Rita has coins worth $3.00. If the coins are all dimes, how many dimes does she have?

The function of the sequence -4,-6,-9,-27/2,-81/2 is f(n) = -4(3/2)^(n - 1)

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

-4,-6,-9,-27/2,-81/2

The above sequence is a geometric sequence

This is because it has a common ratio calculated as

r = -6/-4

So, we have

r = 3/2

The sequence is then represented as

f(n) = ar^n-1

So, we have

f(n) = -4(3/2)^(n - 1)

Hence, the function is f(n) = -4(3/2)^(n - 1)

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Answer: x = -1 and y = 9

Step-by-step explanation:

To solve this system of equations, we can use the substitution method.

First, solve the first equation for y:

y = -x + 8

Now, substitute this expression for y into the second equation and solve for x:

4x + y = 5

4x + (-x + 8) = 5 (substituting -x + 8 for y)

3x + 8 = 5

3x = -3

x = -1

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:

y = -x + 8

y = -(-1) + 8

y = 9

Therefore, the solution to the system of equations is x = -1 and y = 9.

The nearest cent, the amount of money in the account after 13 years is $2,094.18.

The formula for continuous compound interest is:

V = Pe^(rt)

where V is the value of the account after t years, P is the principal (initial amount) invested, e is the base of natural logarithms (approximately 2.71828), r is the annual interest rate (as a decimal), and t is the time period in years.

In this case, P = $741, r = 0.058 (since the annual interest rate is 5.8%), and t = 13. Substituting these values into the formula, we get:

V = 741e^(0.058*13)

Using a calculator, we can evaluate e^(0.058*13) to be approximately 2.8302. Then, we can multiply this value by 741 to get:

V = 741*2.8302

V ≈ $2,094.18

Therefore, to the nearest cent, the amount of money in the account after 13 years is $2,094.18.

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Answer:

To solve this problem, we can use the laws of indices, specifically the law that states that (a^m)^n = a^(m*n).

So, we have:

(1/64)^(2/3) = (1^(2/3))/(64^(2/3))

Since any number raised to the power of 1 is itself, we can simplify the numerator to just 1.

Now, we have:

(1/64)^(2/3) = 1/(64^(2/3))

To evaluate 64^(2/3), we can use the law of indices again, which states that a^(1/n) = nth root of a. In this case, we have:

64^(2/3) = (64^(1/3))^2 = 4^2 = 16

So, substituting this back into the original expression, we have:

(1/64)^(2/3) = 1/16

Therefore, (1/64)^(2/3) simplifies to 1/16.

Step-by-step explanation:

Answer:

Using the law of indices, we have:

(1/64)^(2/3) = (1^(2/3))/(64^(2/3))

Now we need to simplify the denominator by finding the cube root of 64:

64^(1/3) = 4

Substituting this value in the original expression, we get:

(1/64)^(2/3) = (1^(2/3))/(4^2)

Simplifying further, we have:

(1/64)^(2/3) = 1/16

Step-by-step explanation:

The length of the arc that is drawn in a circle of radius 14 cm and angle of arc  135° is approximately 32.67 cm.

An arc is a portion of a curve that is part of a circle. It is defined as a continuous portion of the circumference of a circle. In other words, an arc is a segment of a circle's circumference.

To find the length of an arc of circle, you can use the formula:

arc length = (angle of arc / 360) x (2 x π x radius)

Where π (pi) is a mathematical constant approximately equal to 3.14.

In this problem, the radius of the circle is given as 14 cm and the angle of the arc is 135°. So, By substituting these values in the formula, we get:

arc length = (135/360) x (2 x π x 14)

arc length = (3/8) x (2 x 3.14 x 14)

arc length = (3/8) x (87.92)

arc length = 32.67 cm (rounded to two decimal places)

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The marginal cost function is $ 4000.72.

What is the marginal cost function?

The overall costs involved in producing an additional good are what is referred to as the marginal cost. Hence, it can be evaluated by changes in the costs associated with each extra unit. Marginal Cost is calculated as Total Expenditure Change / Unit Production Change.

Here, we have

Given: C(x) = 20+4000x+0.09x²

We have to find the marginal cost function.

We differentiate the given function and we get

C(x) = 20+4000x+0.09x²

C'(x) = 4000 + 2×0.09x

To determine how fast the cost is increasing when x=4.

C'(4) = 4000 + 2×0.09(4)

C'(4)  = 4000.72

Hence, the marginal cost function is $ 4000.72.

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The composite figure has a total area of 102 square units (80 + 16 + 6 square units). Consequently, the composite figure has a 102 square unit area.

Composite things that are three dimensional (3D) are constructed from two or more separate pieces. Finding each item's outside surface area and adding the surface areas together will yield the surface area of a 3D composite object. Another way to divide it is into a top and a bottom.

We may divide the composite figure into smaller forms and sum up their areas to determine the area of the overall figure. Here is one method for breaking down the figure:

A rectangle and two triangles make up the figure.

The rectangle has an area of 80 square units since it is 10 units long and 8 units wide.

The two triangles have right triangles with four and six unit-long legs, respectively. The equation (base * height) / 2 may be used to calculate each triangle's area.

The area of the triangle on the left is (4 * 8) / 2 or 16 square units since its base is 4 units and its height is 8 units (the length of the rectangle).

The area of the triangle on the right is (6 * 2) / 2 or 6 square units because its base is 6 units and its height is 2 units (the distance between the bottom of the triangle and the bottom of the rectangle).

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For fau/cet filter:

For pitcher-filter:

Let's start with the fau/cet model:

Contribution margin per unit = selling price - variable cost

Contribution margin per unit = $90 - $25

Contribution margin per unit = $65

Contribution margin ratio = contribution margin per unit / selling price

Contribution margin ratio = $65 / $90

Contribution margin ratio = 0.722

The sales mix is 2 faucet models for every 3 pitcher filters sold, so the contribution margin weighted average is:

= (2/5)($65) + (3/5)($90-$20)

= $42

Now we can calculate the break-even point in units for the faucet model:

= Total fixed costs / contribution margin per unit

= $1,200,000 / $42

= 28,571 units

For pitcher filter:

Contribution margin per unit = selling price - variable cost

Contribution margin per unit = $110 - $20

Contribution margin per unit = $90

Contribution margin ratio = contribution margin per unit / selling price

= $90 / $110

Contribution margin ratio = 0.818

Contribution margin weighted average:

= (2/5)($25) + (3/5)($90-$20)

= $54

Break-even point in units for pitc/her filter:

= Total fixed costs / contribution margin per unit

= $1,200,000 / $54

= 22,222 units

Break-even point in dollars for fau/cet model:

= 28,571 units x $90 per unit

= $2,571,390

Break-even point in dollars for pitc/her-filter:

= 22,222 units x $110 per unit

= $2,444,420

Full question "Multiproduct CVP and decision making. Crystal Clear Products produces two types of water filters. One attaches to the faucet and cleans all water that passes through the faucet. The other is a pitcherfilter that only purifies water meant for drinking. The unit that attaches to the faucet is sold for $90 and has variable costs of $25. The pitcherfilter sells for $110 and has variable costs of $20. Crystal Clear sells two faucet models for every three pitchers sold. Fixed costs equal $1,200,000.

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Answer:

Step-by-step explanation:

You want the absolute extremes of f(x) = -x +cos(3πx) in the interval [0, π/6].

The attached graph shows the extremes to be ...

__

Additional comment

The x-value at the minimum is (π+arcsin(1/(3π)))/(3π) ≈ 0.344612473782. The corresponding y-value is about −1.33896758676.

Answer:

natural, whole, integer, rational

Step-by-step explanation:

Natural Number:

All the numbers in the set {1, 2, 3, …} are natural numbers, 1256 lies in this set.

Whole Number:

All the numbers in the set {0, 1, 2, 3, …} are whole numbers, 1256 lies in this set.

Integer:

All the numbers in the set {… ,-1, 0, 1, 2 …} are integers, 1256 lies in this set.

Rational Number:

1256 can be represented as [tex]\dfrac{1256}{1}[/tex] or [tex]\dfrac{2512}{2}[/tex] etc., which is in the rational form (division of two non zero integers). therefore 1256 is also a rational number.

Hopefully this answer helped you!!

Answer:x = π/6 + 2πn , 5π/6 + 2πn, for any integer n

1) The area of the garden in Design A and Design B is 108 [tex]feet^{2}[/tex]and 84[tex]feet^{2}[/tex]

2)The area of the deck not including the garden in Design A and Design B is 342 [tex]feet^{2}[/tex]and 372 [tex]feet^{2}[/tex]

3)The cost of $4.20 per [tex]feet^{2}[/tex]required to install the deck in Design A and Design B is $1890 and $1764 respectively

4) The cost of $1.40 per [tex]feet^{2}[/tex]required to install the garden in Design A and Design B is $151.2 and $117.6

5)Mr. and Mrs. Harper would like to choose Design A because its most affordable than Design A.

Therefore Mr. and Mrs. Harper save money $159.6.

1) The area of the rectangular garden in design A

Area = length * width

From the fig, length = 9 feet

                      width = 12 feet

Area = 12 * 9 = 108 [tex]feet^{2}[/tex]

The area of the triangular garden in Design B

From the fig, Height = 12 feet

                     base = 14 feet

Therefore the area of the triangle = [tex]\frac{1}{2} * base *height\\\frac{1}{2} * 14 * 12[/tex]

                                                         = 84 [tex]feet^{2}[/tex]

2) The area of the rectangular deck is in design A

Area = length * width

        = 18 * 25

        = 450 [tex]feet^{2}[/tex]

The area of the rectangular deck is in design B

Area = length * width

        = 21 * 20

        = 420 [tex]feet^{2}[/tex]

The area of the rectangular deck without a  rectangular garden in design A is =

= 450 - 108 = 342 [tex]feet^{2}[/tex]

The area of the rectangular deck without a triangular garden in design B is =

= 420 - 84[tex]feet^{2}[/tex] = 372 [tex]feet^{2}[/tex]

3) The cost of $4.20 per [tex]feet^{2}[/tex]required to install the deck in Design A and Design B

Therefore the total cost required to install the deck in design A

= 450 * 4.20

= $ 1890

Therefore the total cost required to install the deck in Design B

= 420 * 4.20

= $ 1764

4) The cost of $1.40 per [tex]feet^{2}[/tex]required to install the garden in Design A and Design B

Therefore the total cost required to install the garden in design A

= 108 * 1.40

= $ 151.2

Therefore the total cost required to install the garden in Design B

= 84 * 1.40

= $ 117.6

5) Mr. and Mrs. Harper would like to choose Design A because its most affordable than Design A.

Mr. and Mrs. Harper save money if they choose design B over design A

= (1890 + 151.2) - (1764 +117.6)

= 2041.2 - 1881.6

= $159.6

Therefore Mr. and Mrs. Harper save money $159.6.

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The blue curve represents y = x³ and the red curve represents y = -x³.in the attached image.

What are the quadrants?

The quadrant refers to one of the four regions in a two-dimensional coordinate system, formed by two perpendicular lines that intersect at their common origin, or point of intersection.

a graph of y = x³ and y = -x³ on the same axes:

We can see the graph of equations y = x³ and y = -x³ in the attached image.

The blue curve represents y = x³ and the red curve represents y = -x³.

They are symmetric about the origin, and the blue curve is in the first and third quadrants while the red curve is in the second and fourth quadrants.

Hence, The blue curve represents y = x³ and the red curve represents y = -x³.in the attached image.

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From the diagram the value of v is √6

You should recall that Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.

Using the trigonometrical ratios, we have

Tangent = opposite /adjacent

This implies that

√2/1 = 2√3/v

cross and multiplying to have

v√2 = 2√3

Rationalizing the denominator and making v the subject of the formular we have

v = 2√3/√2 *√2/√2

v = 2√2/2

Therefore the value of v is √6

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41/2 days is equivalent tο 492 hοurs.

Divisiοn is an arithmetic οperatiοn that invοlves splitting a quantity intο equal parts οr determining hοw many times οne quantity is cοntained within anοther. It is cοmmοnly denοted by the symbοl ÷ οr /, and can be written as a fractiοn οr as a ratiο.

We knοw that there are 24 hοurs in day therefοre,

Tο cοnvert 41/2 days tο hοurs, we can use the fact that there are 24 hοurs in οne day:

41/2 days x 24 hοurs/day = 41 x 12 = 492 hοurs

Therefοre, 41/2 days is equal tο 492 hοurs.

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According to the solving time will they take together to wax the same car 16 minutes

The minute is a unit of time usually equal to 160 (the first sexagesimal fraction) of an hour, or 60 seconds.

Let's assume that Andrea takes x minutes to wax the car. Then Mathew takes x/2 minutes to wax the same car since he waxes twice as fast as Andrea.

We know that Andrea takes 24 minutes to wax the car. So we can substitute this value in the equation and solve for x.

x = 24 * 2 = 48

So Andrea takes 48 minutes to wax the car alone.

Now we can use the formula:

1/x + 1/(x/2) = 1/t

where t is the time taken by both of them together to wax the same car.

Substituting x = 48, we get:

1/48 + 1/24 = 1/t

Solving for t, we get:

t = 16minutes

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Tim's score range would be between 20.2 - 56.25 and 20.2 + 56.25, or between -36.05 and 76.45. To find the percentage of games

a. To find the percentage of candy wrappers that would have between 3.4 and 3.6 ounces, we need to calculate the z-scores for each of the values:

[tex]z-score for 3.4 ounces = (3.4 - 3.5) / 0.16 = -0.625[/tex]

[tex]z-score for 3.6 ounces = (3.6 - 3.5) / 0.16 = 0.625[/tex]

Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers between these two values is approximately 47.70%.

b. To find the percentage of candy wrappers that would have less than 3.3 ounces, we need to calculate the z-score for this value:

[tex]z-score for 3.3 ounces = (3.3 - 3.5) / 0.16 = -1.25[/tex]

Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers with less than 3.3 ounces is approximately 10.92%.

To find the percentage of candy wrappers with more than 3.62 ounces, we need to calculate the z-score for this value:

[tex]z-score for 3.62 ounces = (3.62 - 3.5) / 0.16 = 0.75[/tex]

Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers with more than 3.62 ounces is approximately 22.77%.

c. To find how many of the 1358 packets made that day have between 3.35 and 3.65 ounces, we need to convert these values to z-scores:

[tex]z-score for 3.35 ounces = (3.35 - 3.5) / 0.16 = -0.9375[/tex]

[tex]z-score for 3.65 ounces = (3.65 - 3.5) / 0.16 = 0.9375[/tex]

Using a z-table or a calculator with a normal distribution function, we can find the percentage of candy wrappers between these two values, which is approximately 62.97%. To find how many packets this represents, we can multiply this percentage by the total number of packets made:

[tex]0.6297 * 1358 = 856 packets[/tex]

Therefore, approximately 856 packets made that day have between 3.35 and 3.65 ounces.

d. To find how many games Tim would have scored 22 points or more if he plays 32 games, we first need to calculate the z-score for this value:

[tex]z-score for 22 points = (22 - 20.2) / 25 = 0.072[/tex]

Using a z-table or a calculator with a normal distribution function, we can find the percentage of games with a z-score greater than or equal to 0.072, which is approximately 53.10%. To find how many games this represents, we can multiply this percentage by the total number of games:

[tex]0.5310 x 32 = 17 games[/tex]

Therefore, Tim would have scored 22 points or more in approximately 17 games out of 32.

e. To find how many games Tim would have scored within 2.25 standard deviations from his average if he plays 32 games, we first need to calculate 2.25 standard deviations:

[tex]2.25 x 25 = 56.25[/tex]

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a)  The number of units that produces maximum profit is q = 12.

b) The price per unit that produces maximum profit is p = $39.

c)  The maximum profit is P = $386.

What is profit?

a) To find the number of units that produces maximum profit, we need to find the point where revenue equals cost. The revenue function is given by:

R(q) = pq = (63-2q)q = 63q - 2q²

The cost function is given by:

C(q) = 70 + 15q

The profit function is given by:

P(q) = R(q) - C(q) = (63q - 2q²) - (70 + 15q) = -2q² + 48q - 70

To find the number of units that produces maximum profit, we take the derivative of the profit function with respect to q, and set it equal to zero:

P'(q) = -4q + 48 = 0

Solving for q, we get:

q = 12

Therefore, the number of units that produces maximum profit is q = 12.

b) To find the price per unit that produces maximum profit, we substitute q = 12 into the price function:

p = 63 - 2q = 63 - 2(12) = 39

Therefore, the price per unit that produces maximum profit is p = $39.

c) To find the maximum profit, we substitute q = 12 and p = 39 into the profit function:

P = -2q² + 48q - 70 = -2(12)² + 48(12) - 70 = $386

Therefore, the maximum profit is P = $386.

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Answer:

60.5

Step-by-step explanation:

Answer: 60.50

Step-by-step explanation:

.

This transformation of figure 1  has been transformed to produce figure 2, can be described by (x' , y') = (x' -y')

Transformation describes how an item moves, particularly as they are shown on a coordinate plane.

There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or position. The four methods comprise

Pre-Image refers to the item's shape before transformation, whereas Image refers to the object's ultimate location and shape.

The linked image's preimage and image may be examined to determine that reflection is the involved translation.

The transformation rule for reflection over the y-axis is as follows:

(x, y) → (x, -y)

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The percentage of reduction in consumption required to keep the same expenditure is 25%.

Inflation is an economic phenomenon that occurs when the prices of goods and services increase over time.

To find out the percentage of reduction in consumption, we need to calculate the difference between the current and the original prices of the butter.

This can be done by subtracting the original price of the butter from the current price of the butter (25% costlier).

The difference can be expressed as a percentage by dividing the difference by the original price.

Therefore, the percentage of reduction in consumption required to keep the same expenditure is 25%.

This means that a housewife needs to reduce her consumption of butter by 25% in order to keep her expenditure the same.

Thus, the percentage of reduction in consumption required to keep the same expenditure is 25%.

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Answer:

5.0625

Step-by-step explanation:because it is 1.5 as a decimel and that to the power of 4 is 5.0625

Answer:

1.97

Step-by-step explanation:

(3/2)^4

3^4 / 2^4

81/16

Answer:

You can use the formula for the volume of a cuboid, which is Volume = length x width x height

You are given the volume of the cuboid as 108cm^3, the length as 4cm, and the width as 9cm. Let's substitute these values into the formula and solve for the height:

108cm^3 = 4cm x 9cm x height

To solve for height, you can divide both sides by 36 (which is equal to 4cm x 9cm) to isolate height:

108cm^3 ÷ 36 = 4cm x 9cm x height ÷ 36

3cm = height

So the height of the cuboid is 3cm.

We can easily say that the following about this question:

[tex]f(x)=x^2-x+1[/tex]  and  [tex]g(x)=2x+3[/tex]  can be combined as;

The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).

It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.

In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.

Let the capacity of the mug be x.

Given,

Mug is 5/8 full and contains 3/4 of water

So, 5/8 of the mug is filled with water

Therefore,

5/8 of x = 3/4

(5/8 )x = (3/4)

x = (3/4) × (8/5)

x = (24/20)

x = 1.2

Therefore, the capacity of the mug is 1.2.

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