What is "The cube of twice a number"?

Answer:

B is the answer

Step-by-step explanation:

The equation is a shorthand method for writing a mathematical rule.

The answer to your question is b.equation. An equation is a shorthand method for writing a mathematical rule. It represents a relationship between two or more variables using mathematical symbols and operations. Equations are commonly used in algebra, calculus, and other areas of mathematics to solve problems and make predictions. They are written using an equal sign (=) to show that the expression on the left is equal to the expression on the right. Equations are an important tool in mathematics because they allow us to express complex ideas in a concise and precise way. By using equations, we can simplify calculations and solve problems more efficiently.
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Answer:

15.9

Step-by-step explanation:

just because it is the bigger side of the triangle

154 yd ²

the formula is (b • h) / 2 = A

so plug it in (14 • 22) / 2 = 154

Answer: The expression 6xy - 3xy can be simplified to 36 if x = 3 and y = 4.

Step-by-step explanation:

First let's simplify the problem.

6xy - 3xy = 3xy

3xy

Now let's substitute x for 3 and y for 4.

3 x 3 x 4

Finally, let's solve using the associative property!

  (3 x 3) x 4

= 9 x 4

= 36

  3 x (3 x 4)

= 3 x 12

= 36

The expression 6xy - 3xy can be simplified to 36.

Answer:

(-6,8)

Step-by-step explanation:

Answer: 47/100

Step-by-step explanation: 47/100 = 0.47.

The difference between 141.2 and 79.83 is as follows:141.2 - 79.83 = 61.37The sum of 141.2 and 79.83 is:141.2 + 79.83 = 221.03The product of 141.2 and 79.83 is:141.2 × 79.83 = 11250.996 The quotient when 141.2 is divided by 79.83 is:141.2 ÷ 79.83 = 1.7696655174 (approx. 1.77)

Thus, the sum of 141.2 and 79.83 is 221.03. The difference between 141.2 and 79.83 is 61.37. The product of 141.2 and 79.83 is 11250.996. The quotient when 141.2 is divided by 79.83 is approximately 1.77.Thus, the solution can be summarized as follows: Given the two numbers 141.2 and 79.83, we are to find their sum, difference, product, and quotient.

After performing the necessary arithmetic operations, we get that their sum is 221.03, their difference is 61.37, their product is 11250.996, and their quotient is approximately 1.77.

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Answer:

dont post stuff like this on brainly, it is for homework only

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

There are 2 possible approaches to differentiating these.

Expand the factors and differentiate term by term, or

Use the product rule for differentiation.

I feel they are looking for use of product rule.

Given

y = f(x). g(x) , then

\(\frac{dy}{dx}\) = f(x).g'(x) + g(x).f'(x) ← product rule

(a)

y = (2x - 1)(x + 4)²

f(x) = 2x - 1 ⇒ f'(x) = 2

g(x) = (x + 4)²

g'(x) = 2(x + 4) × \(\frac{d}{dx}\) (x + 4) ← chain rule

       = 2(x + 4) × 1

        = 2(x + 4)

Then

\(\frac{dy}{dx}\) = (2x - 1). 2(x + 4) + (x + 4)². 2

    = 2(2x - 1)(x + 4) + 2(x + 4)² ← factor out 2(x + 4) from each term

    = 2(x + 4) (2x - 1 + x + 4)

    = 2(x + 4)(3x + 3) ← factor out 3

    = 6(x + 4)(x + 1)

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

(b)

y =  x(x² - 1)³

f(x) = x ⇒ f'(x) = 1

g(x) = (x² - 1)³

g'(x) = 3(x² - 1)² × \(\frac{d}{dx}\) (x² - 1) ← chain rule

        = 3(x² - 1)² × 2x

        = 6x(x² - 1)²

Then

\(\frac{dy}{dx}\) = x. 6x(x² - 1)² + (x² - 1)³. 1

    = 6x²(x² - 1)² + (x² - 1)³ ← factor out (x² - 1)²

    = (x² - 1)² (6x² + x² - 1)

     = (x² - 1)²(7x² - 1)

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

(c)

y = (x² - 1)(x³ + 1)

f(x) = x² - 1 ⇒ f'(x) = 2x

g(x) = (x³ + 1) ⇒ g'(x) = 3x²

Then

\(\frac{dy}{dx}\) = (x² - 1). 3x² + (x³ + 1), 2x

   = 3x²(x² - 1) + 2x(x³ + 1) ← factor out x

   = x[3x(x² - 1) + 2(x³ + 1) ]

   = x(3x³ - 3x + 2x³ + 2)

   = x(5x³ - 3x + 2) ← distribute

    = 5\(x^{4}\) - 3x² + 2x

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

(d)

y = 3x³(x² + 4)²

f(x) = 3x³ ⇒ f'(x) = 9x²

g(x) = (x² + 4)²

g'(x) = 2(x² + 4) × \(\frac{d}{dx}\)(x² + 4) ← chain rule

       = 2(x² + 4) × 2x

       = 4x(x² + 4)

Then

\(\frac{dy}{dx}\) = 3x³. 4x(x² + 4) + (x² + 4)². 9x²

    = 12\(x^{4}\)(x² + 4) + 9x²(x² + 4)² ← factor out 3x²(x² + 4)

    = 3x²(x² + 4) [ 4x² + 3(x² + 4) ]

    = 3x²(x² + 4)(4x² + 3x² + 12)

    = 3x²(x² + 4)(7x² + 12)

a) The feasible set can be represented as a straight line with a negative slope on a graph.

b) The preferred choice point is (15, 15).

c)  With an entrance fee of $9, the new feasible set shifts vertically upwards.

d)  The change in entrance fee reduced the amount of leftover cash in the feasible set.

a) The x-axis represents the number of pizza slices, and the y-axis represents the leftover cash. The line starts at the point (0, 60) and intersects the x-axis at (20, 0). This means that you can buy a maximum of 20 pizza slices with $60, and if you don't buy any pizza, you will have $60 left.

b) This point represents buying 15 slices of pizza, which costs $45, and having $15 left. It is the preferred choice because it allows for a balance between enjoying pizza and not exhausting all the cash. It provides both a substantial amount of pizza and a reasonable amount of leftover cash.

c) The line now starts at (0, 51) and intersects the x-axis at (20, 9). This means that with the entrance fee, you can buy a maximum of 20 pizza slices and have $9 left.

d) It means that you have less cash available after buying pizza slices. The new preferred choice would likely shift downwards to a point that allows for a reasonable number of pizza slices while still leaving enough money to cover the entrance fee.

The change in entrance fee makes it necessary to consider the balance between the number of pizza slices and the available cash more carefully to ensure you can afford the entrance fee and still enjoy a satisfying amount of pizza.

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Answer:

$4.16

Step-by-step explanation:

To find out how much 8 ounces of frozen yogurt costs if each ounce costs $0.52, we can use an equation that looks like this:

Therefore, for 8 ounces of yogurt is will cost $4.16.

Answer:

$21

Step-by-step explanation:

Answer:

You deposit $2000 in an account that earns 5% annual interest compounded quarterly. Find the account balance after 10 years

The power series ∑ 2^n + n(n+4)x^n has a radius of convergence of 1 and an interval of convergence of [-1,1], and it converges at both endpoints of the interval. The power series diverges for x = ±1, since the terms of the series do not approach zero as n goes to infinity.

To find the radius of convergence of the power series, we use the ratio test to calculate the limit:

lim |a_{n+1}/a_n| = lim |(2+x(n+5)/(2+n+4x))|

As n approaches infinity, the limit simplifies to |x|. The series converges absolutely if |x| < 1, and it diverges if |x| > 1. When |x| = 1, we need to check the endpoints of the interval of convergence.

When x = 1, the series becomes:

∑ n=0[infinity]​2^n + n(n+4)

This is a sum of two convergent series, so it converges. When x = -1, the series becomes:

∑ n=0[infinity]​(-1)^n (2^n + n(n+4))

This is an alternating series that satisfies the conditions of the alternating series test, so it converges.

Therefore, the radius of convergence is 1, and the interval of convergence is [-1,1].

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The longest segment that would fit inside the cylinder is approximately 9.06 centimeters.

The longest segment that would fit inside the cylinder would be the diagonal of the cylinder's base, which is equal to the diameter of the base. The diameter of the base is equal to twice the radius, so it is 6 cm. Using the Pythagorean theorem, we can find the length of the diagonal:

\(diagonal^2 = radius^2 + height^2 \\diagonal^2 = 3^2 + 8^2 \\diagonal^2 = 9 + 64 \\diagonal^2 = 73 \\diagonal = sqrt(73)\)

Therefore, the longest segment that would fit inside the cylinder is approximately 8.54 cm (rounded to the nearest hundredth).
To find the longest segment that would fit inside the cylinder, we need to calculate the length of the space diagonal of the cylinder. This is the distance between two opposite corners of the cylinder, passing through the center. We can use the Pythagorean theorem in 3D for this calculation.

The terms we'll use are:
- Radius (r): 3 cm
- Height (h): 8 cm

To find the space diagonal (d), we can use the following formula:

\(d = \sqrt{r^2 + r^2 + h^2}\)
Plug in the values:

\(d = \sqrt{((3 cm)^2 + (3 cm)^2 + (8 cm)^2)} d = \sqrt{(9 cm^2 + 9 cm^2 + 64 cm^2)} d = \sqrt{(82 cm^2)}\)
d ≈ 9.06 cm

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The longest segment that can fit inside the cylinder is. \($\sqrt{73}$ cm\).

The longest segment that can fit inside a cylinder is a diagonal that connects two opposite vertices of the cylinder.

The length of this diagonal by using the Pythagorean theorem.

Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation:[1]

\({\displaystyle a^{2}+b^{2}=c^{2}.}\)

The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.

The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.

The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.

Consider a right triangle with legs equal to the radius.

\($r$\) and the height \($h$\) of the cylinder, and with the diagonal as the hypotenuse.

Then, by the Pythagorean theorem, the length of the diagonal is:

\($\sqrt{r^2 + h^2} = \sqrt{3^2 + 8^2} = \sqrt{73}$\)

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a. If a passenger arrives at the station between 7 and 8 a.m., then the probability of them taking the train heading for destination A is 50%. This is because, during that hour, two trains heading for destination A will arrive, whereas only one train will head for destination B.

b. If a passenger arrives at the station between 7:15 and 8:15 a.m., then the probability of them taking the train heading for destination A is 66.7%. This is because, during that hour and a half, three trains heading for destination A will arrive, whereas only one train will head for destination B.

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Answer:

y = 0.5x + 11

Step-by-step explanation:

rate = 0.5ft per second

rate = m

(0.5)(6) + 8 = b

3 + 8 = 11

b = 11

y = mx + b

y = 0.5x + 11

the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.

Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.

The ODEs for the transition probabilities can be written as follows:

dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)

dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)

dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)

dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)

dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)

dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)

where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.

Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.

To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.

The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:

total_rate = q₁₂ + q₁₃

Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:

P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate

In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.

Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

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Answer:

Step-by-step explanation:

One of the Answers is C

Answer:

B.

Step-by-step explanation:

Lets break this down piece by piece.

So first, add 500,000 and 30,000. that would be 530,000.

Next, add on 5,000, which is 535,000

After that, add 300. ( 535,300. )

Then add up 50 and 3 which is 53.

Lastly, your answer is 535,353.

Answer:

b

Step-by-step explanation:b

b

Answer:

(y+6)(y-1)

Step-by-step explanation:

literally factorising.

y^2 x -6 = -6y^2

u need two numbers that multiply to make -6 and add them together to make +5 which is +6 and -1.

Answer:

p = 6, q = - 1 , or p = - 1, q = 6

Step-by-step explanation:

Factorise the quadratic expression on the left side

y² + 5y - 6

Consider the factors of the constant term (- 6) which sum to give the coefficient of the y- term (+ 5)

The factors are + 6 and - 1 , since

6 × - 1 = - 6 and 6 - 1 = + 5 , then

y² + 5y - 6

= (y + 6)(y - 1) = (y - 1)(y + 6)

Compare to (y + p)(y + q) , then

p = 6, q = - 1 or p = - 1, q = 6

The following logarithm expressions are,

(a) \(ln e^{-11}\) = -11

(b) \(e^{ln5}\) = 5

(c) \(e^{ln\sqrt{2} }\) = 1.414

(d) \(ln^{\frac{1}{e^{4} } }\) = -4

It is important to remember the following logarithm properties in order to solve the exercise:

\(ln(a) + ln(b) = ln(ab)\)

\(ln(a) -ln(b) = ln(\frac{a}{b} )\)

\(ln(a^{m})= m ln(a)\)

\(ln(e)=1\)

Given data,

(a) \ln e ^ { -11 }

\(ln e^{-11}\) = \(ln_{e} ^{e^{-11} }\)

\(ln e^{-11}\) = -11

(b) e ^ {\ln 5 }

\(e^{ln5}\) = 5

(c) e ^ {\ln \sqrt { 2 } }

\(e^{ln\sqrt{2} }\) = \(\sqrt{2}\)

\(e^{ln\sqrt{2} }\) = 1.414

(d) \ln ( 1/e^ { 4} )

\(ln^{\frac{1}{e^{4} } }\) = \(elne^{-4}\)

\(ln^{\frac{1}{e^{4} } }\) = -4

Therefore,

The following logarithm expressions are,

(a) \(ln e^{-11}\) = -11

(b) \(e^{ln5}\) = 5

(c) \(e^{ln\sqrt{2} }\) = 1.414

(d) \(ln^{\frac{1}{e^{4} } }\) = -4

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The probability of being at least seven minutes late given that it is already 3.5 minutes late is approximately 0.368 (or 36.8%).

What is mean?

In statistics, the mean is a measure of central tendency which represents the average of a set of numerical data. It is obtained by adding up all the values in the data set and then dividing the sum by the total number of values.

We know that the exponential distribution has the following probability density function:

\($f(x) =\)

\(\frac{1}{\mu} e^{-x/\mu} & x \geq 0 \\)

\(0 & x < 0 \\)

where \($\mu$\) is the mean of the distribution.

We are given that \($\mu = 3.5$\) minutes. Let \($X$\) be the time it takes to be late. Then \($X$\) follows an exponential distribution with mean \($\mu = 3.5$\) minutes.

We want to find \($P(X \geq 7 \mid X \geq 3.5)$\). By the definition of conditional probability, we have:

\($P(X \geq 7 \mid X \geq 3.5) = \dfrac{P(X \geq 7 \text{ and } X \geq 3.5)}{P(X \geq 3.5)}$\)

\($= \dfrac{P(X \geq 7)}{P(X \geq 3.5)}$\)

\($= \dfrac{\int_7^\infty \frac{1}{3.5} e^{-x/3.5} dx}{\int_{3.5}^\infty \frac{1}{3.5} e^{-x/3.5} dx}$\)

\($= \dfrac{e^{-2}}{e^{-1}}$\)

\($= e^{-1}$\)

Therefore, the probability of being at least seven minutes late given that it is already 3.5 minutes late is approximately 0.368 (or 36.8%).

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Answer:

15 steps

Step-by-step explanation:

Answer:

w = -8

Step-by-step explanation:

Distribute: -6 = 2w + 10

Remove the 10: -6 -10 = 2w +10 -10 ---> -16 = 2w

Isolate the variable: -16/2 = 2w/2

Answer: -8 = w

The measures of the angles of the triangles are

m∠1 = 55°

m∠2 = 125°

m∠3 = 35°

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔCDE

And ∠BAC = m∠1

And , ∠CDE = m∠3

Now , from the triangle ΔABC

∠ABC = 180° - 110° ( Angle of a straight line is 180° )

So , the measure of angle ∠ABC = 70°

The sides of the triangle AC and BC are similar

So , The angles of the triangle are = 70° + x + x = 180°

On simplifying the equation , we get

70° + m∠1 + m∠1 = 180°

Subtracting 70° on both sides of the equation , we get

2m∠1 = 110°

Divide by 2 on both sides of the equation , we get

m∠1 = 55° = ∠ACB

And , ∠ACB and m∠2 are on a straight line

So , m∠2 = 180° - 55°

On simplifying the equation , we get

m∠2 = 125°

The triangle ΔCDE is a right triangle with ∠DCE = m∠1 ( vertically opposite angles )

So , the angles of the triangle are = 90° + 55° + m∠3 = 180°

On simplifying the equation , we get

145° + m∠3 = 180°

Subtracting 145° on both sides of the equation , we get

m∠3 = 35°

Hence , the measures of the angles of the triangles are are m∠1 = 55° , m∠2 = 125° , m∠3 = 35°

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Answer:

2x-2= -21

Step-by-step explanation:

Answer:

-9.5

Step-by-step explanation:

We can create an equation to represent this, where \(n\) is the missing value.

\(2n - 2 = -21\)

Now we can solve for \(n\) by isolating it on one side of the equation.

Add 2 to both sides:

\(2n - 2 + 2 = -21+2\\\\2n = -19\)

Divide both sides by 2:

\(2n\div2 = -19\div2\\\\n = -9.5\)

Hope this helped!