Determine the exact surface area of the cylinder in terms of 3.14 pi radius 1 3/4 cm and 3 1/4cm height

The answer for the given expression is =1/128[35-56cos2x+28cos4x-8cos6x+cos8x]

What is trignomatric functions?

All trigonometric identities are built upon the foundation of the six trigonometric ratios. Some of their names are sine, cosine, tangent, cosecant, secant, and cotangent. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios.

What is multiple angles?

If angle A is taken as a given, then many angles are 2A, 3A, 4A, etc. The many angle formulas employ the double and triple angles formulas. Sine, cosine, and tangent are the often utilised trigonometric functions for the multiple angle formula.

Answer is attached as a image must check:

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We can rewrite sin⁸x in terms of first powers of the cosines of multiple angles as:

sin⁸x = 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

Trigonometric functions raised to powers can be rewritten using double-angle, half-angle, and Pythagorean identities in power lowering formulas. Equations can be made simpler using them, and trigonometric expressions can be precisely determined.

We can use the power-reducing formulas to rewrite sin⁸x in terms of cosines of multiple angles as follows:

sin²x = 1 - cos²x   (first power-reducing formula)

sin⁴x = (sin²x)² = (1 - cos²x)²

      = 1 - 2cos²x + cos⁴x   (second power-reducing formula)

sin⁶x = (sin⁴x)(sin²x)

      = (1 - 2cos²x + cos⁴x)(1 - cos²x)

      = 1 - 3cos²x + 3cos⁴x - cos⁶x   (third power-reducing formula)

sin⁸x = (sin⁶x)(sin²x)

      = (1 - 3cos²x + 3cos⁴x - cos⁶x)(1 - cos²x)

      = 1 - 4cos²x + 6cos⁴x - 4cos⁶x + cos⁸x

Now we can substitute the expression for sin⁸x into the given expression and simplify it:

1/128 (35 - 56 cos2x + 28 cos4x - 8 cos6x + cos8x)

= 1/128 (35 - 56(2cos²x-1) + 28(4cos⁴x-3cos²x) - 8(8cos⁶x-8cos⁴x+cos²x) + cos⁸x)

= 1/128 (35 - 112cos²x + 56 + 112cos⁴x - 84cos²x - 64cos⁶x + 64cos⁴x - 8cos²x + cos⁸x)

= 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

Therefore, we can rewrite sin⁸x in terms of first powers of the cosines of multiple angles as:

sin⁸x = 1 - 4cos²x + 6cos⁴x - 4cos⁶x + cos⁸x

     = 1/128 (35 - 4cos²x + 40cos⁴x - 64cos⁶x + cos⁸x)

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Answer:

x = 16°

Step-by-step explanation:

What we know:

∠JML = 47°

∠JKL = (7x + 21)°

∠JML is an inscribed angle

∠JKL is an inscribed angle

Inscribed angles are half of the value of their intercepted arc

So if m∠JML = 47° then mArc JL is double that or 94°

And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so

mArc JL + Arc JML = 360°

94 + Arc JML = 360

Subtract 94 from both sides to isolate Arc JML

Arc JML = 266°

So if Arc JML = 266° then it's intercepted inscribed angle is half of that.

Arc JML ÷ 2 = ∠JKL

266 ÷ 2 = ∠JKL

133 °= ∠JKL

Now we can use this value and set it equal to the expression to find the value of x

(7x + 21) = 133

Subtract 21 from both sides to isolate the x

7x = 112

Divide both sides by 7

x = 16

Answer:

1st one is 6.9 X 10^6

2nd one is 2 x 10^5

Step-by-step explanation:

Answer:

There are three steps to find IQR

1. Know how the IQR is used. Essentially, it is a way of understanding the spread or "dispersion" of a set of numbers. The interquartile range is defined as the difference between the upper quartile (the highest 25%) and the lower quartile (the lowest 25%) of a data set.

2. Understand quartiles. To visualize a quartile, chop a list of numbers into four equal parts. Each of these parts is a "quartile."[2] Consider the set: 1, 2, 3, 4, 5, 6, 7, 8.

1 and 2 are the first quartile, or Q1

3 and 4 are the second quartile, or Q2

5 and 6 are the third quartile, or Q3

7 and 8 are the fourth quartile, or Q4

3. Learn the formula. In order to find the difference between the upper and lower quartile, you'll need to subtract the 25th percentile from the 75th percentile.

The formula is written as: Q3 – Q1 = IQR.

Answer:

the answer would be 2.5

Explanation:

The formula for finding the interquartile range takes the third quartile value and subtracts the first quartile value. Equivalently, the interquartile range is the region between the 75th and 25th percentile (75 – 25 = 50% of the data).

The probability that at least 2 students feel like they can do better in their math class is E. 0.9130.

To find the probability that at least 2 students feel like they can do better, we need to calculate P(X >= 2). This can be done using the cumulative distribution function (CDF) of the binomial distribution:

P(X >= 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)

Using the binomial probability formula, we can calculate:

P(X = 0) = (5 choose 0) * 0.6^0 * 0.4^5 = 0.01024

P(X = 1) = (5 choose 1) * 0.6^1 * 0.4^4 = 0.07680

Therefore,

P(X >= 2) = 1 - 0.01024 - 0.07680 = 0.91296

Rounding this to four decimal places, we get: 0.9130

Therefore, the answer is option E: 0.9130.

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To find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.

To find the ratio of edge lengths of two figures given their volume ratio, you need to use the fact that volume is proportional to the cube of the edge length.

If we have two figures, Figure A and Figure B, with edge lengths a and b respectively, and their volumes are in the ratio of V(A) : V(B) = k, then we can set up the following equation:

(Volume of A) / (Volume of B) = (a^3) / (b^3) = k

We can then solve for the ratio of edge lengths:

a / b = (k)^(1/3)

Therefore, to find the ratio of edge lengths given the volume ratio, we need to take the cube root of the volume ratio.

This method works for any shape, as long as the volume formula for that shape involves the cube of the edge length. For example, this method works for cubes, rectangular prisms, cylinders, spheres, and so on.

For triangles, however, we cannot use this method directly because the volume of a triangle is not a function of its edge length. Instead, we can use similar triangles to find the ratio of their edge lengths.

If we have two similar triangles, with corresponding sides in the ratio of a : b, then their areas are in the ratio of (a^2) : (b^2). We can use this fact to find the ratio of their edge lengths:

a / b = sqrt(Area of first triangle / Area of second triangle)

So, to find the ratio of edge lengths of two triangles given their area ratio, we need to take the square root of the area ratio.

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The truth set of the inequality is all values of x greater than -9. In interval notation, this can be written as (-9, ∞)

Multiply both sides by -2 (and reversing the direction of the inequality because we are multiplying by a negative number) gives:

x > -2*(5/2 + 2)

x > -5 - 4

x > -9

Therefore, the truth set of the inequality is all values of x greater than -9. In interval notation, this can be written as:

(-9, ∞)

Below is the complete question:

Find the truth set of x*(-1/2) < 5/2 + 2

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Answer:

Hello... im exhausted but ill solve it i guess

To solve for x in the equation 2/5 + x = 1, we can follow these steps:

Subtract 2/5 from both sides of the equation to isolate the x term:

2/5 + x - 2/5 = 1 - 2/5

This simplifies to:

x = 1 - 2/5

Find a common denominator for 1 and 2/5, which is 5:

x = 5/5 - 2/5

Subtract 2/5 from 5/5:

x = 3/5

So, the solution for x in the given equation is x = 3/5.

the formula for the exponential function N(t) is N(t) = 14 * 59in power (t/6), where N is the population at time t and t is the time in hours, days, or any other unit of time as long as it is consistent with the time unit used in the formula

How to solve the question?

Let N(t) be the exponential function we are trying to find, where N is the population at time t.

From the given information, we know that when t=0, N(0) = 14, which is the initial value of N.

We also know that when t is increased by 6, N is multiplied by 59. In other words,

N(t+6) = 59N(t)

We can use this relationship to express N(t+6) in terms of N(t) by substituting N(t+6) with 59N(t) in the above equation, giving us:

59N(t) = N(t+6)

Now, we can use this equation to solve for N(t) in terms of N(0) by repeatedly substituting N(t) with 59N(t-6), 59²N(t-12), 59³N(t-18), and so on.

N(t) = 59  in power (t/6) * N(0)

Using the initial value of N(0) = 14, we get:

N(t) = 14 * 59 in power (t/6)

Therefore, the formula for the exponential function N(t) is N(t) = 14 * 59^(t/6), where N is the population at time t and t is the time in hours, days, or any other unit of time as long as it is consistent with the time unit used in the formula

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Graph cookies and coffee, slope -2. Ben buys 2 cookies and 2 coffees. To optimize, allocate budget where MU per dollar is equal.

A budget is a financial plan that outlines expected income and expenses over a certain period. It helps individuals or organizations manage their money and make informed decisions about spending and saving.

Consumption refers to the use of goods and services by individuals, households, or organizations. It is an essential part of the economy and can be influenced by factors such as income, preferences, and prices.

According to the given information:

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By using the partial sum of series is

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

and summation n=1 to infinity of [tex]a_{n}[/tex] is =6 .

To obtain the formula for the nth term of the series and its total, we must first discover the formula for the series' general term.

The formula for the series' nth partial sum is as follows:

[tex]sn = 6 - n*5^{-n}[/tex]

The nth term of the series can be obtained by subtracting the (n+1)th and nth partial sums, i.e.,

a = sn+1 - sn

When we substitute the formula for sn, we get:

[tex]a_{n} = [6 - (n+1)5^{(-(n+1))} ] - [6 - n5^{(-n)} ]\\a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

As a result, the formula for the series' nth term is:

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

To calculate the series total, take the limit of the nth partial sum as n approaches infinity:

lim(n->inf) lim(n->inf) sn [6 - n*5^(-n)]

lim(n->inf) [n*5(-n)] = 6

= 6 - 0

= 6

As a result, the series' sum is 6.

As a result, the formula for the nth term in the series is:

[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]

And the series' total is:

a = sum(n=1 to inf) = 6

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The complete table for the pie chart is;

Type of Film             Frequency           Angle in °

Action                            4                           72°

Horror                           11                            198

Comedy                         5                            90

From the given table used to form the pie chart, we see that;

Type of Film             Frequency           Angle in °

Action                            4                           72°

Horror                           11                            

Comedy                         5

We know that the angles in a circle is equal to 360 degrees. Thus;

Angle composed of horror and comedy = 360 - 72 = 288°

Thus;

Angle for horror film = (11/(4 + 11 + 5)) * 360°

= (11/20) * 360°

= 198°

Thus;

Angle for comedy = 288° - 198° = 90°

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The ratio of the areas is given as follows:

1:5.8.

The ratio of the areas is obtained applying the proportions in the context of the problem.

When a prism is dilated by a scale factor of k, we have that:

Hence the ratio of the areas is the cubic root of the ratio of the volumes squared, thus, as the ratio of the volumes is of 1:14, we have that:

(14²)^(1/3) = 5.8.

Hence:

1:5.8.

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Answer:

-9.5.

Step-by-step explanation

To find a reasonable value for n, we need to use the given data points and the equation of the line. We can plug in any pair of x and y values into the equation and solve for m or b. For example, using (4, 2), we get:

2 = m(4) + b

Solving for b, we get:

b = 2 - 4m

Now we can plug in another pair of x and y values, such as (7, 4.5), and use the value of b we just found:

4.5 = m(7) + 2 - 4m

Solving for m, we get:

m = 0.5

Now we have the slope and the y-intercept of the line. The equation is:

y = 0.5x + 2 - 4(0.5)

Simplifying, we get:

y = -1.5x + 4

To find n, we need to plug in x = 9 and solve for y:

y = -1.5(9) + 4

y = -9.5

Answer:

  (I₁, I₂) = (1, 1)

Step-by-step explanation:

You want the matrix version of the given circuit equations, and the solution by matrix methods and by Cramer's rule.

The coefficients of the variables fill matrix A; the constants fill matrix (column vector) B:

  AI = B

  [tex]\left[\begin{array}{cc}15&5\\25&5\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}20\\30\end{array}\right][/tex]

The solution to this matrix equation can be found by left-multiplying both sides by the inverse of matrix A. The inverse of a 2×2 matrix is the transpose of the cofactor matrix, divided by its determinant. It can be written down, as the form is simple: diagonal elements are swapped; off-diagonal elements are negated.

  [tex]A^{-1}=\dfrac{1}{15(5)-25(5)}\left[\begin{array}{cc}5&-5\\-25&15\end{array}\right]=\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\\\\\textsf{Multiplying by $A^{-1}$, we have ...}\\\\\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\left[\begin{array}{cc}15&5\\25&5\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{cc}-0.1&0.1\\0.5&-0.3\end{array}\right]\left[\begin{array}{c}20\\30\end{array}\right][/tex]

  [tex]\left[\begin{array}{cc}1&0\\0&1\end{array}\right]\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}(-0.1)(20+(0.1)(30)\\(0.5)(20)+(-0.3)(30)\end{array}\right]\\\\\\\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}1\\1\end{array}\right][/tex]

Cramer's rule requires we find three determinants. We already found the determinant of the coefficient matrix, above. It is D = -50. The other two are ...

  [tex]D_1=\left|\begin{array}{cc}20&5\\30&5\end{array}\right|=(20)(5)-(30)(5)=-50\\\\\\D_2=\left|\begin{array}{cc}15&20\\25&30\end{array}\right|=(15)(30)-(25)(20)=-50\\\\\\I_1=\dfrac{D_1}{D}=\dfrac{-50}{-50}=1\qquad I_2=\dfrac{D_2}{D}=\dfrac{-50}{-50}=1\\\\\\\left[\begin{array}{c}I_1\\I_2\end{array}\right]=\left[\begin{array}{c}1\\1\end{array}\right][/tex]

Boat is 4.195 miles or  6.749755 km far from the lighthouse B.

The boat has moved 4 kilometers from point A to point x. The distance between B and x is what we're looking for.

Trigonometry can be used to overcome this issue. Let's abbreviate the distance "d" from A to x. Then, we can apply the following formula:

tan(65°) = (9 / d)

We can rearrange this formula to solve for d:

d = 9 / tan(65°)

We find that:

tan(65°) = 2.1445

So, d = 9 / 2.1445

= 4.195 miles (rounded to the nearest tenth)

or  6.749755 km.

Hence, Boat is 4.195 miles or  6.749755 km far from the lighthouse B.

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To determine which of the given fractions is a multiple of 1/9, we need to check if each fraction can be written as the product of 1/9 and another integer.

3/9 = 1/3, which is not a multiple of 1/9

4/9 cannot be simplified further and is therefore a multiple of 1/9

9/12 can be simplified to 3/4, which is not a multiple of 1/9

9/10 cannot be simplified further and is therefore a multiple of 1/9

2/9 cannot be simplified further and is therefore a multiple of 1/9

9/9 = 1, which is not a multiple of 1/9

Therefore, the fractions that are multiples of 1/9 are 4/9, 9/10, and 2/9.

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A single scoop is $0.40 cheaper per scoop than a scoop in a 3-scoop cone.

To compare the cost of each scoop of ice cream in a 3-scoop cone and a single scoop, we need to calculate the cost per scoop for each option.

In a 3-scoop cone, the cost of each scoop can be found by dividing the total cost by the number of scoops. Therefore, the cost of each scoop in a 3-scoop cone is:

4.80 ÷ 3 = 1.60

On the other hand, a single scoop of ice cream costs $2. Therefore, the cost of each scoop in a single scoop is:

2 ÷ 1 = 2

Comparing the two options, we can see that a single scoop of ice cream costs less per scoop than a 3-scoop cone. Specifically, a single scoop is $0.40 cheaper per scoop than a scoop in a 3-scoop cone.

Therefore, choosing a single scoop of ice cream over a 3-scoop cone will result in a cost savings of $0.40 per scoop.

In conclusion, when comparing the cost per scoop of ice cream, a single scoop is cheaper than a scoop in a 3-scoop cone. The cost savings per scoop is $0.40.

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Suppose you are driving a car with the velocity function represented by the following equation: f(x)= 2x^3-3x^2-12x+1. The derivative would be: f'(x) = 6x^2 - 6x - 12

To find the acceleration of the car at a particular moment, we would need to calculate the derivative of the velocity function f(x). In this case, the derivative would be:

f'(x) = 6x^2 - 6x - 12

The result of this calculation would give us the instantaneous acceleration of the car at a given time x.

In terms of the car's motion, a positive value for f'(x) would indicate that the car is accelerating, while a negative value would indicate that the car is decelerating. The magnitude of the value would indicate the rate of change of the car's velocity, with larger values indicating a more rapid change.

Translated question "A derivative problem from everyday life using the following function: f(x)= 2x^3-3x^2-12x+1"

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Answer:d. The inequality that represents "c is between 1/7 and 1/5" is:

1/7 ≤ c ≤ 1/5

e. The inequality that represents "p is not greater than -6" is:

p ≤ -6

f. The inequality that represents "the negative of m is not less than -2" is:

-m ≥ -2

Note that we need to flip the inequality when we multiply or divide both sides by a negative number, which is the case in part (f).

Step-by-step explanation:

Answer:

Step-by-step explanation:

sedimentary, igneous, metamorphic

Answer: sedimentary, igneous, metamorphic.

have an amazing day and crush that homework/class!

branliest?

Answer:

  (a)  52°

  (b)  128°

Step-by-step explanation:

You want the angle whose sine is 0.79 (a) in the interval [0, 90°], and (b) in the interval [90°, 180°].

The inverse sine function is used to find the angle when its sine is known.

  sin(x) = 0.79

  x = arcsin(0.79) ≈ 52°

x ≈ 52° in the domain 0 ≤ x ≤ 90°.

The sine function is symmetrical about x = 90°, so other angles for which sin(x) = 0.79 can be found as 180° -x.

  180° -52° = 128°

x = 128° in the domain 90° ≤ x ≤ 180°.

__

Additional comment

The attachment shows the angles and that their sine is 0.79. Note that the calculator is set to Degrees mode.

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Using the method of mathematical induction, we show that the inequality σ(n) > H(n) holds for all n≥1. Thus, the inequality n≥1 is true for all n≥1.

It is a  a technique used in mathematics to prove that a statement is true for every positive integer or natural number. It consists of two steps:

We can calculate like this:

Base case: Show that the inequality holds for n=1.

Inductive hypothesis: Assume that the inequality holds for some arbitrary positive integer k, i.e., k ≤ 2^(σ(k)/Hk).

Inductive step: Show that the inequality also holds for k+1. Consider σ(k+1) and H(k+1). We can express them as σ(k+1) = σ(k) + k+1 and H(k+1) = H(k) + 1/(k+1).

Using the inductive hypothesis, we have:

So, we can raise both sides to the power of (k+1)/(kH(k+1)) to get:

By the AM-GM inequality, we know that σ(k+1)/k+1 ≥ H(k+1), so we can replace the denominator (kH(k+1)) with H(k+1) and simplify to get

Therefore, we have shown that k+1 ≤ 2^(σ(k+1)/H(k+1)), which means the inequality holds for all positive integers n by mathematical induction.

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Answer:

A nonlinear line is a line that is not straight. So the answers for these question include B and D

B and D  are not straight lines and they are increasing

Step-by-step explanation:

Hope this helps! =D

Mark me brainliest! =D

The value of D represents the vertical displacement or shift of the basic cosine graph. Therefore, the vertical displacement of the given graph is pi - 3.

What is Displacement?

In physics, displacement refers to the distance and direction of an object's change in position from its starting point. It is a vector quantity that measures the overall change in position of an object, regardless of the path it took to get there. Displacement can be positive, negative, or zero depending on the direction and distance of the movement.

To find the vertical displacement of the basic graph to produce a graph of y = pi - 3 cos(x - 2), we need to compare the given equation with the general cosine function y = A cos(Bx - C) + D.

Here, A = 3, B = 1, C = 2, and D = pi - 3.

The value of D represents the vertical displacement or shift of the basic cosine graph. Therefore, the vertical displacement of the given graph is pi - 3.

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Answer:i think it is c

Step-by-step explanation:

Answer:

The answer for Surface area is 332m²

Step-by-step explanation:

S.A=area of 2 triangle +Area of 2 rectangle +Area of rectangle

S.A=2×1/2×4×3 + 2(20×5) + 20×6

S.A=12+2(100)+120

S.A=12+200+120

S.A=212+120

S.A=332m²

2. The total dollar amount for each cash dividend is $23,700.

 1. Calculation of outstanding common shares on each cash dividend date:

2.

Calculation of total dollar amount for each cash dividend:

Therefore, the total dollar amount for each cash dividend is $23,700.

3.

Calculation of the capitalization of retained earnings for the stock dividend:

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The equity sections from Atticus Group’s 2016 and 2017 year-end balance sheets follow Stockholders’ Equity (December 31, 2016)

Common stock—$4 par value, 100,000 shares

authorized, 40,000 shares issued and outstanding . .. . . . . . . . . . $160,000

Paid-in capital in excess of par value, common stock .. . . . . . . . . . . . . . . . 120,000

Retained earnings .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320,000

Total stockholders’ equity .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $600,000

Stockholders’ Equity (December 31, 2017)

Common stock—$4 par value, 100,000 shares

authorized, 47,400 shares issued, 3,000 shares in treasury . .. . . . . . . $189,600

Paid-in capital in excess of par value, common stock . . . . . .. . . . . . . . . . . . 179,200

Retained earnings ($30,000 restricted by treasury stock) .. . . . . . . . . . . . . 400,000

768,800

Less cost of treasury stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (30,000)

Total stockholders’ equity . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . $738,800

The following transactions and events affected its equity during year 2017.

Jan. 5 Declared a $0.50 per share cash dividend, date of record January 10.

Mar. 20 Purchased treasury stock for cash.

Apr. 5 Declared a $0.50 per share cash dividend, date of record April 10.

July 5 Declared a $0.50 per share cash dividend, date of record July 10.

July 31 Declared a 20% stock dividend when the stock’s market value was $12 per share.

Aug. 14 Issued the stock dividend that was declared on July 31.

Oct. 5 Declared a $0.50 per share cash dividend, date of record October 10.

Required

1. How many common shares are outstanding on each cash dividend date?

2. What is the total dollar amount for each of the four cash dividends?

3. What is the amount of the capitalization of retained earnings for the stock dividend?