enter the number that belongs in the green box

The graph of the piecewise function for this problem is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

The definitions to the function in this problem are given as follows:

Hence the graph of the piecewise function for this problem is given by the image presented at the end of the answer.

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Answer:

a)  x = 2 and x = 4

Step-by-step explanation:

A quadratic function is a mathematical function of the form f(x) = ax² + bx + c, where a, b, and c are constants and x represents the independent variable.

The solutions of a graphed quadratic function are the x-values of the points where the parabola crosses the x-axis.

These solutions are also known as the x-intercepts, roots, or zeros of the quadratic function.

From inspection of the given graph, the function crosses the x-axis at x = 2 and x = 4.

Therefore, the solutions of g(x) = -x² + 6x - 8 are:

Answer:

x=2 and x=4.

Step-by-step explanation:

The solution of g(x)=-x^2+6x-8 is the point where the graph of the function intersects the x-axis. This point is (4,0) and (2,0).

Therefore, the solution of g(x)=-x^2+6x-8 is x=4 and x=2.

Another method:

Similarly, we can find the value of x by factorization method too.

g(x)=x^2+6x-8

let g(x)=0

0=x^2+6x-8

x^2-6x+8=0

doing middle-term factorization:

x^2-(4+2)x+8=0

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

x(x-4)-2(x-4)=0

(x-4)(x-2)=0

either

x=4

0r

x=2

Therefore x=4 and x=2.

[tex] \bold{a {}^{n + 3} - 3a {}^{n + 2} - 4a {}^{n + 1} - a {}^{n} \: \: by \: \: - a {}^{n} \: \: x {}^{2} }[/tex]

Case of multiplication of a Polynomial by a monomial. The rule says that, to multiply the monomial by each of the terms of the polynomial, taking into account the law of signs, separating the partial products with their own signs. That is, we apply the Distributive Law of multiplication.

Then, we will solve by Distributive law.

[tex]\bold{(a {}^{n + 3} - 3a {}^{n + 2} - 4a {}^{n + 1} - a {}^{n})( \: \: - a {}^{n} \: \: x {}^{2} ) }[/tex]

[tex] \sf{a {}^{n + 3}( - a {}^{n}x {}^{2}) - 3a {}^{n + 2}( - a {}^{n}x {}^{2}) - 4a {}^{n + 1} ( - a {}^{n} x {}^{2} ) - a {}^{n} ( - a {}^{n} x {}^{2}) }[/tex]

[tex] \sf{ - 1 \cdot 1a {}^{n + 3 + n}x {}^{2} + 3 \cdot1 a{}^{n + 2 + n}x {}^{2} + 4 \cdot1a {}^{n + 1 + n}x {}^{2} + 1 \cdot1a {}^{n + 2}x {}^{2} }[/tex]

[tex]\bold{ Answer}=\sf{- a {}^{2n + 3} x {}^{2} + 3a {}^{2n + 2}x {}^{2} + 4a {}^{2n + 2}x {}^{2} + a {}^{2n} x {}^{2}} [/tex]

To find the value above which the top 25% of scores lie, we need to find the z-score corresponding to the 75th percentile and use it to compute the corresponding raw score.

The z-score corresponding to the 75th percentile can be found using a standard normal distribution table or calculator. The 75th percentile corresponds to a cumulative probability of 0.75, so we need to find the z-score such that the area under the standard normal curve to the left of that score is 0.75.

Using a standard normal distribution table, we can look up the z-score corresponding to a cumulative probability of 0.75, which is approximately 0.67.

Alternatively, we can use the inverse cumulative distribution function (also known as the percent point function) of the standard normal distribution to find the z-score. In Python, we can use the scipy.stats.norm.ppf function to do this:

from scipy.stats import norm

z_score = norm.ppf(0.75)

Either way, we find that the z-score corresponding to the 75th percentile is approximately 0.67.

To find the raw score corresponding to this z-score, we can use the formula:

z = (x - mu) / sigma

where x is the raw score, mu is the mean, and sigma is the standard deviation. Solving for x, we get:

``x = z * sigma + mu

Plugging in the values for `z`, `sigma`, and `mu`, we get:

x = 0.67 * 40 + 300

Simplifying the expression, we get:

x = 326.8

Therefore, the top 25% scores are above the value of 326.8.

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Answer:

It's C: 400

Step-by-step explanation:

The inside dimensions of the tank are:

h = 40 inches

w = 40 inches

l = 48 inches

Convert to Feet:

h = 40 inches / 12 = 3.33 feet

w = 40 inches / 12 = 3.33 feet

l = 48 inches / 12 = 4 feet

Volume of one tank = 3.33 feet * 3.33 feet * 4 feet

= 44 cubic feet (approximately)

Since there are nine tanks, we multiply the volume of one tank by nine to get the total volume:

Total volume = 44 cubic feet * 9

= 396 cubic feet

Rounding the answer to the nearest whole number, the total volume is approximately 396 cubic feet.

Therefore, the correct answer among the given options is 400.

Hope that helped!

The function represented by the graph is f(x) = ln(0.5x).

The graph displays a diminishing curve that begins above the x-axis and moves closer to it as x grows.

Logarithmic functions most  typically take this structure of graph.

Only f(x) = ln(0.5x), where ln stands for the natural logarithm, is one of the many functions that can express a logarithm.

The inverse of the exponential function with base e is the natural logarithm, which has a base of e (about 2.718).

The rate at which the function decrements is determined by the 0.5 coefficient in ln(0.5x).

The argument of the logarithm (0.5x) as it  grows as x increases, causes the function to approach the x-axis more slowly.

This is consistent with how the graph in the provided graphic behaves.

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Answer: Ratio of their investments is 3:4:6:7. Ratio of profits is 13:4:6:7.

Step-by-step explanation:

a. we know that their investments are 30,000 , 40,000 , 60,000 , 70,000 respectively.

so the ratio o their investments is, A:B:C:D = 3:4:6:7

A: (360-120) x (30000/ 30000+40000+60000+70000) = 36

B: (360-120) x (40000/ 30000+40000+60000+70000) = 48

C: (360-120) x (60000/ 30000+40000+60000+70000) = 72

D: (360-120) x (70000/ 30000+40000+60000+70000) = 84

b. For dividing the profit, it is given that 1/3rd of the profit is reserved for the manager. So,

1/3 of360 = 120

A: 120 + (360-120) x (30000/ 30000+40000+60000+70000) = 156

B: (360-120) x (40000/ 30000+40000+60000+70000) = 48

C: (360-120) x (60000/ 30000+40000+60000+70000) = 72

D: (360-120) x (70000/ 30000+40000+60000+70000) = 84

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The number of feet of flat bar needed to complete the gate is 34 feet (rounded up to the nearest whole number).

To calculate the number of feet of flat bar needed to complete a gate with the given specifications of 1/4" x 3/4" flat bar, we can follow these steps:

Step 1: Convert the measurements to Feet To convert the measurements from inches to feet, we can divide them by 12. So, 1/4" = 0.02083 ft and 3/4" = 0.0625 ft.

Step 2: Calculate the length of each flat bar piece Needed For each flat bar piece, we need to add up the length of all the sides that will be made from the flat bar.

From the specifications given, we can see that there will be six pieces of flat bar needed:

four vertical pieces and two horizontal pieces. The length of each vertical piece will be the height of the gate plus an additional 2 inches at the top for the curve, and the length of each horizontal piece will be the width of the gate plus an additional 2 inches on either side for the curves.

So, the length of each piece can be calculated as follows:

Vertical pieces: (48 + 2 + 2) x 2 x 0.02083 ft = 2.083 ft Each Horizontal pieces: (120 + 2 + 2) x 2 x 0.0625 ft = 15.625 ft Each

Step 3: Add up the total length of flat bar Needed Finally, we can add up the total length of flat bar needed by multiplying the length of each piece by the number of pieces, which is 6 in this case:

Total length of flat bar needed = 2.083 ft x 4 + 15.625 ft x 2= 33.33 ft (rounded up to the nearest whole number)

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The arc length of a Curve is given by the formula:`L = int_a^b sqrt(1 + [f'(x)]^2) dx , the correct option is given by `L = int_0^1 sqrt(1 + 4x^2) dx`.

The arc length of a curve is given by the formula:`L = int_a^b sqrt(1 + [f'(x)]^2) dx

where L is the length of the curve between x = a and x = b. In this formula, `f(x)` is the equation of the curve being considered and `f'(x)` is the derivative of `f(x)` with respect to x.

Using this formula, the following integrals can be used to find the length of the curve described by the function:`L = int_0^1 sqrt(1 + 4x^2) dx`This is because the function being described by this integral is the equation of a curve, and the integral finds the length of this curve between `x = 0` and `x = 1`.

To evaluate the integral, we can use trigonometric substitution. Let `x = (1/2) tan(theta)`. Then `dx/dtheta = (1/2) sec^2(theta)`, so `1 + 4x^2 = 1 + 2 tan^2(theta) = sec^2(theta)`.Substituting these expressions into the integral, we have:

`L = int_0^1 sqrt(1 + 4x^2) dx = int_0^(pi/4) sec(theta) (1/2) sec^2(theta) theta = (1/2) int_0^(pi/4) sec^3(theta) dtheta`

This integral can be evaluated using integration by parts, and the final answer will be in terms of trigonometric functions.

Therefore, the correct option is given by `L = int_0^1 sqrt(1 + 4x^2) dx`.

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To compute the arithmetic mean, you would need multiple data points of daily electricity consumption. For example: (30 + 35 + 25 + 40 + 30 + 35 + 40) kWh / 7 days = 33.57 kWh per day

To compute the daily consumption of electricity in units, you need two pieces of information: the total consumption of electricity and the time period over which it was measured. Let's assume you have the total consumption in kilowatt-hours (kWh) and the number of days the consumption was measured.

To calculate the daily consumption, divide the total consumption by the number of days. For example, if the total consumption is 300 kWh and it was measured over 10 days, the daily consumption would be 300 kWh / 10 days = 30 kWh per day.

To compute the arithmetic mean, you would need multiple data points of daily electricity consumption. Let's say you have collected data for a week, with daily consumption values of 30 kWh, 35 kWh, 25 kWh, 40 kWh, 30 kWh, 35 kWh, and 40 kWh. Add up all the daily consumption values and divide the sum by the number of days to calculate the mean.

For example: (30 + 35 + 25 + 40 + 30 + 35 + 40) kWh / 7 days = 33.57 kWh per day.

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Answer:

Set your calculator to degree mode.

[tex] \frac{ \sin(29) }{6.78} = \frac{ \sin(x) }{4} [/tex]

[tex]6.78 \sin(x) = 4 \sin(29) [/tex]

[tex] \sin(x) = \frac{4 \sin(29) }{6.78} [/tex]

[tex]x = {sin}^{ - 1} ( \frac{4 \sin(29) }{6.78} ) = 16.62[/tex]

The number that belongs in the green box is 16.62.

The value of the radical √48 is 4√3.

Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.

Here, we are given the radical √48

To find the value of the radical, we will factorize 48

i.e., 48 = 2×2×2×2×3

           = 16×3

Now, the square root of 48, that is, √48

                                                       = [tex]\sqrt{16\cdot3}[/tex] =[tex]\sqrt{16} \cdot \sqrt{3}[/tex]

We know 16 is a perfect square of 4, that is, the square root of 16= 4

⇒√16=4

Using this, we have √48= 4√3

The correct answer is 4√3.

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Answer:

Answer will be 55898.

Step-by-step explanation:

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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The compound interest earned on a four year investment at $3500 at 4.5% compounded monthly is $724.46 (calculated by subtracting the initial investment amount of $3500 from the total amount of $4224.46).

Compound interest is the interest that is generated on the interest that has been accrued over a certain period of time.

The compound interest that is earned on a four year investment at $3500 at 4.5% compounded monthly can be calculated using the formula for compound interest, which is given as:

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

Where:

A is the total amount of money after the investment period,P is the principal or initial amount of money invested,r is the annual interest rate,n is the number of times the interest is compounded in a year,

t is the total number of years the investment is held.Substituting the given values in the above formula,

we get:A = 3500(1 + 0.045/12)^(12*4)A

= 3500(1 + 0.00375)^(48)A

= 3500(1.00375)^(48)A

= 3500(1.2067)A

= $4,224.46

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The experimental probability of choosing a student who walks to school is given by 0.15625 or 15.625%.

Given data ,

The experimental probability of choosing a student who walks to school can be calculated by dividing the number of students who walk to school by the total number of students in Joe's class.

Number of students who walk to school = 5

Total number of students in the class = 32

Experimental probability = Number of students who walk to school / Total number of students

= 5 / 32

P = 0.15625

Hence , the experimental probability of choosing a student who walks is 0.15625 or 15.625%.

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Answer: Area of Cylinder = 753.982

Step-by-step explanation:

Given:

h = 7 cm

r = 8cm

Formula for cylinder:

A = (Perimeter of base) x height + 2 (Area of Base)

Breakdown:

Perimeter of base = 2[tex]\pi r[/tex]

Perimeter of base = 2 [tex]\pi[/tex] (8)

Perimeter of base = 50.2655

Area of Base = [tex]\pi r^{2}[/tex]

Area of Base = [tex]\pi 8^{2}[/tex]

Area of Base = 201.0619

Area of Cylinder = (Perimeter of base) x height + 2 (Area of Base)

Area of Cylinder = (50.2655)(7) +2(201.0619)

Area of Cylinder = 753.982

The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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Answer:

12

Step-by-step explanation:

Note that the area B of the rectangular base with length x and width 9 units is:

[tex]B=9x[/tex]

Then, the volume [tex]V=468[/tex] cubic units of the pyramid is related to its base area [tex]B=9x[/tex] and height [tex]h=13[/tex] as follows:

[tex]V=\frac{1}{3}Bh\\468=\frac{1}{3}\times 9x\times 13\\x=\frac{468\times3}{9\times 13}=12[/tex]

So, the value of x is 12.

Hello !

Answer:

[tex]\Large \boxed{\sf x=12}[/tex]

Step-by-step explanation:

The volume of a pyramid is given by [tex]\sf V_{pyramid}=\frac{1}{3}\times B\times h[/tex] where B is the area of the base and h is the height.

This is a rectangular pyramid. We have [tex]\sf B=l\times w[/tex] where l is the length and w is the witdth.

So [tex]\sf V_{pyramid}=\frac{1}{3}\times l \times w\times h[/tex]

Given :

Let's substitute l, w and h with their values in the previous formula :

[tex]\sf V_{pyramid}=\frac{1}{3}\times x\times 9 \times 13\\\sf V_{pyramid}=3\times13\times x\\\sf V_{pyramid}=39x[/tex]

Moreover, we know that [tex]\sf V_{pyramid}=468\ units^3[/tex].

Therefore [tex]\sf 39x=468[/tex]

Let's solve for x :

Divide both sides by 39 :

[tex]\sf \frac{39x}{39} =\frac{468}{39} \\\boxed{\sf x=12}[/tex]

Have a nice day ;)

The area of rectangular room with length L and width W is LW/9 square yard.

Given that, a rectangular room has length L and width W, where L and W are measured in feet.

Here, L feet = L/3 yard and W feet = W/3 yard

a) Area = Length×Width

= L/3 × W/3

= LW/9 square yard.

b)  Carpeting costs x dollars per square yard.

Total cost = x×LW/9

= LWx/9 dollars

Therefore, the area of rectangular room with length L and width W is LW/9 square yard.

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Answer:

 (a) at least one x-intercept

  (b) at least one y-intercept

  (e) the domain of x

Step-by-step explanation:

Given g(x) = (-4x² +36)/(x+3) and f(x) as shown in the graph, you want to know what features the functions have in common.

The function g(x) can be simplified:

  [tex]g(x)=\dfrac{-4x^2+36}{x+3}=\dfrac{-4(x^2 -9)}{x+3}=\dfrac{-4(x+3)(x-3)}{x+3}\\\\g(x)=-4(x-3)\quad x\ne-3[/tex]

This is the equation of a straight line with negative slope and a hole at coordinates (-3, 24). That is, the domain excludes x = -3.

The line has x-intercept (3, 0) and y-intercept (0, 12).

Both functions have an x-intercept at (3, 0), at least one x-intercept, choice A.

Both functions have a y-intercept at (0, 12), at least one y-intercept, choice B.

Only function f(x) has an oblique asymptote.

Only function f(x) has a vertical asymptote.

Both functions exclude x = -3 from their domains, so they have the same domain, choice E.

  Choices A, B, E identify the shared features.

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Answer:

Step-by-step explanation:

There is 12 inches in a foot:  therefore, 12inches  x 7ft. = 84 ft.

Answer: 84 inches

Step-by-step explanation:

A conversion factor is a number that is used to multiply or divide one set of units into another.  For instance, 12 inches equals one foot when converting between inches and feet.

Since 1 foot = 12 inches

And we are trying to figure out how much inches are in 7 ft.

We can create a conversion (or cross multiply)

[tex]\frac{12}{1} =\frac{x}{7}[/tex]

Where inches are in the numerator and ft are in demoninator.

When cross multiplying (multiplying in a diagonal) you get:

x = 84 inches

So 7 ft equals 84 inches.

---

A quicker method would be to multiply 7 ft by 12 inches/1 ft (foot), and get 84 inches.

--

The number of brand X batteries that would last more than 14 hours is 12.

Batteries with 14 hours battery life falls in the first quartile which is 25% of the distribution. Hence, 75% lasted more than 14 hours.

From the information we have established, If Mary bought 16 brand X batteries , then;

75% of the number of batteries would give us the answer :

75% of 16

0.75 × 16 = 12.

Therefore, 12 batteries would last more than 14 hours .

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TWO x-values below that lie in the domain of all three functions are

C) x = 0

D) x = -1

Domain values refer to the set of possible input values for a function or mathematical expression. In other words, the domain is the set of all possible x-values for which the function or expression is defined.

The equations is investigated as follows

h(x) = 2x / (x + 4) : would not have a domain of -4

log(x + 2 : would not have a domain of -2

The graph can have a domain of 0 and -1 hence this remains the correct option

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Below are five equations using the digits 7 to 7, each with a negative value for x:

Equation: 7 + x = 0

Explanation: If we subtract 7 from both sides, we get x = -7. Therefore, the value of x in this equation is negative.

Equation: x - 7 = -14

Explanation: If we add 7 to both sides, we get x = -7. Hence, the value of x in this equation is negative.

Equation: 7x - 14 = 0

Explanation: We can rearrange the equation as 7x = 14, and then divide both sides by 7, yielding x = 2. However, we are looking for a negative value of x. By negating the equation, we get -7x + 14 = 0. Solving for x gives x = -2, which is a negative value.

Equation: -7x + 14 = 0

Explanation: We can rearrange the equation as -7x = -14, and then divide both sides by -7. This yields x = 2, which is a positive value. However, we are looking for a negative value of x. By negating the equation, we get 7x - 14 = 0. Solving for x gives x = -2, which is a negative value.

Equation: -7 + x = -14

Explanation: If we subtract x from both sides, we get -7 = -14 - x. By rearranging the equation, we have -x = -7 - 14, which simplifies to -x = -21. Dividing both sides by -1 gives x = 21, but we need a negative value of x. Therefore, we can negate the equation, resulting in 7 - x = 14. Solving for x gives x = -7, which is a negative value.

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Answer:

Step-by-step explanation: 6(1 - cos²0) - 5/3.3cos0

= 6 - 2.3cos²0 - 5/3.3cos0 =  6 - 2.4 - 10/3 = -16/3

Step-by-step explanation:

Just :    5,8374

Answer:

x = 4

Step-by-step explanation:

Vertically opposite angles are equal.

5x + 3 = 2x + 15

Make x the subject:

3x + 3 = 15

3x = 12

x = 4

Based on the information given, it takes 16 days for the whole job to be competed.

Worker's efficiency is a term that is used to describe the effectiveness in which a worker performs their job, therefore increasing productivity.

General, the efficient worker is productive, and tend to organize their time and effort in order to complete daily tasks.

In this case, we know that 10 workers can finish the remaining 15 days

Then 1 worker will do the same job in 15x10= 150 days

Therefore, we have one worker one-day job = 1/150

=>6 workers 5 days job = 6x5/150= 1/5 ..(1)

=>8 workers 3 days job = 8x3/150= 4/25 ..(2)

Hence, 4 more workers joined after 8 days

=> Making a total number of workers now available 12.

=> Work remaining = 1 - 1/5- 4/25= 16/25

=. Remaining work completed by 12 workers in 150/12 x 16/25= 8 days …(3)

Thus, the total work was completed in

5 + 3 +8 = 16 days

Hence, in this case, it is concluded that the correct answer is 16 days.

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The full question

10 workers can finish the job in 15 days. For the first 5 days, only 6workers worked on the job. Then for the 3 next days 2 more workers joined them. To finish the job, 4 more workers joined them. After how many days was the whole job done?

Answer:

11.5 or 11 1/2 (eleven and a half)

Step-by-step explanation:

so we can add the whole numbers together

5 + 6 = 11

then we are left with the fractions

1/3 + 1/6

we need to make both sides equal so we multiply both the upper and lower part of 1/3 by 2

which gives us 2/6

then you simply add 2/6 and 1/6 together which is 3/6

3/6 can be simplified to 1/2 or 0.5

just add that back to the original 11 you added up and your final answer is

11.5 or 11 1/2 (eleven and a half)

Answer:

The answer is

[tex]11 \frac{3}{6} [/tex] or 11.5

or in simplest form

11½

Step-by-step explanation:

5⅓+6⅙

[tex] = \frac{16}{3} + \frac{37}{6} [/tex]

Taking LCM which is 6

[tex] \frac{ \frac{16}{3} + \frac{37}{6} }{6} [/tex]

[tex] \frac{2(16) + 1 \times 37}{6} [/tex]

[tex] \frac{32 + 37}{6} [/tex]

[tex] = \frac{69}{6} [/tex]

[tex] = 11 \frac{3}{6} [/tex]

11½ in simplest form or 11.5