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Answer:

The formula for compound interest is given by:

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

Where:

A = the amount of money accumulated after n years

P = the principal (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $2,500, r = 0.05 (since 5% = 0.05), n = 2 (since interest is compounded semiannually), and t = 15. Substituting these values into the formula, we get:

A = 2500(1 + 0.05/2)^(2*15)

A ≈ $5,551.33

Therefore, Lyla's investment will be worth approximately $5,551.33 after 15 years if interest is compounded semiannually.

10³•10⁵•10³

Step-by-step explanation:

10³means 10×3,10⁵means 10×5and 10³means 10×3 30+50+30=110

The product of the expressions are;

Step 1: (x + 2)(x + 3) and 3(x + 3)/4(x + 5)

Step 3: 4(x + 3) × 3(x + 3)/4(x + 5)

Step 4: 3/x + 5

It is important to note that algebraic expressions are described as expressions that are composed of variables, terms, coefficients, constants and factors.

From the information given, we have the fraction;

4x + 8/x² + 5x + 6 × 3x + 9/4x + 20

To determine the product, let us reduce the expressions to their lowest forms, we have;

4x + 8 = 4(x + 2)

x² + 5x + 6 = (x + 2)(x + 3)

3x + 9 = 3(x +3)

4x + 20 = 4(x + 5)

Substitute the expressions

4(x + 2)/(x + 2)(x + 3)  × 3(x +3)/4(x + 5)

divide the common terms

4(x + 3) × 3(x + 3)/4(x + 5)

Divide further, we have.

3/x + 5

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Answer:i think -81

Step-by-step explanation:3x (-3) = -9.        -9x(-3)=27.       27x(-3)= -81

the pressure at a depth of 66 ft is 197,580 Pa, and the volume of the tank at this depth is 0.000505 L.

To find the pressure at a depth of 66 ft in a liquid, we can use the formula:

pressure = density x gravity x depth

Assuming the liquid in the tank is water, the density is 1000 kg/m³, and gravity is 9.81 m/s².

First, we need to convert 66 ft to meters:

66 ft x 0.3048 m/ft = 20.1168 m

Then, we can find the pressure at this depth:

pressure = 1000 kg/m³ x 9.81 m/s² x 20.1168 m = 197,580 Pa

To find the volume of the tank at this depth, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature:

P₁V₁ = P₂V₂

where P₁ and V₁ are the initial pressure and volume (1 atm and 10 L, respectively), and P₂ and V₂ are the final pressure and volume.

We can rearrange this equation to solve for V₂:

V₂ = (P₁ x V₁) / P₂

Substituting the values, we get:

V₂ = (1 atm x 10 L) / (197,580 Pa / 1 atm) = 0.000505 L

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To answer a student question on Brainly, first, carefully read the question and understand what is being asked. Then, click on an item from the list or group of pictures provided at the bottom of the problem. Hold down the mouse button and drag the item into the correct position in the answer box.

Release the mouse button when the item is placed. If you change your mind, drag the item to the trashcan. Simply click the garbage button to start anew after clearing all your answers. Always be sure to respond with accuracy, professionalism, and friendliness.

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Answer:

x is first angle

y is second angle

and z is third angle

Step-by-step explanation:

This question is solved by a system of equations. We have that:x is the first angle.y is the second angle.z is the third angle.Doing this, we get that:The first angle measures 30º.The second angle measures 67º.The third angle measures 83º.The sum of the measures of the angles of a triangle is 180. This means that The sum of the measures of the second and third angles is five times the measure of the first angle.This means that:From this, the first angle can be found:The measure of the first angle is of 30º.The third angle is 16 more than the second.This means that:Since We get that the second angle is:The second angle measures 67º.For the third angle:The third angle measures 83º.

Each portion of pasta is 2/3 pounds.

Prοpοrtiοn or portion, in general, is referred tο as a part, share, οr number cοnsidered in cοmparative relatiοn tο a whοle. Prοpοrtiοn definitiοn says that when twο ratiοs are equivalent, they are in prοpοrtiοn. It is an equatiοn οr statement used tο depict that twο ratiοs οr fractiοns are equal.

To divide 2 2/3 pounds of pasta into fourths, we can first convert the mixed number to an improper fraction:

2 2/3 = (2 x 3 + 2)/3 = 8/3

Then, we can divide 8/3 by 4 to find the amount of pasta in each portion:

8/3 ÷ 4 = (8/3) x (1/4) = 2/3

Therefore, each portion of pasta is 2/3 pounds.

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Answer:

0.00005

Step-by-step explanation:

you move 5 decimal places left starting from 7 and right it as a decimal.

Ans=0.00007

Answer:

32.67 square meters

Step-by-step explanation:

finding the area of the shaded region.

area of sector = (θ/360°) x πr²

where "θ" is the central angle of the sector in degrees, "r" is the radius of the sector, and π is a mathematical constant approximately equal to 3.14.

Substituting the given values into the formula, we get:

area of sector = (60°/360°) x π(14m)²

area of sector = (1/6) x 3.14 x 196m²

area of sector = 32.67m² (rounded to two decimal places)

Therefore, the area of the section is 32.67 square meters

The gradient of the line is 5, and the y-intercept of the line is 15.

The given equation is in the form of y = mx + c, where m is the gradient (slope) of the line and c is the y-intercept of a straight line represented in 2D plane.

Rearranging the given equation, we get:

y - 6 = 5x + 9

Adding 6 to both sides, we get:

y = 5x + 15

Now we can see that the equation is in the required form of y = mx + c. The gradient (slope) of the line is 5, which is the coefficient of x in the equation. The y-intercept is 15, which is the constant term in the equation.

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x²=22.136

Its the last one

Answer:

This isn't a reasonable scale

Step-by-step explanation:

Using the scale 1 in. = 4 in., the width of the scaled down painting will be:

48 in. ÷ 4 = 12 in.

And the height of the scaled down painting will be:

120 in. ÷ 4 = 30 in.

So the scaled down painting will be 12 in. wide and 30 in. tall. Since Sarah's paper is 12 in. wide and 24 in. tall, the scaled down painting will fit within the paper's width but will be taller than the paper.

Therefore, the scale is not reasonable because the scaled down painting will not fit within the dimensions of Sarah's paper.

(x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.

Functiοn can be define in which it relates an input tο οutput.

If the graph οf a pοlynοmial functiοn P(x) has x-intercepts at x = -4, x = 0, and x = 5, then we knοw that the factοrs οf P(x) are (x + 4), x, and (x - 5). This is because a pοlynοmial has x-intercepts where the value οf P(x) is equal tο zerο, and this οccurs when each factοr is equal tο zerο.

Therefοre, we can cοnclude that (x + 4) and (x - 5) are factοrs οf the pοlynοmial P(x), but x is nοt necessarily a factοr. This is because x is a linear factοr with a zerο intercept, but it cοuld be cancelled οut by anοther factοr in the pοlynοmial.

Thus, the cοrrect statement is:

(x + 5) is nοt necessarily a factοr οf the pοlynοmial.

(x-4) is a factοr οf the pοlynοmial.

The degree οf the pοlynοmial is 3 οr greater since the pοlynοmial has three x-intercepts. Hοwever, we cannοt determine the exact degree οf the pοlynοmial withοut additiοnal infοrmatiοn.

Therefοre, (x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.

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By adding fractions that represent each of the amounts of cupcakes, we can see that you need 9 cupcakes for you and your friends.

Her we know that you want 3 halves of a cupcake for yourself, 8 halves for your friend, and 7 halves for your other friend.

So we just need to add all of these fractions, to do so, we need to solve the follwing opeartion:

3*(1/2) + 8*(1/2) + 7*(1/2)

3/2 + 8/2 + 7/2

All of these have the same denominator so we can directly add them up:

3/2 + 8/2 + 7/2 = (3 + 8 + 7)/2

(3 + 8 + 7)/2 = 18/2

18/2 = 9

You need 9 cupcakes for you and your friends.

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Complete question:

"I want 3 halves of a cupcake for myself, 8 halves for my friend, and 7 halves for our other friend. How many halves we need in total?"

1) y = -3x and y = -3x + 2: inconsistent system of equations.

2) y = x - 5 and -2x + 2y = - 10: consistent and independent.

3) 2x - 5y = 10 and 3x + y = 15 : consistent and independent.

The given equation are:

The graph for each system of equations is plotted.

1) y = -3x and y = -3x + 2

From the graph 1 it is shown that the lines for the each equation form the parallel lines.

Thus, system of equations are inconsistent.

2) y = x - 5 and -2x + 2y = - 10

From the graph 2 it is shown that the lines for the each equation form the coincident lines.

Thus, system of equations are consistent and independent.

3) 2x - 5y = 10 and 3x + y = 15

From the graph 2 it is shown that the lines for the each equation form the coincident lines.

Thus, system of equations are consistent and independent.

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Answer: a) The profit function can be written as:

P(x) = 5x - 400x + 600

To find the asymptotes, we can look at the denominator of the second term, which is (x - 3). This means that there is a vertical asymptote at x = 3. To find the intercepts, we can set P(x) = 0:

5x - 400x + 600 = 0

Solving for x, we get:

x = 1.5 and x = 2.5

Therefore, there are x-intercepts at (1.5, 0) and (2.5, 0). To sketch the graph, we can also note that the coefficient of x^2 is negative, which means that the graph is a downward-facing parabola.

b) The domain of the function is the set of all possible values of x, which in this context represents the amount of coffee sold. Since we cannot sell a negative amount of coffee, the domain is x ≥ 0.

The range of the function is the set of all possible values of P(x), which represents the profit. Since the coefficient of x^2 is negative, the maximum profit occurs at the vertex of the parabola. The vertex has x-coordinate:

x = -b/(2a) = -(-400)/(2(-200)) = 1

Therefore, the maximum profit occurs when x = 1. The vertex has y-coordinate:

P(1) = 5(1) - 400(1) + 600 = 205

Since the coefficient of x^2 is negative, the range is (-∞, 205].

c) The horizontal asymptote of the function is y = -400, which represents the long-term average profit per kilogram of coffee sold. This means that as x gets very large, the profit per kilogram approaches -400. This could happen, for example, if the cost of producing the coffee increased significantly while the price remained the same.

d) To find the amount of coffee that must be sold to make a profit of $4000, we can set P(x) = 4000 and solve for x:

5x - 400x + 600 = 4000

Simplifying, we get:

-395x = -3400

Dividing both sides by -395, we get:

x ≈ 8.61

Therefore, approximately 8.61 kg of coffee must be sold to make a profit of $4000.

Step-by-step explanation:

Therefore, if we are using 27 cups of sugar, we also need 18 cups of wheat.

An ordered combination of integers a and b, rendered as a / b, is a ratio if b is not equal to 0. A percentage is an expression that sets two numbers at the same value. For instance, you could put the percentage as follows: 1: 3 if it's 1 male and 3 girls. (for every one boy there are 3 girls)

If 8 cups of flour are mixed with 12 cups of sugar, then the ratio of flour to sugar is:

8 : 12

Simplifying this ratio by dividing both numbers by 4, we get:

2 : 3

This means that for every 2 cups of flour, we need 3 cups of sugar.

If we are using 27 cups of sugar, we can set up a proportion to find out how much flour we need:

2/3 = x/27

Multiplying both sides by 27:

2 × 27 / 3 = x

Simplifying:

x = 18

Therefore, we need 18 cups of flour if we are using 27 cups of sugar.

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In the given problem,  the displacement vector of the truck with respect to the police car is (-75, 60). This means that the truck is 75 km to the west and 60 km to the north of the police car.

To solve this problem, we can use vector addition. Let's assume that the police car is at the origin, and let the positive x-axis point west and the positive y-axis point north. Then, the initial position of the truck can be represented by the vector (-d, 0), where d is the distance between the police car and the crossroad.

Since the truck is traveling due north, its velocity vector is (0, 60). Similarly, the velocity vector of the police car is (-75, 0). We know that both vehicles will reach the crossroad at the same time, which means that their displacement vectors will have the same magnitude and direction.

Let's call the displacement vector we're looking for "D". Using the formula for displacement, we can write:

D = vt

where v is the average velocity of both vehicles, and t is the time it takes for them to reach the crossroad (which is one hour). The average velocity is given by the vector sum of the velocities of the truck and the police car:

v = (0, 60) + (-75, 0) = (-75, 60)

Substituting in the values for v and t, we get:

D = (-75, 60) * 1 = (-75, 60)

Therefore, the displacement vector of the truck with respect to the police car is (-75, 60). This means that the truck is 75 km to the west and 60 km to the north of the police car.

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Answer:

7/8 - 2/3 = 5/8 pint of water left in the bottle.

Answer:

To calculate the interest rate, we can use the formula for the present value of an annuity:

PV = PMT x [(1 - (1 + r)^(-n)) / r]

where:

PV = present value

PMT = monthly payment

r = interest rate per period

n = number of periods

In this case, we have:

PV = $12,300 (the sticker price)

PMT = $420

n = 36 (36 months)

Substituting these values into the formula, we get:

12,300 = 420 x [(1 - (1 + r)^(-36)) / r]

Simplifying this equation algebraically is not possible, so we need to use numerical methods to solve for r. One way to do this is to use a financial calculator or spreadsheet program, which can find the interest rate that makes the equation true. Using Excel's RATE function, for example, we get:

=RATE(36,-420,12300)

This gives us an interest rate of approximately 3.33% per month or 39.96% per year.

Therefore, Ella is being offered an interest rate of 3.33% per month or 39.96% per year.

Slope is zero and the y-intercept is (0,-5)

What is slope ?

In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points.

In other words, the slope of a line is the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line. It can also be thought of as the rate at which the line rises or falls as it moves horizontally.

The formula for calculating slope is:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

According to the question:
The equation Y = -5 is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Comparing the equation Y = -5 to y = mx + b, we can see that:

The slope, m, is 0, since there is no x-term in the equation.

The y-intercept, b, is -5, since that is the constant value in the equation.

Therefore, the correct answer is:

B. Slope is zero and the y-intercept is (0,-5)


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the probability that they are both Democrats. round to the nearest thousandth if necessary is 0.194

The probability that BOTH is democrats means the probability of "one being democrat" AND "another also being democrat".

The AND means we need to MULTIPLY the individual probability of a person being a democrat.

The probability that a voter is democrat is 44% (0.44) -- stated in the problem

Now, the Probability of BOTH being Democrats is simply MULTIPLYING 0.44 with 0.44

Rounded to the nearest thousandth, 0.194

The last answer choice is correct.

the complete question is-

In one town 44% of all voters are Democrats if two voters are randomly selected for a survey find the probability that they are both Democrats. round to the nearest thousandth if necessary.

0.189

0.880

0.440

0.194

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Answer:

  1759 square meters

Step-by-step explanation:

You want the surface area of a cuboid with a half-cylinder top.

The lateral area of the figure is the product of the length of the mailbox (0.45 m) and the perimeter of the end. The perimeter of the end is the sum of the lengths of the straight sides and half the circumference of a circle with diameter 0.3 m.

  P = 0.3 + 2·0.4 + π/2(0.3) = 1.571 . . . . . meters

  LA = Ph = (1.571 m)(0.45 m) = 0.70695 m²

The end area is twice the area of the rectangular portion of the end, plus the area of a circle 0.3 m in diameter.

 EA = (0.3 m)(0.4 m) + 3.14(0.3/2 m)² = 0.31065 m²

The total area of 1 mailbox is ...

  LA +EA = 0.70695 m² +0.31065 m² = 1.0176 m²

Then the area of 1728 mailboxes is ...

  1728 × 1.0176 m² ≈ 1758.4 m² ≈ 1759 m²

About 1759 square meters of aluminum will be needed for the 1728 mailboxes.

__

Additional comment

This presumes there is no waste in cutting the semicircular shape from the supplied aluminum.

Using geometric progression Rabbits after 5 years will be 5120. Rabbits after 10 years will be 52,428,800.

When each term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the series. It should be mentioned that the common ratio is obtained by dividing any succeeding term by its preceding term.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate organizations or groups.

In this question,

The number of rabbits initially=50=a

rabbits after 6 months=100

common ratio=r= 100/50=2

Since it is a geometric progression, the 11th term will give us the number of rabbits after 5 years.

a₁₁=a₁(r)¹¹⁻¹

   =50(2)¹⁰=5120

the 21th term will give us the number of rabbits after 10 years.

a₂₁=a₁(r)²¹⁻¹

    =50(2)²⁰=52,428,800

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Mr. Oppong's chargeable income for the year of assessment 2022 is GH¢109,100.

Taxes must generally be paid on all types of income, even those derived from a business or profession. Employment. Dividends.

We must take into account Mr. Kwesi Oppong's salary, benefits, and any deductions when determining his chargeable income for the assessment year of 2022.

Let's start by figuring out his gross revenue for 2022. The annual wage scale for Mr. Oppong is GH85,000 X GH5,000 - GH130,000, which denotes a salary range of GH85,000 to GH130,000. To make things easier, we might suppose that his pay is the midpoint of the range, or GH107,500.

His annual acting allowance is GHC 5,000, so the following would be his total income from salary and allowances:

GH107,500 plus GH5,000 plus (GH300 x 12) plus (GH250 x 12) equals GH114,500.

Next, we must look at his advantages. Mr. Oppong is given a vehicle with a designated driver and free fuel, as well as a furnished place to stay. They are taxable benefits, but in order to estimate their worth, we need more details.

Mr. Oppong also holds a life insurance policy with a GHC 70,000 capital and GHC 8,000 yearly premium. This is not a necessary component of his chargeable income.

Let's now explore the inferences made by Mr. Oppong. 5.5% of his income is put into Social Security by him. Since the Social Security rate is set at GH450 every month, Mr. Oppong can only contribute a maximum of GH5,400 (GH450 x 12) in a given year.

As a result, the following would be Mr. Oppong's chargeable income for the year of assessment 2022:

GH114,500 minus GH5,400 equals GH109,100.

Thus, GH 109,100 will be Mr. Oppong's chargeable income for the assessment year 2022.

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Step-by-step explanation:

Area of the trapezoid = height x average of bases

                 area = 4 x (8+13)/2) = 42 in^2

Area of triangle  = 1/2 base * height   = 1/2 (13-8) * 4 = 10 in^2

The volume of the solid is approximately 0.558 cubic units.

To find the volume of the solid, we need to integrate the area of the semi-circles along the a-axis.

We know that the diameter of each semi-circle is the distance between the functions f(x) and g(x), which is:

d(a) = f(a) - g(a) = ln(a) + 1 - (a-1) = ln(a) - a + 2

The radius of each semi-circle is half of the diameter, which is:

r(a) = (ln(a) - a + 2) / 2

The area of each semi-circle is π times the square of its radius, which is:

[tex]A(a) = πr(a)^2 = π/4 (ln(a) - a + 2)^2[/tex]

To find the volume of the solid, we integrate the area of each semi-circle along the a-axis, from a = e to a = 2:

V = ∫[e,2] A(a) da

V = ∫[e,2] π/4 [tex](ln(a) - a + 2)^2 da[/tex]

V ≈ 0.558 (rounded to the nearest thousandth)

Therefore, the volume of the solid is approximately 0.558 cubic units.

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The equation for the function is D(x) = 65 - 0.8x. Where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.

What is a linear function?

A linear function is a mathematical function that has a constant rate of change or slope between the independent variable (x) and the dependent variable (y). It is a function that can be graphically represented as a straight line.

We can use a linear function to approximate the depth of the water in the reservoir x months after the start of the study, since the depth is dropping at a constant rate of 0.8 meters per month. Let D(x) be the depth of the water in meters x months after the start of the study. Then we have:

D(x) = 65 - 0.8x

where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.

Therefore, the equation for the function is D(x) = 65 - 0.8x.

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Answer:

0=-ax^2+bx+c

Step-by-step explanation: