the table shows the volume of gasoline in a gas tank at different times. Find th e rate of change for each time interval. During which time interval did the volume decrease at the greatest rate?

Answers

Answer 1

Final answer:

To find the rate of change for each time interval, calculate the difference in volume for each interval and divide it by the difference in time. Compare the rates of change to determine the time interval with the lowest rate of change.

Explanation:

To find the rate of change for each time interval, we need to calculate the difference in volume for each interval and divide it by the difference in time. Let's assume the time intervals are 12-18 hours, 18-24 hours, and 12-24 hours. The rate of change for each interval can be calculated as follows:

Rate of change for 12-18 hours = (Volume at 18 hours - Volume at 12 hours) / (18 hours - 12 hours)

Rate of change for 18-24 hours = (Volume at 24 hours - Volume at 18 hours) / (24 hours - 18 hours)

Rate of change for 12-24 hours = (Volume at 24 hours - Volume at 12 hours) / (24 hours - 12 hours)

The time interval during which the volume decreased at the greatest rate will be the interval with the lowest rate of change. Compare the rates of change calculated for each interval to find the time interval with the lowest rate of change.

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Related Questions

You have 6 green marbles, 23 blue marbles, and 18 red marbles. what is the probability of choosing a red marble. express your answer as a fraction in lowest terms.

Answers

The probability of choosing a red marble is 18/47.

Use the converse of the pythagorean theorem to determine whether the triangle with the given vertices is a right triangle. (2, 1)(6, 4), (–4, 9)

Answers

hello :
let : A(2, 1) , B(6, 4) , C(–4, 9)
calculate : AB , AC, BC
AB = √((6-2)² + (4-1)²) = √25 = 5
AC= √((-4-2)² + (9-1)²) = √100 = 10
BC= √((-4-6)² + (9-4)²) = √125
by pythagorean theorem : BC² = AC² + AB²
the triangle is rectangle in : A

the total points scored in a basketball game can be calculated using the expression 3c - 3 if c = 41, how many points total were scored

Answers

Answer:

its actually 126

Step-by-step explanation:

Final answer:

The total points scored in the basketball game is 120 points.

Explanation:

To find the total points scored in a basketball game, we can use the expression 3c - 3. Given that c is equal to 41, we can substitute this value into the expression to calculate the total points.

So, 3c - 3 = 3(41) - 3 = 123 - 3 = 120.

Therefore, a total of 120 points were scored in the basketball game.

Find the equation of the line that is perpendicular to the line 3x-y=-4 and contains the point (-2,4)

Answers

3x - y = -4
- 3x - 3x
-------------------
y = -3x - 4

Slope: -3
Opposite Reciprocal Slope: 1/3

Given: (-2,4)

Point Slope Form: y - y₁ = m(x - x₁)
y - 4 = 1/3(x + 2)
y - 4 = 1/3x + 2/3
+ 4 + 4
-----------------------------
y = 1/3x + 14/3

Ohhhhh! I have a Brainliest!

Answers

answers: 1.) 37 & 2.) 1 2/3

1. 4.5+8.75+9.5+10+4.25=37

2. 4 1/3

hope this helps please give brainliest and 5 stars and a thank you

A circle and a square have the same area. find the length of the diagonal of the square divided by the radius of the circle.

Answers

Let us say that the square have edge = sqrt(pi), then its area is pi since A = edge^2, and therefore the diagonal is pi*sqrt(2).

Meanwhile the circle of radius 1 has area pi since area of circle is A = pi *radius^2.

Therefore we get that the diagonal of the square divided by the radius is:

diagonal / radius = pi*sqrt(2) / 1 = pi*sqrt(2)

1) Write the sum or difference in the standard form a + bi. (2 points)
( 7 + 5i) - ( -9 + i)

a) 16+4i
b) -16-4i
c) 16-4i
d) -2+6i

2) Write the product in standard form. (2 points)
( 7 + 7i)( 6 + 7i)

a) -7 + 91i
b) 49i2 + 91i + 42
c) 91 - 7i
d) -7 - 91i

3) Find the product of the complex number and its conjugate. (2 points)
1 + 3i

a) 1 + 9i
b) 10
c) -8
d) 1-9i

4) Write the expression in standard form. (2 points)
three divided by quantity three minus twelve i.

a) - one divided by seventeen. + four divided by seventeen. i
b) one divided by seventeen. - four divided by seventeen. i
c) - one divided by seventeen. - four divided by seventeen. i
d) one divided by seventeen. + four divided by seventeen. i

5) Find the real numbers x and y that make the equation true. (2 points)
5 + yi = x + 3i

Answers

When performing addition and multiplication with constant numbers, we treat i as we would treat any variable x in an expression, with the same rules and properties of addition and multiplication.

1)

[tex]( 7 + 5i) - ( -9 + i)=7+5i+9-i=(7+9)+(5i-i)=16+4i[/tex]

2)
Distribute 7+7i over 6 and 7i:

[tex]( 7 + 7i)( 6 + 7i)=( 7 + 7i)\cdot6+( 7 + 7i)\cdot7i=42+42i+49i+49i^2[/tex]

collecting similar terms, and substituting [tex]i^2[/tex] with -1 we have:

42+91i-49=-7+91 i

3)

The conjugate of a complex number a+bi is a-bi;
the conjugate of 1+3i is 1-3i.

Thus, using the difference of squares formula we have

[tex](1+3i)(1-3i)=1^2-(3i)^2=1-9i^2=1-9(-1)=1+9=10[/tex]

4)

To write a rational expression ( with a complex number in the denominator) in the standard form, we multiply by the conjugate of the denominator both the numerator and the denominator:

[tex]\displaystyle{ \frac{3}{3-12i}= \frac{3(3+12i)}{(3-12i)(3+12i)}= \frac{9+36i}{3^2-(12i)^2} [/tex]

[tex]=\displaystyle{ \frac{9+36i}{9+144}= \frac{9+36i}{153}= \frac{9}{153}+ \frac{36}{153}i [/tex]

simplifying by 9, the complex number is finally written as

[tex]\displaystyle{ \frac{1}{17}+ \frac{4}{17}i [/tex]

5)

2 complex numbers a+bi, and c+di are equal only if a=c, and b=d. (Where a, b, c, d are real numbers.)

Thus, x=5, and y=3 is the solution to the equation.

Answers:

1) A
2) A
3) B
4) D
5) (x, y) =( 5, 3)

The length of a rectangle is 3 meters less than twice the width. if the area of the rectangle is 527 square meters, find the dimensions.

Answers

The rectangle is 17 meters wide and 31 meters long. To solve this problem, first work out the equation for the length of the rectangle. Using the information given, we find that length (L) is given by L=2W-3. Next we setup the formula for the area of a rectangle, A=(W)(L). We are told that the area is 527 sq. meters, so our equation is 527=(W)(L). We also know that L=2W-3, so we can plug that into the equation for area as well which gives us 527=W(2W-3), which can be written 0=2(W^2)-3W-527. We now need to solve this equation for W. Factoring the left side we get, 0=(W-17)(2W+31). Thus, either (W-17)=0 or (2W+31)=0 must equal zero. Solving these two equations, we get W=17 or W=-15.5. Since we are looking for the width (which is a length), we know it cannot be negative and therefore the width must be 17 meters. Now that we know the width, we can plug W=17 back into the equation for length (L=2W-3). Doing this give us L=2(17)-3 which is equal to 31. Thus the length is 31 meters.

Answer:

w=17

l=31

Step-by-step explanation:

correct

Which does not describe the same situation?

Answers

Answer:

4. Option 3rd.

Step-by-step explanation:

In this question, three options are given.

We need to describe the same situation.

First option: y = 3 + 6x

this equation represent the equation of a line. In that line all the points are related with each other with same relation.

So, this equation describe the same situation.

Second equation:

y is two more than six times x.

We write this situation in equation form.

y = 6x + 2

this is also describe the same situation.

Third option:

this table shows the x-y relation table.

Here no two points are describe the same situation.

So, option 3rd doesn't describe same situation.

Question 5:

Please share the options

Answer:

Step-by-step explanation:

It is A

2+1/6y=3x+4 solve for y

Answers

2+1/6y=3x+4 solve for y

Answer y=18x+12

2 + 1/6y = 3x + 4
× 6y throughout
12y + 1 = 18xy + 24y
Send 12y to the other side
12y + 18xy = 1
Y is common
y (12 + 18x) = 1
y = 1/ (12 + 18x)

Hope it helped!

A pool is filled at a rate of 105 gal/min. What is the rate in mL per second?

Answers

Greetings!

(There are 3785.41 mL in a gallon.)
There are 60 seconds in minute. Therefore, if we divided the gallon per minute by 60, we can get the answer.

105/60
=1.75 gallon per second

1.75*3785.41
=6624.4675 mL per second

Hope this helps.
-Benjamin

Is 1.34 a non-terminating decimal

Answers

if it is just 1.34, then it terminates.....1.34 = 1 34/100 = 1 17/50

terminates means ends.. so the answer to your question is no, 1.34 is a TERMINATING decimal

F= 9/5C + 32, solve for F please.

Answers

I believe u would do it this way if it's wrong please let me know hope I helped and don't srew u up

An office uses 478 pounds of paper in one week. The paper comes in packages that hold 18 pounds of paper each. How many packages of paper does the office use each week?

Answers

To solve this, you would divide 478 by 18, which equals 26.5555556. Since you can't have half a package of paper, the answer would be 26. Hope this helps!

The office uses 26 and a half package of papers.

What is division?

Division is the process of splitting a number or an amount into equal parts.

Given that, An office uses 478 pounds of paper in one week. The paper comes in packages that hold 18 pounds of paper each.

To find the number of packages of paper, the office use each week, we will divide the total paper used in one week to paper in 1 package

Therefore, the number of packages of paper, the office use each week = 478 / 18 = 26.5

That means they are using 26 package plus a half package in one week.

Hence, The office uses 26 and a half package of papers.

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what is the sum of the measures of interior angles of a 15-sides polygon

Answers

using
sum = (n-2)180
= (15-2)180 = 13×180 = 2340°

Answer:

2340

Step-by-step explanation:

A P E X

A number sentence is said to be true if both numerical expressions are

Answers

if both expressions are equivalent (that is when both evaluate to the same number)

Cynthia besch wants to buy a rug for a room that is 18 ft wide and 30 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 220 square feet of carpeting. what dimensions should the rugâ have?

Answers

Since the strip around the outside of the rug will be uniform, the dimensions of the rug will have the form (18 - x) in width and (30 - x) in length, where x is equal to twice width of the strip. We can use this data to set up an equation. (18 - x) (30 - x) = 220 x^2 - 48 x + 540 = 220 x^2 - 48 x + 320 = 0 (x - 8) (x - 40) = 0 x = 8 or x = 40 Since x = 40 is too wide for the strip, the correct solution is x = 8 The width of the rug is: 18 - x = 10 feet The length of the rug is: 30 - x = 22 feet The dimensions of the rug are 10 feet x 22 feet. Note that the area is equal to 220 square feet.

A train travels 750 miles in 15 hours. which unit rate describes the speed of the train?
a. 50 miles per hour
b. 75 miles per hour
c. 150 miles per hour
d. 350 miles per hour

Answers

The answer your looking for is A

two cruise ships are sailing towards each other from caribbean islands that are 264 km apart, one ship travels 4 km/h faster than the other. if they both started at the same time. and meet after 6h. how fast is the other ship travelling?

Answers

Final answer:

The slower ship is traveling at a speed of 21 km/h, while the faster ship is traveling at a speed of 25 km/h.

Explanation:

This is a mathematics problem that involves solving for unknown speeds with the given conditions. Lets assume the speed of the slower ship is x km/h. Thus, the speed of the faster ship is x+4 km/h. They are moving towards each other, thus their combined speed is (x+x+4) km/h. As speed is distance over time, we can set up the equation: (2x+4)*6 = 264. Solving this equation, we end up with x=21 km/h as the speed of the slower ship, and hence the speed of the faster ship is 25 km/h.

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Prove that acceleration is perpendicular to velocity

Answers

what are the answers

Which statement is true about the difference 2√7-√28

Answers

It seems like there are answer choices but you forgot to post them. If you want to simplify then

2*sqrt(7) - sqrt(28) = 2*sqrt(7) - sqrt(4*7)
2*sqrt(7) - sqrt(28) = 2*sqrt(7) - sqrt(4)*sqrt(7)
2*sqrt(7) - sqrt(28) = 2*sqrt(7) - 2*sqrt(7)
2*sqrt(7) - sqrt(28) = (2-2)*sqrt(7)
2*sqrt(7) - sqrt(28) = (0)*sqrt(7)
2*sqrt(7) - sqrt(28) = 0

So the whole complicated expression simplifies to 0 (zero)

This is because sqrt(28) = 2*sqrt(7) when you simplify sqrt(28)

Side Note: "sqrt" is shorthand for "square root"

JIMMMMMMMMMMMMMMMM :)

Answers

The completed chart is attached as an image

------------------------------------------------

Plug x = -2 into f(x) to get:
f(x) = 9*x + 7
f(-2) = 9*(-2) + 7
f(-2) = -18 + 7
f(-2) = -11

Do the same for g(x):
g(x) = 5^x
g(-2) = 5^(-2)
g(-2) = 0.04

----------------------------------------
Plug x = -1 into f(x) to get:
f(x) = 9*x + 7
f(-1) = 9*(-1) + 7
f(-1) = -9 + 7
f(-1) = -2

Do the same for g(x):
g(x) = 5^x
g(-1) = 5^(-1)
g(-1) = 0.2

----------------------------------------
Plug x = 0 into f(x) to get:
f(x) = 9*x + 7
f(0) = 9*(0) + 7
f(0) = 0 + 7
f(0) = 7

Do the same for g(x):
g(x) = 5^x
g(0) = 5^(0)
g(0) = 1

----------------------------------------
Plug x = 1 into f(x) to get:
f(x) = 9*x + 7
f(1) = 9*(1) + 7
f(1) = 9 + 7
f(1) = 16

Do the same for g(x):
g(x) = 5^x
g(1) = 5^(1)
g(1) = 5

----------------------------------------
Plug x = 2 into f(x) to get:
f(x) = 9*x + 7
f(2) = 9*(2) + 7
f(2) = 18 + 7
f(2) = 25

Do the same for g(x):
g(x) = 5^x
g(2) = 5^(2)
g(2) = 25

----------------------------------------

Write each of the results into the table (again see attached)

In the last row of that table, we have x = 2 lead to f(x) = 25 and g(x) = 25

So f(x) = g(x) has the solution of x = 2

The solution is x = 2 and not x = 25
25 is the output f(x) and g(x) value. It is not the x value.

Answer: choice C) x = 2

-11 1/25
-2 1/5
7 1
16 5
25 25

x = 25
(I'm guessing your suppose to find a common answer)
hope this helps

If 5 people including mary and bob are arranged randomly in a line, what is the probability that mary and bob are next to one another?

Answers

There are 5! (5 x 4 x 3 x 2 x 1 = 120) potential different arrangements for 5 people picked at random. Of those, let's take a look at all of the possible arrangements with Mary and Bob next to each other:

MBXXX
BMXXX
XMBXX
XBMXX
XXMBX
XXBMX
XXXMB
XXXBM

There are 8 arrangements out of the 120 where Mary and Bob are next to each other, which means that they have an 8/120 = 1/15 chance of ending up in that situation.

Hanks pickup can travel 60miles on 4gallons of gas. How many gallons will hanks pickup need to travel 30miles?

Answers

Hank can go 30 miles with 2 gallons.This is the answer because 30 is half of six so simply do 4 divided by half and get 2. Hope i helped

What is the area of the polygon below

Answers

I got A. 156 for this question.

147 thats the awnser

Reflection : Across the line y = 1

Answers

What is the question supposed to be?

Reflecting across y = 1 means each point's position stays the same horizontally but mirrors vertically across the line.

When reflecting a point or shape across a line, y = 1,

it means that each point is mirrored on the other side of the line while maintaining the same distance from the line.

Here, the line y = 1 acts as a "mirror" or "axis of reflection."

To reflect a point (x, y) across the line y = 1, follow these steps:

Find the vertical distance between the point and the line y = 1. Let's call this distance "d."

If the point is above the line (y > 1), then d = y - 1.

If the point is below the line (y < 1), then d = 1 - y.

Move the point to the same vertical distance on the other side of the line y = 1.

If the point was above the line (y > 1), the new reflected point will be (x, 1 + d).

If the point was below the line (y < 1), the new reflected point will be (x, 1 - d).

Keep in mind that the x-coordinate remains the same in both cases since the line of reflection is vertical (parallel to the y-axis).

By repeating these steps for all points in a shape, obtain the reflection of the entire shape across the line y = 1.

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What is the definition of proof in geometry

Answers

I'm guessing just to show that you did your work to get the answer.

A geometric proof involves writing reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a geometric statement. hope this helped:)

the table represent a linear function

X Y
-2 -2
-1 1
0 4
1 7
2 10
what is the slope of the function?
-3
-2
3
4

Answers

the answer is three work is in picture

Answer:

The answer is 3.

Step-by-step explanation:

In order to determine the slope of the function, we have to know about linear function.

In any linear function, we can get its slope using two pairs of coordinates that belong to the linear function.

m=Slope of the linear function.

P1=(x1,y1)=First pair of coordinate.

P2=(x2,y2)=Second pair of coordinate.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

In this case, we have many pairs of coordinates, so we choose two of them:

[tex]P_1=(-1,1)\\P_2=(0,4)[/tex]

Then, we replace them in the slope formula:

[tex]m=\frac{4-1}{0-(-1)}=\frac{3}{1}=3[/tex]

Finally, the slope of the function is 3.

A restaurant bill before tax is 65.50.if the sales tax is 8% and the a 18% tip is added what is the total cost

Answers

Total $83.47

$65.50 + $5.24 (8%tax ) = $70.74
$70.74 + $12.73 (18%) = $83.47

How do i factor -1/2 out of -1/2x + 6

Answers

-1/2x + 6

-1/2(x - 12)

multiply -2 to the 6 so that when you multiply -1/2 into the expression it will turn into positive 6

hope this helps

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