Question 3: A family is traveling in their RV all summer. They have several propane tanks on their RV. Propane is safe to use between temperatures of −40° F and 120° F.
Write an inequality to represent the temperatures at which the propane is safe to use.

The Perimeter of Harmony's new mural is 13.4 feet.

To determine the perimeter of Harmony's new mural, we need to use the formula for the perimeter of a rectangle, which is:P = 2l + 2w

where P represents the perimeter, l represents the length, and w represents the width of the rectangle. The units of measurement are in feet.

Given that the rectangular mural measures 1.3 feet by 4.8 feet, we can plug these values into the formula to find the perimeter of the original mural:P = 2(1.3) + 2(4.8)P = 2.6 + 9.6P = 12.2

Therefore, the perimeter of the original mural is 12.2 feet.

Now, Harmony creates a new mural that is 0.6 feet longer than the original mural. This means that the length of the new mural is 1.3 + 0.6 = 1.9 feet.

To find the perimeter of the new mural, we need to plug this new length into the same formula:P = 2l + 2wP = 2(1.9) + 2(4.8)P = 3.8 + 9.6P = 13.4

Therefore, the perimeter of Harmony's new mural is 13.4 feet.

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The number of edges that the prism has is

When a plane intersects a prism, the shape formed is known as the cross section. The cross section of the prism will have the same form as the base if it is divided by a plane that runs horizontally and parallel to the base.

A prism is a 3-dimensional object with two congruent and parallel bases (which are polyggonal) connected by rectangular lateral faces. The number of edges of a prism is equal to the sum of the number of edges of the two bases and the number of lateral faces.

Each base of the prism has n edges, so the two bases together have 2n edges. The number of lateral faces of the prism is equal to the number of edges of one of its bases, so there are n lateral faces. Each lateral face has 4 edges, so the total number of edges of the lateral faces is 4n.

Therefore, the total number of edges of the prism is equal to the sum of the number of edges of the two bases (2n) and the number of lateral faces (4n), which is 2n + 4n = 6n.

In conclusion, the cross section of a prism is an n-sided polygon and the prism has n + 2 edges.

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ABCD can be square if the distance between all four points is the same.

A square is a two-dimensional closed shape with four equal sides and four corners. The opposite sides of the square are parallel to each other. A square is also a rectangle with equal length and width. A square is an equilateral quadrilateral with all four equal sides and all four equal angles. Square angles are right angles or 90 degrees. Also, the diagonals of the square are equal and bisect at 90 degrees. A square is just a quadrilateral with four equal sides. There are many rectangular objects around us.

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The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

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The vectors combined sum is equal to (-1, 1)

Given data;

Let 'w' be the vector with an initial point (2,0) and terminal point (3,2).

Let 'v' be the vector with the initial point (2,2) and terminal point (0,1).

To find the sum of two vectors, firstly;

For 'w';

w = (3 - 2)i + (2 - 0)j

w = i + 2j → (I)

For 'v';

v = (0 - 2)i + (1 - 2)j

v = -2i + j → (II)

Now,

From (I) & (II);

w + v = (i + 2j) + (-2i + j)

        = -1, 1

Hence, the sum of the vectors w + v = (-1, 1)

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Answer:

591

Step-by-step explanation:

The length of w from the given triangle UVW is 591 cm.

The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them. The law of cosine states that: a² = b² + c² - 2bc·cosA.

Given that, in ΔUVW, u = 480 cm, v = 180 cm and ∠W=120°.

w² = u² + v² - 2uv·cosW

w² = 480² + 180² − 2×480×180·cos120°

w² = 230400 + 32400 - 172800·(-0.5)

w² = 349200

w = √349200

w = 590.93

w = 591 cm

Therefore, the length of w is 591 cm.

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Answer:

C

Step-by-step explanation:

Answer: 66.548

Step-by-step explanation: 26.2 in = 66.548 so that is how I got my elegant marvelous answer

Answer:

Solve for x

y= x/2 + 2

x= -x +5

Step-by-step explanation:

Answer:

The answer is 106.90in

Step-by-step explanation:

plz tell me if it right

Answer:

Ask her out and make her the happiest girl in the world.

Answer:

Step-by-step explanation:

Price assuming he bought all large flags: \(20*8=160\)

Amount of money more: \(160-112=48\)

Difference of price in both flags: \(20-12=8\)

Medium Flags: \(48\div8=6\)

Large Flags: \(8-6=2\)

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The reason why this works, is because the amount of money more comes from the difference between both flags.

answer:

A≈1039.23

Solution

A=33

2a2=3·3

2·202≈1039.23048

Answer:

3.6

Step-by-step explanation:

Answer:

A is the answer as to me check it

Answer:

The right answer is g(x) = -|x|

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

4/12 = 1/3 yepppp djdkkdkdd

Answer:

Booker:  $103.50 profit

Finley:  $34.50 profit

Step-by-step explanation:

b = # of candles Booker sold

f = # of candles Finley sold

1)  b = 3f

2) f = b - 12    substitute b=3f into this equation to get an expression all in terms of f, then solve for f

f = 3f - 12

-2f = -12

f = -12/2 = 6    now plug this into either equation and solve for b

b = 3(6) = 18

Booker:  18 candles x $5.75 profit/candle = $103.50 profit

Finley:  6 candles x $5.75 profit/candle = $34.50 profit

The Area of the Parallelogram is approximately: 13 square units.

We have a rectangle, remember that the area of a rectangle of length L and width W is equal to:

Area = W * L

Here we can define the length as the distance AB.

A = (3, 6) and B = (6, 5).

Then the distance between these points is:

L = √[(3 - 6)² + (6 - 5)²]

L = √10

The width is the distance AD, then:

A = (3, 6) and D = (2, 2), so we have:

W = √[(3 - 2)² + (6 - 2)²]

W = √17

Area = √10 * √17

Area = √(10 * 17)

Area = √170

Area = 13 square units.

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Answer:

3

Step-by-step explanation:

the absolute value is distance of a number from 0 so +3 absolute value is 0

Answer:

0.7 0.73 0.81 0.9

Step-by-step explanation:

hope this helps

Answer:

....

Step-by-step explanation:

Answer:

If the car gets 30 in city miles per gallon it (MPG) would be 30×15 which would be 450 miles. If its a sportier car like the Chevrolet Camaro ZL1 which gets close to 18 miles per gallon (MPG) it would be 18×15 which would be 270 miles. There is also highway miles where a standard car would get about 40 or more miles per gallon (MPG) 40×15 which would be 600 Miles. For a car like the Toyota Prius which gets 50-58 miles per gallon (MPG) in a city but 48-53 miles per gallon 58×15=870 miles and 53×15=795 miles. It depends on the car's engine, tuning, transmission, aerodynamics, etc.

Step-by-step explanation:

Different cars get different miles per gallon (MPG).

Answer:

C

Step-by-step explanation:

1+3=4

1>0

3>0

so C is correct

The angle of the car's total displacement measured from its starting direction (east) is approximately 36.87°. The magnitude of the car's total displacement from its starting point is approximately 55.97 km.

To determine the car's total displacement, we can treat the individual east and north displacements as vector components and then find their resultant.

Let's denote east as the positive x-axis and north as the positive y-axis.

(a) To find the magnitude of the total displacement, we can use the Pythagorean theorem:

Total displacement = √(east displacement^2 + north displacement^2)

                  = √((47 km)^2 + (21 km)^2 + (22 km * cos 30°)^2)

Calculating the value, we have:

Total displacement ≈ √(2209 km^2 + 441 km^2 + 484 km^2)

                             ≈ √3134 km^2

                             ≈ 55.97 km

Therefore, the magnitude of the car's total displacement from its starting point is approximately 55.97 km.

(b) To find the angle of the total displacement measured from its starting direction, we can use trigonometry:

Angle = arctan(north displacement / east displacement)

        = arctan((21 km + 22 km * sin 30°) / 47 km)

Calculating the value, we have:

Angle ≈ arctan(0.75)

        ≈ 36.87°

Therefore, the angle of the car's total displacement measured from its starting direction (east) is approximately 36.87°.

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Answer:

Mat has 6 cookies. He divides them among his 8 friends. How many cookies does each person get?

Step-by-step explanation:

You divide 6 by 8..?

Answer:

1.3 should be right

Step-by-step explanation:

X = 1.3

We start by using the chain rule to find the derivative of w with respect to t: dw/dt = (∂w/∂x) (dx/dt) + (∂w/∂y) (dy/dt) + (∂w/∂t)

dw/dt = 320 when t = 1.

To find ∂w/∂x, we treat y and t as constants and differentiate w = x^2 y^2 t with respect to x:

∂w/∂x = 2xy^2 t

To find ∂w/∂y, we treat x and t as constants and differentiate w = x^2 y^2 t with respect to y

∂w/∂y = 2x^2 yt

To find ∂w/∂t, we treat x and y as constants and differentiate w = x^2 y^2 t with respect to t:

∂w/∂t = x^2 y^2

Substituting the given values x = 4t and y = 2t, we get:

∂w/∂x = 2(4t)(2t)^2 t = 32t^4

∂w/∂y = 2(4t)^2 (2t) t = 64t^4

∂w/∂t = (4t)^2 (2t)^2 = 64t^4

Using these values, we can write:

dw/dt = (∂w/∂x) (dx/dt) + (∂w/∂y) (dy/dt) + (∂w/∂t)

= (32t^4)(4) + (64t^4)(2) + (64t^4)

= 320t^4

Finally, substituting t = 1, we get:

dw/dt = 320(1)^4 = 320

Therefore, dw/dt = 320 when t = 1.

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It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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