At time t hours after taking the cough suppressant hydrocodone bitartrate, the amount, A, in mg, remaining in the body is given by A = 11(0.81)t. (a) What was the initial amount taken? mg (b) What percent of the drug leaves the body each hour? % leaves the body each hour. (c) How much of the drug is left in the body 6 hours after the dose is administered? NOTE: Round your answer to two decimal places. mg (d) How long is it until only 1 mg of the drug remains in the body? NOTE: Use logarithms to find the answer and round it to two decimal places.

Answer:

(1/2)m - (3/4)(8) = 16

(1/2)m - 6 = 16

(1/2)m = 22

m = 44

Answer:

log8 (2.718) = 0.48

Step-by-step explanation:

In 2.718 ÷ In 8 = 0.999896 ÷ 2.07944

= 0.4808

Expression ㏒₈2.718 = 0.43, since option d. is the correct solution to the given question.

The logarithm is a mathematical function with a number and a base whose solution is the power to which the base needs to be raised to obtain that number.

We need to evaluate ㏒₈2.718.

We will use the base changing formula for the evaluation, which is given by:

㏒ₐX = ㏒ₓX/㏒ₓa

∴㏒₈2.718

= ㏒2.718/㏒8

= 0.4342494523/0.9030899869

= 0.4808484853

Rounding of the answer to two decimal places, ㏒₈2.718 = 0.48.

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While you look behind to see how many people you beat, you are gathering information for your Competitive intelligence via the use of social comparison.

Competitive intelligence is a process of learning as much as possible outside oneself to increase one's competition level.

It tells us about our position in the competition or market .it helps in self-improvement and skill development.

Social comparison helps in determining our own worth in society.

You are gathering information for your Competitive intelligence via the use of social comparison.

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You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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The equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1) is y - 1 = 3/2(x+3)

The equation of a line in point-slope form is expressed as:

y-y0 = m(x-x0)

where:

m is the slope

(x0,y0) is the point on the line

The slope of the given line is as shown:

Slope = 2-(-4)/2-(-2)
Slope = 2+4/2+2
Slope = 6/4 = 3/2

Substitute the slope and the point

y - 1 = 3/2(x-(-3))

y - 1 = 3/2(x+3)

Hence the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1) is y - 1 = 3/2(x+3)

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The first six terms of the sequence defined by each of these recurrence relations and initial conditions are

a) -1, 2, -4, 8, -16, 32.

b) 2, -1, -3, -2, 1, 3.

c) 1, 3, 9, 27, 81, 243.

a) The first recurrence relation is given by an = -2an-1 with an initial condition of a0 = -1. To find the first six terms of this sequence, we need to use the recurrence relation to generate each term, starting with the initial condition. Using the formula, we can find:

a1 = -2a0 = -2(-1) = 2

a2 = -2a1 = -2(2) = -4

a3 = -2a2 = -2(-4) = 8

a4 = -2a3 = -2(8) = -16

a5 = -2a4 = -2(-16) = 32

a6 = -2a5 = -2(32) = -64

Therefore, the first six terms of the sequence defined by an = -2an-1 with a0 = -1 are: -1, 2, -4, 8, -16, 32.

b) The second recurrence relation is given by an = an-1 - an-2 with initial conditions a0 = 2 and a1 = -1. To find the first six terms of this sequence, we need to use the recurrence relation to generate each term, starting with the initial conditions. Using the formula, we can find:

a2 = a1 - a0 = -1 - 2 = -3

a3 = a2 - a1 = -3 - (-1) = -2

a4 = a3 - a2 = -2 - (-3) = 1

a5 = a4 - a3 = 1 - (-2) = 3

a6 = a5 - a4 = 3 - 1 = 2

Therefore, the first six terms of the sequence defined by an = an-1 - an-2 with a0 = 2 and a1 = -1 are: 2, -1, -3, -2, 1, 3.

c) The third recurrence relation is given by an = 3a2n-1 with an initial condition of a0 = 1. To find the first six terms of this sequence, we need to use the recurrence relation to generate each term, starting with the initial condition. Using the formula, we can find:

a1 = 3a0 = 3(1) = 3

a2 = 3a3 = 3(3) = 9

a3 = 3a2 = 3(9) = 27

a4 = 3a7 = 3(27) = 81

a5 = 3a14 = 3(81) = 243

a6 = 3a29 = 3(243) = 729

Therefore, the first six terms of the sequence defined by an = 3a2n-1 with a0 = 1 are: 1, 3, 9, 27, 81, 243.

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Answer:

115 degrees

Step-by-step explanation:

Answer:

356.53

Step-by-step explanation:

Calculate the semicircle and square areas separately. For the semicircle, A = πr²/2, so 100.53

And for the square, A = a², so 256

Hope this helps

a) To prove the inequality (E(X1X2))2≤E(X21)E(X22), we can start by expanding the square on the left-hand side:
(E(X1X2))2 = (cov(X1,X2) + E(X1)E(X2))2
= cov(X1,X2)2 + 2cov(X1,X2)E(X1)E(X2) + (E(X1)E(X2))2
Using the fact that cov(X1,X2) = E(X1X2) - E(X1)E(X2), we can rewrite the above expression as:
E(X1X2)2 - 2E(X1X2)E(X1)E(X2) + E(X1)2E(X2)2
Now, note that for any real number t, E((tX1−X2)2)≥0. This means that the discriminant of the quadratic expression t2E(X1)2 - 2tE(X1X2) + E(X2)2 is non-positive. Therefore,
(E(X1X2))2 - E(X21)E(X22) ≤ 0
which proves the desired inequality.
b) Using part (a), we have:
rho2 = (cov(X1,X2) / (sd(X1)sd(X2)))2 ≤ 1
where sd(X1) and sd(X2) are the standard deviations of X1 and X2, respectively.
Since the standard deviations are positive, we can take the square root of both sides to obtain:
|rho| ≤ 1

Part (a) is proven by expanding the square on the left-hand side and using the fact that E((tX1−X2)2)≥0 for any real number t. Part (b) follows from part (a) and the fact that the correlation coefficient is bounded between -1 and 1.

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Answer:

√{369×369}=√369²=369 is your answer

Answer:

your answer will be 369

Step-by-step explanation:

......

The angle of the rhombus is given as 54 degrees (alternate angles)

A rhombus, a four-sided polygon dotted with sides of the corresponding length, has adjacent angles with equal measure and all four edges culminating in 360 degrees.

If one is seeking to identify the measurements of each angle within a rhombus, they may do so by employing the following formula:

angle measurement = (180 - diagonal angle)/2

To begin, single out one of the diagonal angles; then, take 180 minus that angel and subsequently halve it--this is the measure of each neighboring angle.

Repetition of this procedure on the opposing diagonal angle should enable you to uncover all four side lengths of the rhombus.

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The value of angle 1, 2, 3, and 4 is 42⁰, 48⁰, 42⁰ and 42⁰ respectively.

The value of angle 1, 2, 3, and 4 is calculated as follows;

angle 3 = angle 4 (alternate angles are equal)

angle 3 = 42⁰

let the angle adjacent to 3 = y

y = 90 - 42⁰

y = 48⁰

angle 4 + adjacent angle = 180 - (42 + 48)

angle 4 + angle 2 = 180 - 90

angle 4 + angle 2 = 90

angle 4 = 42⁰ (vertical opposite angles)

angle 2 = 90 - 42⁰

angle 2 = 48⁰

angle 1 = angle 4 = 42⁰ (alternate angles).

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Answer:

1. -6

2. -78

3. 4

4. 504

5. - 236

The smaller eigenvalue of matrix A is -1 and the larger eigenvalue is 9.

To find the eigenvalues of matrix A, we use the characteristic equation det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix. For a 2x2 matrix A, the characteristic equation is given by λ² - tr(A)λ + det(A) = 0. Substituting the given values of tr(A) and det(A), we get λ² - 8λ + 15 = 0. Factoring this quadratic equation, we get (λ - 3)(λ - 5) = 0. Thus, the eigenvalues are λ = 3 and λ = 5.

To determine which of these eigenvalues is larger, we look at the diagonal entries of the matrix A. The sum of the eigenvalues equals the trace of the matrix, so we know that 3 + 5 = 8. Since the determinant of the matrix is positive, we know that the eigenvalues have opposite signs.

Therefore, the larger eigenvalue is 9 (which is the sum of the trace and the absolute value of the difference between the eigenvalues), and the smaller eigenvalue is -1 (which is the difference between the trace and the larger eigenvalue).

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Answer:

There are no tables, but... I made a quick graph.

Step-by-step explanation:

y=2x-1 means that you start at (0,-1), one down from the origin (0,0). From there, you go up 2 and right one (1, 2), as well as down 2 and left 1 (-1, -2), since the slope is 2 (or \(\frac{2}{1\\}\)). The lines continues in both directions, of course.

The table for the equation is y = 2x - 1

x y

0 -1

1 1

2 3

To determine which table represents the equation y = 2x - 1, we substitute the values of x into the equation and check if the resulting y values match those given in the table.

Substitute the values 0, 1, and 2 into the equation y = 2x - 1 and calculate the corresponding y-values:

For x = 0:

y = 2(0) - 1

y = 0 - 1

y = -1

For x = 1:

y = 2(1) - 1

y = 2 - 1

y = 1

For x = 2:

y = 2(2) - 1

y = 4 - 1

y = 3

The corresponding y-values for x = 0, 1, and 2 are -1, 1, and 3, respectively.

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Answer:

i think it is 5

Step-by-step explanation:

Answer:

\(a_{8} = 15\)

Step-by-step explanation:

\(a_{1} + a_{2} + ..... + a_{7} + a_{8} = 8^{2} = 64\)

\(-a_{1} - a_{2} ..... - a_{7} = - 7^{2} = -49\)    Now add the two equations

                                 \(a_{8} = 64 - 49 = 15\)

\(a_{8} = 15\)

Overall, the level, trend, seasonality, and noise components are present in this series, indicating that multiple factors contribute to the sales patterns observed over time

A. To create a well-formatted time plot of the data from the DepartmentStoreSales.csv file, you can follow these steps:

Import the data from the CSV file into a suitable software or programming environment that supports data visualization, such as Python with libraries like pandas and matplotlib, or Excel.

Ensure that the data is properly formatted and organized, with the dates in a consistent date/time format.

Plot the sales data on the y-axis and the corresponding time periods (e.g., quarters or dates) on the x-axis.

Customize the plot by adding axis labels, a title, and any other necessary formatting to make it clear and visually appealing.

B. Analyzing the time plot, we can identify the following components in the series:

Level: The series shows a relatively stable average level of sales over time, with some fluctuations.

Trend: There appears to be an upward trend in sales over the 6-year period, as the sales generally increase.

Seasonality: There may be some seasonality present, as periodic patterns or fluctuations can be observed within each year. For example, there might be higher sales during specific quarters or months.

Noise: There is some random variation or noise present in the series, which causes the sales data to deviate from the trend and seasonal patterns.

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Answer: June had 100 buttercups before she gave any out

Step-by-step explanation:

Let's suppose that June had "x" number of buttercups in the beginning.On Monday, June gives 1/4 of the buttercups to Tess, which means she has only 3/4 of the buttercups left. Therefore, the number of buttercups left with her is 3/4 of x, which can be written as 3x/4.On Tuesday, she gives 1/3 of the remaining buttercups to Gail. Therefore, the number of buttercups remaining with June can be represented as (2/3) × (3x/4), which is equal to 2x/4 or x/2.On Wednesday, she gives 3/5 of the remaining buttercups to George. Therefore, the number of buttercups remaining with June can be represented as (2/5) × (x/2), which is equal to x/5.Given that, June has 20 buttercups left, we can represent the above information in the form of an equation.x/5 = 20Multiplying both sides by 5 gives us,x = 100Therefore, June had 100 buttercups in the beginning.

Answer: I think is A

Step-by-step explanation:

Answer:

a) $26

b) 24.07%

c) $94.3

Step-by-step explanation:

Given that:

Before tax:

Normal price of dress = $62

Discounted price of dress = $48

Normal price of a pair of shoes = $46

Discounted price of a pair of shoes = $34

a) Before the sales tax, total savings = ($64 - $48) + ($46 - $34) = $26

b) Total percentage discount on total sales.

Total bill for original price = $62 + $46 = $108

Percentage discount can be found by the formula:

\(\dfrac{\text{Total discount}}{\text{Total bill for original price}}\times 100\\\Rightarrow \dfrac{26}{108} \times 100 = 24.07\%\)

c) Total amount paid if the sales tax is 15%.

Amount paid with tax = Amount after discount + 15% of amount after discount

Amount after discount = $48 + $34 = $82

15% of $82 = $18.29

Amount paid with sales tax = $82 + $12.3 = $94.3

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Given function is,f(t) ={ t, 0 < t < π π < t < 2π}

where f(t + 2 π) = f(t)

Let's take Laplace Transform of f(t)

                     L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)

∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}

     ⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0

when e^{2πs} ≠ 1 ⇒ s ≠ 0

∴ The Laplace Transform of f(t) is

                       L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                               = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...

                              = (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

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The y-axis reflection of f, followed by a translation 7 units to the right.

A function is a special type of relationship in which each input has exactly one output. In other words, for each input value, the function returns exactly one value. Because one is mapped to two different values, the graph above depicts a relation rather than a function. If the relation above were instead mapped to a single value, it would become a function. Also, output values can be the same as input values.

The function machine is fed the x-values. The function machine then runs its code and returns the y-values. Any function can be found within.

This corresponds to the y-axis graph of f(x).

Step 2 requires us to translate the reflected graph 7 units to the right. To accomplish this, we add 7 to the x-coordinate of each point on the f(-x) graph, yielding:

g(x) = f(-x + 7)

This gives us the equation for the graph of g, which is the y-axis reflection of f, followed by a 7-unit translation to the right.

As a result, f is reflected in the y-axis, followed by a translation 7 units to the right.

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A pair of intersecting lines that forms a pair of complementary angles is as drawn below.

Remember that complementary angles are defined as angles which sum is equal to 90°.

Besides, each of the pairs of opposite angles made by two intersecting lines are called vertical angles. Now, from congruent proofs, we know that that vertical angles are congruent. In another words, they have the same measure.

Thus, we have to draw two vertical angles that measure:

90° ÷2 = 45°

This image is as drawn below in the attached file.

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The first step of calculating the iterated integral involves finding the inner integral by integrating the integrand with respect to the variable x while considering y as a constant. This yields x + 2xy²

To calculate the iterated integral ∫∫(1 + 4xy) dxdy, we follow the process of integrating the inner integral first. In this case, x is treated as the variable while y is considered a constant.To find the inner integral, we integrate (1 + 4xy) with respect to x. Treating y as a constant, we obtain the integral ∫(1 + 4xy) dx. Integrating this expression yields x + 2xy² as the result.

Now, we have an expression for the inner integral: x + 2xy². The next step is to integrate this result with respect to y while considering the limits of integration for y. Without specific limits provided, we cannot determine the exact values for the integral. However, we can express the iterated integral in terms of the variable y, resulting in ∫(x + 2xy²) dy.

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The answer of the question based on the inequality the answer is  Andy can rent up to 20 DVDs in a month and spend no more than $25.

An inequality equation is mathematical statement that compares the two values or expressions using inequality symbol such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

The total cost, C, for renting n DVDs in a month is given by:

C = 10 + 0.75n

The question tells us that Andy wants to spend no more than $25 per month on DVD rentals. Therefore, we can write an inequality:

C ≤ 25

Substituting the expression for C from above, we get:

10 + 0.75n ≤ 25

Simplifying the inequality, we can subtract 10 from both sides:

0.75n ≤ 15

Finally, we can divide both sides by 0.75:

n ≤ 20

Therefore, the inequality that represents how many DVDs Andy can rent in one month that satisfies the condition of spending no more than $25 per month is:

n ≤ 20

So, Andy can rent up to 20 DVDs in a month and spend no more than $25.

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Answer:

9562.000

Step-by-step explanation:

hope this helps with your work

Answer:

9,562 rounded to the nearest thousand is 10,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

The angle is between 3pi/2 and 2pi so it is in the fourth quadrant where both sin and tan are negative.

Given cos(θ) = sqrt(2)/2

cos^2(θ) + sin^2(θ) = 1

sine^2(θ) = 1 - 2/2^2 = 1 - 1/2 = 1/2

sin(θ) = +/1 sqrt(2)/2

As we know sin(θ) is negative,

sin(θ) =  -sqrt(2)/2; the second answer

tan(θ) = sin(θ)/cos(θ) = -1

Answer:

Step-by-step explanation:

using (cosθ)^2 + (sinθ)^2 = 1

2/4 + (sinθ)^2 = 1

sinθ = \(\sqrt{2}/2\)

or -\(\sqrt{2} /2\)

By C-A-S-T, sinθ is -ve

sinθ = -\(\sqrt{2}/2\)

tanθ = sinθ/cosθ = -1