There are 108 flights from an airport, 20 of which are longer than 3 hours. The flight from this airport will be randomly chosen. What is the probability it is longer than 3 hours? Enter your answer as a fraction, in simplest form, in the box.

Since no reaction creates or destroys atoms, every balanced chemical equation must have equal numbers of atoms of each element on each side of the equation. However, the number of molecules does not necessarily have to be the same.

The answer is

No, the total number of molecules can be equal or not

Answer:

No, the number of total molecules on the left side of a balanced equation is not equal to the number of total molecules on the right side of the equation. A molecule is the smallest number of atoms bonded together for a chemical reaction. The total number of atoms must be the same, but not molecules. The reactants and products will bond together in different ways leading to different numbers of reactants and products

Step-by-step explanation:

this is for pennfoster

The arc length of an angle of 2π/3 radians formed on the unit circle is 2π/3.

To find the arc length of an angle of 2π/3 radians on the unit circle, we can use the formula:

Arc Length = Radius * Angle

Since we are considering the unit circle, the radius is 1. Therefore, the arc length is equal to the measure of the angle.

In this case, the angle is 2π/3 radians. So, the arc length is 2π/3.

The correct option is A) π/3.

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Given that the population doubles every ten years, k may be found using the population growth equation dy/dt=ky by computing ln(2)/10, or roughly 0.0693 annually.

We begin by thinking about the solution to the differential equation dy/dt = ky, where the population doubles every ten years, in order to determine the value of k. This differential equation can be solved generally as y(t) = y(0)e^kt, where y(0) is the beginning population.

Since there are ten years between population doubling, we can write: y(10) = 2y(0) = y(0)e^10k.

The result of dividing both sides by y(0) is 2 = e^10k.

We get: ln(2) = 10k by taking the natural logarithm on both sides.

After calculating k, we have k = ln(2)/10 ≈ 0.0693.

Thus, k's value is around 0.0693 per year.

Answer:

Volume of popcorn cup  = 602.88 cm^3

Step-by-step explanation:

Volume of a cone = 1/3 πr^2 h

Given: π = 3.14, r = 12/2 = 6 cm, h = 16 cm

Now plug in these values in the above formula, we get

Volume of popcorn cup = 1/3 * 3.14*6^2*16

= 1/3*3.14 *36*16

= 3.14 *12*16

Volume of popcorn cup  = 602.88 cm^3

Hope this will helpful.

Thank you.

(3,4) would be the answer on e2020/edge

The question involves applying the concept of significant figures and rounding numbers during divisions to determine how many times 54527 must be divided by 5 before it becomes less than 5 without manually performing each division.

The question asks for the number of times the number n = 54527 needs to be divided by 5 and rounded up until it is less than 5. This is a problem that can be solved by understanding exponential decay and the concept of significant figures. It is also an exercise in rounding numbers appropriately. To determine the number of divisions without actually performing each division, one can use logarithms.

The concept of significant figures is important in this context, as each division reduces the number of significant figures by approximately one (since we're dividing by a number that has only one significant figure, 5). The rule is that when dividing, the number of significant figures in the result should be the same as the smallest number of significant figures in the input values.

Here's the process:

The original calculation without the repetition of divisions would use logarithms to solve for x in 5ˣ = 54527, or log5(54527). However, for the purposes of this example and to avoid calculator work, we can estimate that since 5⁴ = 625 and 5⁵ = 3125, it will take more than 4 but significantly fewer than 10 divisions (as 510 is much greater than 54527) to make the number less than 5.

The angle's rate of change when the bottom of the ladder is 8ft from the wall is

[tex]\dfrac{-1.3}{6} rad/s[/tex]

It is given the Length of Ladder [tex](h)[/tex] is [tex]10ft.[/tex]. and the distance between the bottom of the ladder to the wall [tex](r)[/tex] is [tex]8ft.[/tex] as shown in the below figure.

By using the Pythagoras Theorem

[tex]b=\sqrt{10^{2}-8^{2} }\\=\sqrt{36} \\=6ft.[/tex]

and

[tex]cos(\theta)= r/h\\cos(\theta)=r/10[/tex]

Differentiating both sides with respect to [tex]'t'[/tex] by using the chain rule

[tex]-sin(\theta)\dfrac{\mathrm{d}\theta }{\mathrm{d} t}=\dfrac{1}{10} \dfrac{\mathrm{d}r }{\mathrm{d} t}\\\\\dfrac{\mathrm{d}\theta }{\mathrm{d} t}=\dfrac{1}{10} \dfrac{\mathrm{d}r }{\mathrm{d} t} \dfrac{1}{-sin(\theta)} } ......(eq. 1)[/tex]

given

[tex]\dfrac{\mathrm{d}r }{\mathrm{d} t}=1.3ft./s\\sin(\theta)=\frac{6}{10}[/tex]

putting this in eq.1, we get

[tex]\dfrac{\mathrm{d} \theta}{\mathrm{d} t} = \dfrac{1.3}{10} (\dfrac{1}{-\frac{6}{10} }) \\\dfrac{\mathrm{d} \theta}{\mathrm{d} t} =\dfrac{-1.3}{6} rad/s[/tex]

So the angle's rate of change when the bottom of the ladder is 8ft from the wall is[tex]\dfrac{-1.3}{6} rad/s[/tex].

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Answer: The experimental probability that the first cactus he comes across has white flowers is 16/51.

Step-by-step explanation:

Since,

[tex]\text{Experimental probability} = \frac{\text{Number of event occurrence}}{\text{Number of trials}}[/tex]

Let W represents the event of occurrence of white flower and P represents the occurrence of purple flower,

Then, According to the question,

n(P) = 35 and n(W) = 16

Also, the total number of trials, n(S) = 35 + 16 = 51

Thus, the probability of occurring white flower is,

[tex]P(W)=\frac{n(W)}{n(S)}=\frac{16}{51}[/tex]

The general solution of the given second-order differential equation

y'' - y' - 30y = 0 is,

⇒ y = C₁ e⁶ˣ + C₂ e⁻⁵ˣ

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The second-order differential equation is,

⇒ y'' − y' − 30y = 0

Now, We can simplify as;

⇒ y'' − y' − 30y = 0

This gives the general form as;

⇒ m² - m - 30y= 0

⇒ m² - 6m + 5m - 30 = 0

⇒ m (m - 6) + 5 (m - 6) = 0

⇒ (m + 5) (m - 6) = 0

⇒ m = - 5 or m = 6

Hence, The general solution of the given second-order differential equation  y'' - y' - 30y = 0 is,

⇒ y = C₁ e⁶ˣ + C₂ e⁻⁵ˣ

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The largest rectangular box volume in the first octant, with one vertex on [tex]\(x + 2y + 3z = 9\),[/tex] is [tex]\(\frac{486}{125}\).[/tex]

To find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex on the plane [tex]\(x + 2y + 3z = 9\),[/tex]we can set up the problem using optimization techniques.

Let the coordinates of the vertex of the box that lies on the plane [tex]\(x + 2y + 3z = 9\)[/tex] be[tex]\((x, y, z)\).[/tex] Since the other vertices are on the coordinate planes, the dimensions of the box are [tex]\(x\), \(y\), and \(z\).[/tex]

The volume [tex]\(V\)[/tex]of the rectangular box is given by:

[tex]\[V = x \cdot y \cdot z\][/tex]

Given that this vertex lies on the plane [tex]\(x + 2y + 3z = 9\),[/tex] we have the constraint:

[tex]\[x + 2y + 3z = 9\][/tex]

We need to maximize [tex]\(V\)[/tex] subject to this constraint. To do this, we can use the method of Lagrange multipliers. We introduce a Lagrange multiplier [tex]\(\lambda\)[/tex]  and define the Lagrangian function:

[tex]\[\mathcal{L}(x, y, z, \lambda) = x y z + \lambda (9 - x - 2y - 3z)\][/tex]

To find the critical points, we take the partial derivatives of [tex]\(\mathcal{L}\)[/tex] with respect to [tex]\(x\), \(y\), \(z\), and \(\lambda\)[/tex] and set them to zero:

[tex]\[\frac{\partial \mathcal{L}}{\partial x} = yz - \lambda = 0\]\[\frac{\partial \mathcal{L}}{\partial y} = xz - 2\lambda = 0\]\[\frac{\partial \mathcal{L}}{\partial z} = xy - 3\lambda = 0\]\[\frac{\partial \mathcal{L}}{\partial \lambda} = 9 - x - 2y - 3z = 0\][/tex]

From the first three equations, we can express [tex]\(\lambda\)[/tex] as follows:

[tex]\[\lambda = yz\]\[\lambda = \frac{xz}{2}\]\[\lambda = \frac{xy}{3}\][/tex]

Equating these expressions for [tex]\(\lambda\):[/tex]

[tex]\[yz = \frac{xz}{2} \implies 2yz = xz \implies x = 2y \quad \text{(if \(z \neq 0\))}\]\[yz = \frac{xy}{3} \implies 3yz = xy \implies y = 3z \quad \text{(if \(x \neq 0\))}\][/tex]

Substituting [tex]\(y = 3z\) and \(x = 2y = 2(3z) = 6z\)[/tex] into the constraint [tex]\(x + 2y + 3z = 9\):[/tex]

Now, using [tex]\(z = \frac{3}{5}\):[/tex]

[tex]\[y = 3z = 3 \left(\frac{3}{5}\right) = \frac{9}{5}\]\[x = 6z = 6 \left(\frac{3}{5}\right) = \frac{18}{5}\][/tex]

The dimensions of the box are:

[tex]\[x = \frac{18}{5}, \quad y = \frac{9}{5}, \quad z = \frac{3}{5}\][/tex]

The volume[tex]\(V\)[/tex]  is:

[tex]\[V = x \cdot y \cdot z = \left(\frac{18}{5}\right) \left(\frac{9}{5}\right) \left(\frac{3}{5}\right) = \frac{18 \cdot 9 \cdot 3}{5^3} = \frac{486}{125} = 3.888\][/tex]

Therefore, the volume of the largest rectangular box is:

[tex]\[\boxed{\frac{486}{125}}\][/tex]

The volume of the largest rectangular box with one vertex on the plane x + 2y + 3z = 9 is found using Lagrange multipliers. The maximum volume is 4.5 cubic units. The calculations involve the gradient method and substitution.

To find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 9, we need to maximize V = xyz subject to the constraint x + 2y + 3z = 9.

We can use the method of Lagrange multipliers for this problem:

This gives us the following system of equations:

From these equations, we can solve for x, y, z, and λ:

Equating and solving, we obtain x = 1.5, y = 1.5, and z = 2.

Finally, substituting these values into V = xyz gives the volume V = (1.5)  imes (1.5)  imes 2 = 4.5.

Answer:

Step-by-step explanation:

The answer is 25+26+27+28+29=135

Is the correct answer I basically divided 135 by 5 and got 27 then I just worked around that number to get the answer.

Answer:

medical expenses and non-reimbursed work expenses

Step-by-step explanation:

Just did test

Final answer:

The value of x for which the square of the binomial (x+1) is twenty greater than the square of the binomial (x-3) is 3.5.

Explanation:

The student is asking for a value of x for which the square of the binomial (x+1) is twenty greater than the square of the binomial (x-3). To find this value, we set up an equation based on the given information:

(x + 1)² = (x - 3)² + 20

First, we expand both squares:

x² + 2x + 1 = x² - 6x + 9 + 20

Now, simplify and move all terms to one side to solve for x:

8x = 28

Divide both sides by 8 to find the value of x:

x = 28 / 8

x = 3.5

Therefore, the value of x for which the square of (x+1) is twenty greater than the square of (x-3) is 3.5.

Answer:

A. [tex]a_n=200+(n-1)5[/tex]

Step-by-step explanation:

Given,

The initial sprinting of Freya = 200 yards,

Also,  She gradually increases her distance by 5 yards per day,

So, in second day her sprinting = 200 + 5 = 205 yards,

In third day = 205 + 5 = 210 yards,

In fourth day = 210 + 5 = 215 yards,

....................,  so on,.....

Hence, the sequence that shows the given situation,

200, 205, 210, 215, .........

Which is an A.P.

That having first term, a = 200,

Common difference, d = 5,

Thus, the explicit formula for the given situation is,

[tex]a_n=a+(n-1)d[/tex]

[tex]\implies a_n=200+(n-1)5[/tex]

Option A is correct.

Answer:

Option A.

Step-by-step explanation:

The explicit formula of an AP is

[tex]a_n=a+(n-1)d[/tex]              .... (1)

where,

a is the first of the AP,

d is common difference.

It is given that Freya starts by sprinting 200 yards and she gradually increases her distance, adding 5 yards a day.

200, 205, 210,..., 305

Here,

First terms = 200

Common difference = 5

Substitute a=200 and d=5 in equation (1), to find the required explicit model

[tex]a_n=200+(n-1)5[/tex]

Therefore, the correct option is A.