Solve each inequality and graph the solution.
1. 5y + 3y + 5 ≤ ‐2(2y + 4)
2 .4n – 2n ≤ 18
3.
‐(5k – 3) ≤ 15 + 3k

Answer:

36 in.

Step-by-step explanation:

The perimeter is the sum of the length of all the sides.

Perimeter of the figure

= 8 +8 +4 +6 +10

= 36 in

The rate of return for Nichole's investment is approximately 22%.

To calculate the rate of return, we need to determine the percentage increase in value from the initial investment to the final sale.

Nichole bought 500 shares at $8.24 per share, which amounts to a total investment of 500 * $8.24 = $4,120.

After one year, she sold all her shares for $10.10 per share, resulting in a total sale value of 500 * $10.10 = $5,050.

Her profit from the investment is $5,050 - $4,120 = $930.

To find the rate of return, we divide the profit by the initial investment and multiply by 100: ($930 / $4,120) * 100 ≈ 22.6%.

Therefore, her rate of return is approximately 22.6%, which corresponds to option A.

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In both cases, the inequality holds true. The inequality is 415 + d ≥ 500.  

Part A:
To write an inequality that represents the situation, we can use the following format: money raised so far + additional money needed ≥ goal. In this case, the money raised so far is $415, and the goal is $500. Let d represent the additional money needed. So the inequality would be:

415 + d ≥ 500

Part B:

The inequality 415 + d ≥ 500 has infinitely many solutions, as there are countless values of d that can satisfy the inequality. This is because as long as the total amount raised is equal to or greater than $500, the student council meets its goal. For example, if d is 85, then the council would exactly meet its goal (415 + 85 = 500). If d is 100, the council would exceed its goal (415 + 100 = 515). In both cases, the inequality holds true.

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To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ), we need to first plot the curve on a polar graph.

From the graph, we can see that the curve has two loops - one larger loop and one smaller loop. The larger loop encloses the smaller loop.

To find the area inside the larger loop and outside the smaller loop, we can use the formula:

Area = 1/2 ∫[a,b] (r2 - r1)2 dθ

where r2 is the equation of the outer curve (larger loop) and r1 is the equation of the inner curve (smaller loop).

The limits of integration a and b can be found by setting the angle θ such that the curve intersects itself at the x-axis. From the graph, we can see that this occurs at θ = π/2 and θ = 3π/2.

Plugging in the equations for r1 and r2, we get:

r1 = 1/2 + cos(θ)
r2 = 1/2 - cos(θ)

So the area inside the larger loop and outside the smaller loop is:

Area = 1/2 ∫[π/2, 3π/2] ((1/2 - cos(θ))2 - (1/2 + cos(θ))2) dθ

Simplifying and evaluating the integral, we get:

Area = 3π/2 - 3/2 ≈ 1.07

Therefore, the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ) is approximately 1.07. Note that this area is smaller than the total area enclosed by the curve, since it excludes the area inside the smaller loop.
To find the area inside the larger loop and outside the smaller loop of the limaçon given by the polar equation r = 1 + 2cos(θ), follow these steps:

1. Find the points where the loops intersect by setting r = 0:
1 + 2cos(θ) = 0
2cos(θ) = -1
cos(θ) = -1/2
θ = 2π/3, 4π/3

2. Integrate the area inside the larger loop:
Larger loop area = 1/2 * ∫[r^2 dθ] from 0 to 2π
Larger loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 0 to 2π

3. Integrate the area inside the smaller loop:
Smaller loop area = 1/2 * ∫[r^2 dθ] from 2π/3 to 4π/3
Smaller loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 2π/3 to 4π/3

4. Subtract the smaller loop area from the larger loop area:
Desired area = Larger loop area - Smaller loop area

After evaluating the integrals and performing the subtraction, you will find the area inside the larger loop and outside the smaller loop of the given limaçon.

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The time taken by the bug will be 5 seconds and the formula used to calculate time is T = D/S.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

S = D/T or T = D/S

where T is time, D is distance, and S is speed.

If a bug travels 5 meters across the floor if it is traveling 1 meter/second. Then the time taken by the bug will be

T = 5/1

T = 5 seconds

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Answer: they must have used up around 40% of the money if I’m wrong I’m so sorry

Step-by-step explanation: Good luck!

computing the average distance between every pair of observations between two clusters

What is Cluster Analysis?

Grouping "things" into "similar" groups is one of the most fundamental, straightforward, and frequently overlooked techniques (or processes) of comprehending and learning, on which cluster analysis is based. To create clusters of a particular type, this process uses a variety of different algorithms and techniques. It is also a component of data management in statistical analysis.

A multivariate data mining technique called cluster analysis aims to group things (such goods, responders, or other entities) based on a set of user-selected features or characteristics. Data compression, machine learning, pattern recognition, information retrieval, and other areas all use this essential and crucial phase of data mining, which is also a widely used method for statistical data analysis.

Here as per the given question, there are two clusters given.

Hence, computing the average distance between every pair of observations between two clusters.

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Answer:

the slope is 0/-3 or just 0

Step-by-step explanation:

Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

Answer:

P(multiples of 12)=1/25

Step-by-step explanation:

Multiples of 12: 12, 24, 36, 48

That is 4/50=1/25

Yes, the continuous time complex exponential is always periodic, and it is because complex exponentials can be written using Euler's formula.

Euler's formula, in mathematics, is a formula that links five fundamental mathematical constants:

e, the base of the natural logarithm;

pi, a mathematical constant;

i, an imaginary unit;

1, the multiplicative identity; and

0, the additive identity.

The formula is

\(e^{ix} = cos(x) + i sin(x)\)

In the above formula, x is a real number. cos(x) and sin(x) are the trigonometric functions cosine and sine, respectively. And i is the imaginary unit.

In general, periodic functions are mathematical functions that repeat themselves after a certain period. And when complex exponentials can be written using Euler's formula, they can also be expressed as:

\(cos(x) =\frac{1}{2} (e^{ix} + e^{-ix})sin(x) = 1/2i (e^{ix} - e^{-ix})\)

As a result, it can be concluded that the continuous time complex exponential is always periodic since it can be expressed using Euler's formula, and Euler's formula can also be written in a periodic form.

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The answer is Ax = 160, because 180 - (130 + 30) = 20 and 180 - 20 = 160. From the given triangles, we can observe that they are similar triangles. Therefore, their corresponding angles are equal. We can also observe that one of the angles of the first triangle measures 130°.The sum of angles in a triangle is always equal to 180°.The statement that is true about x is Ax = 160°.

Therefore, the sum of the other two angles in the first triangle is equal to:180° - 130° = 50°We can also observe that one of the angles of the second triangle measures 30°.Therefore, the sum of the other two angles in the second triangle is equal to:180° - 30° = 150°From the given information, we can deduce that the two triangles have two corresponding angles that are equal to each other. These angles measure 50° and 30° respectively. We need to find the measure of the third corresponding angle.The sum of the angles of a triangle is 180°. Therefore:50° + 30° + x = 180°Simplifying this equation gives:x = 180° - 80° = 100°From the triangle, we know that Ax + x = 180°Therefore:Ax + 100° = 180°Simplifying this equation gives:Ax = 180° - 100° = 80°From the given information, Ax = 180° - (130° + 30°) = 20°Adding x to both sides of the equation Ax + x = 180° gives:Ax + x = 180°20° + x = 180°Solving this equation gives:x = 160°

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The true statement about x is Ax = 160, because 180 - (130 + 30) = 20 and 180 - 20 = 160. As derived using the Exterior Angle Theorem and the given angles of the triangle.

1. Two triangles are given from which it can be observed that x is the exterior angle of a triangle with interior angles measuring 130° and 30°.

2. Therefore, using the Exterior Angle Theorem which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle, we get:

\(Exterior angle x = Interior angle 1 + Interior angle 2.\)

3. Therefore, x = 130° + 30° = 160°.

4. Based on these triangles, the true statement about x is Ax = 160,

because 180 - (130 + 30) = 20 and 180 - 20 = 160.

The correct statement about x is Ax = 160, as derived using the Exterior Angle Theorem and the given angles of the triangle.

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the more compact hospital. The Law of Large Numbers, which makes intuitive sense, states that when there are more observations, the experimental average tends to approach the true proportion. Large hospitals have more observations, therefore their results are less likely to deviate from 50% or have a wide range of results.

An equation that states that two ratios are equal is a genuine proportion. You can utilise information about one ratio in a proportion to determine values in the other equal ratio.

The sample proportion, p′ = 0.842, which is the point estimate of the population proportion, must be determined in order to calculate the confidence interval. Given that CL = 0.95 is the requested confidence level, = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) follows..

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there are 54,633,624 different collections of 16 coins chosen at random that will contain at least 3 coins of each type.

We have three types of coins, and we need to choose at least 3 coins of each type from a collection of 16 coins.

Let's consider each type of coin separately.

For the first type of coin, we need to choose at least 3 coins from the available coins. There are 8 coins of this type, so the number of ways to choose at least 3 coins is the sum of the number of ways to choose 3, 4, 5, 6, 7, and 8 coins:

C(8,3) + C(8,4) + C(8,5) + C(8,6) + C(8,7) + C(8,8) = 969

Similarly, for the second type of coin, we also have 8 coins to choose from, and we need to choose at least 3 coins. So the number of ways to choose at least 3 coins is also 969.

For the third type of coin, we only have 6 coins to choose from, so the number of ways to choose at least 3 coins is:

C(6,3) + C(6,4) + C(6,5) + C(6,6) = 56

Now, we need to multiply the number of ways to choose coins of each type together, since these choices are independent.

969 x 969 x 56 = 54,633,624

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Step-by-step explanation:

Domain tells us all the possible x values or inputs of a function.

Here the input is n.

The domain here is defined on the interval [-1,3) so the domain can be notated in 3 ways.

Interval Notation: [-1,3]

Words: All inputs that is between -1 and 3, exclusively.

Sign Notation:

\( - 1 \leqslant x \leqslant 3\)

The Range of a function is possible y values or outputs of a function.

For the range, plug in x values to find the y values.

Since the range in this problem, is only defined for -1 to 3. Plug in -1 for n in the function.

\(2( - 1) - 1 = - 3\)

\(2(3) - 1 = 5\)

So the range of is

[-3,5]

Or could be stated

All outputs between -3 and 5 exclusively

\( - 3 \leqslant x \leqslant 5\)

Here's a graph. Look Above

The product of a rational and an irrational number can be either rational or irrational, depending on the specific numbers involved.

To illustrate this, let's consider an example:

Let's say we have the rational number 2/3 and the irrational number √2.

Their product would be (2/3) * √2.

In this case, the product is irrational.

The square root of 2 is an irrational number, and when multiplied by a rational number, the result remains irrational.

However, it's also possible to have a product of a rational and an irrational number that is rational. For example, if we consider the rational number 1/2 and the irrational number √4, their product would be (1/2) * 2, which equals 1. In this case, the product is a rational number.

Therefore, we cannot make a definitive statement that the product of a rational and an irrational number is always rational or always irrational. It depends on the specific numbers involved in the multiplication.

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Answer:

\( {2}^{ - 14} \times {5}^{10} \)

Answer:

6.25

Step-by-step explanation:

Answer:

b must be positive

Step-by-step explanation:

if a is less than -1

that means to get smaller numbers

b needs to be positive

so that when a is multiplied by b you would have

numbers that are more negative

Answer:

b > 1

Step-by-step explanation:

Given:

Substituting a = -1 into ab < a

⇒ (-1)b < -1  

⇒ -b < -1

⇒ b > 1

If a < -1 then a is negative.  If ab < a then ab is also negative.  

In order for ab to be negative (when a is negative) b must be positive.

For ab < a then b > 1.

Proof

If b = 0.5 and a = -1.5 then ab = -0.75

As -0.75 > -1.5 then ab > a so this cannot be true.

If b = 1.5 and a = -1.5 then ab = -2.25

As -2.25 < -1.5 then ab < a so this is true.

Therefore b > 1

The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.

The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.

However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.

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The first step to factorizing a polynomial is taking the Highest Common Factors.

Like Algebraic expressions, polynomials are expressions that consist of both coefficients and variables are called Polynomials.

The factors that are multiplied to obtain the original expressions are known as factors of the given polynomial.

Factorization is the method used to determine the factors of a given polynomial or mathematical expression.  

To factorize a given polynomial first we need to take the Highest common factors from the 4 terms of the polynomial.

Example:

x²-5x -10x +50    

To factorize the polynomial

Take common Highest Common Factors  

=> x(x - 5) -10(x - 5)        

=> (x - 5) (x - 10)

∴ Factors of given polynomial is (x - 5) and (x - 10)

Therefore,

The first step to factorizing a polynomial is taking the Highest Common Factors.

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Answer:

60

Step-by-step explanation:

5*3*4

B is the right response: (6 + 4) 2 = 20.

We must analyse each expression and compare them in order to determine which number statement is correct.

starting with the formula A (6 + 4 2 = 6 + 8 = 14)

Let's now assess expression B:

(6 + 4) × 2 = 10 × 2 = 20

Expression in C: 6 + 4 2 = 6 + 2 =

The final expression is D (6 + 4) 2 = 10 2 = 5.

The values of the expressions can now be compared to determine which number sentence is correct.

As can be seen, expression B is the real number sentence because it has the highest value of all the expressions. As a result, B is the right response: (6 + 4) 2 = 20.

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a) At t = 0.075 s, the position of the piston can be found by substituting the given time into the equation x = (1.88 cm)cos((112 rad/s)t + π/6). Evaluating this equation at t = 0.075 s will give us the position of the piston at that time.

b) The maximum velocity of the piston can be determined by taking the derivative of the position equation with respect to time and finding the maximum value. This will give us the velocity function, from which we can determine the maximum velocity.

c) Similarly, the maximum acceleration of the piston can be found by taking the derivative of the velocity function with respect to time and finding the maximum value.

d) To find the time it takes for the piston to complete one cycle, we need to determine the period of the oscillation. The period is the time it takes for the piston to complete one full oscillation, and it can be calculated by dividing the period of the cosine function, which is 2π, by the coefficient of t in the argument of the cosine function.

a) To find the position of the piston at t = 0.075 s, we substitute t = 0.075 s into the given equation:

x = (1.88 cm)cos((112 rad/s)(0.075 s) + π/6)

Simplifying the equation will give us the position of the piston at that time.

b) To find the maximum velocity, we differentiate the position equation with respect to time:

v = -1.88 cm(112 rad/s)sin((112 rad/s)t + π/6)

The maximum velocity will occur at the points where sin((112 rad/s)t + π/6) takes its maximum value, which is ±1. Evaluating the velocity equation at those points will give us the maximum velocity.

c) To find the maximum acceleration, we differentiate the velocity equation with respect to time:

a = -1.88 cm(112 rad/s)^2cos((112 rad/s)t + π/6)

The maximum acceleration will occur at the points where cos((112 rad/s)t + π/6) takes its maximum value, which is ±1. Evaluating the acceleration equation at those points will give us the maximum acceleration.

d) To find the time it takes for one complete cycle, we divide the period of the cosine function (2π) by the coefficient of t in the argument of the cosine function. In this case, the coefficient is (112 rad/s), so the period will be 2π/(112 rad/s).

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The rocket will take 9 seconds to reach a height given by the equation -16t^(2)+144.

Given that:

The equation is -16t² + 144t.

Time taken by the rocket after it was launched into the air is t seconds.

To solve this equation, we need to factorize the equation and then apply the zero product rule.

Zero product rule: If the product of two factors is zero, then at least one of the factors must be zero.

-16t² + 144t = 0-16t(t - 9) = 0

Here, the product of -16t and (t - 9) gives the equation 0. Then we can say that one of the factors -16t = 0 or (t - 9) = 0 should be equal to 0.

Solving for t,

-16t = 0 or (t - 9) = 0t = 0 or t = 9 seconds

Therefore, the rocket will take 9 seconds to reach a height of 144 feet. Hence the correct option is 9 seconds.

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Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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Answer:

The first is 36,763    second 30 hours

Step-by-step explana