A ladder 35feet long leans against the side of a building. If the angle formed between the ladder and the ground is 60°,how far is the bottom of the ladder from the base of the building?[Given that cos 60° = 0.5]​

One artist not working scenario helps determine domain and range. It shows the max hours one needs to work when the other is not working. C' represents Claude's work hours, and P represents Philipe's work hours on the vertical axis.

The scenario where one of the artists is not working is helpful in finding the domain and range of their work hours. This scenario shows the maximum number of hours one artist would need to work when the other artist is not working. For instance, if Philipe is not working, Claude would have to work for 15 hours (60 caricatures ÷ 4 caricatures per hour) to meet their goal. Similarly, if Claude is not working, Philipe would have to work for 20 hours (60 caricatures ÷ 3 caricatures per hour) to meet their goal. On the horizontal axis, we can represent the hours that Claude works (C'), and on the vertical axis, we can represent the hours that Philipe works (P).

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Answer: g=18

Step-by-step explanation:

g*4=72

g=72/4

g=18

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.

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Step-by-step explanation:

2  2/3 =  8/3

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

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.

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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: 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:

147

Step-by-step explanation:

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

The measure of the side J of the triangle ΔIJK will be 43 units.

The law of sines defines the ratio of triangle sides, and their respective sine angles are equivalent. The law of sines is also known as the sine law, sine rule, and sine formula.

Given that in the triangle i = 100 inches,  m∠I=115° and m∠J=23°. The measure of the length J will be calculated as:-

100 / sin115 = J / sin23

J = (100) x sin23 / sin115

J = 100 x 0.43

J = 43 units

The length of side J will be 43 units.

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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.

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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

Answer:

512 ft and 1,232 ft

Step-by-step explanation:

area is length x width

the pool's area can be calculated doing 32ft x 16ft

the area of the pool is 512 ft

the deck's area can be calculated doing 28ft x 44ft

the area of the deck is 1,232 ft

you're welcome<3

Answer:

8x - 58 ≤ 500

8x ≤ 500 + 58

8x ≤ 558

x ≤ 69.74

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.

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

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

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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.

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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.

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Answer:

X = 61,  Angle 57 and 123

Step-by-step explanation:

If you could provide the exact question that would be great, but from the information given what we know is that the entirety of half of a circle is 180 degrees so the angle at x-4 and the angle and 2x+1 must be equal to 180 degrees.

Therefore:

x-4  +  2x+1 = 180 degrees

X = 61,    Therefore:

x-4 -->  61 -4 = 57 degrees

2x+1 ---> 2(61) +1  = 123 degrees

So:

The angles are 57 degrees for x-4 and 123 for 2x+1 .

Explanation:

She scored 92 points in 4 games. The unit rate is 92/4 = 23 points per game.

Over the course of 17 games, Maria would have a total of 17*23 = 391 points assuming her scoring rate is kept the same.

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:

"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 .

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.

Step-by-step explanation:

Your POST does not match the picture....I will use the equation in the picture

h = - 1/8 d^2 + 4d + 5  

a)     when d = 1   find 'h' by putting '1' in the equation for 'd'

       h = -1/8 *(1^2) + 4(1) + 5 = 8  8/9 ft high

b)  when d = 33

          h = -1/8 ( 33^2) + 4 (33) + 5 =   .875 ft = 7/8 ft high

                yah...it will probably hit your enemy

Answer:0.25

Step-by-step explanation:

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.

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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.

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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.