If Marie were to paint her living room alone, it would take 3 hours. Her sister Fran could do the job in 6 hours. How many hours would it take them working together? Express your answer as a fraction reduced to lowest terms, if needed.

Answer:

147

Step-by-step explanation:

A= h^b b=21*14= 147

Answer:

The given expression is:

3x + 2 / (x + 1)(x² + x + 2)

To simplify this expression, we need to factor the denominator first:

x² + x + 2 = (x + 2)(x + 1)

So the expression becomes:

3x + 2 / (x + 1)(x + 2)(x + 1)

Next, we can use partial fraction decomposition to express the expression in terms of simpler fractions. Let's assume:

3x + 2 / (x + 1)(x + 2)(x + 1) = A/(x + 1) + B/(x + 2) + C/(x + 1)²

Multiplying both sides by the common denominator, we get:

3x + 2 = A(x + 2)(x + 1) + B(x + 1)² + C(x + 2)(x + 1)

Expanding the right side, we get:

3x + 2 = Ax² + 3Ax + 2A + Bx² + 2Bx + B + Cx² + 3Cx + 2C

Combining like terms, we get:

3x + 2 = (A + B + C)x² + (3A + 2B + 3C)x + (2A + B + 2C)

Since this equation holds for all values of x, the coefficients of each power of x must be equal on both sides. We can equate the coefficients of x², x, and the constant term to get a system of three equations for A, B, and C:

A + B + C = 0

3A + 2B + 3C = 3

2A + B + 2C = 2

Solving this system, we get:

A = 2/3

B = -1/3

C = -1/3

Substituting these values back into the partial fraction decomposition equation, we get:

3x + 2 / (x + 1)(x² + x + 2) = 2/3/(x + 1) - 1/3/(x + 2) - 1/3/(x + 1)²

Therefore, the simplified expression is:

3x + 2 / (x + 1)(x² + x + 2) = 2/3/(x + 1) - 1/3/(x + 2) - 1/3/(x + 1)²

A square is not created when a plane slices through a cone.

What is square?

A square is a geometrical shape that has four equal sides and four equal angles of 90 degrees.

What is cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a pointed top or apex. It looks like a funnel or an ice cream cone.

When a plane intersects or slices through a cone, it creates a variety of different shapes depending on the angle of the plane and the position of the cone.

If the plane intersects the cone at an angle perpendicular to its base, it will create a circle. If the plane intersects the cone at an angle that is not perpendicular to its base, it will create an ellipse.

If the plane intersects the cone at an angle that is parallel to one of its generators (the lines that can be drawn from the vertex of the cone to any point on its base), it will create a parabola. If the plane intersects the cone at an angle that is not parallel to one of its generators, it will create a hyperbola.

Therefore, a square is not created when a plane slices through a cone.

To learn more about cone visit:

https://brainly.com/question/1082469

#SPJ9

Therefore , the solution of the given problem of percentage comes out to be the firm expects that each warranty it sells will be worth $1.41.

In statistics, "a%" is used to refer to a figure or number that is expressed as a percentage of 100. Additionally rare are the forms that "pct," "pct," or "pc". It is typically represented by the symbol "%," though. Additionally, there are not any indicators and the proportion of each item to the overall amount is flat. Since percentages typically add up to 100, they are essentially integers. Either the expression "fraction" or the symbol for percentage (%) .

Here,

The price to substitute each item is $200. The anticipated price for each component is thus:

Expected cost per product equals Replacement cost x Failure Probability

=> Cost per product anticipated = 0.008 x $200

=>  Expected price per item is $1.60.

So, the following is the anticipated value of each warranty sold:

Expected worth of the warranty = Failure rate x (Replacement cost - Cost of warranty)

=>   Expected guarantee value = 0.008 * ($200 - $22 - $1.60).

=>  Expected guarantee value = 0.008 * $176.40

=>  Expected warranty worth is $1.41

As a result, the firm expects that each warranty it sells will be worth $1.41.

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ1

Answer:

Lion area: 60

Lion Perimeter: 34

Tiger Area: 60

Tiger perimeter: 64

Step-by-step explanation:

Answer:

To calculate the payback period (PBP) for this project, we need to determine how long it will take for the initial cash outlay of $40,000 to be recovered from the after-tax cash flows.

Year 1 cash flow = $10,000

Year 2 cash flow = $12,000

Year 3 cash flow = $15,000

Year 4 cash flow = $10,000

Year 5 cash flow = $7,000

Total cash inflows for year 1 and year 2 = $10,000 + $12,000 = $22,000

Total cash inflows for year 3 = $15,000

Total cash inflows for year 4 = $10,000

Total cash inflows for year 5 = $7,000

Cumulative cash inflows for year 1 and year 2 = $22,000

Cumulative cash inflows for year 3 = $37,000

Cumulative cash inflows for year 4 = $47,000

Cumulative cash inflows for year 5 = $54,000

It can be seen that the cumulative cash inflows reach the initial cash outlay of $40,000 after year 2, and therefore the payback period for this project is 2 years. Since the payback period is less than the maximum PBP of 3.5 years set by management, this project can be considered acceptable.

So, Hodgman Honest should recommend that Basket Wonders should accept this project as it has a payback period of only 2 years, which is less than the maximum PBP of 3.5 years set by management.

Answer: no they wouldn't be similar

Step-by-step explanation: if x=60 if triangle 1 then the third angle would be (180-(58+60)) =180-118=62
if we decide to calculate the third angle in triangle 2 we will have 180-(50+58) = 180-108=72

therefore not all angles in 1 are similar to angles in 2 so the triangles aren't similar

Answer: 260 ft^2

Step-by-step explanation:

Find the area of the triangle: 0.5*height*base = 0.5*10*20 = 100 ft^2

Find the area of the rectangle: 20*8 = 160 ft^2

Add them together: 160+100 = 260 ft^2

The probability of rolling an even number on a single die is 1/2, or 50%. This can be calculated by considering the possible outcomes of rolling the die.

There are six possible outcomes, and three of these are even numbers (2, 4, and 6). Therefore, there is a 3/6, or 1/2, chance of rolling an even number. In terms of probability, this can be expressed as a fraction, percentage, or decimal. As a fraction, the probability of rolling an even number on a single die is 3/6, or 1/2. As a percentage, the probability of rolling an even number on a single die is 50%. As a decimal, the probability of rolling an even number on a single die is 0.5. No matter how it is expressed, the probability of rolling an even number on a single die is 1/2, or 50%. This can be easily remembered by considering that there are six possible outcomes, and three of them are even numbers.

Learn more about probability here:

https://brainly.com/question/15124899

#SPJ1

Algebraic expressions are useful for solving different and complex equations in mathematics, as well as for modelling real-life situations such as revenue, cost, inference, etc

The algebraic expression is: [tex]6x - 9[/tex].

To represent the sentence as an algebraic expression, we can follow these steps: Identify the variable. In this case, “a number” is x. Identify the operation. In this case, “less than” means subtraction and “times” means multiplication.

An algebraic expression is an expression that contains variables, constants and mathematical operations. Algebraic expressions are useful because they can help us solve different and complex equations.

For example, if you want to calculate the area of a rectangle with length x and width y, you can use the algebraic expression xy to represent the area.

Write the expression using the order of operations. In this case, we need to multiply six by x first, then subtract nine from the result.

Therefore, The algebraic expression is: [tex]6x - 9[/tex]

Learn more about expression here:

https://brainly.com/question/953809

#SPJ1

The expressions can be written as  :a. log5.625 ≈ 0.75.

                                                             b. log6.4 + log6.12 ≈ 1.67.

                                                             c. log3.9^{4} ≈ 2.47.

What is logarithm function?

A logarithm function is a mathematical function that determines the power to which a fixed number, called the base, must be raised to produce a given value and The logarithm function is the inverse of the exponential function. The most commonly used base for logarithmic functions is 10 (log base 10), but other bases such as 2 (log base 2) and the natural logarithm base e (ln) are also used.

a. Since there is no base specified, we assume the base to be 10 by default. Therefore, we can write:

log5.625 = log(5625/1000)

Using the property log(a/b) = log(a) - log(b), we can simplify this expression to:

log5.625 = log(5625) - log(1000)

Using the change of base formula, we can convert the logs to a common base, such as 2 or e:

log5.625 = log(5625)/log(10) - log(1000)/log(10)

Evaluating the logs using a calculator or by simplifying, we get:

log5.625 ≈ 0.75

Therefore, log5.625 ≈ 0.75.

b. Using the property log(a) + log(b) = log(ab), we can simplify the expression:

log6.4 + log6.12 = log(6.4 × 6.12)

Using the change of base formula, we can convert this to a common base:

log6.4 + log6.12 = log(6.4 × 6.12)/log(10)

Evaluating the log using a calculator or by multiplying 6.4 and 6.12 and simplifying, we get:

log6.4 + log6.12 ≈ 1.67

Therefore, log6.4 + log6.12 ≈ 1.67.

c. Using the property log(a^{n}) = n log(a), we can simplify the expression:

log3.9^{4} = 4 log3.9

Using the change of base formula, we can convert this to a common base:

log3.9^{4} = 4 log(3.9)/log(10)

Evaluating the log using a calculator or by simplifying, we get:

log3.9^{4} ≈ 2.47

Therefore, log3.9^{4} ≈ 2.47.

To learn more about logarithm function, visit the link:

https://brainly.com/question/13473114

#SPJ1

The family actually lost purchasing power due to the combination of the wage increase and inflation, as their budget did not keep pace with rising prices.

We need to calculate the inflation-adjusted increase in their wages.

First, we can find the amount of the wage increase by multiplying the original budget by the percentage increase:

Wage increase = $22,300 x 0.03 = $669

Next, we need to adjust for inflation. We can do this by finding the inflation rate as a decimal (5.6% = 0.056) and subtracting it from 1 to get the inflation-adjustment factor:

Inflation-adjustment factor = 1 - 0.056 = 0.944

Finally, we can calculate the inflation-adjusted wage increase by multiplying the wage increase by the inflation-adjustment factor:

Inflation-adjusted wage increase = $669 x 0.944 = $631.08

Therefore, the family's net gain in purchasing power is:

Net gain = Inflation-adjusted wage increase - Original budget

Net gain = $631.08 - $22,300

Net gain = -$21,668.92

So the family actually lost purchasing power due to the combination of the wage increase and inflation, as their budget did not keep pace with rising prices.

Learn more about multiplying here : brainly.com/question/28773316

#SPJ1

The resulting number is 12/5

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

Given that we need to, increase the number 15/16 by 3/5 of it, then increase the resulting number by 3/5 of it

So, performing the operations,

15/16+15/16×3/5

= 15/16(1+3/5)

= 15/16(8/5)

= 120/80

= 3/2

Now,

3/2+3/2×3/5

= 3/2(1+3/5)

= 3/2(8/5)

= 24/10

= 12/5

Hence, the resulting number is 12/5

Learn more about arithmetical operations, click;

https://brainly.com/question/30553381

#SPJ2

Answer:

y=2x+10

Explanation: They start with paying $10 and have to pay and extra $2 for each time at the concession stand.

In the triangle, x has a value of 18.

A right triangle is one with a 90 degree inner angle. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The two arms of a right angle are made up of height and base.

We know that the respective sides of the two triangles in the diagram are proportional since they resemble one another. Namely, we have

AB / AE = BC / CD

Inputting the values provided yields:

x / 12 = 9 / 6

Finding x and simplifying results in:

x = 12 * (9/6) = 18

To know more about triangle visit:-

https://brainly.com/question/2773823

#SPJ1

Answer:

"Undefined slope"

Step-by-step explanation:

The line is vertical on the graph.

Every point on the line has the same x-coordinate.

If the line crosses the x-axis where x=-7, then the

x-coordinate of every point on the line is -7, and the

equation of the line is

                                     x = -7 .

The calculated value of the force of the resistance is 15.62 N

We can use Newton's Second Law of Motion to solve this problem. The formula is:

F = m*a

where F is the net force, m is the mass of the object, and a is the acceleration.

In this case, the brick is falling through water, so there are two forces acting on it:

The net force is the difference between these two forces:

F_net = F_gravity - F_resistance

The weight of the object is:

F_gravity = m*g

So, we have

F_gravity = 2 kg * 9.81 m/s^2 = 19.62 N

Now we can use the formula for net force to find the force of water resistance:

F_net = F_gravity - F_resistance

F_resistance = F_gravity - F_net

F_resistance = 19.62 N - m*a

This gives

F_resistance = 19.62 N - 2 kg * 2 m/s^2 = 15.62 N

Therefore, the force of water resistance is 15.62 N.

Read more about force at

https://brainly.com/question/13370981

#SPJ1

Answer:

Step-by-step explanation:

To calculate the equal monthly payments under this loan, we can use the formula for the present value of an annuity due, since the payments are due at the end of each period. The present value of the equal monthly payments can then be set equal to the loan amount of R250,000, and we can solve for the payment amount.

First, we need to calculate the present value factor for an annuity due with 12 payments per year over a four-year period, using a nominal annual rate of 6%.

PVIFA(due) = (1 - (1 + r/n)^(-nt))/((r/n)(1 + r/n))

Where:

r = nominal annual rate = 6%

n = number of compounding periods per year = 12

t = number of years = 4

PVIFA(due) = (1 - (1 + 0.06/12)^(-12*4))/((0.06/12)(1 + 0.06/12)) = 43.232

Next, we can use the formula for the present value of an annuity due to calculate the equal monthly payments:

PMT = PV / PVIFA(due)

Where:

PV = present value of the loan = R250,000

PMT = 250000 / 43.232 = R5,785.97

Therefore, your equal monthly payments will be R5,785.97. At the end of the four-year period, you will also need to make a final balloon payment of R50,000 to fully pay off the loan.

Option A correctly describes the area of the graph of the function.

How is an area of the graph calculated?

The area of a graph is the area under the function curve enclosed within the X-axis of the graph. Thus, it is the area of the figure formed by enclosing the function graph with the X-axis.

It is the integration of the function polynomial of the possible values of x that the function curve lies in.

Here the function equation is : [tex]f(x) = ( 25 - x^{2} )[/tex]

From the figure, we can see that the value of x varies from -5 to 5.

Initial x-value of integration = minimum value of x

                                          = -5

Final x-value of integration = maximum value of x

                                          = 5

Thus, the area of the graph can be correctly calculated as. :

               [tex]Area = \int\limits^{maxX}_ {minX} \, f(x)dx[/tex]

               [tex]Area = \int\limits^5_ {-5} \, (25-x^{2} )dx[/tex]

Hence, Option A correctly calculates the area of the graph given.

To learn more about Graphs, visit

https://brainly.com/question/29548482

#SPJ1

Step-by-step explanation:

2  2/3 =  8/3

8/3 * 1/4  = 8/12 =   2/3 pound in each portion

Answer:

The product of two numbers is 21.

Step-by-step explanation:

If the first number is -3, which equation represents this situation and what is the second number? A. The equation that represents this situation is x − 3 = 21.

Answer: a) We know that the Revenue equation is a polynomial of order 1, so we can write it in the form:

R(x) = ax + b

where a and b are constants to be determined. We also know that R(1) = 1 and R(5) = 9, so we have two equations:

a(1) + b = 1

a(5) + b = 9

Solving these equations simultaneously, we get:

a = 2, b = -1

Therefore, the Revenue equation is:

R(x) = 2x - 1

Similarly, the Cost equation is a polynomial of order 2, so we can write it in the form:

C(x) = ax^2 + bx + c

where a, b, and c are constants to be determined. We know that C(1) = R(1) = 1 and C(5) = R(5) = 9, so we have two equations:

a(1)^2 + b(1) + c = 1

a(5)^2 + b(5) + c = 9

We also know that C(2) = 0, so we have a third equation:

a(2)^2 + b(2) + c = 0

Solving these equations simultaneously, we get:

a = 1, b = -4, c = 4

Therefore, the Cost equation is:

C(x) = x^2 - 4x + 4

b) The common solutions to the Revenue and Cost equations represent the production level(s) at which the company makes a profit, since the Revenue equation represents the amount of money the company earns and the Cost equation represents the amount of money the company spends. In other words, the common solutions are the values of x for which R(x) - C(x) > 0. At these production levels, the company's revenue is greater than its cost, resulting in a profit. At production levels where R(x) - C(x) < 0, the company is making a loss. At production levels where R(x) - C(x) = 0, the company is breaking even. Therefore, the common solutions to the two equations signify the production levels at which the company makes a profit or breaks even.

Step-by-step explanation:

Answer:

First, we need to find the radius of the base of the cone. We can see from the grid that the diameter is 8 units, so the radius is 4 units (or 4 feet).

Next, we can use the formula for the volume of a cone to find the height:

V = (1/3)πr^2h

Substituting the given volume and radius, and using 3.14 for π, we get:

200.96 = (1/3) x 3.14 x 4^2 x h

Simplifying and solving for h, we get:

h = 200.96 / (1/3 x 3.14 x 4^2)

h = 200.96 / 53.02

h ≈ 3.79 feet (rounded to two decimal places)

To construct the cone vertically on the grid with respect to the center of the base, we can draw a circle with radius 4 units (or 4 feet) centered at the point (4,4) on the grid. Then, we can draw a line from the center of the circle (point (4,4)) up to a point above the circle that is 3.79 units (or 3.79 feet) away from the center. This line represents the height of the cone. Finally, we can connect the endpoint of the line to the points where the circle intersects the grid to complete the cone.

Step-by-step explanation:

To find the percentage that $4250 represents of $6500, we can use the following formula:

percentage = (part / whole) x 100%

where "part" is $4250 and "whole" is $6500.

Substituting these values into the formula, we get:

percentage = (4250 / 6500) x 100%

percentage = 0.6538 x 100%

percentage = 65.38%

Therefore, $4250 represents 65.38% of $6500.

Answer: It is approximately 65%

Step-by-step explanation: Divide $4,250 by $6,500 and your answer without rounding is 65.3846%

Answer:

3. 216 cm^3

4a. A = 5 ft, B = 4 ft.

4b. 88 ft^3

Step-by-step explanation:

3. Separate into two rectangular prisms:

Volume of first one: 4cm*2cm*3cm = 24cm^3

Volume of second one: 4cm*12cm*4cm = 192cm^3

Add them together: 24 + 192 = 216cm^3

4a.

Length A = 8-3 = 5ft.

Width B = 8-4 = 4ft.

4b. Separate into two rectangular prisms:

Volume of first one: 2ft*3ft*4ft = 24ft^3

Volume of second one: 8ft*4ft*2ft = 64ft^3

Add them together: 24 + 64 = 88ft^3

The two square roots of 5 (cos(120°) + i sin(120°)) are sqrt(5) × (cos(60°) + i sin(60°)) and sqrt(5) × (cos(300°) + i sin(300°)).

The complex number in question is the square root of 5, written in trigonometric form as cos(120°) + i sin(120°). To calculate the two individual roots, we can use the identity for the square root of a complex number, which states that for any complex number, z, the square root of z is equal to (sqrt(|z|)) × (cos(θ/2) + i sin(θ/2)), where θ is the argument of z. In this case, we have |z| = 5 and θ = 120°. Therefore, the two individual roots are equal to (sqrt(5)) × (cos(60°) + i sin(60°)) and -(sqrt(5)) × (cos(60°) + i sin(60°)) = sqrt(5) × (cos(300°) + i sin(300°)).

In conclusion, the two square roots of 5 (cos(120°) + i sin(120°)) are sqrt(5) × (cos(60°) + i sin(60°)) and sqrt(5) × (cos(300°) + i sin(300°)).

Learn more about square roots  here:

https://brainly.com/question/29286039

#SPJ1

The quadratic equation in the given graph can be written in the vertex-form as:

y = -2(x - 1)² + 4

We can see the graph of a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)² + k

in the graph we can see that the vertex is (1, 4), replacing that we will get:

y = a*(x - 1)² + 4

In the graph we also can see that the curve passes through the point (0, 2), replacing thesevalues in the equation we will get:

2 = a*(0 - 1)² + 4

2 = a + 4

-2 = a

Then the quadratic is:

y = -2(x - 1)² + 4

Learn more about quadratic equations at:

https://brainly.com/question/1214333

#SPJ1

Part A: The actual dimensions of the pool are 10 feet long and 5 feet wide.

Part B: the cost of the cover for the pool would be $15.00.

Dimension is a measure of a physical property of an object, such as its length, breadth, height, or mass.

Part A: The actual dimensions of the pool can be determined by using the given scale. To do this, we need to convert the given measurements in inches to feet. We can do this by dividing the given measurements in inches by the scale, which is 2 inches equals 7 feet.

The actual length of the pool is 20 ÷ 2 = 10 feet.

The actual width of the pool is 10 ÷ 2 = 5 feet.

Therefore, the actual dimensions of the pool are 10 feet long and 5 feet wide.

Part B: To calculate how much it would cost to buy a cover for the pool, we need to determine the area of the pool. We can do this by multiplying the length by the width of the pool.

Area = length x width

Area = 10 ft x 5 ft

Area = 50 ft²

Therefore, the cost of the cover for the pool would be

$0.30 x 50 ft² = $15.00.

For more questions related to area

https://brainly.com/question/28020161

#SPJ1

Question :

The blueprint of a pool has a scale of 2 inches equals 7 feet. The scale drawing is shown below. the length is 20 and the width is 10

Part A What are the actual dimensions of the pool? Blueprint: 10 in. Actual: ft Blueprint: 20 in. Actual: ft

Part B How much would it cost to buy a cover for the pool that costs $0.30 per square foot?