How many 5 liter gas tanks can you fill from a full 20 liter gas can

Answer:

15

Step-by-step explanation:

The volume of the octahedron is 4000 cubic centimeters.

To find the volume of the octahedron, we'll first find the volume of one pyramid and then multiply it by 2 since the octahedron is made up of two pyramids.

Step 1: Find the height of one pyramid.
Since the overall height of the octahedron is 30 cm and it's made up of two pyramids of equal height, the height of one pyramid is 30 cm / 2 = 15 cm.

Step 2: Calculate the volume of one pyramid.
The formula for the volume of a pyramid is (1/3) * base_area * height.
In this case, the base is a square with sides measuring 20 cm, so the base area is 20 cm * 20 cm = 400 cm².

Step 3: Apply the formula.
Volume of one pyramid = (1/3) * 400 cm² * 15 cm = 2000 cm³.

Step 4: Find the volume of the octahedron.
Since the octahedron consists of two identical pyramids, we'll multiply the volume of one pyramid by 2.
Volume of octahedron = 2 * 2000 cm³ = 4000 cm³.

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Answer: Let's start by subtracting the cost of the glider airplane from the total amount of money you started with:

$20 - $3 = $17

We know that you spent $15 of that $17 on the bouncy ball, since you had $15 left over after buying both items:

$17 - $15 = $2

Therefore, you spent $2 on the bouncy ball.

Answer: $2.

Step-by-step explanation:

Answer:

2.9661582

Step-by-step explanation:

2.9661582e+16 this is the answer

Answer:

110

Step-by-step explanation:

Thus, the probability that two people picked at random both own a dog is 0.1296 or 1296/10000.

To solve this problem, we need to use the formula for calculating the probability of independent events: P(A and B) = P(A) x P(B).

In this case, let A be the event that the first person owns a dog and B be the event that the second person owns a dog.

We know that P(A) = 0.36, or 36% chance that the first person owns a dog. Since the events are independent, P(B) is also 0.36.

So, the probability of both events occurring (both people owning dogs) is:

P(A and B) = P(A) x P(B)
= 0.36 x 0.36
= 0.1296

This can also be expressed as a fraction:

P(A and B) = 36/100 x 36/100
= 1296/10000

Therefore, the probability that two people picked at random both own a dog is 0.1296 or 1296/10000.

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Answer: C. ∠5 and ∠6

Step-by-step explanation:

They are linear pairs meaning they form a straight line.

Angles that form a straight line are ALWAYS supplementary (they add up to 180°)

Hope this helped!

According to the given information, the noise level in a restaurant is normally distributed with an average of 30 decibels. To find the value below which 99% of the time the noise level is, we need to use the Z-table.

We know that 99% of the area under the normal curve is below a Z-score of 2.33 (found from the Z-table).

To find the corresponding noise level value, we use the formula:

Z-score = (X - μ) / σ

where X is the noise level value we want to find, μ is the average (30 decibels), and σ is the standard deviation (which is not given in this question).

However, we can use the empirical rule (68-95-99.7 rule) to estimate the standard deviation. According to the rule, 99.7% of the data falls within 3 standard deviations of the mean. So, if 99% of the time the noise level is below a Z-score of 2.33, then we can estimate that the standard deviation is approximately:

(2.33 x σ) = 3

Solving for σ, we get:

σ = 3 / 2.33 = 1.29 (approx.)

Now we can use the formula above to find the noise level value below which 99% of the time the noise level is:

2.33 = (X - 30) / 1.29

X - 30 = 2.33 x 1.29

X = 33.01

So, 99% of the time, the noise level in the restaurant is below 33.01 decibels (rounded to two decimal places).

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Part A:   70x+50=$250

Part B:   75x-5x+$35=$250

They differ because in Part A they don't lose any money and just gain it, while in part B they lose money, while gaining more in part A.

not 100% sure on Part B

The amount of money Makayla spent on the movies during the year she joined the club will be represented by (m) = 6x + 25.

We have to represent the given situation with a function. The club charges a registration fee of 55 dollars and the discount value for the club members is 6 dollars per ticket. Here, we will use x to represent the number of movie tickets.

The domain is represented by m and so it should be a whole number. It cannot be an integer as integers include negative numbers too. It cannot be a rational number because it cannot include decimals and as we know we can't buy part of a ticket. It can also not be a real number because it can't include irrational numbers.

So, our function will be (m) = 6x + 25.

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Answer:

1.

Step-by-step explanation:

Answer:

x = 61, y = 29

Step-by-step explanation:

29+x = 90

x = 61

x + y = 90

y + 61 = 90

y = 29

Answer:

P(pink) = 0.225

Step-by-step explanation:

We should ignore the spinner picture because it is a trick!

We need to use the data provided in the table

We need to find the probabilty of getting pink out of all the colors:

\(\frac{pink}{purple\ +\ pink\ +\ yellow\ +\ blue} = \frac{9}{12\ +\ 6\ +\ 9\ +\ 13}\\ = \frac{9}{40} = 0.225\ \ (22.5\%)\)

We use the probability notation:

P(pink) = 0.225

Answer:

\(-22\frac{1}{3}\)

Step-by-step explanation:

\(a=\frac{1}{3} , b = -10, c = -3\)

change  \(b^{2} - 9a^{2} + c\)   to  

\(-10 -9\frac{1}{3} + (-3)\)

=

\(-22\frac{1}{3}\)

Answer:

Hey there!

We have that 4/5, or 80% of the 60 students passed the exam.

Thus, we have:

0.8(60)=48

48 students passed the exam.

Let me know if this helps :)

The solution for the given initial-value problem using Laplace transform is :

y(t) = sin(t) + [1 -cos(t-π)]U(t-2π) - [1 - cos(t-2π)]U(t-2π)

To solve this initial value problem using Laplace transform, we first need to take the Laplace transform of both sides of the equation:

L[y''](s) + L[y](s) = L[f(t)](s)

Using the properties of Laplace transform, we can simplify this expression to:

s^2Y(s) + Y(s) = 1/s - e^(-πs)/s + e^(-2πs)/s

We can now solve for Y(s):

Y(s) = 1/(s^2 + 1) - e^(-πs)/(s^2 + 1) + e^(-2πs)/(s^2 + 1)

Using partial fraction decomposition, we can write this as:

Y(s) = (1/s) - (sin(t)/2) + [1/2 - cos(t-π)]e^(-πs) - [1/2 - cos(t-2π)]e^(-2πs)

Taking the inverse Laplace transform of Y(s), we get:

y(t) = sin(t) + [1 -cos(t-π)]U(t-2π) - [1 - cos(t-2π)]U(t-2π)

This is the same answer as given in the book.

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The length of the rectangular book is 5.8cm

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term oblong is occasionally used to refer to a non-square rectangle.

The perimeter of a rectangle is found by adding up the length of all four sides. The formula for the perimeter of a rectangle is,

P = length + breadth + length + breadth. Or, P = 2(length + breadth)

Given:

Perimeter = 16.84 cm.

length = 18/7 cm

substituting in the formula we get

16.84 = 2( 18/7 + width)

8.42 = 18/7 + width

5.8 cm = width

Thus the length of the rectangular book is 5.8cm.

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Answer:

122/3435.35/67

Step-by-step explanation:

Answer:

C, D

Step-by-step explanation:

3 minutes = 180 seconds

A = 165 seconds

B = 150 seconds

C = 240 seconds

D = 195 seconds

E = 150 seconds

Chow,...!

Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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Answer:

Answer: y = 2x + 8

Step-by-step explanation:

• General equation of a line:

\( \hookrightarrow \: { \rm{y = mx + b}}\)

[ for parallel lines, slopes are the same ]

• m is 2

\({ \rm{y = 2x + b}} \)

for point (-2, 4)

\({ \rm{4 = (2 \times - 2) + b}} \\ \\ { \rm{4 = - 4 + b}} \\ \\ { \rm{b = 8}}\)

• therefore, equation is:

\({ \boxed{ \rm{y = 2x + 8}}}\)

Answer:

y=76+2.5x where y is the amount he earns in a day and x is the number of tshirts sold

y=76+2.5(32)

y=76+80

y=156

he earns 156 dollars if he sold 32 tshirts

Step-by-step explanation:

Answer:

New distance = 2do

Step-by-step explanation:

The distance equation :

Distance = speed * time

If speed is doubled ; time stays the same

If speed is doubled,; new speed becomes

Doubled speed = 2* speed

Time remains the same ;

Hence,

New distance becomes : 2 * speed * time

Original dista, Speed * distance

New distance, dn = 2*do = 2do

The density function of the kinetic energy, E = 1/2mV2, can be found by using the formula for the probability density function of a normal distribution. The formula for the probability density function of a normal distribution is: f(x) = (1/σ√2π) e^(-(x-μ)^2/(2σ^2))

Since the velocity, V, is normally distributed with parameters μ = 0 and σ, we can substitute these values into the formula for the probability density function of a normal distribution to find the density function of the kinetic energy, E.

The density function of the kinetic energy, E, is:

f(E) = (1/σ√2π) e^(-(E-0)^2/(2σ^2))

Simplifying the equation gives:

f(E) = (1/σ√2π) e^(-(E^2)/(2σ^2))

Therefore, the density function of the kinetic energy, E, is f(E) = (1/σ√2π) e^(-(E^2)/(2σ^2)).

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Answer:

45

Step-by-step explanation:

x = -30/2(-5)

x = -30/(-10)

x = 3 sec

.

Plug above into equation to find height:

h=-5t^2 + 30t

h=-5*3^2 + 30(3)

h=-5*9 + 30(3)

h=-45 + 90

h=45

The slope of line segments from A to A', B to B' and C to C' is 0.

Given that triangle A'B'C' is translation of triangle ABC which is moved three units right and up 4 units.

We have to find the slope of line segments from A to A', B to B' and C to C'.

To do this we have to find the coordinates of ABC and triangle A'B'C'.

A is (-1, 4) and A' is (1, 4)

Slope= 4-4/2

=0

Bis (0, 3) and B' is (2, 3)

Slope=0

C is (-2, 0) and B' is (0,0)

slope =0

Hence, the slope of line segments from A to A', B to B' and C to C' is 0.

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If the variable h represents how many hours Samantha works, the algebraic expression that describes how much she earns is: 14.55h

This expression represents the total amount of money Samantha earns, based on the number of hours she works and her hourly rate of $14.55.

Another real-life algebraic expression could be:

The total cost of groceries = (number of apples * cost per apple) + (number of bananas * cost per banana) + (number of oranges * cost per orange)

In this expression, the variables are:

Number of apples (a)

Cost per apple (c1)

Number of bananas (b)

Cost per banana (c2)

Number of oranges (o)

Cost per orange (c3)

This expression represents the total cost of groceries, based on the number of each type of fruit purchased and their respective costs.

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