Hypothesis testing question.

From a sample of 30 patients, Divoc Health Group found that the mean days for a patient to discharge is 25 days. The hospitalization duration was assumed to follow a normal distribution. Last year, the mean days for a patient to discharge was 20 days with a standard deviation of 5 days. Divoc Health Group suspects that the mean days for a patient to discharge has increased because of Covid-19 cases and other health-related issues. Divoc Health Group decides to carry out a hypothesis test.

a) State the null and alternative hypotheses.

b) At a 5% significance level, is there sufficient evidence to conclude that the mean days for a patient to discharge has increased? Show all steps clearly. [Express your answers up to 3 decimal places]

Based on the information, Divoc Health Group now samples an additional 10 clients. The mean days for a patient to discharge were 22 days.

c) Using the new information, construct a 95% confidence interval for the mean days for a patient to discharge. [Express your answers up to 3 decimal places]

d) What is the minimum sample size required if Divoc Health Group wants to estimate the mean days for a patient to discharge to within 2 days of error with a 99% confidence?

Answer:

Vertex= (-5, 2)

Step-by-step explanation:

The vertex shifts 5 to the right (x-axis), and 2 up (y-axis) from the point of origin. Then plug in the x values to find other y values.

Answer:

i dont know if this helps, im not sure if you are telling me to do all of these things or B, c, d are answer

Step-by-step explanation:

To find the total amount of money that the photography club will raise to meet their goal, we can multiply the average amount of money each member must raise by the number of members in the club:

Average amount of money each member must raise = m

Number of members in the club = 20

Total amount of money to be raised = Average amount of money each member must raise x Number of members in the club

Total amount of money to be raised = m x 20

We know that the club is trying to raise at least $1,400, and they have already raised $540. Therefore, the amount of money they still need to raise is:

Amount of money still needed to reach goal = $1,400 - $540

Amount of money still needed to reach goal = $860

We can set up an equation to represent the total amount of money the club will raise to meet their goal:

Total amount of money to be raised = Amount of money still needed to reach goal

m x 20 = $860

We can solve for "m" by dividing both sides of the equation by 20:

m = $860 / 20

m = $43

Therefore, the total amount of money the club will raise to meet their goal is:

Total amount of money to be raised = Average amount of money each member must raise x Number of members in the club

Total amount of money to be raised = $43 x 20

Total amount of money to be raised = $860

B))) We can set up an equation to represent the total amount of money the club will raise to meet their goal:

Total amount of money to be raised = Amount of money already raised + Amount of money still needed to reach goal

We know that the club has already raised $540 and they need to raise $860 more to reach their goal of $1,400. Therefore, we can substitute these values in the equation:

Total amount of money to be raised = $540 + $860

Total amount of money to be raised = $1,400

So the equation that represents the club raising all the money is:

$1,400 = $540 + $860

C)))) To solve the equation:

$1,400 = $540 + $860

We can simplify the right-hand side of the equation by adding $540 and $860:

$1,400 = $1,400

This equation is true, which means that it is a consistent equation. The solution to this equation is that the club will be able to raise all the money they need to buy the new photography equipment.

In the context of the scenario, the solution means that the club will be able to meet their goal of raising at least $1,400 for new photography equipment. They have already raised $540, and they need to raise $860 more to reach their goal. The equation shows that the total amount of money they will raise is exactly $1,400, which is the amount they need to meet their goal.

D))))) To represent the amount of money each member must raise, on average, to meet or exceed their goal, we can use the following inequality:

Average amount of money each member must raise ≥ Total amount of money still needed to reach goal / Number of members in the club

We know that the total amount of money still needed to reach the goal is $860, and there are 20 members in the club. Therefore, we can substitute these values in the inequality:

Average amount of money each member must raise ≥ $860 / 20

To simplify the right-hand side of the inequality, we can divide $860 by 20:

Average amount of money each member must raise ≥ $43

This inequality shows that each member must raise at least $43, on average, to meet or exceed their goal of raising $1,400.

To show the possible average amount of money each club member needs to raise, we can use the following inequality:

0 < Average amount of money each member must raise ≤ Total amount of money still needed to reach goal / Number of members in the club

This inequality shows that the average amount of money each member must raise is greater than 0 (since each member must contribute something), but it is less than or equal to $43 (which is the minimum amount each member must raise to meet or exceed their goal).

Answer:

5 (100y -601.39)

3028

Step-by-step explanation:

Answer: A

Step-by-step explanation:

We can use the logarithmic identity logb(a^n) = n*logb(a) to solve this problem.

First, we need to express 4 as a power of 2. We know that 2^2 = 4, so we can write:

log4 = log2^2

Then we can use the identity to rewrite this as:

log4 = 2*log2

Now we can use the given approximation log2 ≈ 0.4307 to approximate log4:

log4 ≈ 2 * 0.4307

log4 ≈ 0.8614

Therefore, the answer is (A) 0.8614.

Josh is incorrect because 100 is perfect square not a perfect cube.

We have the number 100.

Now, factorising the number 100 as

100 = 2 x 2 x 5 x 5

100= (2 x 5)  x ( 2x 5)

100 = 10 x 10

As, 100 can be factorised as 10 x 10 which shows 100 is prefect square of 10.

But 100 is not a perfect cube because for the cube we need pair of three number.

Thus, Josh is incorrect.

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The equation that represents the consecutive odd numbers whose product is 63 is; (x + 9) (x + 7) = 0

Odd numbers have special properties and relationships to other numbers, which make them important in mathematics. For instance, the sum of two odd numbers and the difference between two odd numbers both always equal one.

We can see that we can solve the double brackets by equation them to zero so we have that;

(x + 9) (x + 7) = 0

x = -9

x = -7

Thus;

(-9) (-7) = 63

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Answer:

B’ = (-11, 1)

Step-by-step explanation:

Because the triangle is reflected across the line x = -2, it is being reflected across a vertical line.

Therefore only the x-coordinate will change.

As B is 9 units right of the line x = 2, the coordinates of B’ will be (-2 - 9, 1)

Which will be (-11, 1)

The circumference of the small pizza is approximately 47.1 cm, the circumference of the medium pizza is approximately 69.1 cm, and the circumference of the large pizza is approximately 94.2 cm.

The diameter is the distance across the widest part of a circle. To find the circumference of a circle, we use the formula C = πd, where C is the circumference, π is a mathematical constant (approximated as 3.14), and d is the diameter of the circle. Therefore, to find the circumference of each pizza size, we can simply plug in the given diameter into this formula.

For the small pizza with a diameter of 15 cm, the circumference can be calculated as follows:

C = πd

C = 3.14 x 15

C ≈ 47.1 cm

For the medium pizza with a diameter of 22 cm, the circumference can be calculated as follows:

C = πd

C = 3.14 x 22

C ≈ 69.1 cm

For the large pizza with a diameter of 30 cm, the circumference can be calculated as follows:

C = πd

C = 3.14 x 30

C ≈ 94.2 cm

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The sorted edges algorithm was applied to the pentagon prism graph ABCDEA with edge weights given. The final path is starting and ending at vertex A is  A-B-C-D-A-E.

The sorted edges algorithm starts by sorting the edges in ascending order of their weights. Then, starting from vertex A, the algorithm chooses the next smallest edge that connects to an unvisited vertex until all vertices have been visited.

Sort edges in ascending order

AD = 4, EA = 6, BC = 2, BD = 9, AB = 7, CE = 11, DE = 8, CA = 14, BE = 15, CD = 13

Starting at vertex A, select the next smallest edge that connects to an unvisited vertex AB = 7. Move to vertex B and select the next smallest edge that connects to an unvisited vertex BC = 2. Move to vertex C and select the next smallest edge that connects to an unvisited vertex CD = 13

Move to vertex D and select the next smallest edge that connects to an unvisited vertex AD = 4. Move to vertex A and select the next smallest edge that connects to an unvisited vertex EA = 6. Move to vertex E and all vertices have been visited. The final path is A-B-C-D-A-E.

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Answer:

2π(10^2) + 2π(10)(16)

= 2π(100) + 2π(160)

= 200π + 320π

= 520π ft^2

The solution to the exponential equation is given as follows:

x = 0.8.

The exponential equation in the context of this problem is defined as follows:

[tex]\left(\frac{1}{64}\right)^{0.5x - 3} = 8^{9x - 2}[/tex]

64 is the sixth power of two, while 8 is the third power of two, hence:

Applying the power of power rule, the equation can be given as follows:

[tex]2^{-6(0.5x - 3)} = 2^{3(9x - 2)}[/tex]

[tex]2^{-3x + 18} = 2^{27x - 6}[/tex]

Exponential functions are one-to-one, meaning that the solution is obtained as follows:

-3x + 18 = 27x - 6

30x = 24

x = 0.8.

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5. The answer is option D (12.53, 61.39°)

6. Option D. ((7√2)/2, (-7√2)/2)

7. Option C. (104.40, -16.70°)

Question 5:

Apply the Pythagorean theorem to find the distance r from the fire station to the destination:

r = √(62 + 11²) = 12.53 (rounded to the nearest hundredth)

The angle θ between the positive x-axis and the line connecting the fire station to the destination is found using tangent:

tan(θ) = ¹¹/₆

θ = arctan(¹¹/₆) = 61.39° (rounded to the nearest hundredth)

Therefore, the answer is (12.53, 61.39°), which is option D.

Answer: D. (12.53, 61.39°)

Question 6:

Convert from polar coordinates to rectangular coordinates using the following formulas:

x = r cos(θ)

y = r sin(θ)

Plugging in the values, we get:

x = -7 cos(3π/4) = -7√(2)/2) = 3.5√(2)

y = -7 sin(3π/4) = -7√(2)/2) = -3.5√(2)

Therefore, the rectangular coordinates of the point are (3.5sqrt(2), -3.5sqrt(2)), which can also be written as (-4.95, -4.95) (rounded to the nearest hundredth).

Answer: (7√(2)/2), -7√(2)/2))

Question 7:

Use the Pythagorean theorem to find the distance r from the starting point to the current position:

r = √(100² + 30²) = 104.40 (rounded to the nearest hundredth)

The angle θ between the positive x-axis and the line connecting the starting point to the current position can be found using tangent:

tan(θ) = 30/100

θ = arctan(30/100) = 16.70° (rounded to the nearest hundredth)

However, since the woman is south of the starting point, the angle should be in the negative direction, so we have:

θ = -16.70°

Therefore, the answer is (104.40, -16.70°), which is option C.

Answer: C. (104.40, -16.70°)

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The discontinuity at x = -2 is a removable discontinuity or a hole in the graph of the function.

To identify the discontinuities in the function f(x), we first need to find the values of x that make the denominator zero, since division by zero is undefined.

The denominator of f(x) is x² + x - 2, which can be factored as (x - 1)(x + 2). Therefore, the function f(x) is undefined at x = 1 and x = -2, since they would make the denominator zero.

Now we need to determine the type of discontinuity at these points.

At x = 1, the function f(x) approaches infinity as x approaches 1 from both sides of the graph.

At x = -2, the function f(x) has a hole in the graph.

This means that the function is undefined at x = -2, but if we "plug in" x = -2, we can factor the numerator and cancel out the common factor with the denominator, resulting in a new function that is continuous at x = -2. The new function is:

f(x) = (x⁴ - 5x² + 4) / (x² + x - 2)

= [(x² - 1)(x² - 4)] / [(x - 1)(x + 2)]

= (x - 1)(x + 1)(x - 2), for x ≠ -2

Therefore, the discontinuity at x = -2 is a removable discontinuity or a hole in the graph.

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7:

To find 6% of 45.50=

0.06x45.50= 2.73

and than 17% of 45.50

0.17x45.50= 7.735

so add 2.73 and 7.735= 10.465

than add 10.465 to $45.50 = $55.965 So the answer is $55.965.

8:

again the same thing but with the different numbers.

0.06x105.75= 6.345

0.20x105.75= 21.15

21.15+6.345= 27.495

so than 105.75-27.495= $78.255

9:

same thing again

146.75x0.25= 36.6875

0.09x146.75= 13.2075

But this time add the tax (13.2075)= 146.75+13.2075= 159.9575

but than you subtract the discount which is 25% so 159.9575-36.6875=123.7

So that is the price! $123.7

I hope that helps!

Answer:
A and B

Step-by-step explanation:

-10/3= -3.33333333333

(- (-10))/(-3)= -10/3, (negative sign being erased)

=-3.33333333333

hope it helped:)

Area = 4b² + 16b + 16 square centimeters

The side length of the larger square, L, is equal to the side length of the smaller square plus twice the width of the border:

L = 4 + 2b

Now, we want to find the total area of the decorative tile, which is the area of the larger square. The area of a square is given by the side length squared:

Area = L²

Substitute the expression for L from above:

Area = (4 + 2b)²

Now, we can expand this expression:

Area = (4 + 2b)(4 + 2b)

Area = 16 + 8b + 8b + 4b²

Area = 16 + 16b + 4b²

So, the total area of the decorative tile in terms of b is:

Area = 4b² + 16b + 16 square centimeters

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The value of correct Set-builder form is,

⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }

We have to given that;

The set is,

⇒ {4, 5, 6, 7, 8}

Thus, We can write correct Set-builder form as,

⇒ {4, 5, 6, 7, 8}

⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }

So, The value of correct Set-builder form is,

⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }

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The amount of the down payment and the mortgage amount are $61440 and $194560

From the question, we have the following parameters that can be used in our computation:

Buy a $256,000 home with a down payment of 24%

This means that

down payment = 24% * 256,000

So, we have

down payment = 61440

Next, we have

mortgage amount = (1 - 24%) * 256,000

So, we have

mortgage amount = 194560

Hence, the mortgage amount is 194560

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Answer:

1.Ongoing efforts have been undertaken in Malaysia to improve the financial reporting and accountability in government agencies. Discuss the efforts.

Malaysia has been making efforts to improve financial reporting and accountability in government agencies for several years. In 2015, the Malaysian government introduced a new financial reporting framework for government agencies called the Malaysian Public Sector Accounting Standards (MPSAS). This framework is designed to improve financial reporting and ensure that government agencies are held accountable for their financial performance.

The MPSAS framework is based on international accounting standards and is meant to increase transparency and consistency in financial reporting. It includes guidelines for budgeting, financial management, and reporting of financial performance. Additionally, the Malaysian government has established the Accountant General's Department, which is responsible for overseeing financial reporting in government agencies.

Other initiatives aimed at improving financial reporting and accountability in Malaysia include the implementation of electronic financial management systems, the introduction of new financial management guidelines, and the establishment of a Financial Management Committee to oversee financial management across all government agencies.

2.Discuss the extent of application for the key accounting concepts in the public sector.

The key accounting concepts that are applicable to the public sector are similar to those used in the private sector, with some important differences. One of the key differences is that in the public sector, accounting practices are focused on ensuring accountability to the public and ensuring that public funds are used responsibly.

Some of the key accounting concepts that are applicable in the public sector include accrual accounting, budgeting, and financial reporting. Accrual accounting is used to record financial transactions as they occur, regardless of when payment is made or received. This helps to ensure that all financial transactions are recorded accurately and transparently.

Budgeting is also an important accounting concept in the public sector. Governments typically create budgets to allocate funds to various programs and projects. These budgets are then used to monitor financial performance and ensure that resources are used efficiently.

Financial reporting is another key accounting concept in the public sector. Governments are required to report on their financial performance to ensure transparency and accountability. This includes reporting on revenue and expenses, assets and liabilities, and cash flow.

3.Clearly describe the regulatory framework and procedures for financial reporting in the public sector.

The regulatory framework for financial reporting in the public sector typically involves a combination of national and international accounting standards. In Malaysia, the regulatory framework is based on the Malaysian Public Sector Accounting Standards (MPSAS), which are based on international accounting standards.

Under this framework, government agencies are required to prepare financial statements in accordance with MPSAS. These statements include the statement of financial position, statement of financial performance, statement of changes in equity, and statement of cash flows.

Additionally, the Accountant General's Department is responsible for overseeing financial reporting in government agencies. They are responsible for ensuring compliance with MPSAS and for providing guidance on financial reporting issues.

Government agencies in Malaysia are required to submit their financial statements to the Accountant General's Department for review and approval. Once approved, these statements are published and made available to the public.

Overall, the regulatory framework and procedures for financial reporting in the public sector are designed to ensure transparency and accountability in the use of public funds.

The likelihood that the first question will be true is equally likely and unlikely.

From the question, we have the following parameters that can be used in our computation:

The teacher gave a true and false quiz where P(true) = 0.5 for each question.

This means that

P(true) = 0.5

As a percentage,, we have

P(true) = 50%

When the probability of an event is 50%, then the event is equally likely and unlikely.

Hence, the liikelihood is (c) qually likely and unlikely.

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Answer:

0.00007003 is the standard form of 7.003x10^-5. In scientific notation, the number is expressed as 7.003 multiplied by 10 raised to the power of negative five. To convert it to standard form, the decimal point has to move to the left by five places since the exponent is negative. The resulting number is a decimal with four zeros before the first nonzero digit. Standard form is a way of representing numbers that does not use exponents and is useful in comparing and performing operations on numbers.

P(both poodle) = (3/10)(3/10) = 9/100

Answer: The probability of choosing the same puppy is 9/100

The probability that a red shirt and black slacks are on the floor is 1/10.

Probability is the odds that a random event would happen. The odds that the event would happen has a probability value that lies between 0 and 1.

Probability that a red shirt and black slacks are on the floor = (number of red shirts / total number of shirts) x (number of black slacks / total number of slacks)

Total number of shirts = 2 + 2 + 1 = 5

Total number of slacks = 1 + 1 = 2

(1/5) x (1/2) = 1 /1 0

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695 divided by 70=9.92 hours

The midpoint of the line segment FG is the point (4, 12).

In geometry, the midpoint of a line segment is the point that is exactly halfway between the endpoints of the segment. It is the point that divides the segment into two congruent segments.

The formula for finding the midpoint of a line segment with end points (x₁, y₁) and (x₂, y₂) is:

Midpoint = [(x₁ + x₂)÷2, (y₁ + y₂)÷2]

So, the midpoint of the line segment with endpoints F(-10, 12) and G(18, 12) can be found as:

Midpoint = [(-10 + 18)÷2, (12 + 12)÷2]

= [8÷2, 24÷2]

= [4, 12]

Therefore, the midpoint of the line segment FG is the point (4, 12).

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The percentage rate of change per minute is approximately 0.98%

The mass of the sample decreases by 59% every hour, so we can write the following differential equation:

dm/dt = -0.59m

Rate of change of the mass (dm/dt) is equal to the mass (m) multiplied by the constant -0.59.

We can solve this differential equation using separation of variables:

dm/m = -0.59 dt

Integrating both sides, we get:

ln|m| = -0.59t + C

where C is the constant of integration.

To find C, we can use the initial condition that the mass of the sample is 530 grams at t=0:

ln|530| = C

C = ln(530)

So the solution to the differential equation is:

ln|m| = -0.59t + ln(530)

[tex]m(t) = 530 e^(^-^0^.^5^9^t^)[/tex]

This function represents the mass of the sample after t hours, where the rate of change per minute is given by the constant

k = -0.59/60 = -0.00983 (rounded to 5 decimal places).

To find the percentage rate of change per minute, we can multiply k by 100 to convert it to a percentage:

-0.00983 × 100 = -0.983%

Therefore, the percentage rate of change per minute is approximately 0.98%

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mean = 11+20+38+5+4/5 = 78/5 = 15.6

The coordinates for the centroid of the triangle is (0, 2.67)

The centroid of a triangle is the place where the three medians of the triangle meet or intersect.

To find the centroid of the triangle, we use the formula

(x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3

We add all the x coordinates together and divide by 3, we also do the same for the y coordinates.

It becomes x = (-4 + 0 + 4)/3  

y = (8 + 2 + (-2))/3

Therefore, the centroid is (0, 2.67)

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