Use your choice of equal values, substitution, or elimination to solve the
following System of Equations, and show your work.
i are running a concession stand at a basketball game. You are selling hot
dogs and sodas. Each hot dog costs $3.00 and each soda costs $2.00. At the
end of the night you made a total of $213.00. You sold a total of 87 hot dogs
and sodas combined. You must report the number of hot dogs sold and the
number of sodas sold. How many hot dogs were sold and how many sodas
were sold?

The possible values for |a| are limited to 0, 1, and infinity.

To see why, suppose that |a| is strictly greater than 1. Then by the spectral radius formula, we have that the spectral radius of a is also strictly greater than 1.

Let λ be an eigenvalue of a with maximum absolute value, and let v be a corresponding eigenvector. Then for any positive integer m, we have

|a^m v| = |a^m| |v| = |a|^m |v|,

where the second equality follows from the fact that a is diagonalizable (since it has real entries) and so a^m has the same eigenvectors as a (with eigenvalues raised to the mth power). Thus |a^m v| grows exponentially with m, contradicting the assumption that ak = a for some integer k > 1.

Similarly, if |a| is strictly less than 1, then the spectral radius of a is also strictly less than 1, and the same argument shows that the norm of a^m v decays exponentially with m, again contradicting the assumption that ak = a for some integer k > 1.

Therefore, the only possible values for |a| are 0, 1, and infinity. If |a| = 0, then a is the zero matrix and satisfies ak = a for any k

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The total amount can be obtained by the rule of three:

Then:

Therefore the total amount is $1800.

Answer:

f(x)=X^2+4

f(x)=42

42=X^2+4

X^2+4=42

X^2=42-4

X^2=38

X=sqrt(38)=6.16

\( \sqrt{?} \)

Answer:

Step-by-step explanation:

1. Relation - a set of ordered pairs

2. Vertical line test - a test used to determine if a graph is a function; states that a vertical line can only go through one point on the graph to be a function

3. Function - a relation in which for any given input value, there is only one output value

4. Output -  value generated by a function when an input value is substituted into the function and evaluated

5. Ordered pair - a group of two numbers written in the form (x, y) where the x value represents a horizontal position and the y value represents a vertical position

6. Mapping Diagram - a table or diagram that represents a mathematical relation

7. Input - a value that is substituted in for the variable in a function in order to generate an output value

Answer:

1. Relation - a set of ordered pairs

2. Vertical line test - a test used to determine if a graph is a function; states that a vertical line can only go through one point on the graph to be a function

3. Function - a relation in which for any given input value, there is only one output value

4. Output -  value generated by a function when an input value is substituted into the function and evaluated

5. Ordered pair - a group of two numbers written in the form (x, y) where the x value represents a horizontal position and the y value represents a vertical position

6. Mapping Diagram - a table or diagram that represents a mathematical relation

7. Input - a value that is substituted in for the variable in a function in order to generate an output value

Step-by-step explanation:

Answer:

V = 200.96 m^3

Step-by-step explanation:

V=1/3hπr²

h=12, r=4

V = 1/3 (12) (3.14) (4^2)

V = 1/3 (12) (3.14) (16)

V = 200.96 m^3

Answer:

602.88m³

Step-by-step explanation:

volume = base area x height

            = πr²x h

            = (3.14)(4)² x 12

            =602.88

Answer:

Step-by-step explanation:

( 2x - 8 )° = ( x + 28 )° ⇒ x = 36

m∠1 = m∠4 = 180° - ( 36 + 28 )° = 116 °

m∠2 = 123° - 64° = 59 °

m∠3 = 123 °

Answer:

acute isosceles

Step-by-step explanation:

both legs have an equal length, and angles are less than 90º

Answer:

1/4

Step-by-step explanation:

\( \frac{3}5 \div x = \frac{12}{5} \\ \\ \frac{3}{5 } \times \frac{1}{x} = \frac{12}{5} \\ \\ \frac{3}{5x} = \frac{12}{5} \\ \\ x = \frac{3 \times 5}{12 \times 5} \\ \\ x = \frac{1}{4} \)

Answer:

D \(\sqrt{3}\)

Step-by-step explanation:

tan60 is the same for all values when you plug it into a calculator you will get \(\sqrt{3}\)

Given a ray passing through a line at an angle of 29 degrees, the angle opposite to it (angle R) can be found by subtracting 29 degrees from 180 degrees. Therefore, the value of angle R is 151 degrees.

We are given that a ray passes through a line, making an angle of 29 degrees with the line. Let us represent this situation as follows

The angle R represents the angle opposite to the angle of 29 degrees. Since the ray and the line form a straight line, their angles add up to 180 degrees. Therefore, we can write

angle R + 29 degrees = 180 degrees

To solve for angle R, we can subtract 29 degrees from both sides of the equation

angle R = 180 degrees - 29 degrees

Simplifying the expression, we get

angle R = 151 degrees

Therefore, the value of angle R is 151 degrees.

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The probability that the 3 companies will be the 3 with the best future earnings is 5/100 .

There are a total of 20 possible combinations of 3 companies that Mr. Way can sell stocks from. However, we are only interested in the probability of him selecting the 3 companies with the best future earnings. Since we do not know the actual future earnings of each company, we can assume that all 6 companies have an equal chance of being in the top 3.

Therefore, the probability of Mr. Way selecting the 3 companies with the best future earnings is the same as the probability of selecting any specific set of 3 companies out of the 6.

The number of ways to select 3 companies out of 6 is given by the combination formula, which is:

6! / (3! x 3!) = 20

Therefore, the probability of Mr. Way selecting the 3 companies with the best future earnings is 1/20. So, the answer is:

Probability = 1/20

This can also be written as a fraction, which is probability = 0.05 or 5/100

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Answer:

16=x

Step-by-step explanation:

the two sides are equal, soo i set them equal to each other and add 18 to 16 then divide each side by two and get 16 = x

Answer:

74º

Step-by-step explanation:

The recent fervor surrounding personal privacy has a significant impact on direct marketing and promotions, particularly in the context of email advertising and collecting information at events.

As you design a campaign, it is essential to consider and address these privacy concerns to build trust and ensure compliance with relevant regulations. Here are some key considerations:

Consent and Permission: Obtain explicit consent from individuals before sending them marketing emails or collecting their personal information at events.

Implement clear opt-in mechanisms and provide transparency regarding the purpose and use of their data.

Privacy Policies: Clearly communicate your privacy policies, outlining how you collect, store, and use personal information.

Make it easily accessible to individuals and ensure compliance with applicable data protection laws, such as the General Data Protection Regulation (GDPR) or the California Consumer Privacy Act (CCPA).

Data Security: Implement robust data security measures to protect the personal information you collect. This includes encryption, secure storage, and regular data audits to mitigate the risk of data breaches.

Data Minimization: Only collect the necessary information required for your marketing campaign. Minimize the data you collect to reduce privacy risks and ensure compliance with the principle of data minimization.

Opt-out Options: Provide individuals with clear and simple mechanisms to opt out of receiving marketing emails or having their data collected. Respect their preferences and promptly honor any opt-out requests.

Third-Party Data: Be cautious when using third-party data sources for your marketing campaigns. Ensure that the data providers have obtained proper consent and comply with privacy regulations.

Personalization and Relevance: Focus on delivering personalized and relevant content to individuals based on their preferences and interests. This can help build trust and engagement while respecting privacy boundaries.

By considering these factors and addressing personal privacy concerns, you can develop a campaign that respects individuals' privacy rights, builds trust, and maintains compliance with privacy regulations.

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For 63 pounds of the bag, Eileen will have to pay $10.71.

Given is that the fee to check luggage with a new airline is based on the weight of each bag. Brett paid $7.14 to check a 42 pound.

Brett paid $7.14 to check a 42 pound.

Then, for 1 pound, Brett will have to pay $(7.14/42) or $0.17.

So, for 63 pounds of the bag, Eileen will have to pay -

63 x 0.17

10.71

Therefore, for 63 pounds of the bag, Eileen will have to pay $10.71.

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In a given case where two suppliers, A and B where 8 out of 200 chips from supplier A and 13 out of 250 chips from supplier B is defective, there is not enough evidence to show that the two suppliers are different.

Considering sample from supplier A, the proportion of defective chip, p^a = 8/ 200 = 0.04

And the sample size, n = 200

Considering sample from supplier B, the proportion of defective chip, p^b = 13/250 = 0.052

And sample size, m = 250

To know whether the two suppliers are different we calculate a two-sided confidence interval for pA − pB. There is no proof that the two population proportions differ if the confidence interval comprises 0, which indicates that pA = pB.

Let us consider a confidence interval of 95%, α = 0.05. Null hypothesis, H0 : pA = pB and alternate hypothesis H1 : pA ≠ pB.

p^a − p^b = 0.04 - 0.052 = -0.012

A pooled estimate of the common success probability, p^

p^ = (8 + 13)/ (200 + 250)

= 21/ 450

= 7/ 150

≈ 0.047

Thus, the z-statistic can be obtained by

z = (p^a − p^b)/ (p^ × (1 - p^) × (1/ n + 1/m))⁽⁰.⁵⁾

= -0.012/ √(0.047 × (1 - 0.047) × (1/200 - 1/250))

= -0.600

Also, zα/2 = 1.960

The two-sided confidence interval for pA − pB is

8/ 200 − 13/ 250 ± 1.960 ×√(8×(200−8)/ 200³ + 13×(250−13)/ 250³

= (−0.051, 0.027)

p-value = 2Ф(-z) = 2× Ф(-0.600) = 0.549

Therefore there is not enough evidence that the two suppliers are different.

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\(\huge \boxed{\sf x < -3} \\\\\\ \displaystyle \sf 15 < -5x \\\\ Divide\ each\ side\ by\ -5\ and\ switch\ the\ symbol. \\\\ \frac{15}{-5} > \frac{-5x}{-5} \\\\-3 > x\)

1second because 70 beats =1 second

Answer:

2x^2-3

Step-by-step explanation:

factor out 7x from the numerator to get

7x (2x^2-3)/7x

reduce the fractions by canceling out the 7x

2x^2-3

Answer:

The answer is -16n-41

Step-by-step explanation:

Simplify the expression.

1 / 10 = 3 / 30

2 / 3 = 20 / 30

Elk lives 17 / 30 miles closer

Answer:

  7360 ft·lb

Step-by-step explanation:

You want the work done by a 320-lb gorilla climbing to a height of 23 feet.

Work is the product of force and distance:

  W = (weight)·(height) = (320 lb)(23 ft) = 7360 ft·lb

The gorilla does 7360 ft·lb of work.

__

Additional comment

Time comes into play when you want the power involved. If the climbing is done in 10 seconds, the power required is about 1.34 horsepower. (1 hp = 550 ft·lb/s)

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The following are the solutions to the problems that the central hospital in Suva, Fiji wants for good record management: Staffing (Skill matrix and Activity matrix)

The hospital requires 30 constant rooms and doctors (including the head doctor) and other staff. Each doctor can take up to 40 patients per day, and the hospital also needs to take into account the occurrence of emergencies that would allow for more or fewer patients. With this in mind, the hospital should establish a staffing schedule that takes into account each staff member's skill set and the tasks that need to be performed. They should use both the skill matrix and activity matrix to ensure that each member is assigned a role that aligns with their skills.

Basic Layout (Architecture) - The hospital's basic layout, or architecture, should be designed in such a way that it allows for easy patient flow and provides a comfortable environment for both patients and staff. This includes having sufficient space in each department, strategically locating each department, and incorporating elements such as natural lighting to promote healing. In addition, they should ensure that the layout is designed with technology in mind, allowing for seamless integration of the new system.

Project Schedule - To ensure that the system is delivered on time, the hospital should create a project schedule that outlines all the activities required to develop, implement, and test the new system. They should also allocate sufficient resources to each activity, determine the critical path, and establish milestones to track progress. Regular project status meetings should be held to ensure that the project is on track and that any deviations are addressed in a timely manner.

Final Recommendation - The hospital's management should consider the following recommendations to ensure that the new system meets the stakeholders' requirements: Ensure that the system is designed to capture the patient's details, health conditions, allergies, medications, vaccinations, surgeries, hospitalizations, social history, family history, contraindications and more. Establish a module for appointment scheduling with email/SMS/push notifications to patients and providers. This should include each doctor's calendar defining their services and timings, non-working days, as well as the ability to view appointments to confirm, reschedule and cancel patient appointment bookings. Additionally, automated appointment reminders should be sent to ensure patients do not miss their appointments. Design a platform/page for updating the patient's record and information after seeing them. This will allow doctors to update a patient's record after seeing them, making it easier to track the patient's progress.

In conclusion, developing a new system for the central hospital in Suva, Fiji requires careful planning and execution to ensure that all stakeholders' needs are met. The hospital should consider the staffing, basic layout, project schedule, and final recommendations outlined above to develop a system that meets the hospital's needs and is easy to use for all stakeholders involved.

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The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

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Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

Step-by-step explanation:

(6-√2)(6+√2)=36-6√2+6√2-2

=36-2

=34

Answer:

£312

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{y varies inversely with x}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=8\\ y=6 \end{cases} \\\\\\ 6=\cfrac{k}{8}\implies 48=k\hspace{10em}\boxed{y=\cfrac{48}{x}}\)