A patient is given 3 mg of morphine to control pain. About 31% of any morphine in the blood is washed out every hour. (a) Construct a function that models the level M of morphine (in mg) in the blood t hours after one dose. M = (b) How much morphine (in mg) remains in the blood after 5 hours? (Round your answer to two decimal places.) mg (c) Estimate how long, in hours, it will take for the amount of morphine left to drop to 0.1 mg. (Round your answer to two decimal places.) h

If the grocery bill before tax is $265.24 and you have to pay 7.3% tax, then he has to pay $284.6 for the grocery bill

The amount of the grocery bill before tax = $265.24
The percentage of tax = 7.3%

The amount of tax = The price of the grocery bill before tax × (7.3/100)

Substitute the values in the equation

= 265.24 × (7.3/100)

= 265.24 × 0.073

= $19.36

The final bill including tax = The price of the grocery bill before tax + The amount of tax

Substitute the values in the equation

= 265.24 + 19.36

= $284.6

Therefore, the grocery bill including tax = $284.6

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For the expression y = x + 3, the different y values is obtained as -

x     x+3       y

-1    (-1)+3    2

0    (0)+3     3

1     (1)+3      4

2     (2)+3    5

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

To evaluate each expression, we simply substitute the given value of x into the equation y = x + 3 -

The first expression is -

y = (-1) + 2

y = 2

The second expression is -

y = (0) + 3

y = 3

The third expression is -

y = (1) + 3

y = 4

The fourth expression is -

y = (2) + 3

y = 5

So now, the missing values of y for each value of x are -

For x = -1, y = 2

For x = 0, y = 3

For x = 1, y = 4

For x = 2, y = 5

Therefore, the y values are 2, 3, 4 and 5.

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The maximum production is 3.334 at the point (k, l) is (4.022, 5.029)

To maximize production, we need to maximize the production function:

\(p = k^{(2/5)} * l^{(3/5)}\)

subject to the budget constraint:

b = 4k + 5l = 100

We can use the method of Lagrange multipliers to solve this problem. The Lagrangian function is:

\(L = k^{(2/5)} * l^{(3/5)} + \lambda(100 - 4k - 5l)\)

where λ is the Lagrange multiplier.

To find the critical points, we need to take the partial derivatives of L with respect to k, l, and λ, and set them equal to zero:

∂L/∂k = \(2/5 * k^{(-3/5)} * l^{(3/5)} - 4\lambda\) = 0

∂L/∂l =\(3/5 * k^{(2/5)} * l^{(-2/5)} - 5\lambda\) = 0

∂L/∂λ = 100 - 4k - 5l = 0

Solving these equations, we get:

k = \((25/6)^{(5/7)}\) ≈ 4.022

l = \((20/3)^{(5/7)}\) ≈ 5.029

λ =\((2/5) * (25/6)^{(-2/7)} * (20/3)^{(-3/7)}\)≈ 0.327

Therefore, the maximum production is:

p =\(k^{(2/5)} * l^{(3/5)}\) ≈ 3.334

at the point (k, l) ≈ (4.022, 5.029), subject to the budget constraint 4k + 5l = 100.

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Answer:
45.2x0.784

Step-by-step explanation:

This problem equals 35.4368, which has four decimal points

The volume of the cuboid is 1152 ft³

A cuboid is a solid shape or a three-dimensional shape. A convex polyhedron that is bounded by six rectangular faces with eight vertices and twelve edges is called a cuboid.

A rectangular prism is called a cuboid and the volume of a cuboid is expressed as;

V = base area × height

The base is rectangle, the area of a rectangle is expressed as;

A = l× w

A = 18 × 8

A = 144 ft²

V = base area × height

V = 144 × 8

V = 1152 ft³

Therefore, the volume of the cuboid is 1152 ft³

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The probability that a randomly selected adult scores between 11 - 5 and 11 + 2 * 5 on the Modified Dental Anxiety Scale is approximately 0.3174, or 31.74%.

To find the probability that a randomly selected adult scores between 11 - 5 and 11 + 2 * 5 on the Modified Dental Anxiety Scale, we need to calculate the probability of falling within this range in a standard normal distribution.

First, we need to standardize the values using the formula z = (x - µ) / σ, where x is the given value, µ is the mean, and σ is the standard deviation.

For the lower bound, we have z_lower = (11 - 5 - 11) / 5 = -1.

For the upper bound, we have z_upper = (11 + 2 * 5 - 11) / 5 = 1.

Next, we can find the corresponding probabilities using a standard normal distribution table or a calculator.

P(z_lower < Z < z_upper) = P(-1 < Z < 1).

Looking up the values in the standard normal distribution table, we find that the probability corresponding to z = -1 is approximately 0.1587, and the probability corresponding to z = 1 is also approximately 0.1587.

Therefore, P(-1 < Z < 1) = 0.1587 - 0.1587 = 0.3174.

Hence, the probability that a randomly selected adult scores between 11 - 5 and 11 + 2 * 5 on the Modified Dental Anxiety Scale is approximately 0.3174, or 31.74%.

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The horse's average speed for the race in units of kilometers per hour will be 178.06.

The winning horse in a recent race covered the 5.50-furlong distance in 22.37 seconds.

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

We know that the average speed formula is given as,

Average speed = Total distance / Total time

The conversion is given as,

1 furlong = 0.201168 km

5.50-furlong = 0.201168 x 5.5 km

5.50-furlong = 1.10642 km

1 second = 1/3600 hour

22.37 seconds = 22.37/3600 hour

22.37 seconds = 0.0062 hour

The average speed is calculated as,

Average speed = 1.10642 / 0.0062

Average speed = 178.06 km per hour

The horse's average speed for the race in units of kilometers per hour will be 178.06.

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Answer:

it will be option 3 if isnt pls tell me and I'll work if out

(8 x 3) - 2³+ 17 = 33 is the true statement and so Option 3 is the correct answer.

An equation is a statement that links variables to constants and even with other variables and is helpful in solving complex problems.

The options given below needs to be checked for

Left Hand Side =  Right Hand Side

Option 1

LHS = -133.33

RHS = 33

Option 2

LHS = -125

RHS = 33

Option 3

LHS = 33

RHS = 33

Therefore Option 3 is the correct answer.

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The probability that one of the scores in the sample is less than 1484 is 0.2437 .

a)Given that mean u = 1403

standard deviation σ = 200

sample size n = 32

P(x>1484) = P(X-u/σ > 1484-1403/200)

                = P (z > 0.405)

P(x>1484) = 0.2437 .

hence the probability that one score is greater than 1484 is 0.405 .

b) Now we have to find the average of the scores of 48 samples.

P(x>1484)

= P(x-μ/ σ/√n> 1484-1403 /200/√48)

= P(z>2.805.)

Now we will use the normal distribution table to calculate the p value to be 0.002516.

p-value = 0.0025

Normal distributions are very crucial to statistics because not only they are commonly used in the natural and social sciences but also to describe real-valued random variables with uncertain distributions.

They are important in part because of the central limit theorem. This claim states that, in some cases, the average of many samples (observations) of a random process with infinite mean and variance is itself a random variable, whose distribution tends to become normal as the number of samples increases.

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Using complex numbers and radicals, it is found that the correct option is C.

When a complex number is a root of a polynomial function, it's conjugate also has to be.

The same is valid for radicals, as they are in the \(\pm\) format.

Hence, option C is correct.

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If the speed and the charge of a particle moving across a magnetic field are each doubled, the deflecting force will be:

d. The deflecting force will be quadrupled.

The deflecting force experienced by a charged particle moving across a magnetic field is given by the equation F = qvBsinθ, where F is the deflecting force, q is the charge of the particle, v is its velocity, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field vector.

If both the speed (v) and charge (q) of the particle are doubled, the deflecting force (F) can be calculated by substituting the new values into the equation:

F' = (2q)(2v)Bsinθ = 4(qvBsinθ) = 4F

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Answer:

$0.14

Step-by-step explanation:

$15.12/9

ans/12

Answer:

500 pennies

Step-by-step explanation:

Given that

Carmen saved 592 pennies.

Her sister saved 128 pennies.

Together, they put 250 pennies in wrappers and took them to the bank

We need to find out the total number of pennies Carmen and her sister have left

So,

= 592 pennies + 128 pennies  - 250 pennies

= 470 pennies

= 500 pennies

The total materials cost before sales tax is $297.21.

The total materials cost is the result of the addition of the total cost of posts, wire mesh, gate, and staples, as follows.

The length of the rectangular space = 6 meters

The width of the space = 10.5 meters'

The perimeter of the space = 33 meters [2(6 + 10.5)]

The space between posts = 1.5 meters

The number of posts = 22 (33 ÷ 1.5)

The cost per post = $2.69

a) The cost of the posts = $59.18 ($2.69 x 22)

The cost of wire mesh:

Cost per meter = $5.96

The number of meters of wire mesh = 33 meters

b) Total cost of the wire mesh = $196.68 ($5.96 x 33)

c) Cost of the gate = $25.39

Cost of Staples:

The number of staples per post = 7

The total number of staples required = 154 (22 x 7)

The number of boxes of staples = 4

The cost per box = $3.99

d) The total cost of staples = $15.96 (4 x $3.99)

The total cost of materials = $297.21 ($59.18 + $196.68 + $25.39 + $15.96)

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These agencies use statistics to provide reliable and timely information that supports evidence-based decision-making, policy formulation, economic planning, and monitoring of global and national development goals.

1. United States Census Bureau: The U.S. Census Bureau is a federal agency responsible for collecting and analyzing demographic, social, and economic data about the United States. It conducts the decennial census, as well as numerous surveys and studies that provide statistical information for policy-making, research, and decision-making purposes.

2. National Center for Health Statistics (NCHS): NCHS is a division of the U.S. Centers for Disease Control and Prevention (CDC) that collects and disseminates vital health statistics for the country. It conducts surveys, gathers data from various sources, and produces reports on topics such as mortality, morbidity, birth rates, and health behaviors, which help inform public health policies and programs.

3. Eurostat: Eurostat is the statistical office of the European Union (EU), responsible for collecting and publishing statistical information on various aspects of the EU member countries and their economies. It provides data on areas such as population, economy, agriculture, environment, and social conditions, facilitating evidence-based decision-making and monitoring of EU policies.

4. Australian Bureau of Statistics (ABS): The ABS is Australia's national statistical agency, collecting, analyzing, and disseminating a wide range of statistical data on the country's population, economy, and society. It conducts regular surveys and censuses, providing insights into areas like labor market, population trends, housing, and social well-being, to support informed decision-making by government, businesses, and the public.

5. Statistics Canada: Statistics Canada is the national statistical agency of Canada, responsible for gathering and analyzing statistical data on various aspects of the country. It conducts surveys, censuses, and administrative data collection to produce information related to population, economy, agriculture, and social conditions. The data generated by Statistics Canada is used to inform government policies, business strategies, and research activities.

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It should be noted that z^4 will be -32 in rectangular form.

Based on the information, z = r(cos θ + i sin θ), and provided positive integer n, then it is implied that:

z^n = r^n (cos nθ + i sin nθ)

In this instance, we need to solve for z^4 in rectangular form when z = -2 - 2i. Firstly, we must calculate |z| and arg(z):

|z| = √((-2)^2 + (-2)^2) = 2√2

arg(z) = arctan(-2/-2) = π/4

Leveraging De Moivre's theorem, we can effectively deduce the value of z^4 as:

z^4 = (2√2)^4 (cos (4π/4) + i sin (4π/4))

= 32 (cos π + i sin π)

= -32

Concludedly, z^4  resolved in rectangular form is -32.

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Answer:

Step-by-step explanation:

\(|FE| = |CB| = 4\cdot2=8\,cm\\\\|ED|=|DC|= \sqrt{(3\cdot2)^2+(4\cdot2)^2}= \sqrt{6^2+8^2}=\sqrt{100}=10\,cm\\\\|FA|=|AB|= \sqrt{(6\cdot2)^2+(8\cdot2)^2}= \sqrt{144+256}=\sqrt{400}=20\,cm\\\\\\Circumference = FE+ED+DC+CA+AB+FA\\\\Circumference =8+10+10+8+20+20=76\,cm\)

Answer: 5 1/12

Step-by-step explanation:

1. Conversion a mixed number 1  3/4 to a improper fraction: 1 3/4 = 1  3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4

2. Conversion a mixed number 3  1/3 to a improper fraction: 3 1/3 = 3  1/3 = 3 · 3 + 1/3 = 9 + 1/3 = 10/3

3. Add: 7/4 + 10/3 = 7 · 3/4 · 3 + 10 · 4/3 · 4 = 21/12 + 40/12 = 21 + 40/12 = 61/12 

Multiply 72 by 4/9.

First multiply 72 by 4:

72 x 4 = 288

Now divide by 9

288/9 = 32

Answer: 32

Answer:

32

Step by Step

Divide 72 by 9 which is 8

then times 8 by 4 which is 32

There fore 4/9 of 72 is 32

If you still find it complicated then remember the saying:

Divide by the bottom and times by the top

Answer: x=4+2i , x=4-2i hope this helps tho :>

Step-by-step explanation

The solutions to the equation x 2 −8x+20=0 are x= 10,-2.

The equation  x 2 −8x+20=0  can be written as (x-10) (x+2) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-10=0

x+2=0

so, the solution to the equation x 2 −8x+20=0 are x=10 and x=-2.

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Answer:

Step-by-step explanation:

S is3/4

Intercept is 5

Given:

The graph of a curve.

To find:

The domain and range for the given graph in interval notation.

Solution:

Domain: It is the set of input values.

Range: It is the set of output values.

Closed circle: It means that point is included in the solution set.

Open circle: It means that point is not included in the solution set.

(a) From the given graph it is clear that the function is defined between x=-5 to x=4. There is a closed circle at x=-5 and an open circle x=4, it means x=-5 is included and x=4 is not included in the domain.

\(Domain=-5\leq x<4\)

\(Domain=[-5,4)\)

(b) From the given graph it is clear that the values of the function lie between y=-3 to y=3. There is a closed circle at y=-3 and an open circle y=3, it means y=-3 is included and y=3 is not included in the range.

\(Range=-3\leq y<3\)

\(Range=[-3,3)\)

Therefore (a) \(Domain=[-5,4)\) and (b) \(Range=[-3,3)\).

Answer:

1

Step-by-step explanation:

Answer:

i think like the 2nd one im not sure i cant see the lines

Step-by-step explanation:

Answer:

b) \(a_{n}\) = 2 + 2/5n

Step-by-step explanation:

Given :-

a = 12/5

d = 2/5

To Find :-

\(a_{n}\)

Solving :-

\(a_{n}\) = a + (n - 1)d

= 12/5 + 2/5n - 2/5

= 2 + 2/5n

Solution :-

b) \(a_{n}\) = 2 + 2/5n

If \(y=x^m\) is a solution to the ODE

\(x^2 y'' - 7xy' + 15y = 0\)

then substituting \(y\) and its derivatives

\(y' = mx^{m-1} \text{ and } y'' = m(m-1)x^{m-2}\)

gives

\(m(m-1)x^2x^{m-2} - 7mxx^{m-1} + 15x^m = 0\)

\(m(m-1)x^{m} - 7mx^{m} + 15x^m = 0\)

\((m(m-1) - 7m + 15)x^{m} = 0\)

We ignore the trivial case of \(y=x^m=0\). Solve for \(m\).

\(m(m-1) - 7m + 15 = 0\)

\(m^2 - 8m + 15 = 0\)

\((m - 3) (m - 5) = 0\)

\(\implies \boxed{m=3} \text{ or } \boxed{m=5}\)

The amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59, which is the difference between the future value and the present value.

The future value represents the amount that will be in the account after the present value investment is compounded at an interest rate periodically.

The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.

Where:

A = future value

P = Present value of investment

i = interest rate

n = number of periods.

The future value of the investment can also be determined using an online finance calculator, as follows.

Then the interest is the difference between the future value and the present value.

Initial deposit = $8,241.78

Interest rate = 5.5% compounded daily

Investment period = 31 days

N (# of periods) = 31 days

I/Y (Interest per year) = 5.5%

PV (Present Value) = $8,241.78

PMT (Periodic Payment) = $0

Results:

FV = $8,280.37

Total Interest $38.59 ($8,280.37 - $8,241.78)

Thus, the amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59.

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Serial correlation refers to the degree to which a variable is correlated with a past version of itself.

Serial correlation violates the classical assumption that error terms are independent of each other.

What is Serial Correlation?

Serial correlation is a statistical concept that describes the correlation between a variable and a lagged version of itself. In simpler terms, it refers to the degree to which a variable is correlated with a past version of itself.

Serial correlation violates the classical assumption that error terms are independent of each other.

The error terms of a regression model are random variables that are used to capture the unexplained variability in the response variable. When these error terms are not independent, it means that there is a pattern in their distribution that is not explained by the model.

This can lead to biased parameter estimates and invalid hypothesis testing results.

Therefore, it is important to test for serial correlation in regression models and adjust for it if necessary.

This can be done using techniques such as the Durbin-Watson test and the Cochrane-Orcutt procedure.

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To calculate the residual for observation 6, we first need to find the forecast for observation 6. Based on the given information, the forecast for observation 6 is 34. Therefore, the residual for observation 6 would be:

Residual = Actual Demand - Forecast
Residual = 38 - 34
Residual = 4

So the residual for observation 6 is 4.
Hi! To find the residual for observation 6, we need to subtract the forecast (F) from the actual demand (A). In this case, the observation 6 values are:

Actual Demand (A): 38
Forecast (F): 28

Now, we'll calculate the residual:

Residual = Actual Demand (A) - Forecast (F)
Residual = 38 - 28
Residual = 10

So, the residual for observation 6 is 10.

The fraction of sweets that does she eat is 7/20

In this case, we will be using fractions to describe the portion of sweets that Hanna eats from her bag of 20.

Hanna has a bag of 20 sweets, and she eats 7 of them. To find out what fraction of the sweets she eats, we need to determine the ratio of the number of sweets she eats to the total number of sweets in the bag.

So in this case, Hanna eats 7 sweets, and there are 20 sweets in the bag. Therefore, the fraction of sweets she eats can be written as:

=> 7/20

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