Find the product of (x − 3)2

The total number of sides of a regular polygon with each exterior angle of measure 30 degrees is equal to 12.

Let us consider 'n' be the number of sides of the regular polygon.

Let 'y' be the measure of each of the exterior angle of regular polygon.

y = 30 degrees

Measure of each of the exterior angle of regular polygon 'y'

= ( 360° ) / n

⇒ n = ( 360° / y )

Substitute the value we get,

⇒ n = ( 360° / 30° )

⇒ n = 12

Therefore, the number of sides of a regular polygon with each of the exterior angle 30 degrees is equal to 12.

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The above question is incomplete, the complete question is:

How many sides does a regular polygon have when each exterior angle measures 30 degrees?

Answer:

16.67

Step-by-step explanation:

Answer:

16.67

Step-by-step explanation:

70:420*100 =

(70*100):420 =

7000:420 = 16.67

Using the vertex form of a parabola f(x) = a(x - h)2 + k where (h,k) is the vertex of the parabola

The axis of symmetry is y = 0 so h also equals 0

Substitute each point from the parabola into the vertex form:

4 = a(1 - 0)2 + k

4 = a(1) + k

4 = a + k

7 = a(2 - 0)2 + k

7 = a(4) + k

7 = 4a + k

We know have a linear system:

4 = a + k

7 = 4a + k

Subtracting the two equations gives us:

-3 = -3a

a = 1

Substituting the a value into the first equation of the linear system:

4 = 1 + k

k = 3

f(x) = (x - 0)2 + 3

f(1) = 4 = (1 - 0)2 + 3 = 1 + 3

f(2) = 7 = (2 - 0)2 + 3 = 4 + 3

The equation of the parabola through the given points and axis of symmetry is

f(x) = (x - 0)2 + 3 = x2 + 3

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Answer:

$1053

Step-by-step explanation:

If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.

To do this multiplication, we can break 1.62 down  simply into $1.00 +$0.6+$0.02

650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.

When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053

For constructing a confidence interval for the mean of a Normal population with unknown population standard deviation, taking a larger sample size would reduce the margin of error.

However, if increasing the sample size is not feasible, then using a lower level of confidence can also reduce the margin of error.

This is because a lower level of confidence requires a smaller critical value, resulting in a narrower confidence interval, and thus a smaller margin of error.

Using z-methods instead of t-methods or converting data into categorical values will not necessarily reduce the margin of error.

Hypothesis testing is a statistical method used to determine whether there is enough evidence to reject or fail to reject a null hypothesis (H0).

In this case, the null hypothesis is that the proportion of people who believe that the state of the economy is the country’s most significant concern is equal to 75%.

Since we are testing for a difference in proportion in either direction, the appropriate alternative hypothesis is Ha: p ≠ 0.75.

This is a two-tailed test, which means we are interested in deviations from 75% in both directions.

Option (a) and (b) are incorrect because they only consider one tail of the distribution. Option (c) is incorrect because it tests for a difference only in one direction (greater than).

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Answer:

y=-4

Step-by-step explanation:

The answer is going to be -4 as when y=-16 x=8.

(1) A = 1

(2) P(0.1 ≤ X ≤ 0.5) = 0.999

(3) Possible PDF(probability density function): fx(x) = 3Ax² for x < 1, fx(x) = 0 for x ≥ 1

(1) Find the value of A:

The cumulative distribution function (CDF) is given by Fx(x) = Ax³ for x < 1 and Fx(x) = 1 for x ≥ 1.

To find the value of A, we need to ensure that the CDF is continuous at x = 1. This means that the limit of Fx(x) as x approaches 1 from the left side should be equal to the value of Fx(x) at x = 1.

Taking the limit as x approaches 1 from the left side, we have:

lim(x→1-) Ax³ = A(1)³ = A.

Since the CDF is equal to 1 at x = 1, we have:

Fx(1) = 1.

Equating the limit and the CDF value, we get:

A = 1.

Therefore, the value of A is 1.

(2) Calculate the probability that X is between 0.1 and 0.5:

To calculate the probability that X is between 0.1 and 0.5, we need to find the difference in the CDF values at those points.

P(0.1 ≤ X ≤ 0.5) = Fx(0.5) - Fx(0.1).

Using the given CDF, we have:

Fx(0.5) = 1 (since 0.5 ≥ 1),

Fx(0.1) = (1)(0.1)³ = 0.001.

Therefore, P(0.1 ≤ X ≤ 0.5) = 1 - 0.001 = 0.999.

The probability that X is between 0.1 and 0.5 is 0.999.

(3) Find a possible probability density function (PDF) fx(x) of X:

The PDF, denoted as fx(x), is the derivative of the CDF Fx(x).

For x < 1, we have:

Fx(x) = Ax³,

Differentiating both sides with respect to x, we get:

fx(x) = d/dx (Ax³) = 3Ax².

For x ≥ 1, we have:

Fx(x) = 1,

Since the CDF is constant, the PDF is zero: fx(x) = 0.

Therefore, a possible PDF fx(x) of X is:

fx(x) = 3Ax² for x < 1, and fx(x) = 0 for x ≥ 1.

In summary, the value of A is 1, the probability that X is between 0.1 and 0.5 is 0.999, and a possible PDF fx(x) of X is 3Ax² for x < 1 and 0 for x ≥ 1.

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Answer:

The monthly growth rate is 2.1%

Step-by-step explanation:

To find the monthly growth rate, we have to consider what is inside the bracket

Mathematically, what we have in the bracket should be written as;

1 + r

Thus;

1 + r = 1.021

r = 1.021-1

r = 0.021

This is same as 2.1%

Answer:

1) x = 6

2) x = 14

3) x = 4

4) x = 7

Step-by-step explanation:

1) x+5=11

x = 11-5

x =6

2) x-6=8

x = 8+6

x = 14

3) 3+x=7

x = 7-3

x = 4

4) 12=x+5

12-5 = x

7 = x

(a) The generating function for distributing r identical crayons to 5 kids and 2 adults if each adult gets at most 3 crayons is given by:\(G(x) = (1 + x + x^2 + ...)^5 (1 + x + x^2 + x^3)^2\)

(b) The generating function for the number of election outcomes where no candidate gets a majority of the votes is given by:\(G(x) = (1 + x)^{100} - \binom{100}{ > 50} - \binom{100}{ > 50}\)

(c) The generating function for the number of ways to get a sum of r when 4 distinct dice are rolled is given by:

\(G(x) = (x + x^2 + x^3 + x^4 + x^5 + x^6)^4\)

(d) The generating function for the number of ways to make r cents change in pennies and dimes is given by:

\(G(x) = (1 + x + x^2 + ...)(1 + x^{10} + x^{20} + ...)\)

(a) To distribute r identical crayons to 5 kids and 2 adults, we can use a generating function where the coefficient of \(x^r\) represents the number of ways to distribute r crayons to the kids and adults.

Let's consider the generating function:

\(G(x) = (1 + x + x^2 + ...)^5 (1 + x + x^2 + x^3)^2\)

The term \((1 + x + x^2 + ...)^5\) represents the number of ways to distribute r crayons to the 5 kids without any restrictions.

The term \((1 + x + x^2 + x^3)^2\) represents the number of ways to distribute the remaining crayons to the 2 adults, where each adult gets at most 3 crayons (the maximum power of x is 3).

(b) To count the number of election outcomes where no candidate gets a majority of the votes, we can use a generating function where the coefficient of\(x^r\) represents the number of outcomes where r votes are not received by any candidate.

Let's consider the generating function:

\(G(x) = (1 + x)^{100} - \binom{100}{ > 50} - \binom{100}{ > 50}\)

The term\((1 + x)^{100}\) represents the total number of outcomes where each voter votes for one of the 3 candidates.

The terms\(\binom{100}{ > 50}\)  represent the number of outcomes where one candidate receives more than 50 votes (a majority).

We subtract these terms twice to exclude the cases where one candidate or the other receives a majority, but then we double subtract the cases where both candidates receive a majority.

The resulting generating function counts the number of outcomes where no candidate receives a majority.

(c) To count the number of ways to get a sum of r when 4 distinct dice are rolled, we can use a generating function where the coefficient of\(x^r\)represents the number of ways to obtain a sum of r.

Let's consider the generating function:

\(G(x) = (x + x^2 + x^3 + x^4 + x^5 + x^6)^4\)

The term \((x + x^2 + x^3 + x^4 + x^5 + x^6)\)  represents the possible outcomes of rolling one die. Raising this term to the fourth power gives all possible outcomes of rolling 4 dice.

The coefficient of\(x^r\) in this generating function gives the number of ways to get a sum of r.

(d) To count the number of ways to make r cents change in pennies and dimes, we can use a generating function where the coefficient of\(x^r\)represents the number of ways to make r cents using pennies and dimes.

Let's consider the generating function:

\(G(x) = (1 + x + x^2 + ...)(1 + x^{10} + x^{20} + ...)\)

The term\((1 + x + x^2 + ...)\) represents the possible numbers of pennies we can use, and the term \((1 + x^{10} + x^{20} + ...)\)  represents the possible numbers of dimes we can use. Multiplying these two terms together gives all possible combinations of pennies and dimes that can be used to make r cents.

The coefficient of \(x^r\)  in this generating function gives the number of ways to make r cents change in pennies and dimes.

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Answer:

The answer is 7 meters

Step-by-step explanation:

Its 7 meters because if you divide the area by the width you would get the length (49 divided by 7 = 7)

The precision and accuracy of the data for warfarin are as follows:

Sample 1:

Sample 2:

Sample 3:

To determine the precision and accuracy of the data for warfarin, we can calculate the relative standard deviation as a measure of precision and the relative error as a measure of accuracy.

The relative standard deviation (RSD) is a measure of the precision of the data. It is calculated by dividing the standard deviation of the data by the mean and multiplying by 100 to express it as a percentage.

For Sample 1:

Mean: (21.1 + 26.4 + 23.2 + 23.1 + 27.3) / 5 = 24.42 ng/mL

Standard Deviation: 2.88 ng/mL

RSD = (2.88 / 24.42) * 100 = 11.8%

For Sample 2:

Mean: (59.1 + 71.7 + 91.0 + 70.6 + 73.7) / 5 = 73.22 ng/mL

Standard Deviation: 9.58 ng/mL

RSD = (9.58 / 73.22) * 100 = 13.1%

For Sample 3:

Mean: (229 + 207 + 253 + 199 + 225) / 5 = 222.6 ng/mL

Standard Deviation: 19.42 ng/mL

RSD = (19.42 / 222.6) * 100 = 8.73%

The relative error is a measure of the accuracy of the data. It is calculated by taking the absolute difference between the experimentally determined value and the known concentration, dividing it by the known concentration, and multiplying by 100 to express it as a percentage.

For Sample 1:

Relative Error = (|21.1 - 24.7| / 24.7) * 100 = 14.59%

For Sample 2:

Relative Error = (|59.1 - 78.5| / 78.5) * 100 = 24.67%

For Sample 3:

Relative Error = (|229 - 237| / 237) * 100 = 3.38%

The complete question:

Determine the precision and accuracy of these data for warfarin:

Sample 1 precision (relative standard deviation)

Sample 1 accuracy (relative error):

%%

Sample 2 precision (relative standard deviation):

%%

Sample 2 accuracy (relative error):

%%

Sample 3 precision (relative standard deviation):

%%

Sample 3 accuracy (relative error)

                                                    Sample 1    Sample 2     Sample 3

_______________________________________________________

Known concentration (ng/mL):      24.7            78.5               237

_______________________________________________________                                                                                    

                                                       36.0             72.9            249

Experimentally determined            21.1              59.1             229

values (ng/mL):                                26.4             71.7            207

                                                        23.2             91.0            253

                                                         23.1             70.6            199

                                                          27.3            73.7            225

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Answer:

10−(9)(−6)

=10−(−54)

=64

hope i helped

Answer:

an infinite is a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integer s {1, 2, 3, ...}.

Step-by-step explanation:

Answer:

(49,0)(0,-35)

y intercept (0,-35)

x intercept (49,0)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

2n-6=28

We move all terms to the left:

2n-6-(28)=0

We add all the numbers together, and all the variables

2n-34=0

We move all terms containing n to the left, all other terms to the right

2n=34

n=34/2

n=17

Answer:

x =2

Step-by-step explanation:

14x - 10 = 3(4 + x)

Distribute

14x -10 = 12 +3x

Subtract 3x from each side

14x -10 -3x = 12+3x-3x

11x -10 = 12

Add 10 to each side

11x -10+10 = 12+10

11x = 22

Divide each side by 11

11x/11 =22/11

x =2

Answer:

x = 2

Step-by-step explanation:

14x - 10 = 3(4 + x)

Distribute the 3 on the right side of the equation.

14x - 10 = 12 + 3x

Add 10 to both sides of the equation.

14x = 22 + 3x

Subtract 3x from both sides of the equation.

11x = 22

Divide both sides of the equation by 11.

x = 2

So we have found that x = 2.

x = 2 would be the solution to the equation.

I hope you find my answer and explanation to be helpful. Happy studying.

Answer:

that is the correct answer.

Step-by-step explanation:

If the slope of the line is -1/10, the value of j is: 8.

Slope of a line = change in y / change in x = (y2 - y1) / (x2 - x1).

Given the following:

(-2, 6) = (x1, y1)

(j, 5) = (x2, y2)

Slope (m) = -1/10.

Plug in the values:

-1/10 = (5 - 6) / (j -(-2))

-1/10 = -1/(j + 2)

-1(j + 2) = -1(10)

-j - 2 = -10

-j = -10 + 2

-j = -8

j = 8

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The expressions that have 3 as the greatest common factor are b + 3 + 6c, 27n + 66p, and 36 - 9j + 6k.

Thus,

b + 3 + 6c         - Yes

-30 - 24z           - No

27n + 66p         - Yes

36 - 9j + 6k       - Yes

From the question, we are to determine if 3 is the greatest common factor of the given expressions

b + 3 + 6c

3(b + 1 + 2c)

The greatest common factor is 3

-30 - 24z

6(-5 -4z)

The greatest common factor is not 3. The greatest common factor is 6

27n + 66p

3(9n + 22p)

The greatest common factor is 3

36 - 9j + 6k

3(12 - 3j + 2k)

Thus, The greatest common factor is 3

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Answer:

$7 per pound

Step-by-step explanation:

28/4

The statement "Flexible exchange rates ..." is incomplete, and without further clarification, it is uncertain to determine whether it is true or false. A complete statement is required to provide a clear context for discussing the nature and implications of flexible exchange rates.

Flexible exchange rates refer to a system in which currency exchange rates are determined by market forces, such as supply and demand. Under this system, exchange rates fluctuate freely based on various economic factors, including inflation rates, interest rates, trade balances, and investor sentiment.

Flexible exchange rates offer advantages such as the ability to adjust to changing economic conditions and promote trade balance adjustments. They can also help absorb external shocks and enhance monetary policy autonomy. However, they may also introduce volatility and uncertainty in international trade and investment. To assess the accuracy of the statement, additional information or context is needed.

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Answer:

Step-by-step explanation:

Objective: finding the distance

Formula: speed × time =  distance

75 × 2 = 150

final answer: 150 mph

According to the question The total cost of a table and a chair is $60.30 and the chair costs $20.10.

Let's assume the cost of the chair as \(\(x\)\) dollars. Since the table costs twice as much as the chair, the cost of the table is \(\(2x\)\) dollars.

The total cost of the table and chair is given as $60.30. We can set up the equation:

\(\(x + 2x = 60.30\)\)

Combining like terms:

\(\(3x = 60.30\)\)

To solve for \(\(x\)\), we divide both sides of the equation by 3:

\(\(x = \frac{60.30}{3}\)\)

\(\(x = 20.10\)\)

Therefore, the chair costs $20.10.

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Answer:

y=65

x=50

Step-by-step explanation:

exterior angle of a triamgle is equal to sum of two interior angles

so

2y=130(as it is isosceles triangle)

y=65

we know y+y+x=180(sum of all angles of triangle)and (vertically opposite angle)

therefore, x=50

Answer:

x=50°

y=65°

Step-by-step explanation:

I guess it would be better if there were alphabets representing each vertices otherwise it would difficult for you to understand

Let's take the point of intersection as O

Since It is a straight line(on both sides of O)=180°

Therefore x=180°-130°=50°

In the second triangle the angle at the top = 50° because x and that angle are vertically opposite to each other and therefore are equal

When the two sides of a triangle are equal, The base angles are always equal

Second triangle is 180°

The top angle is 50°

the base angles (which y and the angle below it)

is equal to 180°-50°=130°

Since base angles are equal and their sum is 130°, One base angle which is Y = 130°÷2=65°

As a result, the solid's volume in the first octant, which is restricted by the paraboloid z = 4 + 2 x + 2 y, is 9.

We must determine the limits of integration for x, y, and z in order to determine the volume of the solid in the first octant bounded by the paraboloid z = 4 + 2x + 2y + 2 and the plane z = 10.

At z = 10, where the paraboloid and plane overlap, we put the two equations equal and find z:

4 + 2x^2 + 2y^2 = 10

2x^2 + 2y^2 = 6

x^2 + y^2 = 3

This is the equation for a circle in the xy plane with a radius of 3, centred at the origin. We just need to take into account the area of the circle where x and y are both positive as we are only interested in the first octant.

Integrating over the circle in the xy-plane, we may determine the limits of integration for x and y:

∫∫[x^2 + y^2 ≤ 3] dx dy

Switching to polar coordinates, we have:

∫[0,π/2]∫[0,√3] r dr dθ

Integrating with respect to r first gives:

∫[0,π/2] [(1/2)(√3)^2] dθ

= (3/2)π

So the volume of the solid is:

V = ∫∫[4 + 2x^2 + 2y^2 ≤ 10] dV

= (3/2)π(10-4)

= 9π

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Given:

A number line from -10 to 10 with 20 tick marks.

Point D is 1 tick mark to the left of 5.

To find:

The integer value that represents point D.

Solution:

A number line from -10 to 10 with 20 tick marks. It means, each mark represents the integer values from -10 to 10.

We know that, as we move towards left on a number line the value decreases and as we move towards right the value increases.

Point D is 1 tick mark to the left of 5. It means, point D represents the integer value which is 1 less than 5.

\(5-1=4\)

Therefore, point D represents the integer 4.

Answer:y

=

4

3

x

−

9

Explanation:

Given -

x

1

=

6

y

1

=

−

1

Slope

m

=

4

3

Given the slope and a point, the formula for the straight line equation is

(

y

−

y

1

)

=

m

(

x

−

x

1

)

y

−

(

−

1

)

=

4

3

(

x

−

6

)

y

+

1

=

4

3

x

−

6

.

4

3

y

+

1

=

4

3

x

−

8

y

=

4

3

x

−

8

−

1

y

=

4

3

x

−

9