A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 10 inches long, and the height of the equilateral triangle is 8. 7 inches. The pyramid's slant height is 11 inches. What is its surface area?

The post-war period of the 1950s and 1960s saw the emergence of a number of important voices in literature, art, and politics. Here are some examples:

Ginsberg was a prominent poet and a leading figure in the Beat Generation, a group of writers who rejected conventional norms and values. His most famous work, "Howl," was published in 1956 and became a landmark in American literature.

Baldwin was an African-American writer whose novels and essays explored issues of race and sexuality in America. His most famous works include "Go Tell It on the Mountain" (1953) and "The Fire Next Time" (1963).

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Explain the Post-War voices that emerge in (1950s-1960s)

Answer:

AB = √(4^2 + 1^2) = √(16 + 1) = √17

GH = √(4^2 + 4^2) = √(16 + 16) = √32

= 4√2

The arrow reaches a maximum height of 245 meters and stays in flight for 14 seconds.

To find the maximum height and flight time for the arrow, we'll use the given height equation and concepts of projectile motion.
Maximum height:
1. First, we need to find the time (t) at which the arrow reaches its maximum height. This occurs when the vertical velocity is zero. The velocity equation is the derivative of the height equation: v = dh/dt = -10t + 70.
2. Set the velocity equation to zero and solve for t: 0 = -10t + 70. Solve for t: t = 7 seconds.
3. Now that we have the time, plug it into the height equation to find the maximum height: h = -5(7^2) + 70(7) = -245 + 490 = 245 meters.
Flight time:
1. The arrow's flight time is the time it takes to reach the ground (h = 0) after reaching its maximum height.
2. Set the height equation to zero and solve for t: 0 = -5t^2 + 70t. Factor out a common term: 0 = 5t(-t + 14). This gives two possible solutions for t: t = 0 seconds (initial time) and t = 14 seconds.
3. The arrow stays in flight for 14 seconds, as the 0 seconds correspond to the initial time.
In summary, the arrow reaches a maximum height of 245 meters and stays in flight for 14 seconds.

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To determine the level of service of the four-lane freeway, we need to consider the geometric design, traffic volume, vehicle mix, and the presence of ramps and obstructions. The HCM methodology can be used to estimate the level of service based on various parameters.

To determine the level of service of the four-lane freeway, we need to consider several factors, including the geometric design, traffic volume, vehicle mix, and the presence of ramps and obstructions.

First, the four-lane freeway has two lanes in each direction with 12-ft lanes, and obstructions 3 ft from the right edge of the traveled pavement. This geometric design may affect the traffic flow, especially when heavy vehicles and RVs are present. These types of vehicles require more space to maneuver, and the presence of obstructions may limit their ability to do so.

Second, the directional weekday peak-hour volume of 2100 vehicles is observed. This traffic volume is relatively high and may lead to congestion and delay, especially during peak hours. To estimate the level of service, we need to use the Highway Capacity Manual (HCM) methodology, which considers various parameters such as speed, travel time, and density.

Third, we need to account for the vehicle mix, which includes 5% heavy vehicles and 10% RVs. These types of vehicles have different characteristics than passenger cars and may affect the traffic flow differently. For example, heavy vehicles may cause more congestion due to their slower speed and larger size, while RVs may require more space to maneuver and may have limited visibility.

Finally, we need to consider the presence of ramps within 2 miles upstream and 2 miles downstream of the midpoint of the analysis segment. Ramps can affect the traffic flow by adding or removing vehicles from the mainline, and their location and design can affect the merging and weaving maneuvers.

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Therefore, the DFT of x∗[n] is obtained by taking the complex conjugate of each element in the DFT spectrum of x[n].

The DFT (Discrete Fourier Transform) of the conjugate sequence x∗[n] is the complex conjugate of the DFT of the original sequence x[n]. In other words, if x[k] is the N-point DFT of the sequence x[n], then the DFT of x∗[n] is given by x∗[k], where the asterisk (*) denotes complex conjugation.

Mathematically, if X[k] is the N-point DFT of x[n], then the DFT of x∗[n] is given by:

x∗[k] = conj(X[k])

Here, conj(.) represents the complex conjugate operation.

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The triangle AEB is similar to triangle DEC based on congruent angles or equal angles principle.

The proof of similarity of the triangles is determined by applying angle - angle (AA) theorem as shown below.

triangle AEB will be similar to triangle DEC if the following conditions are met;

From the given diagram, the line XY bisects angle E, and it is also perpendicular to line AB and line CD.

Let angle AED = θ

then angle YEC = ¹/₂θ and angle YED = ¹/₂θ

Considering triangle AEB, we will have;

angle XEB = ¹/₂θ and angle XEA = ¹/₂θ

So the values of angle YCE  and angle XBE will be equal, hence triangle AEB will be similar to triangle DEC, proved.

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If we reference the given temperature data, the village where the temperature fell in the morning and then rose over the afternoon is Village B.

Temperature is described as  a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.

In Village B, the daytime high is 15 degrees, followed by lows of 10 degrees at 10:00 and 5 degrees at 12:00 (morning).

Nevertheless, the temperature begins to rise from 12:00 and eventually rises to +5 degrees at 18:00 (afternoon), reaching 0 degrees at 14:00.

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The response variable in this experiment is the scores on the midterm exam. The response variable is the one that is measured or observed to determine whether it has been affected by the explanatory variable.

The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.

The explanatory variable in this experiment is the type of music played in the background during the exam. The explanatory variable is the one that is deliberately manipulated or changed by the researcher in order to observe its effect on the response variable. In this case, the researcher wanted to investigate whether the type of music played during the exam would have an effect on the students' performance, so they manipulated the type of music and observed its effect on the exam scores.

The response variable in this experiment is the scores on the midterm exam. The response variable is the one that is measured or observed to determine whether it has been affected by the explanatory variable. In this case, the researcher measured the exam scores of the two groups to see if there was a difference between the group that listened to Dave Matthews Band and the group that listened to Death Cab for Cutie.

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The actual area of Logo 1 is given as follows:

A = 0.9747 ft².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.

The circumference of the circle is given as follows:

C = 0.5 in = 7 x 0.5 = 3.5 ft.

Hence the radius of the circle is obtained as follows:

2πr = 3.5

r = 3.5/(2π)

r = 0.557 ft.

Hence the area of the circle is given as follows:

A = π x 0.557²

A = 0.9747 ft².

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The resulting displacement of the cyclist is approximately [tex]19.2[/tex] miles. (option C)

To find the resulting displacement of the cyclist, we can use the Pythagorean theorem since the cyclist traveled north and east, forming a right triangle.

The distance traveled north is 15 miles, and the distance traveled east is 12 miles. Let's call the northward distance "a" and the eastward distance "b."

Using the Pythagorean theorem, the resulting displacement "c" is given by:

[tex]\(c = \sqrt{a^2 + b^2}\)[/tex]

Plugging in the values, we have:

[tex]\(c = \sqrt{15^2 + 12^2}\)\\\c = \sqrt{225 + 144}\)\\\c = \sqrt{369}\)\(c \approx 19.2\) miles[/tex]

Therefore, the resulting displacement of the cyclist is approximately 19.2 miles.

So, the correct answer is option C: 19.2 miles.

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Picard's theorem states that a first-order ordinary differential equation of the form y' = f(x, y) with an initial condition y(x0) = y0 has a unique solution if the function f(x, y) is continuous and satisfies the Lipschitz condition with respect to y in some region containing the initial point (x0, y0).

For the given differential equations, we can apply Picard's theorem to determine whether they have unique solutions.

(i) The function f(x, y) = t cos^-1(y) is continuous and satisfies the Lipschitz condition with respect to y in some neighborhood of (0, 1), so by Picard's theorem, the equation has a unique solution.

(ii) The function f(x, y) = tx is continuous and satisfies the Lipschitz condition with respect to y in some neighborhood of (0, y0), so by Picard's theorem, the equation has a unique solution.

(iii) The function f(x, y) = 1/(t^2*y^2) is not continuous at (0, 0), so we cannot apply Picard's theorem to determine whether the equation has a unique solution.

(iv) The function f(x, y) = y^(2/3) is continuous and satisfies the Lipschitz condition with respect to y in some neighborhood of (0, 0), so by Picard's theorem, the equation has a unique solution.

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Answer: I'm in 2nd grade

Step-by-step explanation: Fortnight is a acrobatic FIRST PERSON SHOOTER GAME

The values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

√15/(y + 2) = y/√15 {opposite/adjacent}

y(y + 2) = (√15)² {cross multiplication}

y² + 2y = 15

y² + 2y - 15 = 0

by factorization;

(y - 3)(y + 5) = 0

y = 3 or y = -5

by Pythagoras rule:

(√15)² = x² + y²

15 = x² + 3²

x = √(15 - 9)

x = √6

z² = (√6)² + 2²

z = √(6 + 4)

z = √10

Therefore, the values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

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Answer:

C

Step-by-step explanation:

the range is from the bottom line to top

the IQR is the length of the box in the middle

C. The range is 37 and the IQR is 20.

The range is the difference between the highest and lowest values in the data set. In this case, the highest value is 50 and the lowest value is 13, so the range is 50 - 13 = 37.

The interquartile range (IQR) is the difference between the first and third quartiles. In this case, the first quartile is 24 and the third quartile is 44, so the IQR is 44 - 24 = 20.

Therefore, the range is 37 and the IQR is 20 which is option c.

The other options are incorrect. Option A is incorrect because the IQR is 21, not 20. Option B is incorrect because the range is 37, not 38. Option D is incorrect because the range is 37 and the IQR is 20, not 21.

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The third graph is the graph of the quadratic function f(x) = 2(x - 4)² + 1.

The quadratic function of vertex(h,k) is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The function for this problem is given as follows:

f(x) = 2(x - 4)² + 1.

Hence the coordinates of the vertex are given as follows:

x = 4, y = 1.

The vertex is the turning point of the graph of the quadratic function, hence the third graph is the correct option for this problem.

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The graph that represents the given quadratic equation is: Graph C which is the third graph

The general form of the quadratic equation is:

ax² + bx + c = 0

We are given the equation as:

f(x) = 2(x - 4)² + 1

Thus, at x = 0, f(x) = 33

at x = 1, f(x) = 19

Thus, only graphs C or D are correct

The quadratic function of vertex (h,k) is given by the expression:

y = a(x - h)² + k

where:

h is the x-coordinate of the vertex.

k is the y-coordinate of the vertex.

a is the leading coefficient.

Thus, graph C is correct because the coordinate of the vertex is (4, 1)

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No, because P(A|B) = 0.79 and the P(A) = 0.48 they are not equal.

The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes.

We have the information:

P(A)= 0.48  

P(B) = 0.42

P(A∩B) = 0.38

To find out if watching a movie and buying a popcorn are independent,

The formula is used:

P(A|B) = P(A∩B)/P(A)

Plug all the values in above formula:

P(A|B) = 0.38/0.48 = 0.79166

P(A|B) = 0.79

From the deductions above;

Hence, the answer is

No, because P(A|B) = 0.79 and the P(A) = 0.48 they are not equal.

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For complete question, to see the attachment

Answer: The formula for finding the area of a sector of a circle with a radius r is θ/360° × π[tex]r^{2}[/tex].

Explanation: The formula for finding the area of a sector of a circle with a radius r is θ/360° × π[tex]r^{2}[/tex],

where θ is the angle of the sector and r is the radius of the circle.

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Check the picture below.

so the way I see it, we have a bunch of semicircies going from 0 to 5, and we're looking at the bottom of the object, the provided picture above is not very useful btw.

so we're looking at the bottom of the object and the semicircles are going from 0 to 5, however from 0 to 1 they vary, from small to large, then they reach a diameter of 6 and go steady with that 6 all the way to 5.

so we can say that from 1 to 5, we can simply get the integral of a semicircle with a steady radius of 3, in which case that'd be the fixed value of 4.5π for the area.

now, we can also say that from 0 to 1 it varies, now, the radius varies, the radius is really the vertical value of the line or namely the y-value of that slanted line from 0 to 1, anyhow, not to bore you to death, but if we use the points (0 , 0) and (1 , 3) to get the equation of the line, we end up with y = 3x, and that's our radius, and we'll get the integral of those semicircles from 0 to 1 with a radius of 3x, with an area of 4.5πx²

[tex]\stackrel{ \textit{areas from 0 to 1} }{\cfrac{1}{2}\cdot \pi (3x)^2\implies 4.5\pi x^2}\hspace{9em}\stackrel{ \textit{areas from 1 to 5} }{\cfrac{1}{2}\cdot \pi (3)^2\implies 4.5\pi} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \int_0^{1}4.5\pi x^2dx~~ + ~~\int_{1}^{5}4.5\pi dx\implies 4.5\pi\int_0^{1} x^2dx~~ + ~~\int_{1}^{5}4.5\pi dx \\\\\\ 4.5\pi \left. \cfrac{x^3}{3} \right]_{0}^{1}~~ + ~~4.5\pi \left. x\cfrac{}{} \right]_{0}^{1}\implies 4.5\pi ~~ + ~~18\pi \implies \boxed{22.5\pi}[/tex]

The value of perimeter of the base of the cube is,

⇒ 24 units

We have to given that;

The volume of cube is, 216 cubic units

Since, The volume of cube is,

V = side³

Substitute the values, we get;

⇒ ∛216

⇒ 6

Hence, The value of perimeter of the base of the cube is,

⇒ 4 x 6

⇒ 24 units

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The expression that gives the simplified expression for the value of f'(1) is option D) lim0 (3h + 7), which evaluates to 9. The function f(x) can be written as f(x) = 3x^3.

To find f'(x), we need to take the derivative of f(x) with respect to x. Using the power rule of differentiation, we get:

f'(x) = 9x^2

To find the value of f'(1), we substitute x = 1 in the expression for f'(x):

f'(1) = 9(1)^2 = 9

Now, we need to find the expression that gives the simplified expression for the limit of the difference quotient, which is the definition of the derivative. The difference quotient is given by:

[f(x + h) - f(x)] / h

Substituting f(x) = 3x^3, we get:

[f(x + h) - f(x)] / h = [3(x + h)^3 - 3x^3] / h

Expanding the cube, we get:

[f(x + h) - f(x)] / h = [3(x^3 + 3x^2h + 3xh^2 + h^3) - 3x^3] / h

Canceling out the terms and simplifying, we get:

[f(x + h) - f(x)] / h = 9x^2 + 9xh + 3h^2

Now, we need to find the expression that gives the simplified expression for the limit of the difference quotient as h approaches 0. We can simplify the expression above as follows:

[f(x + h) - f(x)] / h = 9x^2 + 9xh + 3h^2
= 9x^2 + (9xh + 3h^2)
= 9x^2 + 3h(3x + h)

As h approaches 0, the second term in the expression above approaches 0. Therefore, the simplified expression for the limit of the difference quotient is:

lim(h → 0) [f(x + h) - f(x)] / h = 9x^2

Substituting x = 1, we get:

lim(h → 0) [f(1 + h) - f(1)] / h = 9(1)^2 = 9

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Answer:

C

Step-by-step explanation:

sinx=9/19

sinx=0.47

opposite function on calculator

x= ~28

Answer:

28˚

Step-by-step explanation:

The range of the data in the 4th of July parade is greater than the range of the data in the New Years's Day parade.

A dataset's range, which reflects the gap among its greatest and lowest values, is measured statistically. By deducting lowest value from the greatest value, it is computed. If range of total data is wider in Fourth of July parade than it is in the New Year's Day parade, then highest and lowest figures in Fourth of July parade will be further apart than highest and lowest values in New Year's Day parade.

For example, if highest value in 4th of July parade is 100 and lowest value is 10, then total range is 100 - 20 = 80. If the highest value in the New Year's Day parade is 60 and the lowest value is 20, then the range is 60 - 20 = 40. Thus, here range of the data in 4th of July parade is greater than range of the data in the New Year's Day parade.

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Option C (chi-square distribution) and Option D (F distribution) have only positive values.

The chi-square distribution is a continuous probability distribution that is used in statistical tests to compare observed data with expected data. It has only positive values and is right-skewed. It is commonly used in hypothesis testing, goodness-of-fit tests, and in confidence interval calculations.

The F distribution is also a continuous probability distribution that arises in the analysis of variance (ANOVA) and regression analysis. It is used to test the equality of variances of two or more populations. Like the chi-square distribution, it is also right-skewed and has only positive values.

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The quotient of expression is,

⇒ 7x² - x/7 + 92/49

We have to given that;

Expression is,

⇒ (7x³ - 8x² - 13x + 2) / (7x - 1)

By using division method as;

(7x - 1) ) 7x³ - 8x² - 13x + 2 ( 7x² - x/7 + 92/49

           7x³ - 7x²

          --------------

                 - x² - 13x

                 - x² + x/7

                 ------------

                      92/7x + 2

                       92/7x - 92/49

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

                                 190/49

Thus, The quotient of expression is,

⇒ 7x² - x/7 + 92/49

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The equations that correctly apply properties of operations include:

The equation of 15 b + 10c = 5 ( 3b+ 2c ) is correct in using the property of operations because it uses the distributive property correctly.

a + a + a = 3a uses the repeated addition property, to show that when you add the same number a certain number of time, the result is the same as multiplying that number by the certain number of times.

6 ( 3 + y ) = 18 + 6y like option B, uses the distributive property correctly.

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We do not have sufficient evidence to claim that the vans outperform the manufacturer's mpg rating at the 0.01 level of significance, the null and alternative hypotheses are H₀: μ = 25.3, Hₐ: μ > 25.3.

To determine if there is sufficient evidence that the vans outperform the manufacturer's mpg rating, we need to conduct a hypothesis test. The null hypothesis (H₀) is that the vans have an average mpg of 25.3, while the alternative hypothesis (Hₐ) is that the vans have an average mpg greater than 25.3.

H₀: μ = 25.3

Hₐ: μ > 25.3

We will use a one-tailed t-test since the alternative hypothesis is directional (greater than). To conduct the test, we need to calculate the t-statistic and compare it to the critical value at the 0.01 level of significance with 18 degrees of freedom (19 vans - 1).

t = (x' - μ) / (s / √n)

t = (25.4 - 25.3) / (√(5.29 / 19)) = 0.90

Using a t-distribution table or a statistical software, we find that the critical value for a one-tailed test at the 0.01 level of significance with 18 degrees of freedom is 2.552.

Since the calculated t-statistic (0.90) is less than the critical value (2.552), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to claim that the vans outperform the manufacturer's mpg rating at the 0.01 level of significance.

In summary, we can use a hypothesis test to determine if there is sufficient evidence that the vans outperform the manufacturer's mpg rating. We set up the null and alternative hypotheses, calculate the t-statistic, compare it to the critical value, and make a decision based on the level of significance.

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We can use the formula for the area enclosed by a parametric curve. Therefore, the area enclosed by the parametric equation is given by

A = 27[(1/5)b^5 - (8/3)b^3] - 27[(1/5)a^5 - (8/3)a^3]

A = ∫[a,b] y(t) x'(t) dt

where x'(t) is the derivative of x(t) with respect to t.

Using the given parametric equations, we have:

x(t) = t^3 - 8t

y(t) = 9t^2

Taking the derivative of x(t), we have:

x'(t) = 3t^2 - 8

Substituting these expressions into the formula for A, we get:

A = ∫[a,b] y(t) x'(t) dt

= ∫[a,b] 9t^2 (3t^2 - 8) dt

= 27∫[a,b] t^4 - 8t^2 dt

= 27[(1/5)t^5 - (8/3)t^3]∣[a,b]

Using the bounds of the integral, which are not given in the problem, we get:

A = 27[(1/5)b^5 - (8/3)b^3] - 27[(1/5)a^5 - (8/3)a^3]

Therefore, the area enclosed by the parametric equation is given by:

A = 27[(1/5)b^5 - (8/3)b^3] - 27[(1/5)a^5 - (8/3)a^3]

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Answer:

8

Step-by-step explanation:

+, the overall volume of moisturising bath powder is: V=4/3 π×R³×12 = 4/3 π×2³×12=128π(cm³)

=>the number of spherical molds with a diameter of 5cm she could fill with the same amount of powder is: N=V/(4/3 π×R'³)= 8

Using the mean value theorem, we can find an upper bound for f(7) given the information provided. The mean value theorem states that for a differentiable function f(x) on the interval [a,b], there exists at least one point c in the interval such that:

f'(c) = (f(b) - f(a))/(b - a)

If we apply this theorem to the interval [4,7], we get:

f'(c) = (f(7) - f(4))/(7 - 4)

Since f '(x) ≥ 3 for 4 ≤ x ≤ 7, we know that f'(c) ≥ 3. We can use this inequality to find an upper bound for f(7):

3 ≤ (f(7) - 6)/3

9 ≤ f(7) - 6

f(7) ≥ 15

Therefore, the smallest possible value for f(7) is 15. This means that f(x) must be increasing at a rate of at least 3 between x=4 and x=7, and the smallest possible value of f(7) occurs when f(x) is increasing at a constant rate of 3.

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To find the numbers "a" and "c" such that Norman scored lower than approximately "percent" of people who took the test, we need to use the standard normal distribution.

First, we calculate the z-score for Norman's score using the formula:

z = (x - mean) / standard deviation

In this case, x = 72, mean = 50, and standard deviation = 20.

z = (72 - 50) / 20 = 1.1

Next, we find the percentile corresponding to the z-score of 1.1 using a standard normal distribution table or a calculator. Let's assume it is "percent".

To find "c", we need to calculate the complement of "percent" and convert it to a decimal:

complement = 1 - (percent / 100)

Finally, to find "a", we use the formula:

a = mean + (c * standard deviation)

a = 50 + (complement * 20)

100c a can be obtained by multiplying "a" by 100.

Therefore, 100c a = 100 * a.

Please provide the value of "percent" to calculate the exact values for "c" and "100c a".

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