Which rectangular prism has the greatest volume?
5 cm 7 cm 5 cm
10 cm 3 cm 4 cm
7 cm 7 cm 3 cm
5cm 3 cm 7 cm

Answer:

Option C

20, 21, 29 represents three sides of a right triangle

Step-by-step explanation:

By Using Pythagorean Triplet we can say that

20, 21, 29 represents three sides of a right triangle

(20)² + (21)² = (29)²

400 + 441 = 841

841 = 841

Thus, 20, 21, 29 represents three sides of a right triangle

-TheUnknownScientist

Let S be the sum of the first n terms of the left side:

\(S = \dfrac23 + \left(\dfrac23\right)^2 + \left(\dfrac23\right)^3 + \cdots + \left(\dfrac23\right)^n\)

Multiply both sides by 2/3 :

\(\dfrac23 S = \left(\dfrac23\right)^2 + \left(\dfrac23\right)^3 + \left(\dfrac23\right)^4 + \cdots + \left(\dfrac23\right)^{n+1}\)

Subtract this from S :

\(S - \dfrac23 S = \dfrac23 - \left(\dfrac23\right)^{n+1}\)

Solve for S :

\(\dfrac13 S = \dfrac23 - \left(\dfrac23\right)^{n+1}\)

\(S = 2 - 3 \left(\dfrac23\right)^{n+1}\)

As n gets larger and larger, S converges to the given sum, and the term (2/3)ⁿ⁺¹ converges to zero, which leaves us with

\(\displaystyle \lim_{n\to\infty} S = \boxed{x = 2}\)

Step-by-step explanation:

rocket : 26 mpg

Glimmer : 484/18 = 26.89 mpg

cambria : 392/16 = 24.5 mpg

Avenger : 60/2 = 30 mpg

a. Avenger, has the highest mileage

b. cambria, has the lowest mileage

c. Avenger,Glimmer, rocket, cambria

Answer:

72 ounces of bananas

Answer:

72

Step-by-step explanation:

4.5 ties 16 = 72

Answer:

3(5-y)=4

Step-by-step explanation:

Key Words:

The difference

equals

times

When using parenthesis, you multiply. The difference means to subtract. And equals means something is equal to it.

The equation of the osculating circle to \(y = x^4 - 2x^2 at x = 1\) is: \((x - 1/2)^2 + (y + 1)^2 = (1/8)^2\)

The first step in finding the equation of the osculating circle to \(y = x^4 - 2x^2\) at x = 1 is to find the values of the first and second derivatives of y with respect to x at x = 1.

\(y = x^4 - 2x^2\)

\(y' = 4x^3 - 4x\)

\(y'' = 12x^2 - 4\)

Evaluate y', y'', and y at x = 1:

\(y(1) = 1^4 - 2(1)^2 = -1\)

\(y'(1) = 4(1)^3 - 4(1) = 0\)

\(y''(1) = 12(1)^2 - 4 = 8\)

The equation of the osculating circle can be expressed as:

\((x - a)^2 + (y - b)^2 = r^2\)

where (a, b) is the center of the circle and r is its radius. To find (a, b) and r, we use the following formulas:

\(a = x - [(y')^2 + 1]^(^3^/^2^)^/ ^|^y''^|\)

\(b = y + y'[(y')^2 + 1]^(^1^/^2^) ^/ ^|^y^''|\)

\(r = [(1 + (y')^2)^(^3^/^2^)^] ^/ ^|^y''^|\)

Substituting the values of x, y, y', and y'' at x = 1, we get:

\(a = 1 - [0^2 + 1]^(^3^/^2^) ^/ ^|^8^| = 1 - 1/2 = 1/2\)

\(b = -1 + 0[0^2 + 1]^(^1^/^2) ^/ ^|^8^| = -1\)

\(r = [(1 + 0^2)^(^3^/^2^)^] ^/ ^|^8^| = 1/8\)

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the slope of the staircase is approximately 0.727.

The slope of the staircase is the ratio of the rise (vertical distance) to the run (horizontal distance) of each step.

In this case, the rise is 8 inches and the run is 11 inches, so the slope of each step is:

Slope = Rise/Run

     = 8/11

The slope can be expressed as a fraction or a decimal. In decimal form, the slope is:

Slope = 8/11 ≈ 0.727

what is Slope?

Slope is a measure of the steepness of a line or a curve on a graph. It is defined as the ratio of the change in the y-coordinates of two points on the line or curve to the corresponding change in the x-coordinates of those points. In other words, slope is the change in y divided by the change in x, and is often denoted by the letter m.

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The value of cos 45 in a right angle triangle is 1/√2.

The trigonometry ratios are ratios that can be used to determine the side and angles of a triangle depending on the known parameter. The basic trigonometry ratios are denoted by the acronym: SOH CAH TOA

i.e.

From the given diagram, we are to find the Cos 45°

i.e.

θ = 45°

Let's recall the angle 45 45 90 theorem that states that right angles have the following values for the sides:

Since

Cos θ = adj/hyp

Cos 45 = 1/√2

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An angle that turns through 1/360 of a circle is called a “one-degree angle” and can be used to measure angles.

A degree, generally represented by the symbol ° (the degree), is a unit of measurement for a plane angle, where one full revolution equals 360 degrees.

A degree is the name given to the mathematical unit of measurement for an angle. A protractor is a device used to determine the degree of an angle. Angles can be measured at different angles with different degrees, such as 30°, 45°, 60°, and so on. A complete circle rotates at 360°.

One-degree angles are used to measure angles because they turn around 1/360 of a circle; an angle is said to have an angle measure of n degrees if it turns through n one-degree angles.

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Answer:

153.94 cm

Step-by-step explanation:

d=2r (need radius (r) to solve for the area)

14=2r

r=7

A=πr²

A=π(7)²

A=π49

A=153.94

Answer:

Variable B is the area of triangular base.

B = 38.5 \(in^{2}\).

Variable h is the height of pyramid.

In the given prism, h is 9 inches.

The volume of prism is 346.5 \(in^{3}\).

Step-by-step explanation:

Please refer to the attached image for the detailed labeling of all the sides.

\(\triangle ABC\) is the triangular base of the prism.

BC is the base of triangular base of the prism.

AP is the height of triangular base.

Area of triangular base is represented by B and is calculated by following formula of area of a triangle.

\(Area = \dfrac{1}{2} \times \text{Base}\times \text{Height}\)

\(\Rightarrow \dfrac{1}{2} \times 11 \times 7\\\Rightarrow 38.5\ in^{2}\)

Hence, B = 38.5 \(in^{2}\).

Height of prism, h = 9 in

h is represented as side BE in the attached image.

It is know that volume of prism is given as :

V = Bh

Putting values of B and h:

\(V = 38.5 \times 9\\\Rightarrow V = 346.5\ in^{3}\)

Answer:

The formula for volume of a prism is V = Bh.

The variable B stands for the ✔ area of the base.

In this prism, B equals ✔ 38.5  in.².

The variable h stands for ✔ height.

In this prism, h is ✔ 9 in.

The volume of the prism is ✔ 346.5  in.³.

Explanation:

The answer above mine is correct. I hope this helps!

Answer:

25

Step-by-step explanation:

f(x)= 3x-5

Let x= 10

f(10)= 3*10-5

     = 30-5

     = 25

Step 1:

Concept:

The cost of wire varies directly to the length in inches

Step 2:

Final answer

14 inches will cost = 14 x 0.04 = $0.56 = 56 cents

56 cents

Answer:

A

Step-by-step explanation:

union is U

A U B = m,e,a,t,i

a.{ m,e,a,i,t} This answer is certain

It would take approximately 7.83 hours (or 7 hours and 50 minutes) to fill a 470-gallon hot tub with a hose that fills at a rate of 1 gallon per minute.

To determine how many hours it will take to fill a 470-gallon hot tub with a hose that fills at a rate of 1 gallon per minute, divide the total volume of the hot tub by the filling rate.

Given that the hose fills the hot tub at a rate of 1 gallon per minute, we need to calculate the time it will take to fill a 470-gallon hot tub.

To do this, we divide the total volume of the hot tub (470 gallons) by the filling rate (1 gallon per minute).

Dividing 470 by 1 gives us 470. This means that it would take 470 minutes to fill the hot tub using the given hose.

Since there are 60 minutes in an hour, we can convert the minutes to hours by dividing 470 by 60. The result is approximately 7.83 hours.

Therefore, it would take approximately 7.83 hours (or 7 hours and 50 minutes) to fill a 470-gallon hot tub with a hose that fills at a rate of 1 gallon per minute.

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The Fahrenheit temperature of the cup of water, after 4.5 minutes, is given as follows:

155ºF.

The temperature function is defined as follows:

\(T(t) = T_a + (T_0 - T_a)e^{-kt}\)

Considering the surrounding and initial temperature, we have that the function is given as follows:

\(T(t) = 69 + 135e^{-kt}\)

The temperature after 1.5 minutes is of 185ºF, hence the coefficient k is obtained as follows:

\(185 = 69 + 135e^{-1.5k}\)

\(e^{-1.5k} = \frac{116}{135}\)

\(k = -\frac{\ln{\left(\frac{116}{135}\right)}}{1.5}\)

k = 0.1011.

Hence:

\(T(t) = 69 + 135e^{-0.1011t}\)

Hence the temperature after 4.5 minutes is given as follows:

\(T(4.5) = 69 + 135e^{-0.1011 \times 4.5}\)

T(4.5) = 155ºF.

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Answer:

4

Step-by-step explanation:

because The square root of 16 is 4, which is a rational number.

Answer:

4

Step-by-step explanation:

option 3

The mean is the same as the average.

The two cars are 10.5 kilometers apart, measured in a straight line.

This is calculated by taking the square root of the sum of the squares of the distances traveled by the two cars (3.1 km and 8.3 km). The square root of (3.1² + 8.3²) is 10.47, which can be rounded up to 10.5.

To calculate the distance between the two cars, we first need to calculate the sum of the squares of the distances traveled by the two cars (3.1 km and 8.3 km).

3.1² + 8.3² = 68.49

Next, we take the square root of this sum to get the distance between the two cars in a straight line:

√68.49 = 8.25

Finally, we round this number up to the nearest tenth, giving us the final answer of 10.5 kilometers.

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Answer:

6

Step-by-step explanation:

The x intercept is the value of x when y equals zero. The table tells us that when x goes up by one, y goes down by two.

Knowing this, all we have to do is increase x by 1 and decrease y by two until y is zero, and we can look and see what x is.

I also made a visual in the file below if this is confusing

The independent variable for Scenario A is given as follows:

a. The employee benefits package.

In the case of a relation, we have that the independent and dependent variables are defined by the standard presented as follows:

In the context of this problem, we have that the input and the output of the relation are given as follows:

Hence the independent variable for Scenario A is given as follows:

a. The employee benefits package.

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Answer:

the answer is 5

Step-by-step explanation:

it is right jk

Answer:

Step-by-step explanation:

We know area of a rectangle is xy where x and y are its dimensions.

A=xy

If we factor the area we will get the dimensions.

A=15k^4+35k^3+20k^2

(this can be factored in many ways to produce the same area, the answer choices you are given can be any given combination of factors.)

A=15k^4+15k^3+20k^3+20k^2

A=15k^3(k+1)+20k^2(k+1)

A=(15k^3+20k^2)(k+1) (this is one way)

A=5k(3k^2+4k)(k+1)

A=(3k^2+4k)(5k^2+5k) (and another way)

Either expression would give you width and length (or length and width) as they all produce the area of the original equation.

Answer:

Step-by-step explanation:

3

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

Answer:

If you don't agree or there's an error, let me know so I can edit.

Step-by-step explanation:

f(x) = x⁴ + 2

differentiate

f(x) = 4x³ + 0 =0

x(4x²) = 0

at x= 0 f(x) = 0 points = (0,0)

at x= 1. f(x) = 3 points = (4,3)......

The ordered pair is (4,3).

An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension. The numeric values in an ordered pair can be integers or fractions.

Given:

f(x) = x⁴ + 2

Now, differentiate the above function for the small values

f(x) = 4x³ + 0 =0

x(4x²) = 0

When x= 0

f(x) = 0

So, the points = (0,0)

when x= 1

f(x) = 3

so, the points = (4,3).

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The probability that the reporter gets an assignment in the United States or Asia is 15/37.

To find the probability that the reporter gets an assignment in the United States or Asia, we first need to determine the total number of assignments in the pool.

Total number of assignments = 8 + 29 + 15 + 22 = 74

Next, we need to determine the number of assignments that are in the United States or Asia.

Number of assignments in the United States or Asia = 8 + 22 = 30

Finally, we can calculate the probability of the reporter getting an assignment in the United States or Asia by dividing the number of assignments in the United States or Asia by the total number of assignments:

Probability of getting an assignment in the United States or Asia = (Number of assignments in the United States or Asia) / (Total number of assignments)

Probability of getting an assignment in the United States or Asia = 30/74

Therefore, the probability of the reporter getting an assignment in the United States or Asia is 30/74, which can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF), which in this case is 2:

Probability of getting an assignment in the United States or Asia = 15/37

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The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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An independent basic service set (IBSS) does not consist of any access points.

In an IBSS, devices such as laptops or smartphones connect with each other on a peer-to-peer basis, forming a temporary network. This type of network can be useful in situations where there is no existing infrastructure or when devices need to communicate with each other directly.

Since an IBSS does not involve any access points, it is not limited by the number of access points. Instead, the number of devices that can be part of an IBSS depends on the capabilities of the devices themselves and the network protocols being used.

To summarize, an IBSS does not consist of any access points. Instead, it is a network configuration where wireless devices communicate directly with each other. The number of devices that can be part of an IBSS depends on the capabilities of the devices and the network protocols being used.

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(D) the floor of a classroom is a perfect example of a line segment.

Therefore, (D) the floor of a classroom is a perfect example of a line segment.

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The correct form of the question is given below;
Which is an example of a line segment?

(A) the edge of a book

(B) the corner of a box

(C) a beam of light

(D) the floor of a classroom