if a coin is tossed five times: find the probability of getting at least one tail. give answer as simplified fraction.

Answer:

(100/500) *200 =40%

Step-by-step explanation:

The given sequence appears to be an arithmetic sequence, as the common difference between consecutive terms is 4.

The nth term of an arithmetic sequence is given by the formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference and n is the nth term.

Given that the first term of the sequence is 2, the common difference is 4.

To find the 41st term of the sequence, we can use the formula:

a_41 = 2 + (41-1) * 4 = 2 + 40 * 4 = 2 + 160 = 162

Therefore, the 41st term of the sequence is 162.

The proof of the circumcenter theorem states that given three points A, B and C, drawing lines AB and AC or AB and BC and finding the perpendicular bisector of the corresponding segment will intersect at the circumcenter of triangle ABC.

Column 1:

1. Given three points A, B and C, draw lines AB and AC.

2. A bisector of angle BAC is the perpendicular bisector of segment AC.

3. The perpendicular bisector of segment AC intersects line AB at the circumcenter of triangle ABC.

Column 2:

1. Given three points A, B and C, draw lines AB and BC.

2. A bisector of angle ABC is the perpendicular bisector of segment BC.

3. The perpendicular bisector of segment BC intersects line AB at the circumcenter of triangle ABC.

The proof of the circumcenter theorem states that given three points A, B and C, drawing lines AB and AC or AB and BC and finding the perpendicular bisector of the corresponding segment will intersect at the circumcenter of triangle ABC. Therefore, it is enough to work on two edges to find the circumcenter.

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Answer:

A polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial (ignoring the coefficients).

For example: 6x4 + 2x3+ 3 is a polynomial. Here 6x4, 2x3, 3 are the terms where 6x4 is a leading term and 3 is a constant term. The coefficients of the polynomial are 6 and 2.

The degree of the polynomial 6x4 + 2x3+ 3 is 4.

Answer:

Here is your answer. Hope this helps.

To calculate the mcg/kg/minute, first divide 800 mg by 500 ml to get 1.6 mg/ml. Then, multiply 1.6 mg/ml by 5 ml/hour to get 8 mg/hour. Finally, divide 8 mg/hour by 70 kg to get 0.114 mcg/kg/minute.

To calculate the mcg/kg/minute, first divide 800 mg by 500 ml to get 1.6 mg/ml, which is the concentration of dopamine in the solution. Next, multiply 1.6 mg/ml by 5 ml/hour to get 8 mg/hour, which is the rate of infusion. Finally, divide 8 mg/hour by 70 kg to get 0.114 mcg/kg/minute, which is the mcg/kg/minute the client is receiving. This calculation can also be done by dividing 800 mg by 500 ml to get 1.6 mg/ml, then multiplying 1.6 mg/ml by 5 ml/hour to get 8 mg/hour, and finally dividing 8 mg/hour by 70 kg to get 0.114 mcg/kg/minute. By doing this calculation, the client is receiving 0.114 mcg/kg/minute of dopamine solution.

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Answer:129.7

Step-by-step explanation:

Literally just used a calculator but if you need explanation lmk

The numbers that have been omitted from the given series of a number with comparable discrepancies between them are known as missing numbers.

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Slope is y is -1x + 1.

To enter data and find the equation's solution, we can utilize the equation's point-slope form.

use the point ( 2, 3) and the slope of 1.

m \s= \s− \s1

x \s1 \s= \s− \s2

y \s1 \s= \s3

In the point-slope formula,

y \s− \sy \s1 \s= \sm \s( \sx \s− \sx \s1 \s)

the values into the plug

y \s− \s3 \s= \s− \s1 \s( \sx \s− \s( \s− \s2 \s) \s)

symbol reduction

Distribute the 1 according to y 3 = 1 (x + 2).

Use additive inverse to find the y in the equation y = 3 = 1 x 2

y \s− \s3 \s+ \s3 \s= \s− \s1 \sx \s− \s2 \s+ \s3

simplify

y \s= \s− \s1 \sx \s+ \s1.

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Answer: A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller). Therefore, The scale factor would be 1/2

The value of  [tex]tan^{-1}(0.2)[/tex] = -0.19739 + ... i.e. [tex]tan^{-1} (0.2)= (0.2) - \frac{(0.2)^{3} }{3} +\frac{(0.2)^{5} }{5} -\frac{(0.2)^{7} }{7}+...[/tex]

The power series of  [tex]tan^{-1}(x)[/tex] obtained in example 6 is called the Gregory's series. The Gregory series is an infinite series of fractions or rational numbers

After the Scottish mathematician James Gregory (1638-1675) who had anticipated some of Newton's discoveries we have shown that  the Gregory's series is valid when -1 < x < 1.

But it turns out (although it isn't easy to prove) that it is also valid when:

x = 1 or ≠ 1.

According to Example 6, The radius of convergence of the series for

[tex]1/(1 +x^{2} )[/tex]  is 1, the radius of convergence of this series for [tex]tan^{-1}(x)[/tex] is also 1.

                          [tex]tan^{-1} x = x - \frac{x^{3} }{3} +\frac{x^{5} }{y} -\frac{x^{7} }{y} +....[/tex]  

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Answer:28

Step-by-step explanation:

Trick: just check if it's divisible by both numbers

Answer:

1,576,800 minutes

Answer:

250u2

Step-by-step explanation:

The volume of a cube is found by multiplying LxWxH. 5x5x5-125, 125x2-250

Hope this helped :)

Answer:

2. <

Step-by-step explanation:

To compare these two fractions we can first find them a common denominator. A common denominator between 4 and 16 is 16.

To get from 16 from 4 we multiply by 4 so we do the same to the numerator, changing 1/4 to 4/16.

5/16 already has a denominator of 16 so we can leave that one as is.

4/16___5/16

In this form it is obvious that 5/16 is the larger fraction because 5 is larger than 4, meaning that 5/16 is larger than 1/4.

Answer: Since the company is running short of cash they have failed or late to pay the shareholders' share of the profit which is the dividend.

An ellipse is defined as the set of all points such that the sum of the distances between the point and the two foci is constant. The equation of an ellipse can be represented in the standard form as:

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

where (h, k) is the center of the ellipse, a is the distance from the center to a vertex, and b is the distance from the center to the focus.

Given that the center of the ellipse is at (2, 1), one vertex is at (2, -4), and one focus is at (2, -2), we can use this information to find the values of a and b, and represent the equation of the ellipse:

a = distance from center to vertex = |1 - (-4)|/2 = 2.5

b = distance from center to focus = |1 - (-2)|/2 = 1.5

The equation of the ellipse is:

(x-2)^2/2.5^2 + (y-1)^2/1.5^2 = 1

which can also be written as:

(x-2)^2/6.25 + (y-1)^2/2.25 = 1

This equation represents the ellipse with center at (2, 1), one vertex at (2, -4), and one focus at (2, -2)

Consequently, x∈R denotes that x belongs to the set of Real numbers. This means that x is a real number.

Hence, As a result, the symbol x∈R indicates that x is a member of the Real number set. Thus, x must be a real number.

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If the dealership decided to use a 20% markup instead, then they earn $700 more.

percentage, a relative value indicating hundredth parts of any quantity.

Given that A car dealership pays a wholesale price of $14,000 to purchase a vehicle.

They sell the car for $16,100

If the dealership decided to use a 20% markup instead, we have to find the hu=ow much more would they make.

Let us find 20% of 14000

20/100×14000

0.2×14000

2800

So with 20% the price will become $16800.

As they sell the car for $16100.

The difference between $16800-$16100 is $700

Hence, If the dealership decided to use a 20% markup instead, then they earn $700 more.

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The picture explains it all. We use tangent rule to find out the measure of angle A.

The measure of angle unknown angle is 30°.

Use the concept of the triangle defined as:

A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.

Given that,

Side AC = 6 units

Side BC = 3 units

Let ∠BAC = θ

Since we know that,

Sin θ = opposite/Hypotenuse

Sin θ = BC/AC

Put the values,

Sin θ = 3/6

Sin θ = 1/2

Since we know that,

sin(π/6) = 1/2

Therefore,

Sin θ = sin(π/6)

Take the inverse of sin on both sides we get,

θ = π/6 or 30°

Hence,

The measure of angle unknown angle is 30°.

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The solution to the differential equation (x^3 + y^3) dx − xy^2 dy = 0 is y/x^3 = Ce^(−(y/x)^3), where C is an arbitrary constant.

Substituting y = vx and dy = x dv + v dx, we get:

(x^3 + (vx)^3)dx − x(vx)^2(x dv + v dx) = 0

Simplifying and rearranging, we get:

x^2v dx + (x^3 + 3xv^2 − v^3x^2)dv = 0

Dividing both sides by x^2v and rearranging, we get:

dx/x + (1/v)dv + (3/xv - v^2)dv = 0

Integrating both sides, we get:

ln|x| + ln|v| + 3ln|v/x| − v^3 = C

Where C is an arbitrary constant. Simplifying, we get:

ln|vx/x^3| = C − v^3

Rearranging, we get:

vx/x^3 = Ce^(−v^3)

Finally, we can express this in terms of x and y as:

y/x^3 = Ce^(−(y/x)^3)

The solution to the differential equation (x^3 + y^3) dx − xy^2 dy = 0 is y/x^3 = Ce^(−(y/x)^3), where C is an arbitrary constant.

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Cotangent is the inverse of tangent:

cotΘ = 1/tanΘ

cotΘ = [tex]1/\frac{\sqrt{6} }{2}[/tex]

         =[tex]\frac{2}{\sqrt{6}}[/tex]

         =[tex]\frac{2}{\sqrt{6}}*\frac{\sqrt{6}}{\sqrt{6}}=\frac{2\sqrt{6}}{6}[/tex] Rationalize the denominator

cotΘ = [tex]\frac{\sqrt{6}}{3}[/tex]

Plug and solve.

[tex]\frac{\frac{\sqrt{6}}{2}+\frac{\sqrt{6}}{3} }{\frac{\sqrt{6}}{2}-\frac{\sqrt{6}}{3}}[/tex]

We'll break the problem into 2, simplify the denominator, then simplify the numerator.

Simplify the denominator with the common denominator 6, of 2 and 3:

[tex]{\frac{\sqrt{6}}{2}-\frac{\sqrt{6}}{3} = {\frac{3\sqrt{6}}{6}-\frac{2\sqrt{6}}{6} = {\frac{3\sqrt{6}-2\sqrt{6}}{6} = {\frac{\sqrt{6}}{6}[/tex]

Simplify the Numerator with the common denominator 6, of 2 and 3:

[tex]{\frac{\sqrt{6}}{2}+\frac{\sqrt{6}}{3} = {\frac{3\sqrt{6}}{6}+\frac{2\sqrt{6}}{6} = {\frac{3\sqrt{6}+2\sqrt{6}}{6} = {\frac{5\sqrt{6}}{6}[/tex]

Back in original equation with simplified numerator and denominator:

[tex]\frac{\frac{5\sqrt{6}}{6}}{\frac{\sqrt{6}}{6}}[/tex]

Multiply by reciprocal and simplify:

[tex]\frac{5\sqrt{6}}{6}*\frac{6}{\sqrt{6}} = \frac{5\sqrt{6} * 6}{6\sqrt{6}} = 5*\frac{6\sqrt{6}}{6\sqrt{6}} = 5*1 = 5[/tex]

The answer to the problem is: row

To have the determinant negative, at least one Eigenvalue has to be negative but the reverse of this statement may or may not be true.

If we add all the diagonal elements of the square matrix, we get the trace of the given matrix.

Eigenvalues is a scalar that associates with a set linear equation described as -

(A - λ I) X = 0

If we take the product of all the eigenvalues of a matrix, we'll get the determinant of the matrix. If we consider a case in which the trace of the matrix is +ve, and its determinant is -ve, then at least one or an odd no. of Eigenvalues must be negative, since their product has to be positive when we solve for the determinant of the matrix

Therefore, to have the determinant negative, at least one Eigenvalue has to be negative but reverse may or may not be true.

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The odd_sum method accepts an array of numbers and returns the total sum of all odd numbers found in the array.

def odd_sum(numbers)

 sum = 0

 numbers.each do |num|

   if num.odd?

     sum += num

   end

 end

 sum

end

1. We define a method called odd_sum that accepts an array of numbers as an argument.

2. We set a variable called sum and set it to 0.

3. We iterate through the array using the each method.

4. We check if the number is odd using the odd? method.

5. If the number is odd we add it to the sum variable.

6. We return the sum variable at the end of the method.

The odd_sum method accepts an array of numbers and returns the total sum of all odd numbers found in the array

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.

The area above x axis is 12.6 sq units while the area under the y-axis is 42.443 sq units. The change in the average phone bill is 29.843 units.

a) Here we see that the graph is in the shape of a right-angled triangle above the x-axis

The area of a triangle = 1/2 X Base X Height

Here the base will be the measure of the distance of co-ordinates on the x-axis

The height is the distance between the coordinates on the axis for that triangle

= 1/2 X (16 - 8) X (3.15 - 0)

= 1/2 X 8 X 3.15

= 12.60 sq units

b)

Below the x-axis, the graph is a rectangle and a triangle

The area of the rectangle = length X width

Here length is the distance of the co-ordinates of the y-axis and width is the distance between the coordinates for the x-axis

Hence we get

(0 - (-5.14))(8 - 0)

= 5.14 X 8

= 41.12 sq units for the rectangle.

The area of the triangle will be

1/2 X (18 - 15.48) X (0 - (-1.05))

1/2 X 2.52 X 1.05

= 1.323 sq unit

Hence, the total area is

41.12 + 1.323

= 42.443 sq unit

c)

Since the area under the graph represents change,

Here we see that the change in the average cell phone bill will be

42.443 + 12.6

= 55.043

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Complete Question

(Image Attached)

The general solution with the initial condition y(-1)=C is y=-(1+x)/(6+x)=-2/7.

The general solution to the differential equation -6y = 1+x+y+xy is y = -(1+x)/(6+x). To apply the initial condition, we can substitute x=-1 and y=C into the above equation and solve for C. We get C=-(2/7). Therefore, the general solution to the differential equation with the initial condition y(-1)=C is y=-(1+x)/(6+x)=-2/7.

Substituting x=-1 and y=C into the equation:

-6C = 1-1+C+(-1)C

-7C = 1

C = -1/7

Therefore, the general solution with the initial condition y(-1)=C is y=-(1+x)/(6+x)=-2/7.

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The difference (Dogs – Cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.054 from the true difference in proportions.

The third option is correct.

What is the standard deviation?

Standard deviation is a statistical measure of the spread of a dataset, defined as the square root of its variance. It is a way to quantify the amount of variation or dispersion of a set of data values.

Percentage of Dogs getting their teeth cleaned = 48% = pD

Percentage of Cats getting their teeth cleaned = 35% = pC

Number of Dogs selected = nD = 25

Number of Cats selected = nc = 32

As the sample sizes are large enough, we can apply Central Limit Theorem

According to Central Limit Theorem for proportions –

pD-hat ~ Normal(pD, {pD*(1-pD)}/nD)

Thus, pD-hat ~ Normal(0.48, 0.009984)

Similarly,

pC-hat ~ Normal(pC, {pC*(1-pC)}/nC)

Thus, pC-hat ~ Normal(0.35, 0.0071094)

Now if X ~ N(E(X), Var(X)) and Y ~ N(E(Y), Var(Y))

then X -Y ~ N(E(X)-E(Y), Var(X)-Var(Y)) (If X and Y are Independent)

Thus,

pD-hat - pC-hat ~ Normal(0.48-0.35, 0.009984 – 0.0071094)

pD-hat - pC-hat ~ Normal(0.13, 0.0028746)

Thus, Standard Deviation of pD-hat - pC-hat = (0.0028746^0.5) = 0.0536 that is 0.054 approximately

Hence, the difference (Dogs – Cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.054 from the true difference in proportions.

Third Option is correct.

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