B. Mason put sticky notes on some pages of his math book. The page numbers for this sequence 3, 5, 8, 13, 21,34, ... Describe the rule for the sequence. I Find the next two terms of the sequence. Show your work.​

Answer:

If you were to factor this inequality the answer would be

-6(4p+15)

If you were to simplify this inequality the answer would be

-24p-90

I don't really know how your question is set up or how your teachers teach this but here are two possible answers. I hope this helps

Answer:

b

Step-by-step explanation:

The equation that represents the graph will be y > 3x + 2. Then the correct option is B.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,

\(\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)\)

From the graph, the two points are (0, 2) and (-3, -7). The region above the line is considered, then the equation is written as,

(y - 2) > [(2 + 7) / (0 + 3)] (x - 0)

y - 2 > 3x

y > 3x + 2

The equation that represents the graph will be y > 3x + 2. Then the correct option is B.

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The measure of each exterior angle of a regular 12-sided figure is 30 degrees.

For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).

Exterior angle is an measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended. Also, due to polygon being regular, let it be having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.

We are given that;

The number of side of figure=12

Now,

The sum of the exterior angles of any polygon is 360 degrees. For a regular n-sided polygon, each exterior angle measures 360/n degrees.

So for a regular 12-sided figure (dodecagon), each exterior angle measures:

360/12 = 30 degrees

Therefore, the value of the angle will be 30 degrees.

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Answer:

The y-intercept is $1000

Step-by-step explanation:

What this means is the the value of the antique when first found/created was 1000 dollars

The derivative of the function f(t) = t^7(t + 1) is f'(t) = 8t^6 + 7t^7. To find the derivative of the given function, we will apply the product rule and the power rule of differentiation.

The product rule states that if we have two functions u(t) and v(t), the derivative of their product is given by (u(t)v'(t) + v(t)u'(t)).

Let's apply the product rule to the function f(t) = t^7(t + 1):

f'(t) = (t^7)'(t + 1) + t^7(t + 1)'

Now, let's find the derivative of each term using the power rule:

The derivative of t^7 is given by (t^7)' = 7t^(7-1) = 7t^6.

The derivative of (t + 1) is simply 1.

Substituting these derivatives back into the product rule formula, we have:

f'(t) = 7t^6(t + 1) + t^7(1)

Simplifying further:

f'(t) = 7t^7 + 7t^6 + t^7

Combining like terms:

f'(t) = 8t^6 + 7t^7

Therefore, the derivative of the function f(t) = t^7(t + 1) is f'(t) = 8t^6 + 7t^7.

In summary, the derivative of the function f(t) = t^7(t + 1) is given by f'(t) = 8t^6 + 7t^7.

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(a) The mean number of buses arriving in any interval of minutes is λ = 1.

(b) The probability of buses arriving in a t-minute interval is P(X > 0) = 1 - P(X = 0), where X is a Poisson random variable with parameter λt.

(c) The probability of no buses arriving in a t-minute interval is P(X = 0) = \(e^{(-λt)}\) = \(e^{(-t)}\).

(d) The probability of at least one bus arriving in a t-minute interval is

P(X ≥ 1) = 1 - P(X = 0) = 1 - \(e^{(-t)}\).

To guarantee at least one bus with a certain percentage of probability, we need to solve the inequality:

where p is the desired probability. Solving for t, we get:

Therefore, the minimum wait time necessary to guarantee at least one bus with a probability of p is -ln(1-p) minutes.

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Answer:

Step-by-step explanation:

Given line ;

\(y = \frac{5}{4} x -3\\\\m = slope\\m = \frac{5}{4}\)

1. Perpendicular and passes through (4,-6)

\(m_1 = \frac{5}{4} \\\\m_2 = \frac{-1}{m_1} \\\\m_2 = \frac{-1}{\frac{5}{4} } \\\\m_2 = -\frac{4}{5} \\\\(4,-6)=(x ,y)\\\)

Substitute the values above into slope intercept form ; y=mx+b and solve for b.

\(y =mx+b\\\\-6 = -\frac{4}{5} (4) + b\\\\-6 = -\frac{16}{5} + b\\\\-6 + \frac{16}{5} = b\\\\-\frac{14}{5} = b\\\\b = -\frac{14}{5}\\\\m = - \frac{4}{5}\)

Substitute new values into ; y =mx+b.

\(y = -\frac{4}{5} (x)- (\frac{14}{5} )\\\\y = -\frac{4}{5} x - \frac{14}{5}\)

2.Parallel and passes through (4,-6)

\(m = \frac{5}{4} \\\\(4,-6)=(x_1,y_1)\)

Substitute values into point slope  form and simplify

\(y-y_1=m(x-x_1)\\\\y - (-6) = \frac{5}{4} (x -4)\\\\y+6 = \frac{5}{4} x -5\\\\y = \frac{5}{4} x -5-6\\\\y = \frac{5}{4} x -11\)

Answer:

EF = -120 inches

Step-by-step explanation:

AB + BC + CD + EF = 4G

AB + 2BC + 4CD + EF = 140

AB + 2(2AB) + 4(2(2AB)) + EF = 140

AB + 4AB + 8AB + EF = 140

13AB + EF = 140

EF = 140 - 13AB

EF = 140 - (13)(20)

EF = 140 - 260

EF = -120 inches

The length of EF is 40 inches long.

The triangle proportionality theorem states that if a line is drawn inside the triangle which is parallel to any side of the given triangle, then the line intersects other two sides at two different points. Then the division of the other two sides of the triangle will be in the same ratio.

Here we can use the proportionality theorem to find the length of EF.

Using the proportionality theorem,

AD / AG = BC / EF  [Equation 1]

Given that,

BC = 2 AB ⇒ AB = BC / 2

CD = 2 BC

Now, AD = AB + BC + CD

               = (BC / 2) + BC + 2 BC

               = 7/2  BC

AG is given as 140 inches.

Substituting the values in the Equation 1,

(7/2 BC) / 140 = BC / EF

BC get cancelled on both sides.

7 / (2 × 140) = 1 / EF

Cross multiplying,

7 EF = (2 × 140)

EF = 40 inches

Hence the length of EF is 40 inches long.

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The complete question is given below.

0.688 will be the probability of getting a nickel from the jar.

Given,

Probability;-

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The number of fortunate situations divided by the total number of coins would be the product between the probability of each occurrence and the likelihood of each event.

Therefore,

P(nickel) = 19/69

P(penny) = 17/68

That is,

P = 19/69 × 17/68

P = 323/4692

P = 0.0688

That is,

The probability of getting nickel from the jar is 0.06888

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Answer:

BD = 26

The measure of angle ADB = 59 degrees

The measure of angle DEC = 118 degrees

Step-by-step explanation:

BD = 2 * EC = 2 * 13 = 26

The measure of angle ADB = 90 - 31 = 59 degrees

The measure of angle DEC = 180 - 2(31) = 180-62 = 118 degrees

To find the eigenvalues and eigenvectors of a 2x2 matrix, follow these steps:

Calculate the characteristic equation by subtracting the identity matrix I multiplied by the scalar λ from matrix A, and set the determinant of this resulting matrix equal to zero. The characteristic equation is given by det(A - λI) = 0.Solve the characteristic equation to find the eigenvalues (λ).

Let's assume we have a 2x2 matrix A:

  | a  b |

A = | c d |

To find the eigenvalues, we need to calculate the characteristic equation:

det(A - λI) = 0,

where I is the 2x2 identity matrix and λ is the eigenvalue.

A - λI = | a-λ b |

| c d-λ |

The determinant of this matrix is:

(a-λ)(d-λ) - bc = 0,

which simplifies to:

λ² - (a+d)λ + (ad - bc) = 0.

This quadratic equation gives us the eigenvalues.

Solve the quadratic equation to find the values of λ. The solutions will be the eigenvalues.

Once you have the eigenvalues, substitute each value back into the equation (A - λI)v = 0 and solve for v to find the corresponding eigenvectors.

For each eigenvalue, set up the homogeneous system of equations:

(A - λI)v = 0,

where v is the eigenvector.

Solve this system of equations to find the eigenvectors corresponding to each eigenvalue.

To find the eigenvalues and eigenvectors of a 2x2 matrix, follow the steps mentioned above. The characteristic equation gives the eigenvalues, and by solving the corresponding homogeneous system of equations, you can determine the eigenvectors.

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Strategies such as fast-tracking, crashing, prioritization, and resource optimization can be employed to reduce the project completion time by 5 weeks.


To reduce the completion time of the project by 5 weeks, we need to analyze the provided information and make appropriate adjustments. The initial completion time of the project is 25 weeks.

To achieve a reduction of 5 weeks, we can consider several strategies:

1. Fast-tracking: This involves overlapping or parallelizing certain project activities that were initially planned to be executed sequentially. By identifying tasks that can be performed concurrently, we can potentially save time. However, it's important to evaluate the impact on resource allocation and potential risks associated with fast-tracking.

2. Crashing: This strategy focuses on expediting critical activities by adding more resources or adopting alternative approaches to complete them faster. By compressing the schedule of critical tasks, we can reduce the overall project duration. However, this may come at an additional cost.

3. Prioritization: By reevaluating the project tasks and their priorities, we can allocate resources more efficiently. This ensures that critical activities receive higher attention and are completed earlier, resulting in an accelerated project timeline.

4. Resource optimization: Analyzing the resource allocation and identifying potential areas for optimization can lead to time savings. By ensuring that resources are utilized effectively and efficiently, we can streamline the project execution process.

It's important to note that implementing any of these strategies requires careful evaluation, considering factors such as project constraints, risks, cost implications, and stakeholder agreements. A comprehensive analysis of the project plan, resource availability, and critical path can guide the decision-making process for reducing the project completion time.

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The value of ∠MON is 57.

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

Here, we have

Given the following angle

We want to find the angle MON

∠LON = 113°

∠MON = 2x+33

∠LOM =3x+20​

we notice that the sum of angle MON and angle LOM equals angle LON.

∠MON + ∠LOM = ∠LON

2x + 33 + 3x + 20 = 113

5x + 53 = 113

5x = 113 - 53

5x = 60

x = 12

Now, we put the value of x on ∠MON and we get

∠MON = 2(12) + 33

∠MON = 57

Hence, the value of ∠MON is 57.

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The matter that occupies more space, assuming a similar number of molecules, is the one that has a lower density than the other.

The space occupied by a matter depends on its density. The higher the density of the matter, the more space it occupies. Density can be defined as the amount of matter present per unit volume.

The matter that occupies more space is the one that has a lower density than the other, assuming a similar number of molecules. Density is a key physical property that helps scientists identify a substance.

The density of a substance remains constant at a given temperature and pressure. Density is important for many applications such as calculating the weight of a particular amount of material, measuring the concentration of a solution, and determining whether a substance will float or sink in a liquid.

The mass of the substance will determine the density of the substance. The relationship between mass, volume, and density can be given by the following formula:

Density = Mass/VolumeIf we have the same number of molecules of two different substances, the substance with the lower density will occupy more space. Let's say we have a balloon with helium gas and another balloon with oxygen gas, and both balloons have the same number of molecules.

Since helium gas has a lower density than oxygen gas, the balloon with helium gas will occupy more space than the balloon with oxygen gas.

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Answer:C

Step-by-step explanation:

Answer

20 - 12x

Step-by-step explanation

We distribute 4 through the parenthesis:

\(\bf{4(5-3x)}\)

\(\bf{4*5-3x*4}\)

\(\bf{20-12x}\)

Therefore, the answer is 20 - 12x

Answer:

Step-by-step explanation:

no way i can do math like that

The product of 2 and 4√147 in simplest radical form is 56√3.

We have,

We can simplify the product of 2 and 4√147 as follows:

2 x 4√147

= 8√147

(multiply 2 and 4)

= 8√(49 x 3)

(factor 147 as 49 x 3)

= 8√49 √3

(apply the product rule of radicals)

= 8 x 7 √3

(simplify √49 to 7)

= 56√3

(multiply 8 and 7)

Therefore,

The product of 2 and 4√147 in simplest radical form is 56√3.

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Answer:

Ok, the rules of the exponent come from a logic construction.

If we have x^n

this means that n is multiplied by itself n times.

If we decompose n into a + b, we have:

x by itself a times, and then x by itself b times, and for how the product works, this is equivalent:

if n = 5, a= 2 and b = 3

x^5 = (x*x*x*x*x)   5 times-

x^5 = x^(2 + 3) = (x^2)*(x^3) = (x*x*)*(x*x*x) = x*x*x*x*x = x^5

And the same for the other rules:

(x^n)^b = x^n*b and such.

Obviusly, this only works when we have a common base.

So the correct answer is that we constructed the exponential rules in a way that only can be used when we have a common base, and this happens because to construct them, we started with common bases.

Answer: One of the ways you can do all this is by zearn or by listening by your teacher.

Answer:

1 e

2 a

3 b

4 c

5 d

Step-by-step explanation:

i did the answers to the first question i dont know the rest sorry

ANSWER

a. 1.25 + 1.5x = 8.75

b. 5 games

EXPLANATION

We have that:

Shoe rental = $1.25

Games = $1.50 per game

He spent a total of $8.75.

a. Let the number of games played be x.

This means that the cost of shoe rental and the total cost of x games must be equal to $8.75. Therefore:

1.25 + (1.50 * x) = 8.75

1.25 + 1.5x = 8.75

That is the equation that represents Frank's situation.

b. To find the number of games he bowled, we have to find x:

1.25 + 1.5x = 8.75

=> 1.5x = 8.75 - 1.25

1.5x = 7.5

Divide both sides by 1.5:

x = 7.5 / 1.5

x = 5

He bowled 5 games.

The estimated cost of the new 3000-ft2 heat exchange system for the plant retrofit can be calculated using the power-sizing exponent and the price index. Based on the given information, the rough estimate for the cost of the new heat exchanger system is approximately $108,984.

To estimate the cost of the new heat exchange system, we need to consider the price index and the power-sizing exponent. The price index provides a measure of the change in prices over time. In this case, the price index 7 years ago was 1360, and the current price index is 1478.

To calculate the cost estimate, we can use the following formula:

Cost estimate = (Cost of previous heat exchanger) × (Current price index / Previous price index) × (New size / Previous size) ^ power-sizing exponent

Using the given information, the cost of the previous heat exchanger was $75,000, the previous size was 1200 ft2, and the new size is 3000 ft2.

Plugging in these values into the formula, we get:

Cost estimate = ($75,000) × (1478 / 1360) × (3000 / 1200) ^ 0.55

Simplifying the calculation, we find:

Cost estimate ≈ $108,984

Therefore, a rough estimate for the cost of the new 3000-ft2 heat exchanger system for the plant retrofit is approximately $108,984. It's important to note that this is just an estimate and the actual cost may vary based on specific factors and market conditions.

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The range of the graphed function is expressed as: -∞ < y < ∞

Range corresponds to the values on the y-axis while the Domain corresponds to values on the x-axis.

From the graph of a function h(x), we want to find the range of the function in inequality notation.

The range is all possible y-values of the function. Thus, let's find all possible y-values from the graph.

If we look at the graph closely, we see that it has a vertical asymptote at x = 1 and a slant asymptote.

But it includes all y values from -infinity to infinity.

Thus, we can write range as -∞< y < ∞ because both sides of the function go and so on below the x-axis and go and so on above the x-axis.

The range is  -∞< y < ∞ .

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