Justin has a loyalty card good for 11% discount at his local grocery store. What number should he multiply the prices on the tags by to find the price he would have to pay, before tax in one step?

Answer:

Step-by-step explanation:

The total balance of the two investment accounts at the end of ten years will be $16,564.08. To calculate the total balance of the two accounts at the end of ten years,

we need to use the formulas for simple interest and compound interest.

For Account I, the simple interest formula is:

I = Prt

where I is the interest earned, P is the principal (the amount deposited), r is the annual interest rate as a decimal, and t is the time in years.

Plugging in the values for Account I, we get:

I = (3500)(0.065)(10) = $2,275

So, after ten years, the balance in Account I will be:

B1 = P + I = 3500 + 2275 = $5,775

For Account II, the compound interest formula is:

A = P(1 + r/n)^(nt)

where A is the balance at the end of the time period, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.

Plugging in the values for Account II, we get:

A = 5900(1 + 0.06/1)^(1*10) = $10,789.08

So, after ten years, the balance in Account II will be $10,789.08.

Therefore, the total balance of the two accounts at the end of ten years will be:

Total balance = Balance in Account I + Balance in Account II

= $5,775 + $10,789.08

= $16,564.08

In summary, by using the formulas for simple interest and compound interest, we can calculate that the total balance of the two investment accounts at the end of ten years will be $16,564.08.

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-5 and 7

Step-by-step explanation

lets try putting -5 and 7

-5 +7=2

and the difference is 8

i am not smart sorry

Answer:

67. 50

Step-by-step explanation:

15x4.50= 67.5

The correct answer is option (d) (x, y) → (x + 1/3, y + 1/3).

The dilation is a type of transformation that changes the size of the object, but not the shape. It can be represented by a rule in which each point of the original object is multiplied or divided by a constant factor. In this case, since the center of dilation is the origin, we can find the constant factor by dividing the coordinates of the corresponding points of the two rectangles.

Let's take the point Q(x, y) in rectangle QRST and its corresponding point Q'(x', y') in rectangle Q'R'S'T'. Since the dilation is centered at the origin, we have:

x' = k * x

y' = k * y

where k is the constant factor of dilation. We can find k by dividing the corresponding sides of the rectangles. For example, the length of QR is 4 units, and the length of Q'R' is 4/3 units. Therefore, k = 4/3.

Using this value of k, we can find the coordinates of any point in rectangle QRST that corresponds to a point in rectangle Q'R'S'T'. For example, point R(6, 2) in rectangle QRST corresponds to point R'(6 + 1/3, 2 + 1/3) = (20/3, 7/3) in rectangle Q'R'S'T'.

Hence, the correct answer is (x, y) → (x + 1/3, y + 1/3).

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La fuerza resultante sobre q3 debe calcularse considerando la interacción de las cargas q1, q2 y q3.

Para determinar la fuerza resultante sobre q3, debemos calcular la magnitud y la dirección de las fuerzas ejercidas por q1 y q2 sobre q3.

Usando la Ley de Coulomb, podemos calcular la fuerza entre dos cargas puntuales utilizando la fórmula: F = k * (|q1| * |q2|) / r^2, donde k es la constante de Coulomb, |q1| y |q2| son los valores absolutos de las cargas, y r es la distancia entre las cargas.

Dado que las cargas q1 y q3 son iguales, y q2 tiene una carga negativa, las fuerzas ejercidas por q1 y q2 en q3 tendrán direcciones opuestas. Debido a la simetría del triángulo rectángulo, las fuerzas tendrán componentes horizontales y verticales iguales en magnitud.

La magnitud de la fuerza resultante sobre q3 se calcula sumando las magnitudes de las fuerzas ejercidas por q1 y q2. La dirección de la fuerza resultante será la misma que la de las fuerzas individuales ejercidas por q1 y q2.

Por lo tanto, para calcular la fuerza resultante sobre q3, debemos encontrar la magnitud de la fuerza ejercida por q1 y la magnitud de la fuerza ejercida por q2, y luego sumarlas. La dirección será la misma que las fuerzas individuales.

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The first step in solving the equation is to isolate the radical term, and the second step is to eliminate the radical by raising both sides to the power of 3. Solving this equation for x initially yields x = 0, x = 2, and x = -2. Checking the solutions shows that it is not a real solution.

The first step in solving the equation (4x)[tex]^{1/3}[/tex] - x = 0 is to isolate the radical term by adding x to both sides of the equation. This gives us

(4x)[tex]^{1/3}[/tex]= x.
The second step is to raise both sides of the equation to the power of 3, which eliminates the radical. This results in 4x = x³.

Solving this equation for x initially yields x = 0, x = 2, and x = -2.
Checking the solutions shows that only x = 2 is a valid solution, as plugging it back into the original equation yields (4*2)[tex]^{1/3}[/tex] - 2 = 0. However, plugging in x = 0 results in a division by zero, and plugging in x = -2 yields a negative number under the radical, which is not a real solution.

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Carl pays his broker a total of $200 in fees for the 40 trades he made during the year.

To calculate how much Carl pays his broker, we need to first determine how many trades he made in a year. Looking at the table, we can see that Carl made a total of 40 trades - 20 buys and 20 sells. Since each trade incurs a $5 charge, we can multiply the number of trades by the cost per trade to get the total amount paid to the broker.

40 trades x $5 per trade = $200 paid to the broker in a year

It's important to note that transaction costs can have a significant impact on investment returns, especially for small accounts, so it's important to consider these costs when making investment decisions. Some brokers may offer lower transaction fees or other incentives to attract clients, so it's worth shopping around and comparing fees before choosing a broker. Additionally, it may be more cost-effective to use a robo-advisor or invest in index funds or exchange-traded funds (ETFs) that have lower fees compared to actively managed funds.

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The value of the expression 11C7 is 330. This can be calculated using the formula for combinations, which is nCr = n!/r!(n-r)!, where n is the total number of objects and r is the number of objects being selected. So, the correct answer is A).

To calculate the value of the expression 11C7, we need to use the formula for combinations or binomial coefficients, which is

nCr = n! / (r! * (n-r)!)

where n is the total number of items, r is the number of items to be chosen, and ! denotes the factorial operation (the product of all positive integers up to n).

In this case, we have

n = 11 and r = 7

So, we can substitute these values into the formula

11C7 = 11! / (7! * (11-7)!)

= 11! / (7! * 4!)

= (11 * 10 * 9 * 8 * 7 * 6 * 5) / (4 * 3 * 2 * 1)

= 330

Therefore, the value of the expression 11C7 is 330. So, the correct answer is A).

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--The given question is incomplete, the complete question is given

"Pls respond quick | what is the value of the expression? ₁₁C₇

a)330

b)1,663,200

c)5040

d)7920"--

The population density of the fish is 0.0061sharks/m²

Population density is a measurement of population per unit land area. Therefore the population density can be expressed as;

population density = population/ area

The number of fish in the tank is 3

The area of the tank is given as!

A = 2πr( r+h)

h = 3meters

r = d/2 = 15/2 = 7.5

A = 2 × 3.14 × 7.5(7.5+3)

A = 47.1( 10.5)

A = 494.55 m²

Therefore population density = 3/494.55

= 0.0061sharks/m²

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Answer:

The expression 625y^2 + 400y - 36 + 20z - z^2 can be rearranged and simplified as follows:

625y^2 + 400y - 36 + 20z - z^2

= (25y)^2 + 2(25y)(8) + 8^2 - 8^2 - 36 + 20z - z^2 (adding and subtracting (25y)(8) and 8^2 inside the parentheses)

= (25y + 8)^2 - (8^2 + 36) + 20z - z^2 (expanding the squared term and simplifying)

= (25y + 8)^2 - 100 + 20z - z^2 (simplifying)

Therefore, the simplified form of the expression is:

(25y + 8)^2 - 100 + 20z - z^2.

Note that this expression can also be written as:

(5y + 2)^2(5y - 12)^2 - (z - 10)(z + 10),

Using the difference of squares factorization. However, this is not necessarily simpler than the previous form, and it depends on the context and the purpose of the expression.

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The probability that a randomly selected balloon animal is green and shaped like a dog is 0.231.

The probability is found using the data table given below:

Purple and giraffe = 3; Purple and dog =  3; Green and giraffe = 4; Green and dog = 3

Out of the total number of balloon animals made, the number of green dog balloon animals is 3.

The probability of randomly selecting a green dog balloon animal is found using the formula:

Probability = 3 / (3 + 3 + 4 + 3) = 3/13

Probability = 0.231

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the height of the pyramid is 99 inches.

(explain)

To solve this problem, we can use the formula for the volume of a square pyramid which is:

Volume = (1/3) x (base area) x (height)

Since the base of our pyramid is a square with a side length of 10 inches, the base area would be:

Base area = (side length)^2 = 10^2 = 100 square inches

Substituting the values given in the problem, we get:

3300 = (1/3) x 100 x height

Multiplying both sides by 3, we get:

9900 = 100 x height

Dividing both sides by 100, we get:

height = 99 inches

Therefore, the height of the pyramid is 99 inches.

If combine harvester able to cut a 2450 square meters field in 5 hours and other one can do the same job in 7 hours then the area that the two combines cut in 9 hours is equals to the 7,560 square meters.

We have two harvester which can cut a area into different time.

The time taken by first harvester cuts into 2450 square meters field =5 hours.

The time taken by second harvester cuts into 2450 square meters field = 7 hours.

We have to determine the area can the two combines cut in 9 hours.

Here, total work = 2450 square meters

Work ability or efficiency of first harvester = 2450/5 = 490

Work efficiency of second harvester

= 2450/7= 350

Efficiency of both harvester in combine

= 350 + 490 = 840

So, area they cut into 9 hours = 840 × 9

=7560 square meters

Hence, required area is 7,560 square meters.

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The value of m that makes the inequality  4m + 8 < 36 true is m = 1 for the set of numbers 1 7 11 and 36 contains values for m.

An inequality is a mathematical expression in which the values on the left side of an equation are not equal to the values on the right side, but instead are either greater than or less than the values on the right side.

To find the value of m that makes the inequality 4m + 8 < 36 true, given the set of numbers {1, 7, 11, 36},

Now, we know that the value of m should be less than 7. From the given set of numbers {1, 7, 11, 36}, only 1 is less than 7. Therefore, the value of m that makes the inequality true is m = 1.

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The value of the side lengths b and h in the right-angle triangle is [tex]3\sqrt{2} , and[/tex] 8.

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent are three often used trigonometric ratios. (tan).

The given figure is a right-angle triangle.

To find the value of b and h we need to apply the trigonometric ratio.

In the first triangle,

[tex]cos45 = \frac{adjacent}{hypotenuse}[/tex]

[tex]cos45 = \frac{b}{6}[/tex]

[tex]\frac{1}{\sqrt{2} } = \frac{b}{6}[/tex]

[tex]b = \frac{1}{\sqrt{2} } * 6[/tex]

[tex]b = 3\sqrt{2}[/tex]

In the second triangle

[tex]cos60 = \frac{adjacent}{hypotenuse} \\cos60 = \frac{4}{h} \\\frac{1}{2} = \frac{4}{h} \\h= 2 *4\\h = 8[/tex]

Therefore the value of the b and h is [tex]3\sqrt{2}[/tex] , and 8 respectively.

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Answer:

j: 0, m: (-4)

Step-by-step explanation:

RECALL:

Rational function is the func. expressed by polynomials p(x) and q(x) as:

p(x)/q(x) where q(x) is non-zero

j(m+4) must be non zero, or

j(m+4)≠0

j≠0 and m+4≠0

j≠0 and m≠(-4)

The measure of angle TUV, given that line segment UT is tangent to circle V, and angle VTS is 145, is 55°.

Based on the information provided, you are looking to find the measure of angle TUV, given that line segment UT is tangent to circle V, and angle VTS is 145º.

Since UT is tangent to circle V, it means that angle UTV is a right angle (90º). Now, we know that the sum of the angles in a triangle is 180º. Therefore, to find the measure of angle TUV (m∠TUV), we can use the following formula:

m∠TUV + m∠UTV + m∠VTS = 180º

Substitute the given values:

m∠TUV + 90º + 145º = 180º

Solve for m∠TUV:

m∠TUV = 180º - 90º - 145º
m∠TUV = -55º

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Marlene will need to buy approximately 44 feet of fencing to enclose her circular vegetable garden.

To determine the amount of fencing Marlene needs, we'll need to calculate the circumference of her circular vegetable garden. Here's a step-by-step explanation:

1. Given the diameter of the garden is 14 feet, we can find the radius by dividing the diameter by 2: Radius = Diameter / 2 = 14 feet / 2 = 7 feet.

2. Now, we will use the formula for the circumference of a circle, which is: Circumference = 2 * pi * radius.

3. Plug in the radius value we found in step 1: Circumference = 2 * pi * 7 feet.

4. Calculate the circumference: Circumference ≈ 2 * 3.1416 * 7 feet ≈ 43.98 feet.

5. Since fencing is sold by the linear foot, Marlene needs to buy approximately 44 linear feet of fencing to enclose her circular vegetable garden and keep the rabbits away.

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The resultant component of the vector addition is (-9, 0).

The resultant component of the vector is calculated as follows;

a = (-9, 6)

b = (3, 1)

The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)

The result of 2b = 2(3, 1) = (6, 2)

The result of the vector addition is calculated as follows;

1/3a - 2b

= (-3, 2) - (6, 2)

= (-3 -6, 2 -2)

= (-9, 0)

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Let's call the initial number of bacteria in the petri dish as $N_0 = 100$. After 12 hours, the number of bacteria triples, which means there are now $3N_0$ bacteria. After another 12 hours, the number of bacteria triples again, which means there are now $3(3N_0) = 9N_0$ bacteria.

We can see a pattern here that after every 12 hours, the number of bacteria is multiplied by 3. Let's calculate the number of bacteria after 1 hour:

$\sf\implies\:N_1 = N_0 \times 3^{1/12}$

After simplifying:

$\sf\implies\:N_1 = 100 \times 3^{1/12}$

Using a calculator, we can find that $\sf\:3^{1/12} \approx 1.1548$. Therefore:

$\sf\implies\:N_1 \approx{\boxed{115.48}}$

So the equivalent hourly rate at which the number of bacteria is increasing is approximately 15.48% per hour.

In general, if the number of bacteria triples every $t$ hours, the equivalent hourly rate can be calculated as:

$\sf\implies\:r = 3^{1/t} - 1$

where $r$ is the hourly rate expressed as a decimal.

[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]

The solution to the composite function (f + g)(x) is: 8x + 7

Composite functions are said to occur when the output of one function is used as the input of another. If we have a function f and another function g, it means that the function fg(x), said as “ f of g of x”, is the composition of the two functions.

Now, we are given two functions as:

f(x) = x + 3

g(x) = 7x + 4

Thus, we can say that:

(f + g)(x) = f(x) + g(x)

= x + 3 + 7x + 4

= 8x + 7

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The critical point x = 0 does not yield a local minimum or maximum. The function is always decreasing.

To find the critical points and intervals for the function y = x^3 / (x^2 + 1), we'll first find the derivative using the Quotient Rule:

y'(x) = [(x^2 + 1)(3x^2) - x^3(2x)] / (x^2 + 1)^2

y'(x) = (3x^4 + 3x^2 - 2x^4) / (x^2 + 1)^2

y'(x) = (x^2 - 2x^2) / (x^2 + 1)^2

Now, we'll find the critical points by setting the derivative equal to zero:

0 = (x^2 - 2x^2) / (x^2 + 1)^2

0 = x^2(1 - 2) / (x^2 + 1)^2

0 = -x^2 / (x^2 + 1)^2

This equation is equal to zero only when x = 0. So, the critical point is x = 0.

Next, we'll use the First Derivative Test to determine if the critical point yields a local min or max. To do this, we'll evaluate the sign of y'(x) to the left and right of x = 0.

1. Left of x = 0 (for example, x = -1):
y'(-1) = (-1)^2(1 - 2) / (-1^2 + 1)^2 = -1 / 1^2 = -1 (negative)

2. Right of x = 0 (for example, x = 1):
y'(1) = (1)^2(1 - 2) / (1^2 + 1)^2 = -1 / 2^2 = -1/4 (negative)

Since the derivative is negative on both sides of the critical point, the function is decreasing for all x. Thus, the critical point x = 0 does not yield a local minimum or maximum. The function is always decreasing.

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PJ's design is best described as a randomized controlled trial (RCT), which is a type of experimental study that randomly assigns participants to a control group or an intervention group.

In this case, the control group did not receive the soft music during high stakes science testing, while the intervention group did. By administering both a pretest and a posttest, PJ was able to measure any differences in performance between the two groups. The use of randomization helps to ensure that any differences observed between the groups can be attributed to the intervention (soft music) rather than to other factors that may have influenced the results. Overall, PJ's RCT design is a rigorous way to test the effects of a specific intervention on a particular outcome.

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The distance the plane traveled from point A to point B is approximately y - x:

Distance = y - x

≈ 14046.99 feet - 20246.71 feet

≈ -6200.72 feet.

To find the distance the plane traveled from point A to point B, we can use trigonometry and the concept of similar triangles.

Let's denote the distance from point A to the plane as x, and the distance from point B to the plane as y. We are given the altitude of the plane (constant) as 7275 feet.

At point A, Carlos measures an angle of elevation of 20 degrees to the plane, and at point B, he measures an angle of elevation of 37 degrees to the plane.

Using trigonometry, we can set up the following equations:

tan(20 degrees) = 7275 / x,

tan(37 degrees) = 7275 / y.

We can rearrange these equations to solve for x and y:

x = 7275 / tan(20 degrees),

y = 7275 / tan(37 degrees).

Using a calculator, we can evaluate these expressions:

x ≈ 20246.71 feet,

y ≈ 14046.99 feet.

Therefore, the distance the plane traveled from point A to point B is approximately y - x:

Distance = y - x

≈ 14046.99 feet - 20246.71 feet

≈ -6200.72 feet.

Since the distance cannot be negative, we can round the absolute value of the result to the nearest foot:

Distance ≈ 6201 feet.

To find the distance the plane traveled from point A to point B, we can use trigonometry and the concept of similar triangles.

Let's denote the distance from point A to the plane as x, and the distance from point B to the plane as y. We are given the altitude of the plane (constant) as 7275 feet.

At point A, Carlos measures an angle of elevation of 20 degrees to the plane, and at point B, he measures an angle of elevation of 37 degrees to the plane.

Using trigonometry, we can set up the following equations:

tan(20 degrees) = 7275 / x,

tan(37 degrees) = 7275 / y.

We can rearrange these equations to solve for x and y:

x = 7275 / tan(20 degrees),

y = 7275 / tan(37 degrees).

Using a calculator, we can evaluate these expressions:

x ≈ 20246.71 feet,

y ≈ 14046.99 feet.

Therefore, the distance the plane traveled from point A to point B is approximately y - x:

Distance = y - x

≈ 14046.99 feet - 20246.71 feet

≈ -6200.72 feet.

Since the distance cannot be negative, we can round the absolute value of the result to the nearest foot:

Distance ≈ 6201 feet.

Therefore, the distance the plane traveled from point A to point B is approximately 6201 feet.

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Gastronomy is a way of promoting understanding among different cultures, and of bringing people and traditions closer together.

The practise of choosing, preparing, presenting, and consuming exquisite cuisine. The foundation of gastronomy lies in the connections between food, culture, and tradition. Gastronomy has emerged through time as a more potent cultural force than language or other influences among the peoples of the world.

Molecular gastronomy is a relatively recent branch of science that studies the physical and chemical changes that take place during cooking. Molecular cuisine is the name of the new culinary movement based on this emerging discipline.

Nowadays, the world may be broken down into separate gastronomic zones, where different cuisines are popular and similar cooking techniques are used. Throughout much of Southeast Asia, rice is the main food. The abundant and creative use of spices to give meals an extra flavour is what makes Indian and Indonesian cuisine unique. The prevalent ingredient in Mediterranean recipes is olive oil.

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Complete question:

How can gastronomy help us live harmoniously?

3/4 + (1/3 divided by 1/6) - (-1/2) when simplified give 3 1/4

How to determine this

3/4 + (1/3 divided by 1/6) - (-1/2)

3/4 + (1/3 ÷ 1/6) - (-1/2)

Using the rule of BODMAS

Whee B = Bracket

O = Order

D = Division

M = Multiplication

A = Addition

S = Subtraction

By removing the bracket

3/4 + 1/3 ÷ 1/6 + 1/2

By dividing

3/4 + 1/3 * 6/1 + 1/2

3/4 + 6/3 + 1/2

3/4 +2 + 1/2

By finding the LCM

The LCM is lowest common factor of the denominator which is 4

= [tex]\frac{3+8+2}{4}[/tex]

= 13/4

= 3 1/4

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To verify that the function f(x) = -4x^2 + 12x - 4ln x attains an absolute maximum and absolute minimum on [1/2,2], we can use the Extreme Value Theorem.

First, we need to check if the function is continuous on the interval [1/2,2] and differentiable on the open interval (1/2,2).

The function is continuous on [1/2,2] because it is a polynomial and the natural logarithm function is continuous on its domain.

To check if it is differentiable on (1/2,2), we need to take the derivative:

f'(x) = -8x + 12 - 4/x

This is defined and continuous on the open interval (1/2,2).

Now we can find the critical points by setting f'(x) = 0:

-8x + 12 - 4/x = 0

Multiplying both sides by x and rearranging, we get:

-8x^2 + 12x - 4 = 0

Dividing by -4, we get:

2x^2 - 3x + 1 = 0

This factors as (2x - 1)(x - 1) = 0, so the critical points are x = 1/2 and x = 1.

We also need to check the endpoints of the interval:

f(1/2) = -4(1/4) + 6 - 4ln(1/2) = 2 - 4ln(1/2)

f(2) = -4(4) + 12(2) - 4ln(2) = 8 - 4ln(2)

Now we can compare the function values at the critical points and endpoints to find the absolute maximum and minimum:

f(1/2) = 2 - 4ln(1/2) ≈ 5.39

f(1) = -4(1) + 12(1) - 4ln(1) = 8

f(2) = 8 - 4ln(2) ≈ 0.31

So the absolute maximum value is 8, which occurs at x = 1, and the absolute minimum value is 0.31, which occurs at x = 2.

Therefore, the function f(x) = -4x^2 + 12x - 4ln x attains an absolute maximum and absolute minimum on [1/2,2], and the absolute maximum value is 8 and the absolute minimum value is 0.31.
To verify that the function f(x) = -4x^2 + 12x - 4ln(x) attains an absolute maximum and minimum on the interval [1/2, 2], we will first find its critical points by taking the first derivative and setting it to zero, and then evaluate the function at the critical points and endpoints.

The first derivative of f(x) is:

f'(x) = -8x + 12 - 4/x

Setting f'(x) to zero, we have:

-8x + 12 - 4/x = 0

Multiplying by x to remove the fraction, we get:

-8x^2 + 12x - 4 = 0

Dividing by -4, we have:

2x^2 - 3x + 1 = 0

Factoring, we get:

(x-1)(2x-1) = 0

This gives us the critical points x = 1 and x = 1/2.

Now, we evaluate f(x) at the critical points and endpoints:

f(1/2) = -4(1/2)^2 + 12(1/2) - 4ln(1/2)
f(1) = -4(1)^2 + 12(1) - 4ln(1)
f(2) = -4(2)^2 + 12(2) - 4ln(2)

Calculating these values, we get:

f(1/2) ≈ 5.386
f(1) = 4
f(2) ≈ -4

The absolute maximum value is ≈ 5.386 at x = 1/2, and the absolute minimum value is ≈ -4 at x = 2.

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To solve for the surface area of a rectangular prism, you'll need to find the area of each of its six faces and add them together.

A rectangular prism has three pairs of faces: two each for length (L), width (W), and height (H).

First, find the area of the two faces with dimensions L x W. The area is calculated by multiplying length by width: A₁ = L * W. Since there are two such faces, the total area for these is 2A₁ = 2(L * W).

Next, find the area of the two faces with dimensions L x H. The area is calculated by multiplying length by height: A₂ = L * H. The total area for these faces is 2A₂ = 2(L * H).

Finally, find the area of the two faces with dimensions W x H. The area is calculated by multiplying width by height: A₃ = W * H. The total area for these faces is 2A₃ = 2(W * H).

To find the total surface area of the rectangular prism, add the areas of all six faces together: Surface Area = 2A₁ + 2A₂ + 2A₃ = 2(L * W) + 2(L * H) + 2(W * H).

So, the formula for the surface area of a rectangular prism is Surface Area = 2(L * W + L * H + W * H).

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The sequence (n){(1-2)/(3^n+1) + 3} is bounded and decreasing. The GLB is 3 and the LUB is 1.

To determine the boundedness and monotonicity of the sequence, we can look at the limit as n approaches infinity.

Taking the limit of the sequence, we have:

lim(n→∞) [(1-2)/(3^n+1) + 3] = 3

This means that the sequence approaches a finite value as n gets larger, so the sequence is bounded.

Next, to check the monotonicity of the sequence, we can take the first derivative of the sequence with respect to n:

d/dn [(1-2)/(3^n+1) + 3] = [(2-1)(-ln3)(3^n+1)]/[(3^n+1)^2]

Simplifying, we get:

d/dn [(1-2)/(3^n+1) + 3] = (-ln3)/(3^n+1)^2

Since the derivative is negative for all n, the sequence is decreasing.

To find the GLB and LUB, we can use the fact that the sequence is decreasing and bounded. Since the sequence approaches 3 as n approaches infinity, 3 is the lower bound.

To find the upper bound, we can use the fact that the sequence is decreasing and start with the second term, which is 2. Therefore, the upper bound is 2. Since 1 < 2, we can conclude that the LUB is 1.

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(I) The new selling price per kilogram of the tomatoes is 0.4576.

(II) The percentage profit on the whole transaction is 24.77% if she threw away 5kg of bad tomatoes.

The new selling price is calculated as follows;

The cost per kilogram of the tomatoes is;

Cost per kg = Total cost / Total weight

Cost per kg = 52 / 130

Cost per kg = 0.4

Selling price per kg = Cost per kg + (Profit percentage x Cost per kg)

Selling price per kg = 0.4 + (0.3 x 0.4)

Selling price per kg = 0.52

The new selling price per kilogram is:

= Selling price per kg - (Reduction percentage x Selling price per kg)

= 0.52 - (0.12 x 0.52)

= 0.4576

The total revenue from selling the tomatoes is calculated as;

The woman sold half of the 130kg of tomatoes, = 130 / 2 = 65kg

Revenue = (amount sold x selling price per kg) + (amount left x new selling price per kg)

Revenue = (65 x 0.52) + (65 x 0.4576)

Revenue = 33.8 + 29.68

Revenue = 63.48

New total cost = Total cost / Total weight x (Total weight - Bad tomatoes)

New total cost = 0.4 x (130 - 5)

New total cost = 50.6

The profit on the whole transaction  is calculated as;

Profit = Total revenue - New total cost

Profit = 63.48 - 50.6

Profit = 12.88

The profit percentage on the whole transaction is calculated as;

Profit percentage = (Profit / Total cost) x 100%

Profit percentage = (12.88 / 52) x 100%

Profit percentage = 24.77%

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