Activity 3
Write in increasing order according to their capacity:

Answer:

The amount of money the painter earns, in dollars, depends on the number of rooms he paints.

For each room painted, the painter charges $25. Therefore, the amount of money earned, y, is given by the equation:

y = 25x + 100

where x is the number of rooms painted and 100 is the cost of supplies.

To graph this equation, we can plot a point on the y-axis where x=0 (the fixed cost of supplies) at (0, 100), and then use the slope of 25 to find additional points. For example, when x=1, y=125; when x=2, y=150; and so on.

With this information, we can eliminate options (b) and (d) because they both show negative slopes, which would mean the painter loses money as he paints more rooms.

Option (c) shows a positive slope, but the line goes through the point (0,100) and (4,200), which means the painter earns $200 after painting 4 rooms, but this contradicts the given information that the painter charges $25 per room. Therefore, option (c) is also incorrect.

Option (a) correctly shows the slope of 25 and goes through the point (0, 100), and the line reaches the x-axis when x=4, indicating that the painter earns $0 after painting 4 rooms. This matches the given information that the painter charges $25 per room. Therefore, the correct answer is option (a).

Therefore, the graph that shows the relationship between the amount of money the painter earns, in dollars, and the number of rooms he paints is:

a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 0

Answer:

The correct answer is a C. coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 200.

The painter pays $100 for supplies, so he will only earn money for the rooms he paints after he has recouped that cost. The first room he paints will earn him $25, the second will earn him $50, and so on. After he has painted 4 rooms, he will have earned $200.

The graph of this relationship would be a line that starts at the point (0, 100) and goes up to the point (4, 200).

Step-by-step explanation:

The integral of 1/(2+4x²+25x²) using partial integration is (1/2) arctan(10x) + C, where C is the constant of integration.

To solve this integral, we will use the technique of partial integration. This technique is also known as integration by parts and is used to find the integral of a product of two functions. The formula for integration by parts is as follows:

∫u dv = uv - ∫v du

where u and v are functions, and du/dx is the derivative of u with respect to x, and dv/dx is the derivative of v with respect to x.

Let's apply this formula to our integral:

∫1/(2+4x²+25x²) dx

We need to choose two functions, u and dv, such that when we differentiate u, we get a simpler function, and when we integrate dv, we get a simpler function. In this case, we can choose:

u = 1, and dv = 1/(2+4x²+25x²) dx

Now, let's find du/dx and v:

du/dx = 0 (since u is a constant)

To find v, we need to integrate dv. We can use the substitution method to evaluate the integral:

Let u = 5x

du/dx = 5

dv = 1/(2+4x²+25x²) dx

Substituting u and dv:

v = ∫ dv/dx du = ∫1/(2+4u²) du

v = (1/2) arctan(2u)

v = (1/2) arctan(2(5x))

v = (1/2) arctan(10x)

Now, we can apply the formula for integration by parts:

∫1/(2+4x²+25x²) dx = uv - ∫vdu

∫1/(2+4x²+25x²) dx = (1) x (1/2) arctan(10x) - ∫(1/2) arctan(10x) x 0 dx

∫1/(2+4x²+25x²) dx = (1/2) arctan(10x) + C

where C is the constant of integration.

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The calculated range of the amount of rainfall in mm is 20.5 mm

From the question, we have the following parameters that can be used in our computation:

Data values in mm

0.0, 12.2, 2.1, 0.0, 20.5, 5.5 and 1.0

The range of the rainfall  is the difference between the least and the highest amount of rainfalls

Using the above as a guide, we have the following:

Range = 20.5 - 0.00

Evaluate

Range = 20.5

Hence, the range of rainfall is 20.5 mm

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Answer:

Y=1

Step-by-step explanation:

Answer:

a = 48

b = 28

Step-by-step explanation:

b = 0.5 × 56

b = 28

52 = 0.5 × (56 + a)

104 = 56 + a

a = 48

The coordinates of a vertex of the image of D are (3, 1)

From the question, we have the following parameters that can be used in our computation:

The coordinates of point D is

D = (1, 3)

The transformation rule is given as

y = x

Mathematically, this is represented as

(x, y) = (y, x)

Substitute the known values in the above equation, so, we have the following representation

D' = (3, 1)

Hence, the image of point D is D' = (3, 1)

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Answer:

C -1

Step-by-step explanation:

in such a case the simplest way is to simply try the 4 numbers and see :

x² - 3x - 4 = |x + 3| - 2

x² - 3x - 2 = |x + 3|

A x = -4

(-4)² - 3×-4 - 2 = |-4 + 3|

16 + 12 - 2 = 1

26 = 1

wrong.

B x = -3

(-3)² - 3×-3 - 2 = |-3 + 3|

9 + 9 - 2 = 0

16 = 0

wrong.

C x = -1

(-1)² - 3×-1 - 2 = |-1 + 3|

1 + 3 - 2 = 2

2 = 2

correct.

D x = 4

4² - 3×4 - 2 = |4 + 3|

16 - 12 - 2 = 7

2 = 7

wrong.

According to the given function.

There were approximately 24.9 million international Netflix subscriptions in the year 2012.

There were approximately 167.7 million international Netflix subscriptions in the year 2020,

We have,

a.

Since the function N(x) gives the number of international Netflix subscriptions x years after 2012, to find the number of Netflix subscriptions in the year 2012,

We need to set x = 0.

So,

N(0) = 24.9(1.736)^0

       = 24.9 million

b.

To estimate the number of Netflix subscriptions in the year 2020, we need to set x = 8 (since 2020 is 8 years after 2012).

N(8) = 24.9(1.736)^8

       =  167.7 million

Thus,

According to the given function.

There were approximately 24.9 million international Netflix subscriptions in the year 2012.

There were approximately 167.7 million international Netflix subscriptions in the year 2020,

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Answer:

Step-by-step explanation:

(4 – 5) – (13 – 18 + 2).

= -1-(13+2-18).

= -1-(15-18).

= -1-(-3).

= -1+3.

= 2.

Answer:

Step-by-step explanation:

To combine the terms 12a + 26b - 4b - 16a, you first simplify the like terms. Add the coefficients of a terms and add the coefficients of b terms separately. You get 12a - 16a + 26b - 4b which results in -4a + 22b. Therefore, the correct answer is (c) -4a + 22b.

Answer:

Figure A is greater.

Step-by-step explanation:

Figure A has 60 cubic units in volume, if you do length x width x height you get 60. And for figure B the volume is 40 because of again l x w x h.

The probability that the point that is selected randomly would be in the semicircular region would be = 0.28.

To calculate the probability of a selected point, the formula for probability should be chosen. That is;

Probably = possible outcome/sample space

Possible outcome is the area of the semicircle = πr²/2

where r = 5 in

Area of semicircle = 3.14×5×5/2

=78.5/2 = 39.25 in²

The sample space = area of semicircle+area of square.

But Area of the square;

= length×width

= 10×10 = 100in²

sample space = 100+39.25 =139.25

Probability = 39.25/139.25 = 0.28

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Based on the survey, we can say that between 12,776 and 14,000 citizens in the town would support a new coffee shop.

The margin of error is a measure of the uncertainty in the survey results. It is based on the sample size and the level of confidence desired. In this case, the margin of error is 1.7%.

This means that the actual percentage of citizens in the town who would support a new coffee shop could be as much as 1.7% higher or lower than the survey result of 37%.

To calculate the range of possible values for the percentage of citizens who would support a new coffee shop, we add and subtract the margin of error from the survey result:

37% + 1.7% = 38.7%

37% - 1.7% = 35.3%

Therefore, based on the survey, we can say that between 35.3% and 38.7% of the citizens in the town would support a new coffee shop.

To determine the number of people who would support a new coffee shop, we need to multiply the percentage by the population of the town:

35.3% of 36,170 = 12,776

38.7% of 36,170 = 14,000

Therefore, based on the survey, we can say that between 12,776 and 14,000 citizens in the town would support a new coffee shop.

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The two sets of possible dimensions for the rectangular plot of land are:

11 m x 22 m

8 m x 28 m

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be A

Now , the length of the rectangle be L

Let the width of the rectangle be W

Let's assume that the length of the rectangular plot of land is L meters and the width is W meters. Since Jamal has only 44 meters of fencing available, the perimeter of the enclosure will be 44 meters:

Perimeter = 2L + W = 44

W = 44 - 2L

The area of the rectangular plot of land is given as 192 square meters

Area = L x W = L x (44 - 2L) = 192

2L² - 44L + 192 = 0

Solving for L using the quadratic formula, we get:

L = (44 ± √(44² - 4 x 2 x 192)) / (2 x 2)

L = (44 ± √(1600)) / 4

L = (44 ± 40) / 4

So, the possible values of L are 11 and 8

If L = 11, then W = 44 - 2L = 22, and the dimensions of the rectangular plot of land are 11 m x 22 m

If L = 8, then W = 44 - 2L = 28, and the dimensions of the rectangular plot of land are 8 m x 28 m

Hence , the two sets of possible dimensions for the rectangular plot of land are 11 m x 22 m and 8 m x 28 m

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Answer:

Sure give me a sec

Step-by-step explanation:

1) A system of equations has no solution if the graphs of the equations do not intersect.  2) A system of equations has exactly one solution if the graphs of the equations intersect at exactly one point.  3) A system of equations has exactly two solutions if the graphs of the equations intersect at exactly two points.

Systems with no solution

A system of equations has no solution if the graphs of the equations do not intersect. This can happen if the graphs are parallel, or if one graph is completely contained within the other graph.

For example, the graph of a linear equation is a line, and the graph of a quadratic equation is a parabola. If the line and the parabola are parallel, then they will never intersect, and the system will have no solution.

Another way for a system to have no solution is if one graph is completely contained within the other graph. For example, the graph of the equation y = x is completely contained within the graph of the equation y = [tex]x^2[/tex]. This means that there are no points that satisfy both equations, and the system will have no solution.

Systems with exactly one solution

A system of equations has exactly one solution if the graphs of the equations intersect at exactly one point. This can happen if the graphs are intersecting lines, or if the graphs are intersecting parabolas.

For example, the graph of the equations y = x and y = [tex]x^2[/tex] intersect at exactly one point, which is the point (0,0). This is because the two graphs intersect when x = 0, and there is no other point where they intersect.

Systems with exactly two solutions

A system of equations has exactly two solutions if the graphs of the equations intersect at exactly two points. This can happen if the graphs are intersecting parabolas that have different slopes.

For example, the graph of the equations y = [tex]x^2[/tex] and y = 2[tex]x^2[/tex] intersect at exactly two points, which are the points (0,0) and (1,1). This is because the two graphs intersect when x = 0 and when x = 1, and there are no other points where they intersect.

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The solution is the area of triangle ABC is 9.56 square units .

Given:

The objective is to find the area of triangle ABC

Explanation:

The general formula to find the area of a triangle is,

A = 1/2 *b*h

To find the area of triangle ABC:

The height of the triangle DC can be calculated using the Pythagorean theorem of triangle ADC.

DC  = √ 9 - 6.25

      =1.65

On plugging the given values in equation

Thus, the height of triangle ABC is 2.5

So the base of the triangle CB = 6 + 1.65 = 7.65.

Now, substitute the obtained values in equation

area = 1/2 * 7.65 * 2.5

        = 9.56

Hence, the area of triangle ABC is 9.56 square units .

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The three consecutive even integers are 6, 8, and 10, which satisfy the Pythagorean Theorem.

We have,

The Pythagorean Theorem in a right-angled triangle,

a² + b² = c²

To find three consecutive even integers that satisfy this theorem, we can start by assuming that one of the even integers is x.

Then, the next two consecutive even integers would be x+2 and x+4.

We can then use the Pythagorean Theorem to set up an equation and solve for x:

x² + (x+2)² = (x+4)²

Expanding and simplifying:

x² + x² + 4x + 4 = x² + 8x + 16

Simplifying further:

x² - 4x - 12 = 0

Now we can use the quadratic formula to solve for x:

x = [4 ± √(4² - 4(1)(-12))] / (2 x 1)

x = [4 ± √64] / 2

x = [4 ± 8] / 2

x = 6 or x = -2

Since we are looking for three consecutive even integers, we can discard the negative solution and choose x = 6.

This gives us the three consecutive even integers: 6, 8, and 10, which satisfy the Pythagorean Theorem:

6² + 8 = 10²

36 + 64 = 100

100 = 100

Thus,

The three consecutive even integers are 6, 8, and 10, which satisfy the Pythagorean Theorem.

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The complete question.

Find three consecutive even integers that satisfy the Pythagorean Theorem.

Answer:

1.

[tex]p(t) = 2000({2}^{ \frac{t}{4} }) [/tex]

2.

[tex]p(8) = 2000( {2}^{ \frac{8}{4} } ) = 2000( {2}^{2} ) = 2000(4) = 8000[/tex]

3. p'(t) = 2,000(1/4)(2^(t/4))(ln 2)

= (500 ln 2)(2^(t/4))

p'(t) = 2,000 ln 2 cells/hour

= about 1,386 cells/hour

Answer:

Step-by-step explanation:

Barbara read the first 100 pages from a 320-page in the last four days

Judy read the first 54 pages of a 260-page book in the previous three days.

Nancy read the first 160 pages from a 480-page book in the  previous  five days

Order the friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book(Show all work)

Answer:

Step-by-step explanation:

To divide 18 by 5.5, we can use long division method as follows:

       _________

   5.5 | 18.0000

       -16.5

       ------

        1.5

We first divide 5.5 into the first digit of 18, which is 1. This gives us 0 as the whole number part of the quotient. We then multiply 0 by 5.5 to get 0, and subtract it from 1, which gives us 1.

We then bring down the next digit 0 and get 10. We then divide 5.5 into 15, which gives us 2 as the whole number part of the quotient. We then multiply 2 by 5.5 to get 11, and subtract it from 15, which gives us 4.

We then bring down the next digit 0 and get 40. We then divide 5.5 into 40, which gives us 7 as the whole number part of the quotient. We then multiply 7 by 5.5 to get 38.5, and subtract it from 40, which gives us 1.5.

Since there are no more digits to bring down and the remainder is less than the divisor 5.5, we can stop here. Therefore, the result of 18 divided by 5.5 is approximately 3.27, which we get from the quotient of 0.327 rounded to two decimal places.

So 18 divided by 5.5 is approximately 3.27 or 3.27 to two decimal places.

Answer:

3.27 to 2dp

Step-by-step explanation:

18÷5.5

18/1×11/2

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"z" varies directly with }x^2}{z = k(x^2)}\hspace{5em}\textit{we also know that} \begin{cases} z=96\\ x=4 \end{cases} \\\\\\ 96=k(4^2)\implies \cfrac{96}{4^2}=k\implies 6=k\hspace{8em}\boxed{z=6x^2} \\\\\\ \textit{when x = 3, what's "z"?}\qquad z=6(3^2)\implies z=54[/tex]

Answer:

-506

Step-by-step explanation:

Answer:

-506

Step-by-step explanation:

2 - ([tex]2^{2}[/tex]) + [tex](-8)^{3}[/tex] + 8

2 - 4 -512 + 8

-2 - 512 + 8

-514 + 8

-506

Helping in the name of Jesus.

Answer:

The sum of the interior angle measures of a regular hexagon is 720°.

Step-by-step explanation:

To find the sum of the interior angle measures of a regular hexagon, we can use the fact that any polygon can be divided into triangles. The formula to find the sum of the interior angles of any polygon with n sides is:

Sum of interior angles = (n - 2) × 180°

In the case of a hexagon, n = 6. So, we can plug this value into the formula:

Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

To explain this using triangles, let's divide the hexagon into triangles. A hexagon can be divided into four triangles by drawing three diagonals from one vertex to the three non-adjacent vertices. Since the sum of the interior angles of each triangle is 180°, and we have four triangles:

Sum of interior angles of hexagon = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

The time to take the money to triple is, 15.2 years

We have to given that;

It is invested $9000 in an account earning 7.5% interest compounded continuously.

Hence, We can formulate;

27,000 = 9000 (1 + 7.5/100)ⁿ

3 = (1 + 0.075)ⁿ

3 = (1.075)ⁿ

log 3 = n log (1.075)

0.477 = n x 0.0314

n = 0.477 / 0.0314

n = 15.2 years

Thus, The time to take the money to triple is, 15.2 years

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Answer:

Arc length = (147/360) x (2π x 7)

Arc length = (0.40833) x (2 x 3.14159 x 7)

Arc length = 0.40833 x 43.9823

Arc length = 17.9955

Answer: 1:4

Step-by-step explanation:

In order to do this, we have to know that the octagon has an area which is four times less than the other area. Because of this, it shuld be 1:4

The absolute value inequality that has the solution set x ≤ –9 or x ≥ –5 is

|x + 7| ≤ 2

We have,

To write an absolute value inequality with a solution set x ≤ –9 or x ≥ –5, we first need to find the midpoint of the two given values:

Midpoint of –9 and –5

= (-9 + (-5)) / 2

= -7

We can now use the midpoint and one of the given values to write the absolute value inequality.

Since the solution set includes both values, we need to use the form

|x – b | ≤ c.

We can choose to use either value, let's use x ≤ –9:

|x – (-7)| ≤ |-9 – (-7)|

|x + 7| ≤ 2

Therefore,

The absolute value inequality that has the solution set x ≤ –9 or x ≥ –5 is

|x + 7| ≤ 2

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Reflecting a point across the x-axis changes the sign of its y-coordinate while keeping the x-coordinate intact. As such, Z' can be rewritten in terms of (x, -y).

If a rectangle shifts downward by five units and rightward by three units, the transformation rule can be expressed as: (x, y) → (x + 3, y - 5).

Conversely, the given equation for this specified action is: (x, y) → (x - 3, y - 4).

Similar but reversed in reflection across the y-axis, where instead it is the x-coordinate that sees its sign changed, given the conditions that the y-coordinate stays constant. Hence, the transformation can be stated as: (x, y) → (-x, y).

The same applies for a mathematical exchange when it comes to reflecting about the x-axis; here the y-coordinate has its signs reversed with no transition in the x-coordinate – simply put, we have as follows: (x, y) → (x, -y).

Finally, observing what occurs when rototating clockwise 270° around the origin reveals each point experiencing an equal shift from said anchor point; permitting us to formalize the related rule accurately as: (x, y) → (y, -x).

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Answer:

The height of the desk is 8 cubic inches.

Hope this helps!

Step-by-step explanation:

The formula for the volume of a rectangular prism is Width × Length × Height or Base × Height.

Because the Base is already given ( 400 in² ), that means the height of the desk can be found by dividing 3200 by 400.

3200 ÷ 400 = 8

The height of the desk will be 8 cubic inches.

Answer:

It’s 2.07 pounds/in 3

Step-by-step explanation:

1 kilogram = 2.2 × pounds, so,2.07 × 1 kilogram = 2.07 × 2.2 pounds (rounded), or2.07 kilograms = 4.554 pounds.Step 2: Convert the decimal part in pounds to ouncesAn answer like "4.554 pounds" might not mean much to you because you may want to express the decimal part, which is in pounds, in ounces which is a smaller unit.So, take everything after the decimal point (0.55), then multiply that by 16 to turn it into ounces. This works because one pound equals 16 ounces. Thus,4.55 pounds = 4 + 0.55 pounds = 4 pounds + 0.55 × 16 ounces = 4 pounds + 8.8 ounces. So, 4.55 pounds = 4 pounds and 8 ounces (when rounded). Obviously, this is equivalent to 2.07 kilograms. Step 3: Convert from decimal ounces to a usable fraction of ounceThe previous step gave you the answer in decimal ounces (8.8), but how to express it as a fraction? See below a procedure, which can also be made using a calculator, to convert the decimal ounces to the nearest usable fraction: a) Subtract 8, the number of whole ounces, from 8.8:8.8 - 8 = 0.8. This is the fractional part of the value in ounces.b) Multiply 0.8 times 16 (it could be 2, 4, 8, 16, 32, 64, ... depending on the exactness you want) to get the number of 16th's ounces:0.8 × 16 = 12.8.c) Take the integer part int(12.8) = 13. This is the number of 16th's of a pound and also the numerator of the fraction.Finalmente, 2.07 quilogramas = 4 pounds 8 3/4 ounces.A fração 12/16 não está simplificada, e ainda pode ser reduzida para 3/4 para que possamos expressar como a fração mais simples possível.In short:2.07 kg = 4 pounds 8 3/4 ounces