the correct alternative corresponding to the location, so we have:
Letter A
The following information was then given by the statement:
Lucy starts from home and travels 3 miles south to the post officeFrom the post office, she travels 4 miles east to the gas station.Imagining the paths made by lucy as a triangle, we know that the longest path that corresponds to the hypotenuse will be from the gas station to her house, so:
HP=3;PG=4;GH=5;P=90°.We have:
[tex]180-90=90\\90/2=45\\45-15=30[/tex]
The smallest angle is at the gas station.
See more about triangles at brainly.com/question/25813512
Avery owns stocks in Ever Rise Corporation. The stock price increased by 120% over the past week. If the stock price was p last week, write two equivalent expressions that represent the current stock price and explain what their equivalence means. Substitute one or more variables into the expressions to prove them equivalent.
Answers
Answer:
Expression 1. P+1.2p
Expression 2. 2.2p
Step-by-step explanation:
These 2 equivalent expressions state that increasing a value by 120% is the same as multiplying the original value by 2.2.
Example: assume that p=50. The first expression gives p+1.2p=50+1.2(50) =110. The second expression gives 2.2p=2.2(50)=110
The two expressions 1.2p and p + 0.2p are equivalent, as they both represent the same relationship between the current stock price and the stock price last week.
What is the expression?
Expressions are defined as mathematical statements that have a minimum of two terms containing that variables or numbers.
If the stock price increased by 120% over the past week, then the current stock price is 120% of the stock price last week. This can be represented by the equation:
current price = 1.2p
Another way to represent the same relationship is to say that the current price is the stock price last week plus 120% of the stock price last week. This can be represented by the equation:
current price = p + 0.2p
To prove that these two expressions are equivalent, we can substitute a value for p into both equations and show that they give the same result. For example, if the stock price last week was $100, then:
current price = 1.2100 = $120
current price = 100 + 0.2100 = $120
Therefore, the two expressions are equivalent, as they both represent the same relationship between the current stock price and the stock price last week.
Learn more about Expressions here :
brainly.com/question/21751419
#SPJ2
How do variables help you model real-world situations? Give an example of a model that uses variables and explain how it helps people make predictions.
Answers
You are given 4x-2y=12 and -4x-9=54. You are asked to find the order of the ladder. However, you did not specify which variable represents the ladder. I will just solve for both of the variables. I will be applying the substitution method.
Let 4x-2y=12 equals equation one and equation 2 for -4x-9=54.
4x-2y=12
4x=12+2y
x=3+1/2y
substitute this x to the equation 2
-4x-9y=54
-4(3+1/2y )-9y=54
Y=-6
X=3+1/2y = 3+1/2(-6) = 3+(-3) = 0