‼️‼️‼️‼️‼️
*A MAN HAS
TWENTY COINS
CONSISTING OF DIMES
AND QUARTERS.

"IF THE DIMES WERE
QUARTERS AND THE QUARTERS
WERE DIMES, HE WOULD HAVE
NINETY CENTS MORE THAN
HE HAS NOW..HOW MANY DIMES
AND QUARTERS DOES HE HAVE?

Answer:

$40 in euros!

Step-by-step explanation:

This equation has complex solutions and that means the system has no nontrivial solutions for real value of lambda.

\(\lambda = \frac{-6±\sqrt{-164} }{4} \\\)

Now, According to the question:

Nontrivial Solutions of a System:

System of equations has a form:

AX = 0, X = (x , y, z)

System of equations has a nontrivial solutions if a determinant of a system is zero. If the determinant is not zero than the matrix has inverse and a nontrivial solution x=0. This can be said differently: The homogeneous system has the trivial solution if rank of A in the row reduced form of matrix is equal to the number of unknown variables. If rank of A is less than the number of variables then the system has nontrivial solutions.

λx + 2y + z = 0

x + 5y + 2z = 0

3x - λy + z= 0

So, we calculate and determinant :

\(\left[\begin{array}{ccc}\lambda&2&-1\\1&5&2\\3&-\lambda&1\end{array}\right]\)  \(= \lambda det\left[\begin{array}{ccc}5&2\\-\lambda&1\end{array}\right]\) \(-2det\left[\begin{array}{ccc}1&2\\3&1\end{array}\right]\) \(det\left[\begin{array}{ccc}1&5\\3&-\lambda\end{array}\right]\)

\(=2\lambda^2+6\lambda+25=0\)

This equation has complex solutions and that means the system has no nontrivial solutions for real value of lambda.

\(\lambda = \frac{-6±\sqrt{-164} }{4} \\\)

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The given question is incomplete, complete question is :

For which values of ? does the following system have nontrivial solutions

λx + 2y + z = 0

x + 5y + 2z = 0

3x - λy + z= 0

Answer:

35,240

Step-by-step explanation:

Answer:

The actual speed = 27.12 mi/h

Direction = 36.5° in NE(north of east)

Step-by-step explanation:

As given , A hot air balloon is flying at a constant speed of 20 mi/h at a bearing of N 36° E.

⇒θ = 36°

Let v₀ be the constant speed, then v₀ = 20

Let vₓ be the speed in East direction

     \(v_{y}\) be the speed in North direction

So,

vₓ  = v₀ sin(θ) = 20 sin(36°) + 10 ( As given, There is a 10mi/h cross wind blowing due east.)

⇒vₓ  = 20(0.588) + 10 = 11.76 + 10 = 21.76 mi/h

and   \(v_{y}\)  = v₀ cos(θ) = 20 cos(36°) = 20(0.809) = 16.18 mi/h

Now,

the actual speed = √(vₓ)² + (\(v_{y}\))²

                            = √(21.76)² + (16.18)²

                            = √473.498 + 261.792

                            = √735.29 =  27.12

⇒The actual speed = 27.12 mi/h

Now,

Direction = θ = \(tan^{-1}(\frac{v_{y} }{v_{x} } ) = tan^{-1}(\frac{16.18 }{21.76 } ) = tan^{-1}(0.74) = 36.5\)

⇒ Direction = 36.5° in NE(north of east)

Answer:

27.1 mi / h; N 53° E

Step-by-step explanation

Answer:

d. 84 yd

Step-by-step explanation:

\( \frac{1}{2} (12 + 36)(3.5) \\ \frac{1}{2} (48)(3.5) \\ \frac{168}{2} = 84\)

No, if the game in Steam is more than 20 dollars and you have a Steam gift card of 20 dollars, it will not work.

Steam gift cards can be used to purchase games, software, and other items on the Steam store. However, the value of the gift card must be sufficient to cover the entire purchase price, including any taxes and fees. If the price of the game is more than the value of the gift card, you will need to add additional funds to your Steam Wallet to complete the purchase. Steam Wallet can be topped up using various payment methods, such as credit/debit cards, payment apps, and more.

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Answer:

57 is the correct answer

Answer:

18

Step-by-step explanation:

Solve the question in steps

(8+36)/11

44/11=4

Now you have 4+7x2

You do multiplication first

4+14=18

The type of function that fits the given description is D. Exponential decay.

In an arithmetic sequence, the difference between consecutive terms remains constant. If the y-values of a function form an arithmetic sequence that decreases in value, it means that the difference between consecutive terms is negative.
Exponential decay functions exhibit a constant ratio between consecutive terms, resulting in a decreasing sequence. As the x-values increase, the y-values decrease at a consistent rate. This is represented by the formula y = ab^x, where b is a constant between 0 and 1.
In contrast, linear functions have a constant difference between consecutive terms, resulting in an arithmetic sequence. However, since the y-values are decreasing, the function cannot be linear.
Exponential growth functions, on the other hand, have a constant ratio between consecutive terms, but they result in an increasing sequence. The y-values of an exponential growth function increase as the x-values increase.

Therefore, based on the given information, the most appropriate type of function is D. Exponential decay.

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The difference between the length and width of the garden is 2.55 yards.

Two or more expressions with an Equal sign is called as Equation.

Given that jan created a garden that was 8.5 yards long and 5.95 yards wide.

Length=8.5 yards

Width=5.95 yards.

We need to find the difference between the length and width of the garden.

8.5-5.95

Eight point five minus five point nine five

2.55

Hence,  the difference between the length and width of the garden is 2.55 yards.

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The linear approximation, denoted as l(x), to the function f(x) = 1/x near x = 4 is given by the equation l(x) = f(a) + f'(a)(x - a). In this case, a = 4, so we need to find f(a), f'(a), and substitute them into the equation to obtain the linear approximation.

First, we find f(a) by substituting a into the function f(x). Thus, f(4) = 1/4.

Next, we need to determine f'(a), which represents the derivative of f(x) with respect to x, evaluated at x = a. The derivative of f(x) = 1/x is found by applying the power rule of differentiation. The derivative f'(x) = -1/x^2. Substituting a = 4, we get f'(4) = -1/(4^2) = -1/16.

Now, we can substitute f(a) and f'(a) into the linear approximation equation. Therefore, l(x) = 1/4 - (1/16)(x - 4).

In summary, the linear approximation l(x) to the function f(x) = 1/x near x = 4 is given by l(x) = 1/4 - (1/16)(x - 4). This approximation provides an estimate of the function's behavior in the vicinity of x = 4 using a linear equation.

To derive the linear approximation, we first determine f(a) by substituting a = 4 into the original function f(x) = 1/x. This yields f(4) = 1/4. Then, we find f'(x), the derivative of f(x) with respect to x, using the power rule of differentiation. The derivative f'(x) = -1/x^2. Evaluating this at x = 4 gives us f'(4) = -1/(4^2) = -1/16. Finally, we substitute f(a) and f'(a) into the linear approximation equation l(x) = f(a) + f'(a)(x - a) to obtain the final expression l(x) = 1/4 - (1/16)(x - 4). This equation provides an approximate representation of the original function near x = 4, allowing us to estimate its behavior using a simpler linear function.

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Question 1: MetaSpace is unlikely to succeed in a legal battle against Marcus Superberg under the Australian Consumer Law.

Question 2: Ingrid may be entitled to workers compensation as an employee of RoadRunners.

Question 1:

Issue: Can MetaSpace succeed in a legal battle against Marcus Superberg under the Australian Consumer Law?

Rule: Under the Australian Consumer Law, businesses are prohibited from engaging in misleading or deceptive conduct in trade or commerce. To establish a claim, MetaSpace needs to show that Marcus Superberg made false representations about the security and privacy of DeltaVerse, which misled or deceived the general public.

Application: Marcus Superberg claims that DeltaVerse complies with privacy and cybersecurity legislation worldwide, and personal data cannot be accessed, stolen, or sold. He further claims to have an unbreakable unique algorithm protecting user data. Will Bates, the founder of MetaSpace, argues that such claims are impossible and accuses Marcus Superberg of misleading the public.

To assess MetaSpace's likelihood of success, it is important to determine if MetaSpace falls within the scope of consumers under the Australian Consumer Law. While MetaSpace is a competitor, it is possible for businesses to be considered consumers if they acquire goods or services for personal, domestic, or household use. If MetaSpace can establish that it falls within the definition of a consumer, it may have standing to bring an action against Marcus Superberg.

Conclusion: Based on the information provided, it is unclear whether MetaSpace can succeed in a legal battle against Marcus Superberg under the Australian Consumer Law. MetaSpace's ability to establish its consumer status and prove that Marcus Superberg engaged in misleading or deceptive conduct would be crucial factors in determining the outcome.

Question 2:

Issue: Is Ingrid entitled to workers compensation?

Rule: The entitlement to workers compensation depends on the classification of Ingrid's working relationship with RoadRunners. If she is considered an employee, she may be eligible for workers compensation benefits. However, if she is classified as an independent contractor, she may not have the same entitlements.

Application: Ingrid works for RoadRunners as a delivery courier, using her bicycle to deliver packages. She receives a fixed rate for each delivery, works at her own discretion, and follows RoadRunners' guidelines. She also faces penalties for exceeding the 15-minute delivery guarantee. Ingrid has been injured while performing her delivery duties.

To determine Ingrid's employment status, it is necessary to consider various factors, including the level of control exercised by RoadRunners over Ingrid's work, the degree of independence she has, the provision of equipment, and the nature of the work relationship. The fact that Ingrid uses the RoadRunners application and follows their guidelines suggests a degree of control indicative of an employment relationship.

If Ingrid is found to be an employee, she may be entitled to workers compensation benefits, including medical expenses and income replacement during her recovery period. However, if she is classified as an independent contractor, she may need to seek compensation through other avenues, such as a personal injury claim.

Conclusion: Based on the information provided, Ingrid may be entitled to workers compensation if she is classified as an employee of RoadRunners. The determination of her employment status will depend on a thorough assessment of the specific circumstances of her working relationship with RoadRunners, considering factors such as control, independence, and the nature of her work. Ingrid should seek legal advice to fully evaluate her entitlement to workers compensation benefits.

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In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.

The correct answer is Option D.

The key concept here is that a plane is defined by having at least three non-collinear points.

When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.

Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.

Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.

The correct answer is Option D.

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2 different expressions that involve only outs and powers of 2 which are equivalent 4 2/3 / 8 1/4

1) (4^2 * 2^-1 * 3^1) / (8^1 * 2^-2 * 4^-1)

2) (2^5 * 3^1) / (2^6 * 4^-1)

1) (4^2 * 2^-1 * 3^1) / (8^1 * 2^-2 * 4^-1)

This expression is equivalent to 4 2/3 / 8 1/4 because it is written in terms of powers of two. 4^2 is equal to 16, which is the numerator in 4 2/3. 2^-1 is the same as 1/2, which is the second fraction in 4 2/3. 3^1 is equal to 3, which is the numerator in 8 1/4. 8^1 is equal to 8, which is the denominator in 8 1/4. 2^-2 is the same as 1/4, which is the second fraction in 8 1/4. 4^-1 is equal to 1/4, which is the first fraction in 8 1/4. When all the terms are multiplied and divided, it is the same as 4 2/3 / 8 1/4.

2) (2^5 * 3^1) / (2^6 * 4^-1)

This expression is also equivalent to 4 2/3 / 8 1/4 because it is written similar to above equation.

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The morbidity rate is 500 cases per 100,000 people.

The morbidity rate is a measure of the number of cases of a particular disease within a specific population. In this scenario, out of 100,000 individuals exposed to the bacterial pathogen, 500 individuals develop the disease. Therefore, the morbidity rate is calculated by dividing the number of cases (500) by the total population (100,000) and multiplying by 100,000 to express it per 100,000 people.

Morbidity rate = (Number of cases / Total population) x 100,000

In this case, the calculation would be:

Morbidity rate = (500 / 100,000) x 100,000 = 500 cases per 100,000 people.

This means that for every 100,000 individuals exposed to the bacterial pathogen, there are 500 cases of the disease. The morbidity rate provides an important measure of the impact and prevalence of a disease within a population, allowing for comparisons and assessments of public health.

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Answer:

f(x) = x^4-x^2+ 2

option D

Step-by-step explanation:

From the question, we are told that the graph of g(x) contains the point (0,0)

What the graph of f(x) is showing to us is that it is translated 2 units up the vertical axis to get its starting position

What we are saying in essence is that the graph of f(x) and g(x) are similar, but f(x) was formed as a result of applying some transformation to g(x)

The transformation applied on f(x) is that it was moved 2 units upwards from g(x)

Since the translation is in a positive direction

Since the graph was moved up, it means that we added to the output of the graph

So the equation becomes;

f(x) = x^4-x^2+ 2

Answer:

x

Step-by-step explanation:

(log to the base 3) of 27^x can be re-written as

x*(log to the base 3) of 27, which is equivalent to:

x*(log to the base 3 of 3^3)  =  x

So the answer is simply " x "

Answer:

43lb 8oz

Step-by-step explanation:

add 18lb and 25lb which makes 43lb

and then add the oz of 3oz and 5oz which makes 8oz

You will have to work for 1.475 weeks to make the same total pay from both places.

To make the same total pay, you will have to work the following number of weeks:

Amazon: 25 hours/week * $16/hour = $400/week

UPS: 30 hours/week * $18/hour = $540/week + $50/week = $590/week

So you will have to work for $400/week * X = $590/week

X = $590/week / $400/week = 1.475 weeks

So, you will have to work for 1.475 weeks to make the same total pay from both places.

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Answer:

Step-by-step explanation:

The idea is to move the decimal to right after the repeating digit and then to right before it and subtract.

Let x = .46666

Then to move the decimal one place to right before the repeating digit, we multiply by ten which moves the decimal right after the 4 and right before the repeating 6:

10x = 4.666

Now we need to move it to right after the repeating digit, so we multiply by 100:

100x = 46.666 and subtract:

100x = 46.666

-10x =    4.666

99x = 42 so

x = 42/99

The LP problem min z = -2x1 - x² s.t. x - x² = 2, x + x² = 6, x , x2 =(non-negativity), the basic feasible solution in standard form is (x, x², s, s²) = (0, 0, 2, 6).

For the linear programming (LP) problem. The given problem is:
Minimize z = -2x - x²
Subject to:
x - x² <= 2
x + x² <= 6
x, x² >= 0 (non-negativity)
First, let's convert the problem into standard form by introducing slack variables to eliminate inequalities:
x- x² + s = 2
x + x² + s² = 6
x, x², s, s² >= 0
Now, let's construct a basic feasible solution at which (x1, x2) = (0, 0):
0 - 0 + s = 2 => s = 2
0 + 0 + s² = 6 => s² = 6
So, the basic feasible solution in standard form is (x, x², s, s²) = (0, 0, 2, 6).

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Answer: search it up

Step-by-step explanation:

Answer:

52x

Step-by-step explanation:

There are 52 weeks in one year

x times 52 = 52x

Answer:

c will be the answer mark me brainliest

To graph the polar equation and find the common interior of r = 6 - 4 sin(θ) and r = -6 + 4 sin(θ), we can use a graphing utility such as Desmos or Wolfram Alpha. These tools allow us to visualize polar equations and explore their graphs.

When we enter the given polar equations into a graphing utility, it will plot the curves corresponding to each equation on the same graph. We can then observe the region where the curves overlap, indicating the common interior of the two equations.

The polar equation r = 6 - 4 sin(θ) represents a cardioid, a heart-shaped curve centered at the pole (origin) with a radius that varies based on the angle θ. The term 6 represents the distance from the origin to the furthest point on the cardioid, while the term -4 sin(θ) determines the variation in radius as the angle changes.

Similarly, the polar equation r = -6 + 4 sin(θ) also represents a cardioid but with a radius that is the mirror image of the first equation. The negative sign in front of the term indicates that the cardioid is reflected across the x-axis.

Using a graphing utility, we can plot both equations and observe the graph to determine the common interior. The graphing utility will provide a visual representation of the region where the two cardioids intersect or overlap.

In the graph, we can see the heart-shaped curves corresponding to each equation. The cardioids intersect in two regions, forming a figure-eight shape. This figure-eight region represents the common interior of the two polar equations.

The common interior of the two cardioids is the region where the radius values from both equations are positive. In this case, the figure-eight region is entirely within the positive region of the coordinate plane, indicating that the common interior consists of points with positive radius values.

To summarize, by graphing the polar equations r = 6 - 4 sin(θ) and r = -6 + 4 sin(θ) using a graphing utility, we can observe their overlapping regions, which form a figure-eight shape. This figure-eight represents the common interior of the two equations and consists of points with positive radius values.

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Answer:

19/4 = 4 3 4

Step-by-step explanation:

Answer: 20%

Explanation:

1. Turn it into a fraction (224/280)

2. Divide the numerator (224) by the denominator (280). (224÷280=0.8)

3. Subtract 1 by 0.8 (or 100% by 80%) that should give you the answer 0.2 (20%)

Checking work:

280x0.2=56

280-56=224