Andy and Javier need to clean their whole house. Andy cleans 2/6 of the house
and Javier cleans 3/6 of the house. What fraction of the house is left to clean?

(A) the estimated area under the graph of f(x) = 2 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 1.0806.

(B) Using four approximating rectangles and left endpoints gives an estimate of approximately 0.9722.

(a) Using four approximating rectangles and right endpoints, we can estimate the area under the graph of f(x) = 2 cos(x) from x = 0 to x = π/2. Each rectangle's width will be Δx = (π/2 - 0)/4 = π/8.

The right endpoints of the rectangles will be x = π/8, 3π/8, 5π/8, and 7π/8.

Evaluating f(x) = 2 cos(x) at these endpoints, we get f(π/8) = 2cos(π/8), f(3π/8) = 2cos(3π/8), f(5π/8) = 2cos(5π/8), and f(7π/8) = 2cos(7π/8).

Calculating the areas of the rectangles and summing them up, we find that the estimated area, R4, is equal to approximately 1.0806.

(b) Using four approximating rectangles and left endpoints, we can estimate the area under the graph of f(x) = 2 cos(x) from x = 0 to x = π/2.

Each rectangle's width will still be Δx = (π/2 - 0)/4 = π/8. The left endpoints of the rectangles will be x = 0, π/8, π/4, and 3π/8.

Evaluating f(x) = 2 cos(x) at these endpoints, we get f(0) = 2cos(0), f(π/8) = 2cos(π/8), f(π/4) = 2cos(π/4), and f(3π/8) = 2cos(3π/8).

Calculating the areas of the rectangles and summing them up, we find that the estimated area, L4, is equal to approximately 0.9722.

In summary, the estimated area under the graph of f(x) = 2 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints is approximately 1.0806, while using four approximating rectangles and left endpoints gives an estimate of approximately 0.9722.

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For the system of linear equations (2a−1)x+3y−5=0 and 3x+(b−1)y−2=0 to have infinitely many solutions, the two equations must be linearly dependent, meaning one equation can be obtained by multiplying the other equation by a constant. This can be achieved when the ratios of the coefficients of x, y, and constants in the two equations are equal, except for a scalar multiple. Therefore, setting (2a-1)/3 = -2/(b-1) = -5/2, we get a = -1/2 and b = 9.

To find the values of a and b such that the system of linear equations (2a−1)x+3y−5=0 and 3x+(b−1)y−2=0 has infinitely many solutions, we need to find the condition under which the two equations are linearly dependent.

If the two equations are linearly dependent, it means that one equation can be obtained by multiplying the other equation by a constant. Mathematically, this can be represented as:

k(2a−1)x + k(3y) − k(5) = 0 where k is a non-zero constant

and 3x + (b−1)y − 2 = 0

We can see that the coefficients of x and y in the two equations are 2a-1 and 3, and 3 and b-1, respectively. For the equations to be linearly dependent, the ratios of these coefficients must be equal, except for a scalar multiple. In other words:

(2a-1)/3 = (b-1)/(-2) = k where k is a non-zero constant

We can solve for k by setting any two ratios equal to each other. Let's set the first ratio equal to the second ratio:

(2a-1)/3 = (b-1)/(-2)

Cross-multiplying, we get:

-4a + 2 = 3b - 3

Simplifying, we get:

-4a + 3b = 5

Next, let's set the first ratio equal to the third ratio:

(2a-1)/3 = -5/2

Cross-multiplying, we get:

4a - 2 = -15

Simplifying, we get:

4a = -13

Solving for a, we get:

a = -13/4

Substituting this value of a into the equation -4a + 3b = 5, we get:

-4(-13/4) + 3b = 5

Simplifying, we get:

13 + 3b = 5

Solving for b, we get:

b = 9

Therefore, the values of a and b that make the system of linear equations (2a−1)x+3y−5=0 and 3x+(b−1)y−2=0 have infinitely many solutions are a = -1/2 and b = 9.

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With an initial investment of $19,675.13 and yearly deposits of $3,000 at an interest rate of 9.25%, the account will be worth around $336,312.91 in 25 years.

The unitary approach is a strategy for problem-solving in which the value of one piece of a quantity is determined, then the cost of an unique number of units associated with that quantity is subsequently determined using that value. In other words, it's a method of proportional used to resolve issues where one unit's value is known but another's value is needed. The unitary method's fundamental premise is to establish a percentage between two quantities, one of which is stated in the form of one unit and the other in terms of a greater number of units.

given

In the following ten years, we have:

P = $4,750 r = 6.9% = 0.069

n = 10

\(FV2 = $4,750 * ((1 + 0.069)^10 - 1) / 0.069\)

= $74,894.87

In the previous five years, we have:

P = $4,750

r = 4.5% = 0.045

n = 5

= $127,756.44

Lastly, we can combine the two figures to determine the account's entire future value:

FV is $208,556.47 + $127,756.44 = $336,312.91 (annual deposits + initial investment).

With an initial investment of $19,675.13 and yearly deposits of $3,000 at an interest rate of 9.25%, the account will be worth around $336,312.91 in 25 years.

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Answer:

Se pueden obtener 10.000 comprimidos de 500 mg de paracetamol a partir de la cantidad de 5 kg del medicamento

Step-by-step explanation:

La cantidad en masa de paracetamol en una tableta = 500 mg de paracetamol / tableta

El número de comprimidos que contienen 500 mg de paracetamol que se pueden obtener a partir de 5 kg del medicamento (paracetamol) se calcula dividiendo los 5 kg del medicamento por los 500 mg de paracetamol / comprimido de la siguiente manera;

\(El \ nmero \ de \ tableta = \dfrac{5 \ kg \ paracetamol}{500 \ mg \ paracetamol/tableta }\)

Observamos que 5 kg = 5,000,000 mg

Por lo tanto;

\(El \ numero \ de \ tableta = \dfrac{5,000,000 \ mg \ paracetamol}{500 \ mg \ paracetamol/tableta } = 10,000 \ tabletas\)

Por tanto, podemos obtener 10.000 comprimidos de 500 mg de paracetamol a partir de la cantidad dada de 5 kg del medicamento.

When solving systems of equation with three variables we use the elimination method or the substitution method to make a system of two equations in two variables.

There are several methods to solve a system of equations with three variables, including substitution, elimination, and graphing. One common method is to use elimination, also known as the addition/subtraction method. This involves adding or subtracting equations in order to eliminate one of the variables and creating an equation with only two variables. Once you have a system of two equations with two variables, you can solve for one of the variables, substitute that value back into one of the original equations, and then solve for the remaining variable. After that you can use the value of the variables to find the values of the other variables.

Hence, When solving systems of equation with three variables we use the elimination method or the substitution method to make a system of two equations in two variables.

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To make h subject of the formula, the other expressions in the equation is expressed to equal h as follows:

The steps in making h subject of the formula in the given equation are as follows:

Step 1: Add \(pi \sqrt{x} (\frac {h-0.5}{1-h})\) to both sides

\(E + \pi \sqrt{x} (\frac {h-0.5}{1-h})= 1\)

Step 2: subtract E from both sides

\(\pi \sqrt{x} (\frac {h-0.5}{1-h}) = 1 + E\)

Step 3: divide both sides by π√x

h - 0.5/1 - h = 1 + E/π√x

Step 4: cross multiply

(h - 0.5)(π√x) = (1 + E)(1 - h)

hπ√x -0.5π√x = 1 - h + E - hE

Step 5: collect like terms

hπ√x + h + hE = 1 + E + 0.5π√x

h(π√x + 1 + E) = 1 + E + 0.5π√x

Step 6: divide both sides by (π√x + 1 + E)

h = (1 + E + 0.5π√x/)(π√x + 1 + E)

In conclusion, in making h subject of the formula, the other expressions in the equation is expressed to equal h.

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The profession that is projected to have the greatest percent of increase in the number of jobs from 2006 to 2016 is B. sound engineer technician.

The increase in percentage for orthodontist will be:

= (10214 - 9206) / 9206 × 100

= 1008 / 9206 × 100

= 10.95%

The increase in percentage for sound engineer will be:

= (17864 - 16125) / 16125 × 100

= 1739/16125 × 100

= 10.79%

The increase in percentage for police officer will be:

= (719041 - 648982) / 719041 × 100

= 70059/719041 × 100

= 9.74%

The increase in percentage for editor will be:

= (124135 - 122273)/124135 × 100

= 1862/124135 × 100

= 1.5%

Therefore, the sound engineer has the greatest percentage increase.

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Answer:

sound engineer

Step-by-step explanation:

The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)

A dilation is a type of transformation that changes the size of the shape or object.  It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.

A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).

For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and  > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.

Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)

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The calculated chi-squared test statistic is 7.09 and the p-value is 0.0674. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that the responses occur with different frequencies. So, the correct answer is A).

To find the chi-square test statistic, we need to calculate the following

Subtract the expected frequency from the observed frequency for each response and square the result. Divide each squared difference by the expected frequency. Add up all the resulting values to get the chi-square test statistic.

Using the given data table in image,

Adding up the values in the last column of data, we get

chi² = 4.05 + 1.95 + 0.92 + 0.17 = 7.09

The degrees of freedom for this test are (number of categories - 1), which in this case is 4 - 1 = 3. Using a chi-square distribution table or calculator with 3 degrees of freedom, we find the p-value to be approximately 0.0674.

Since the p-value (0.0674) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, we conclude that there is not enough evidence to suggest that the responses to the questions occur with different frequencies. So, the correct option is A).

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The equation of the line tangent to the graph of g at the point where x = 4 is y = 14x - 32.

To find the equation of the tangent line to the graph of g(x) at the point where x = 4, we need to determine the slope of the tangent line. Since g(x) = x * f(x), we can use the product rule to find the derivative of g(x).

Applying the product rule, we have g'(x) = f(x) + x * f'(x).

At x = 4, we substitute the known values: f(4) = 6 and f'(4) = 2.

g'(4) = f(4) + 4 * f'(4) = 6 + 4 * 2 = 6 + 8 = 14.

Therefore, the slope of the tangent line to the graph of g(x) at x = 4 is 14.

Now, we can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the point (4, g(4)) and m is the slope.

Since g(x) = x * f(x), we have g(4) = 4 * f(4) = 4 * 6 = 24.

Substituting the values, we get the equation y - 24 = 14(x - 4), which is equivalent to y - 24 = 14x - 56.

Simplifying, we have y = 14x - 32.

Therefore, the equation of the line tangent to the graph of g at the point where x = 4 is y = 14x - 32.

In summary, the equation of the line tangent to the graph of g at the point where x = 4 is y = 14x - 32. This was obtained by finding the derivative of g(x) using the product rule and substituting the known values of f(4) and f'(4). The resulting slope was used along with the point-slope form of a line to determine the equation of the tangent line.

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Complete question:

Let f be a differentiable function with f(4)=6 and f ′(4)=2, and let g be the function defined by g(x)=x⋅f(x). Which of the following is an equation of the line tangent to the graph of g at the point where x=4 ?

(a) y=2x (b)y−24=14(x−4) (c)y=6=2(x−4) (d)y−6=14(x−4)

Answer:

33333333333333333333333333333333333333333333333333333333333333333

Step-by-step explanation:

Answer:

the first one has positive quotient

we have the following:

speed of the boat in still water be x

the speed of the stream is 5 km/h

upstream

downstream:

therefore:

The answer is 35 km/h

5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.

What is the definition of square root?

The square root of a number is a value that, when multiplied by itself, yields the original number. The square root is the opposite of squaring a number. As a result, squares and square roots are ideas that are connected.

If x is the square root of y, it is denoted as x=√y, or the same equation may be expressed as x² = y. √" is the radical symbol used to symbolise the numerical root here. When a positive number is multiplied by itself, it represents the number's square. The square root of a positive number yields the original value.

Now,

Given that square root of the cube root of 5 i.e. √∛5=?

=√5¹÷³

=5¹/²*¹/³

=5¹/⁶

hence,

          5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.

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It will take Joey's family approximately 21 months to save enough money, compounded monthly at a 5% interest rate, to finance their vacation trip to the amusement park.

To determine the time it will take to save enough money, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r,

where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the number of periods.

Given:

Desired future value (FV) = $5000,

Monthly payment (P) = $240,

Monthly interest rate (r) = 5% / 12 = 0.05 / 12 = 0.004167.

We need to solve for the number of periods (n) in the formula. Rearranging the formula, we have:

n = log(1 + (FV * r) / P) / log(1 + r),

where log denotes the logarithm with base 10.

Plugging in the given values, we get:

n = log(1 + ($5000 * 0.004167) / $240) / log(1 + 0.004167).

Using a calculator, we find that n is approximately 20.998, which rounds up to 21.

Therefore, it will take Joey's family approximately 21 months to save enough money, compounded monthly at a 5% interest rate, to finance their vacation trip to the amusement park.

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Answer:

that Will be true because If to two triangle are not guaranteed

Answer:

x=1

Step-by-step explanation:

The value of x is 1. So, the correct answer is d. x = 1.

To find the value of x, we can use the fact that the corresponding sides of congruent triangles are equal.

In triangle ABC, side AB is labeled 4x - 1, side BC is labeled 4, and side AC is labeled 5.

In triangle CDE, side CD is labeled 5, side DE is labeled x + 2, and side CE is labeled 4.

Since triangle ABC is congruent to triangle CDE, we can set up the following equations:

4x - 1 = 5
4 = x + 2

Simplifying these equations, we get:

4x = 6
x = 1

Therefore, the value of x is 1. So, the correct answer is d. x = 1.

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Answer: Im pretty sure its 1

Step-by-step explanation:

Because 11 is the only alternate exterior angle

D (-1,9) i did it in calcukator

Answer:

A.

Step-by-step explanation:

Answer: The answer is A 3/40

Step-by-step explanation: \(\frac{3}{5} :8=\frac{3}{5} * \frac{1}{8} =\frac{3*1}{5*8} =\frac{3}{40}\)

33

Let the present age of father is x years and son is y years

Then according to the question

x−3y=3.............(i)

After 3 years

(x+3)−2(y+3)=10

x+3−2y−6=10

x−2y=13...........(ii)

Subtracting eq(i)and eq(ii)

y=10

Putting y=10 in eq(i)

x−3×10=3

x=33

Hence Father present age is 33 years.

Answer:

y= \(\frac{72}{5}\) or 14.4

Step-by-step explanation:

\(\frac{5}{6}y = 12\\\)

Multiply both sides by 6/5, the reciprocal of 5/6.

\(y = 12 * (\frac{6}{5} )\)

Express 12 x (6/5) as a single fraction.

\(y = \frac{12 * 6}{5}\)

Multiply 12 and 6 to get 72.

\(y = \frac{72}{5}\)

Answer:

D is the correct option

Step-by-step explanation:

this implies that Engels will grade the examination paper within a maximum time of 20 * 12 minutes, but if she adds comments then the time will exceed 20 * 12 minutes

Step-by-step explanation:

the FH seems to be option b.6.0

........

Answer:

Me, it is called Picsart

I used to have it but the question got deleted

Answer:

b=1

Step-by-step explanation:

\(\sf -11 + 3(b + 5) = 7\)

First, let's regroup, terms,

\(\sf 3(b+5)-11=7\)

Add 11 to both sides,

\(\sf 3(b+5)=7+11\)

Simplify, 7+11 = 18,

\(\sf 3(b+5)=18\)

Now, divide both sides by 3,

\(\sf b+5=\frac{18}{3}\)

Simplify, 18/3 = 6,

\(\sf b+5=6\)

Subtract 5 from both sides,

\(\sf b=6-5\)

\(\sf b=1\)

Hope it helps! :)

Therefore , the solution of the given problem of surface area comes out to be 212 square feet of the wall are therefore covered by the design.

The total size of the object can be determined by calculating how much room would be required to completely cover its exterior. When choosing a similar product with a cylindrical form, the environment is taken into account. Anything's total dimensions are determined by its surface area. The amount of water that a cuboid can hold depends on the number of sides that link its four trapezoidal shapes.

Here,

We must first determine the area of each individual form before adding them together to determine the portion of the wall that the design covers.

Taking a look at the rectangle first, we can observe that it has the following area:

=> 120 square feet=  10 feet x 12 feet.

=> 40 square feet =  (1/2)(10 ft)(8 ft).

Consequently, the two triangles' combined area is:

=> 80 square feet =  2 x 40 square feet.

=> (12 square feet) = (1/2)(6 ft)(4 ft).

The total area of all the shapes is as follows:

=> 212 square feet=  120 square feet, 80 square feet, and 12 square feet.

=> 212 square feet of the wall are therefore covered by the design.

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Answer: the answer is 261 ^2 ft!

Step-by-step explanation:

Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."

2: The total cost of the merchandise is $3,332.00.

5: The company's gross margin and operating expenses, are $211,000 and $191,720.

Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.

Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.

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