Graph the image of the figure after a dilation with a scale factor of 3 centered at (2, −7).

The area of the large pizza is approximately 824 square inches.

Let d be the diameter of the small pizza. We know that the area of the small pizza is 203 in².

Therefore, we can use the formula for the area of a circle to find the radius of the small pizza:

A = πr²

203 = π(d/2)²

203 = π(d²/4)

d² = 812/π

d ≈ 16.2

Therefore, the diameter of the small pizza is approximately 16.2 inches.

The diameter of the large pizza is twice that of the small pizza, so it is:

2d ≈ 32.4

Since the diameter of the large pizza is 32.4 inches, the radius is half of that:

r = 16.2

Therefore, the area of the large pizza is:

A = πr²

A = π(16.2)²

A ≈ 824 in²

Therefore, the area of the large pizza is approximately 824 square inches.

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Answer:

-----------------

Multiply both the numerator and denominator by √2 to rationalize the denominator.

Distribute and simplify:

Answer:

[tex]\sqrt{2} +3\sqrt{3}[/tex]

Step-by-step explanation:

To solve this you have to rationalize the denominator. That is, you have to multiply both numerator and denominator by √2.

Let us do it now.

[tex]\sf \dfrac{2+3\sqrt{6} }{\sqrt{2} } \\\\\sf \dfrac{\sqrt{2}* (2+3\sqrt{6} )}{\sqrt{2} *\sqrt{2} }\\\\\sf \dfrac{2\sqrt{2} +3\sqrt{6}\sqrt{2} }{\sqrt{2*2} }\\\\\sf \dfrac{2\sqrt{2} +3\sqrt{12}}{\sqrt{4} }\\\\\sf \dfrac{2\sqrt{2} +3*2\sqrt{3} }{2} }\\\\\sf \dfrac{2\sqrt{2} +6\sqrt{3} }{2} }\\\\\sf \dfrac{2\sqrt{2}} {2}+\dfrac{6\sqrt{3} }{2} \\\\\sqrt{2} +3\sqrt{3}[/tex]

Step-by-step explanation:

How to solve a system of equations using substitution:

1. Choose one of the equations and solve for one of the variables in terms of the other variable.

2. Substitute the expression you found in step 1 into the other equation for the variable you solved for.

3. Solve for the remaining variable.

4. Substitute the value you found in step 3 into either of the original equations to find the value of the other variable.

5. Check your solution by plugging in the values you found in both original equations to make sure they are true.

Example:

Solve the system of equations below using substitution:

2x + y = 8

x - y = 2

1. Solve the second equation for x in terms of y:

x = y + 2

2. Substitute the expression for x from step 1 into the first equation:

2(y + 2) + y = 8

3. Simplify and solve for y:

2y + 4 + y = 8

3y = 4

y = 4/3

4. Substitute the value of y into either of the original equations to find x:

x - (4/3) = 2

x = 8/3

5. Check the solution by plugging in both values into both original equations:

2(8/3) + (4/3) = 8 (true)

(8/3) - (4/3) = 2 (true)

Therefore, the solution to the system of equations is (8/3, 4/3).

How to solve a system of equations by graphing:

1. Rewrite each equation in slope-intercept form, y = mx + b.

2. Graph each equation on the same coordinate plane.

3. Find the point of intersection of the two lines. This is the solution to the system of equations.

4. Check your solution by plugging in the values into both original equations to make sure they are true.

Example:

Solve the system of equations below by graphing:

y = 2x - 1

y = -x + 3

1. Rewrite each equation in slope-intercept form:

y = 2x - 1 is already in slope-intercept form.

y = -x + 3 can be rewritten as y = -1x + 3.

2. Graph each equation on the same coordinate plane:

The two lines intersect at the point (1, 1).

3. Check the solution by plugging in both values into both original equations:

y = 2x - 1: 1 = 2(1) - 1 (true)

y = -x + 3: 1 = -(1) + 3 (true)

Therefore, the solution to the system of equations is (1, 1).

Answer:

Substitution:

Solve one of the equations for either variable.

Substitute the expression from Step 1 into the other equation.

Solve the resulting equation.

Substitute the solution in Step 3 into one of the original equations to find the other variable.

Write the solution as an ordered pair.

Check that the ordered pair is a solution to both original equations.

Graphing:

Graph the first equation.

Graph the second equation on the same rectangular coordinate system.

Determine whether the lines intersect, are parallel, or are the same line.

Identify the solution to the system.

If the lines intersect, identify the point of intersection. Check to make sure it is a solution to both equations. This is the solution to the system.

If the lines are parallel, the system has no solution.

If the lines are the same, the system has an infinite number of solutions.

that the statistic being collected is the mean difference in scores from the beginning and the end of the semester.

In this scenario, the fourth grade class is given a standardized math test at the beginning and end of the semester. The scores from both tests are compared, and the difference between the two scores is calculated for each student. The mean difference in scores is then considered as a statistic to evaluate the overall progress of the class.

Mean difference is a statistical measure that represents the average difference between two sets of data. It is calculated by subtracting the mean of one set from the mean of the other set and then dividing the result by the number of data points.

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Vlad should sample 1733 soldiers to estimate the proportion with a margin of error of less than 0.007 and a 97% confidence level.

We can use the formula for the margin of error of a proportion:

ME = zsqrt(p(1-p)/n)

where ME is the margin of error, z is the critical value for a 97% confidence interval (which can be found using a table or calculator and is approximately 2.17), p is the estimated proportion (0.62), and n is the sample size.

We want to find n, so we can rearrange the formula and solve for n:

n = (z^2 * p * (1-p)) / ME^2

Substituting the values given, we get:

n = (2.17^2 * 0.62 * 0.38) / 0.007^2

n ≈ 1732.92

Since we need a whole number of soldiers, we round up to n = 1733.

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Answer:

17

Step-by-step explanation:

A straight angle is 180

180 = 6z + 1 + 77 combine like terms

180 = 6z + 78  Subtract 78 from both sides

180 - 78 = 6z + 78 - 78

102 = 6z  Divide both sides by 6

17 = z

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

what you have to do is

hope this helps!

The equation 4(x-1) + 5y = 4(-1) + 5 is transformed by moving 5 spaces right, 2 spaces down, and reflecting. The resulting equation is -4(x+6) - 5y = -44.

To move an equation 5 spaces right, we need to replace x with x-5. Then, to move it 2 spaces down, we replace y with y+2.

The equation now becomes 4(x-1-5) + 5(y+2) = 4(-1) + 5. Simplifying this, we get 4(x-6) + 5y = -16 + 5, which simplifies to 4(x-6) + 5y = -11.

To reflect the equation, we need to negate the coefficients of x and y. This gives us -4(x-6) - 5y = -11, which simplifies to -4x + 24 - 5y = -11.

Finally, we can simplify this further to get -4x - 5y = -35, or alternatively, multiply both sides by -1 to get 4x + 5y = 35.

Therefore, the new equation after the transformations is -4(x+6) - 5y = -44.

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The set {x∈R:[tex]x^2\geq 0[/tex]}^c is the empty set, as there are no real numbers that are not included in the set of all real numbers.

To find the set {x∈R:[tex]x^2\geq 0[/tex]}^c, we first need to understand what the statement [tex]x^2\geq 0[/tex] means. This inequality simply states that any real number squared is always non-negative. Therefore, the set {x∈R:[tex]x^2\geq 0[/tex]} is equivalent to the set of all real numbers.

Now, to find the complement of this set, we need to look for all the elements that are not in the set of all real numbers. Since the universal set is R, which is the set of all real numbers, the complement of {x∈R:[tex]x^2\geq 0[/tex]} will be the empty set, since there are no real numbers that are not included in the set of all real numbers.
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The opening price on the following days are,

April 28 = 20 thousand

May 2 = 50 thousand

And, the closing price on the following days are,

April 29 = 22 thousand

May 1 = 22 thousand

Given that;

The following stock bar chart depicts the market action for the Washington petroleum Corp. during the week of April 28.

Hence, By graph;

The opening price on the following days are,

April 28 = 20,000

May 2 = 50,000

And, the closing price on the following days?

April 29 = 22,000

May 1 = 22,000

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Answer:

Step-by-step explanation:

mass of the urine lol

When sample observations can be paired or we have dependent samples, treating these as independent samples will reduce the power of the test.

The power of a statistical test is the probability of correctly rejecting the null hypothesis when it is false. In other words, it measures the test's ability to detect a significant effect or difference when one actually exists. When we treat dependent samples as independent, we do not take into account the relationship between the paired observations, which can lead to a loss of information and ultimately reduce the test's power.

In summary, when we have dependent samples and treat them as independent, it will reduce the power of the test, leading to an increased chance of a Type II error. This means that we are more likely to fail to detect a true effect or difference when one actually exists. It is important to properly account for the relationship between paired observations in order to maintain the test's power and decrease the likelihood of making errors in our conclusions.

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Answer:

±0.6

Step-by-step explanation:

Pythagorean identity:

sin² x + cos² x = 1

sin² x + (0.8)² = 1

sin² x + 0.64 = 1

sin² x = 0.36

sin x = ±0.6

The length of KL to millimeters is  460 millimeters

To convert the measurements, we need to take into considerations the following.

We have that;

Idm = 10 cm

1000 centimeter = 1 liter

100 millimeters = 1cm

From the information given, we have that;

The length of line KL is 4.6cm

If 100 millimeters = 1cm

Then, x = 4. 6cm

cross multiply the values, we get;

x = 460 millimeters

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Based on the information, we can infer that the three cylinders have a similar volume. However, option 3 would be the best option for buyers.

To find the area of the cylinders we must apply the following formula:

According to the above, the area of the cylinders would be:

option 1

option 2

option 3

On the other hand, to find the volume of the cylinders we must perform the following formula:

option 1

option 2

option 3

Based on the above, we can infer that the three cylinders have a similar volume, so the amount of content would be the same in any of them. However, option 3 would be the best option for buyers because it uses fewer materials and that lowers its value.

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The cost of running the electric water heater for one month (30 days) would be $36, assuming the electricity costs 12 cents per kilowatt-hour.

To calculate the cost of running the electric water heater for one month, we need to determine the total energy consumption and multiply it by the cost per kilowatt-hour.

The water heater consumes 5 kW for 2 hours per day, so the daily energy consumption can be calculated as follows:

Daily energy consumption = Power (kW) × Time (hours) = 5 kW × 2 hours = 10 kWh

Next, we calculate the total energy consumption for one month (30 days):

Total energy consumption = Daily energy consumption × Number of days = 10 kWh/day × 30 days = 300 kWh

Finally, we multiply the total energy consumption by the cost per kilowatt-hour (12 cents/kWh) to find the cost of running the water heater for one month:

Cost = Total energy consumption × Cost per kilowatt-hour = 300 kWh × $0.12/kWh = $36

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Answer:

Step-by-step explanation:

To solve this problem, we can use the fact that a regular hexagon can be divided into six equilateral triangles.The radius of the hexagon is given as 12. Let's draw a diagram to better visualize the hexagon / \ / \ / \ /_______\ B C |\ /| | \ / | | \ / | | \ / | |____D____| | / \ | | / \ | | / \ | |/_______\| E FIn the diagram above, A, B, C, D, E, and F are the vertices of the hexagon.To find the apothem of the hexagon, we need to find the height of one of the equilateral triangles. We know that the side length of each triangle is equal to the radius of the hexagon, which is 12. Using the Pythagorean theorem, we can find the height of one of the triangles/| / | h /__| b/2 (b/2)^2 + h^2 = 12^2 b^2/4 + h^2 = 144 h^2 = 144 - b^2/4Since the hexagon is regular, each side length is equal to 12. Therefore, b = 12.scssCopy codeh^2 = 144 - 12^2/4 h^2 = 144 - 36 h^2 = 108 h = sqrt(108) h = 6*sqrt(3)So the apothem of the hexagon is 6*sqrt(3).To find the area of the hexagon, we can use the formula:makefileCopy codeArea = (1/2) * apothem * perimeterThe perimeter of the hexagon is equal to six times the length of one side, which is 6*12 = 72.scssCopy codeArea = (1/2) * 6*sqrt(3) * 72 Area = 216*sqrt(3)So the area of the hexagon is 216*sqrt(3).Finally, the length of one side of the hexagon is simply equal to the radius, which is 12.

the radius of convergence (R) is ∞, and the interval of convergence (I) is (-∞, ∞).

To find the radius of convergence (R) and the interval of convergence (I) of the series given by:

∑ 7(-1)^(n-1) n^n x^n

We can apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L as n approaches infinity, then the series converges absolutely if L < 1, diverges if L > 1, and the test is inconclusive if L = 1.

Let's apply the ratio test to the given series:

L = lim(n→∞) |(7(-1)^(n-1) (n+1)^(n+1) x^(n+1)) / (7(-1)^(n) n^n x^n)|

Simplifying and canceling out common factors:

L = lim(n→∞) |(7(n+1) x) / (n^n)|

Taking the absolute value:

L = lim(n→∞) |7(n+1) x / n^n|

Now, let's evaluate the limit:

L = |7x| lim(n→∞) (n+1) / n^n

The limit can be further simplified by applying the ratio test for the sequence:

lim(n→∞) (n+1) / n^n = 0

Therefore, the limit L simplifies to:

L = |7x| * 0 = 0

Since L = 0, which is less than 1, the ratio test indicates that the series converges absolutely for all values of x. Thus, the series converges for all x.

For a series that converges for all x, the radius of convergence (R) is infinite (∞), and the interval of convergence (I) is the entire real number line (-∞, ∞).

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The poster width is 21.7 inches.

Given that the original print of the figure is 3.5 inches wide and 5 inches long,

Here we will use the concept of scale factors,

Scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape. It is used to increase or decrease the size of an object.

The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known.

For example, a rectangle has a length of 5 units and a width of 2 units. Now, if we increase the size of this rectangle by a scale factor of 2, the sides will become 10 units and 4 units, respectively.

Hence, we can use the scale factor to get the dimensions of the changed figures.

The scale factor (k) = ratio of the corresponding sides,

We need to find the width of the poster if it is 6.2 times wider than the photo,

So, the original width = 3.5 in

Therefore, the poster size = 3.5 x 6.2 = 21.7 inches.

Hence the poster width is 21.7 inches.

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The airplane traveling from New York to Berlin, Germany, has covered 2100 miles in the first 5 hours of its 7-hour journey, leaving a remaining distance of 1860 miles to cover to reach its destination.

To determine the remaining distance that the airplane needs to cover to reach Berlin, we can subtract the distance already traveled from the total distance of the flight. In this case, the airplane has covered 2100 miles in the first 5 hours of its 7-hour journey. Therefore, the remaining distance can be calculated as:

Total distance - Distance covered = 3960 - 2100 = 1860 miles

This means that the airplane still needs to cover a distance of 1860 miles to reach Berlin. We can use this information to estimate the speed at which the airplane needs to travel for the remaining two hours to reach its destination on time. To do this, we can divide the remaining distance by the remaining time:

Speed = Distance / Time = 1860 / 2 = 930 miles per hour

Therefore, the airplane needs to maintain a speed of 930 miles per hour to reach Berlin on time. It's important to note that weather conditions, air traffic, and other factors can affect the actual speed of the airplane during the remaining two hours of the flight, which should be taken into account by the pilot and the flight crew to ensure a safe and timely arrival at the destination.

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The range of the function f include the following: [-20, ∞].

In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range and domain:

Range = [-20, ∞] or -20 ≤ y ≤ ∞.

Domain = [-∞, ∞] or -1 < x < ∞.

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Answer:

Step-by-step explanation:

You want the volume, cost, and weight of a concrete pipe 2 m long with an outside diameter of 40 cm, and an inside diameter of 30 cm. The cost is $135 per cubic meter, and the weight is 2430 kg per cubic meter.

The area of a circle in terms of its diameter is ...

  A = π/4·d²

The area of the end of the pipe will be the difference between the overall area (using the outside diameter) and the area of the missing center part (using the inside diameter). It is ...

  End area = (π/4)(0.40 m)² -(π/4)(0.30 m)² = 7π/400 m² ≈ 0.05498 m²

The area of the end of the pipe is about 0.05498 m².

The volume of the pipe is the product of its base area and its length:

  V = Bh

  V = (0.05498 m²)(2 m) ≈ 0.10996 m³

The volume of the pipe is about 0.10996 m³.

At $135 per cubic meter, the cost of the concrete for the pipe is ...

  ($135/m³)(0.10996 m³) ≈ $14.84

The concrete cost for the pipe is about $14.84.

The density of 2.43 g/cm³ is equivalent to 2430 kg/m³. Since our volume is in cubic meters, we need the density to have these units.

  m = (2430 kg/m³)(0.10996 m³) ≈ 267.19 kg

The weight of the pipe is about 267 kg.

__

Additional comment

The cost is given in units of dollars per cubic meter. This suggests that it will be convenient to use meters as the unit of length. The calculations are done with 30 cm and 40 cm converted to 0.30 m and 0.40 m, respectively.

Similarly, the density is converted to units of kg per cubic meter. This facilitates finding the weight in kg from the volume in m³.

  1 g/cm³ = (0.001 kg)/(0.01 m)³ = 1000 kg/m³

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Answer: #4- both graphs intersect the x-axis to the right of 0

Step-by-step explanation: put them in a graphing calculator or work it out by first solving for x then imputing that answer into the equation

The mason's assistant's pay for the job is $165.

To find the mason's assistant's pay for the job, we need to multiply the rate of pay per cubic foot by the number of cubic feet moved.

Rate of pay per cubic foot = $0.75
Number of cubic feet moved = 220

Pay for the job = $0.75 x 220 = $165

Therefore, the mason's assistant's pay for the job is $165.
The mason's assistant will earn $165 for this job.


To calculate the pay for the mason's assistant, follow these steps:

1. Determine the rate of pay per cubic foot: $0.75
2. Determine the total amount of cubic feet moved: 220 cubic feet
3. Multiply the rate of pay by the total cubic feet moved: $0.75 x 220

By multiplying the rate of pay ($0.75) by the total cubic feet moved (220), you get the total pay for the job:

$0.75 x 220 = $165


The mason's assistant will be paid $165 for moving 220 cubic feet of earth to dig the trench.

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The number of required tiles including the breakage and cut-offs are 37.

Firstly we will calculate the number of required tiles based on below mentioned formula-

Number of tiles required to cover the floor = Area covered by one tile × Total area to be tiled

Number of required tiles = 33.984

Rounding off the number

Number of required tiles = 34

Number of extra tiles required for breakage and cut-offs = 34 + 10% × 34

Number of extra tiles = 34 + 10/100×34

Performing multiplication, division, addition along with cancelling common zeroes of the number

Number of extra tiles = 34 + 3.4

Adding the values

Number of extra tiles = 37.4

Again rounding off the number

Number of extra tiles = 37

Hence, the total required number of tiles are 37 according to stated percentage of waste.

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The solution is: red<yellow<green<blue<violet are the colors.

The light spectrum contains waves with specific wavelength which can be classified into groups. Most of the groups are invisible to the eye (like infrared, microwaves, radio waves, gamma rays, etc.) however, there is one group that is known as visible light.

Visible light allows us to see colors from red all the way to violet. The colors have different frequencies and wavelengths. The wave with the highest frequency also has the highest energy (which in this case is violet). Hence, as the frequency decreases, the energy will also decrease, making violet have the highest energy, and red have the lowest energy.

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complete question:

which answer has the colors in order from the lowest energy to the highest? group of answer choices red, blue, green blue, red, green blue, green, red red, green, blue

In school suspension

Yes, the chain rule in calculus involves multiplying the derivative of the outside function by the derivative of the inside function.

The chain rule is a fundamental concept in calculus that allows us to find the derivative of a composite function. When a function is composed of two or more functions nested inside each other, the chain rule enables us to differentiate the composite function by taking into account the derivatives of the individual functions.

Mathematically, if we have a composite function f(g(x)), where g(x) represents the inside function and f(u) represents the outside function, the chain rule states that the derivative of the composite function is given by the product of the derivative of the outside function f'(u) and the derivative of the inside function g'(x). In other words, it is the prime of the outside function multiplied by the prime of the inside function.

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The interquartile range of the two data sets are:

Band members = $100.

Choir members = $150.

The difference between the median amounts raised by this group is

A statement that is best supported by the random samples is: A. the amounts raised by band members are more varied than the amounts raised by choir members.

In Mathematics and Statistics, the interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) of band members = Q₃ - Q₁

Interquartile range (IQR) of band members = 250 - 150

Interquartile range (IQR) of band members = $100.

For the choir members, we have;

Interquartile range (IQR) of choir members = 400 - 250

Interquartile range (IQR) of choir members = $150.

Median of band members = $200.

Median of choir members = $350.

Therefore, the median difference can be calculated as follows;

median difference = 350 - 200 = $150

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