Divide
266 divided by 15
Hint: The remainder is not a decimal it is the number that is leftover and can no longer be divided

For a sample of hospitals related to shorten the average length of stay (LOS) of their patients,

A) The 90% confidence interval to estimate the population mean LOS are 3.3362 and 4.2638.

B) The Interpreted interval in terms of this application is equals to (3.3362,4.2638).

C) The meaning of phrase "90% confidence interval" is number that fall within the upper as well as lower boundaries of distribution.

We have a health insurers and federal government ordered to hospitals regarding to short or decrease the average length of stay of their patients.

population Mean of LOS = 4.5 days

Sample size of hospitals, n = 20

Sample mean, \( \bar x\) = 3.8days

Standard deviations, \( \sigma\)

= 1.2 days

A) The population estimate mean LOS for the state's hospitals at 90% confidence interval,

The degrees of freedom, df = 20 -1

= 19

90% confidence interval then the confidence interval is 0.90. So, 1 −∝

= 0.90

=> ∝ = 0.1

=> ∝/2= 0.05

The critical t value for confidence 0.05 and degree of freedom 19 is equals 1.72.

Using the confidence interval formula,

\( \bar x ± t_{(0.05, 19)} \frac{\sigma}{\sqrt{n}}\)

\( 3.8 ± 1.729\frac{1.2}{\sqrt{20}}\)

= (3.3362,4.2638)

So, required values are 3.3362 and 4.2638.

(b) In terms of this application, the interval, 90 percent confident that the populations mean length of remain (LOS) for the state’s hospitals(μ) lies among 3.3362 and 4.2638.

c) The term 90% confidence interval expresses a number that will fall within the upper as well as lower boundaries of a probability distribution.

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Given:

8.90ft³ for 30 balloons

Let h be the volume of helium and b be the number of balloons.

Using proportion;

b/h = 30 /8.90

Multiply both-side by h

Hence, the answer to blank 1 is the above.

when b=50, substitute for b in the above and solve for the volume (h).

That is;

Multiply both-side by 8.90/30

Hence, the answer to blank 2 is 14.83ft³.

Step-by-step explanation:

The area of the target outside the bull's eye is  226.1 in²

To do so, we need to find the total area of the target and subtract the area of the bull's eye.

Remember that the area of a circle of radius R is:

A = 3.14*R²

Then the total area is:

A = 3.14*(9in)²

And the area of the bull's eye is:

A' = 3.14*(3in)²

The difference will give:

area = 3.14*(9in)² -  3.14*(3in)² = 226.1 in²

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The derivative of f(x) = cos(x² - x) is \(3(2x - 1)cos(x^{2} - x)sin(x^{2} - x).\)

To find the derivative of the function f(x) = cos(x² - x), we can use the chain rule.

The chain rule states that if we have a composite function, such as cos(g(x)), the derivative of this composite function is given by the derivative of the outer function multiplied by the derivative of the inner function.

In this case, the outer function is cos(u), where u = x² - x, and the inner function is u = x² - x.

The derivative of the outer function cos(u) is -sin(u).

To find the derivative of the inner function u = x² - x, we apply the power rule and the constant rule. The power rule states that the derivative of x^n, where n is a constant, is nx^(n-1), and the constant rule states that the derivative of a constant times a function is equal to the constant times the derivative of the function.

Applying the power rule and the constant rule, we find that the derivative of u = x² - x is du/dx = 2x - 1.

Now, using the chain rule, the derivative of f(x) = cos(x² - x) is given by:

df/dx = \(-sin(x^{2} - x) * (2x - 1)\)

Simplifying, we have:

df/dx = -\(2xsin(xx^{2} - x) + sin(x^{2} - x)\)

Therefore, the correct answer is option a. 3(2x-1)cos(x²-x)sin(x²-x).

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Answer:

Step-by-step explanation:

1. Solution for 3(6a)a=3 equation:

Simplifying

3(6a) * a = 3

Remove parenthesis around (6a)

3 * 6a * a = 3

Multiply 3 * 6

18a * a = 3

Multiply a * a

18a2 = 3

Solving

18a2 = 3

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Divide each side by '18'.

a2 = 0.1666666667

Simplifying

a2 = 0.1666666667

Take the square root of each side:

a = {-0.408248291, 0.408248291}

2.Solution for 5d(4)d=-2 equation:

Simplifying

5d(4) * d = -2

Reorder the terms for easier multiplication:

5 * 4d * d = -2

Multiply 5 * 4

20d * d = -2

Multiply d * d

20d2 = -2

Solving

20d2 = -2

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Divide each side by '20'.

d2 = -0.1

Simplifying

d2 = -0.1

Reorder the terms:

0.1 + d2 = -0.1 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0

0.1 + d2 = 0.0

So after one hour, the amount of chlorine in the tank has decreased from 20 g to 8.6 g using differential equation.

Let's start by finding the initial amount of chlorine in the tank:

The tank has a capacity of 400 liters and a concentration of 0.05 g of chlorine per liter, so the initial amount of chlorine in the tank is:

400 liters * 0.05 g of chlorine per liter = 20 g of chlorine

Next, we can set up a differential equation to describe how the amount of chlorine in the tank changes over time. We know that the concentration of chlorine in the tank is being diluted by the addition of fresh water at a rate of 4 liters per second, and being removed from the tank at a rate of 10 liters per second. Let C(t) be the amount of chlorine in the tank at time t, in grams. Then we have:

dC/dt = (0.05 g/L * 4 L/s) - (C(t)/400 L * 10 L/s)

The first term on the right-hand side represents the rate at which chlorine is being added to the tank, and the second term represents the rate at which chlorine is being removed from the tank. The factor C(t)/400 L represents the concentration of chlorine in the tank at time t.

We can simplify this equation by multiplying through by 400 L and rearranging:

dC/dt = 2 - (5/2) * C(t)

This is a first-order linear ordinary differential equation. We can solve it using separation of variables:

dC/(2 - (5/2) * C) = dt

Integrating both sides:

(-2/5) * ln|2 - (5/2) * C| = t + constant

Solving for C:

\(C(t) = (2/5) * (2 - e^{(-5t/2)})\)

Now we have a formula for the amount of chlorine in the tank as a function of time. To find the amount of chlorine in the tank at a particular time, we can substitute that time into the formula for C(t). For example, to find the amount of chlorine in the tank after 1 hour (3600 seconds), we can calculate:

\(C(3600) = (2/5) * (2 - e^{(-5/2 * 3600)})\)

\(= (2/5) * (2 - e^{(-9000)})\)

≈ 8.6 g

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The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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The equation to determine the number of hours it will take to fill the pool, given the current level of the pool, the rate at which the pool is being filled, and the pool's capacity can be found using the following steps.

To write an equation that can be used to find the number of hours it will take to fill the pool from its current level, we need to use the following information:

The pool's capacity: 43,000 gallons

The current level of the pool: 20,000 gallons

The rate of filling the pool: 130 gallons per minute

We can start by using the formula:

time = (amount needed to fill)/(rate of filling)

The amount needed to fill the pool is the difference between the pool's capacity and the current level of the pool.

amount needed to fill = 43,000 - 20,000 = 23,000 gallons

Now we can substitute this value in the formula above:

time = (23,000 gallons)/(130 gallons/minute)

To convert the time to hours, we divide the time in minutes by 60

time = (23,000 gallons)/(130 gallons/minute) × (1 hour/60 minutes)

So, the equation that can be used to find h, the number of hours it will take to fill the pool from its current level is:

h = (23,000 gallons) / (130 gallons/minute) × (1 hour/60 minutes)

Note that this equation is not simplified, you can simplify it by canceling out common factors, you'll get:

h = (23000 / 130) × (1/60)

This equation can be used to find the number of hours it will take to fill the pool, given the current level of the pool, the rate at which the pool is being filled, and the pool's capacity.

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The travelers need to remove 1/10 kilograms (or 0.1 kilograms) of baggage in order to board the airplane.

To determine how many kilograms of baggage the travelers need to remove in order to board the airplane, we need to calculate the total weight of their baggage and then subtract it from the weight limit.

The weight of the first passenger's baggage is 1 and 2/7 kilograms. We can represent this as a fraction: 1 + 2/7 = 9/7 + 2/7 = 11/7 kilograms.

The weight of the second passenger's baggage is 2 and 1/2 kilograms. We can represent this as a fraction: 2 + 1/2 = 4/2 + 1/2 = 5/2 kilograms.

Now, let's find the total weight of their baggage:

Total weight = (11/7) + (5/2)

To add these fractions, we need to find a common denominator:

Common denominator = 7 * 2 = 14

Now, we can rewrite the fractions with the common denominator:

Total weight = (11/7)*(2/2) + (5/2)*(7/7)

           = 22/14 + 35/14

           = 57/14 kilograms

The weight limit for each group of travelers is 4 and 1/6 kilograms. We can represent this as a fraction: 4 + 1/6 = 24/6 + 1/6 = 25/6 kilograms.

To determine how many kilograms of baggage they need to remove, we subtract the total weight of their baggage from the weight limit:

Weight to remove = (25/6) - (57/14)

To subtract these fractions, we need to find a common denominator:

Common denominator = 6 * 14 = 84

Now, we can rewrite the fractions with the common denominator:

Weight to remove = (25/6)*(14/14) - (57/14)*(6/6)

               = 350/84 - 342/84

               = (350 - 342)/84

               = 8/84 kilograms

Simplifying the fraction, we have:

Weight to remove = 1/10 kilograms

Therefore, to board the airplane, the travelers must reduce their baggage by 1/10 kilograms (equivalent to 0.1 kilograms).

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Jon understands the correct way to add expressions with the same base, while Don's approach is incorrect. The correct method is to keep the base the same and add the exponents. However, it is unclear from the given information whether Jon or Don knows how to multiply expressions with the same base.

    Jon's explanation is correct. When adding expressions with the same base, such as 3^4 + 3^5, we keep the base (in this case, 3) the same and add the exponents (4 + 5), resulting in 3^9. Therefore, Jon's approach is accurate.

On the other hand, Don's explanation is incorrect. He suggests adding the bases (3 + 3) and the exponents (4 + 5) together, resulting in 6^9. This is an incorrect method of simplification for expressions with the same base. Don's understanding of how to simplify expressions with exponents needs clarification.

The given information does not provide details about how Jon and Don approach multiplying expressions with the same base. Therefore, it is uncertain whether they know the correct method for multiplication.

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The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

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Answer:

it's c the slop is 3 your welcome

Answer:

A) x=3

Step-by-step explanation:

5^2-4^2=9

x=sq rt 9=3

Answer:

r = \(\sqrt{\frac{V}{h\pi } }\)

Step-by-step explanation:

V = πr²h ( isolate r² by dividing both sides by hπ )

\(\frac{V}{h\pi }\) = r² ( take square root of both sides )

\(\sqrt{\frac{V}{h\pi } }\) = r

Answer:

B, C, A.

Step-by-step explanation:

A = C + 3A = C + 3

A = C + 3

A = C + 3A

C + 3A = C + 3

3A = 3

A = 1

A = C + 3

1 = C + 3

C + 3 = 1

C = -2

B = 2C

B = 2(-2)

B = -4.

So, from least to greatest, B = -4, C = -2, and A = 1.

Hope this helps!

Answer:

2:3

Step-by-step explanation:

2a/3a a is out

cya a

The ratio 2a/3a in the simplest form is 2/3.

Ratio is the way to compare one thing that is related to another thing.

Simplifying ratio means reducing its terms to the lowest possible digits by dividing them with the possible common factor

For example if we have a ratio 3/6 then we divide both terms by 3 to get 3/6 = 1/2 which is the simplest form of ratio 3/6

Given that a ratio 2a/ 3a

2 and 3 have nothing in common . therefore a is the common factor between 2a and 3a

Then divide the terms of ratio by a

⇒ 2a/ 3a = (2a/a)/(3a/a) = (2/1)/(3/1) = 2/3

Therefore, the simplest form of the ratio 2a/3a is 2/3.

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The standard deviation of the sample proportion i 0.05.

Given a population of size 1000 with a proportion of 0.5, the proportion and standard deviation of the sample proportion for samples of size 100 are as follows: Proportion of sample proportion: 0.5 (same as population proportion)

The standard deviation of sample proportion: To find the standard deviation of the sample proportion, we use the formula: Standard deviation = √(pq/n)

where p is the population proportion, q is the complement of p (q = 1 - p), and n is the sample size.

Substituting the given values, we get:q = 1 - p = 1 - 0.5 = 0.5n = 100

Therefore, the standard deviation of the sample proportion is: Standard deviation = √(pq/n)= √(0.5 × 0.5/100)≈ 0.05.

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Answer:

more than witney

Step-by-step explanation:

Answer:

$21.78

Step-by-step explanation:

2.79 X 5 = 13.95

13.95 + 7.83 = 21.78

Answer:

part a is c

part b is d

Step-by-step explanation:

The following is an example of a quadratic inequality: x^2 + 2x - 8 > 0.

This is an example of a quadratic inequality because it is an inequality involving a quadratic function (x^2 + 2x - 8) which is of the form ax^2 + bx + c where a, b, and c are constants.

Quadratic inequalities can be solved by factoring the quadratic expression, using the Quadratic Formula, or graphing the inequality. In order to solve a quadratic inequality, it is important to understand the types of solutions that can be expected.

Solutions may include one solution, two solutions, or no solutions. Additionally, when graphing a quadratic inequality, the graph may be a line or a region. To determine which type of graph to use, the type of inequality must be identified (greater than or less than). If the inequality is a greater than or less than inequality, then the graph will be a region. If the inequality is an equal to inequality, then the graph will be a line.

Solving and graphing quadratic inequalities is an important skill in algebra as it allows us to visualize and solve complex problems.

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Answer:

16.4

Step-by-step explanation:

80/5 = 16

2/5 = 0.4

16 + 0.4 = 16.4

Answer:

A

Step-by-step explanation:

Answer:...

Step-by-step explanation:

These standardization methods are crucial in chromatography to ensure accurate quantification and comparability of results.

In chromatography, standardization methods are used to ensure accurate and reliable results by establishing reference points or calibration standards. Here are three common methods of standardization in chromatography: External Standardization: In this method, a set of known standard samples with known concentrations or properties is prepared separately from the sample being analyzed. These standards are then analyzed using the same chromatographic conditions as the sample. By comparing the response of the sample to that of the standards, the concentration or properties of the sample can be determined. Internal Standardization: This method involves the addition of a known compound (internal standard) to both the standard solutions and the sample. The internal standard should ideally have similar properties to the analyte of interest but be different enough to be easily distinguished. The response of the internal standard is used as a reference to correct for variations in sample preparation, injection volume, and instrumental response. Internal standardization helps improve the accuracy and precision of the analysis. Standard Addition: This method is useful when the matrix of the sample interferes with the analysis or when the analyte concentration is unknown. It involves adding known amounts of the analyte of interest to different aliquots of the sample. The response of the analyte is then measured, and the concentration is determined by comparing the response with that of the standards. The difference in response between the sample and the standards allows for the determination of the analyte concentration in the original sample.

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It will take 4 hours for Ashley to clean the house alone.Answer: Ashley will take 4 hours to clean the house alone.

Given:Ashley and Rod cleaned the house in 4 hours. Rod can clean the house alone in 2 hours.To find:How long will it take for Ashley to clean the house alone?Solution:Let's suppose the time Ashley takes to clean the house alone is x hours.Then, Ashley and Rod can clean the house in 4 hours.Thus, using the concept of work, we have:\begin{aligned} \text { Work done by Ashley in 1 hour } + \text { Work done by Rod in 1 hour } &= \text { Work done by Ashley and Rod in 1 hour } \\ \Rightarrow \frac {1}{x} + \frac {1}{2} &= \frac {1}{4} \\ \Rightarrow \frac {2 + x}{2x} &= \frac {1}{4} \\ \Rightarrow 8 + 4x &= 2x \\ \Rightarrow 2x - 4x &= -8 \\ \Rightarrow x &= 4 \end{aligned}Therefore, it will take 4 hours for Ashley to clean the house alone.Answer: Ashley will take 4 hours to clean the house alone.

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Answer:

On the y axis

Step-by-step explanation:

If x is zero, it automatically has to be on the y axis because x=0 is where the x and y axis intersect.

Answer:

30 inches

Step-by-step explanation:

Length of road A = 1¼ miles

Length of road A on map = 1½ inches

Unit rate for inches per miles on the map = 1½ inches ÷ 1¼ miles = ³/2 ÷ ⁵/4 = ³/2 × ⅘ = ⁶/5 inches per mile

Length big Road B on map:

Road B actual length = 10 miles

Thus, using the unit rate of ⁶/5 inches to 1 mile, length of road B on map would be calculated as shown below:

⁶/5 × 10 = 6*5 = 30 inches

Road B is 30 inches long on the map.