After returning to South Africa from Algeria in 1964, Nelson Mandela was
Arrested and imprisoned
Elected to the presidency
Educated in guerrilla tactics
Finally granted his freedom

The antiderivatives of the function -14x are -7x^2 + C and e^x + C, where C is a constant.

The expression |(2-2) dx simplifies to |0 dx. The integral of 0 with respect to x is always equal to a constant. Therefore, the result of this integral is C, where C is a constant.

[(x2–5x+2) dx=0

The integral of (x^2 - 5x + 2) dx can be found by applying the power rule for integration. Each term is integrated separately:

∫ x^2 dx - ∫ 5x dx + ∫ 2 dx

Integrating term by term:

= (1/3)x^3 - (5/2)x^2 + 2x + C, where C is a constant.

To find the antiderivative of -14x, we can apply the power rule for integration. The power rule states that the antiderivative of x^n is (1/(n+1))x^(n+1), except for the case when n = -1, where the antiderivative is ln|x|.

Applying the power rule to -14x, we get:

∫ -14x dx = (-14/2)x^2 + C = -7x^2 + C, where C is a constant.

For the function f(x) = e, the antiderivative is simply e^x.

Therefore, the antiderivatives of the function -14x are -7x^2 + C and e^x + C, where C is a constant.

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The screen aspect ratio of a high-definition television is 16:9, which means the width is 16 units and the height is 9 units. We are given that the width of the HDTV is 41 inches.

To find the screen size, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the diagonal distance across the screen) is equal to the sum of the squares of the other two sides (width and height).

Let's assume the height is h inches. Using the Pythagorean theorem, we have:

(41^2) = (16^2) + (9^2) + (h^2)

Simplifying this equation, we get:

1681 = 256 + 81 + h^2

1681 = 337 + h^2

h^2 = 1681 - 337

h^2 = 1344

Taking the square root of both sides, we find:

h ≈ 36.65 inches

Therefore, the screen size of the HDTV is approximately 36.65 inches.

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The slope of the line passing through the points (-9, 5) and (-6, 2) will be [m] = - 1

The slope intercept of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is a straight line passing through the points (-9, 5) and (-6, 2)

Given is a straight line that passes through the coordinates as follows -

(-9, 5)    

(-6, 2)      

The slope of the line can be calculated using the formula -

m = (y₂ - y₁)/(x₂ - x₁)

m = (2 - 5)/(- 6 + 9)

m = -3/3

m = - 1

Therefore, the slope of the line passing through the points (-9, 5) and (-6, 2) be [m] = - 1.

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Answer:

x > 8

Step-by-step explanation:

Solve for x to find the solution.

10 - 4x < -22

Subtract 10 from both sides.

-4x < -32

Divide both sides by -4. Flip the sign when dividing by negative.

x > 8.

Answer:

x>8

Step-by-step explanation:

MARK AS BRAINLIESTT!!

Answer:

b

Step-by-step explanation:

.because -10 plus 4 is -6

Answer:

The volume of the cylinder ≅ 197.82\(cm^{2}\)

Step-by-step explanation:

The volume of a cylinder is equal to the area of the base times the height. We know the radius, therefore we can find the area of the base. The formula for the volume of the cylinder is as follows:

V = π\(r^{2}\)\(h\)

(now substitute the values of "r" and "h", and get...)

V = π\(r^{2}\)\(h\)

\(V = (3^{2} )(7)\) x π

V = (9)(7)π

V = 63π

V ≅ 197.82\(cm^{2}\)

Answer:

The answer should be A......

If there is sufficient evidence exist to conclude the mean amount of milk in cartons is less than 32 ounces, then we have to use one sample t test (option b).

In this case, we have a sample of 22 cartons and we want to determine if the mean amount of milk in the cartons is less than 32 ounces. Since we are only dealing with one sample and comparing its mean to a known population mean of 32 ounces, we can use a one sample t test. This test will help us determine if the sample mean is significantly different from 32 ounces.

To perform a one sample t test, we need to calculate the sample mean and sample standard deviation of the amount of milk in the 22 quart cartons. We can then use these values, along with the known population mean of 32 ounces, to calculate the t statistic. This t statistic will tell us how many standard errors the sample mean is away from the hypothesized population mean of 32 ounces.

We can then calculate the p-value, which is the probability of getting a t statistic as extreme as the one we calculated, assuming the null hypothesis is true.

If the p-value is less than our chosen significance level (usually 0.05), we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the mean amount of milk in the cartons is less than 32 ounces.

Hence the correct option s (b).

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You will need 37 meters of fencing to erect a fence 2 meters from the edge of a rectangular area that is 11.5 meters long and 5 meters wide.

To calculate the amount of fencing needed, you will need to find the perimeter of the given rectangular area. The formula for the perimeter of a rectangle is P = 2(length + width). Given that the length is 11.5 meters and the width is 5 meters, we can substitute these values into the formula.

P = 2(11.5 + 5)
P = 2(16.5)
P = 33

So, the perimeter of the given rectangular area is 33 meters.

To calculate the amount of fencing needed for the erecting the fence 2 meters from the edge, we need to add 2 meters to each side of the perimeter.

P' = P + (2 x 2)
P' = 33 + 4
P' = 37

Therefore, you will need 37 meters of fencing to erect a fence 2 meters from the edge of a rectangular area that is 11.5 meters long and 5 meters wide.

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To create a slope field for the differential equation ds/dm = S(0.25M-0.75)/M(1-0.5s), we can choose different values of S and M and calculate the corresponding slopes at various points on the S-M plane.

To sketch the slope field for the differential equation dw/dt = 12W^0.6, we can choose various values of W and plot the corresponding slopes at different points on the W-t plane.

Let's choose a few values of W, such as 1, 2, 4, and 8. For each value of W, we calculate the corresponding slope using the given equation dw/dt = 12W^0.6. The slope at each point (t, W) will be given by 12W^0.6.

Based on the slope values, we can draw short line segments or arrows at each point in the W-t plane, indicating the direction and magnitude of the slope.

The slope field helps us visualize the relationship between the weight (W) of the catfish and its age (t). The slope at each point represents the rate of change of the catfish's weight at that specific age. In this case, the slope field will show that as the catfish gets older, its weight increases at a faster rate.

To deduce a solution satisfying W(0) = 2 ounces, we can integrate the differential equation dw/dt = 12W^0.6 with respect to t.

∫(1/W^0.6) dW = ∫12 dt

Integrating both sides, we have:

(5/3)W^0.4 = 12t + C

Where C is the constant of integration.

Applying the initial condition W(0) = 2, we can solve for C:

(5/3)2^0.4 = 12(0) + C

(5/3)(2^0.4) = C

Now we can substitute C back into the equation:

(5/3)W^0.4 = 12t + (5/3)(2^0.4)

Simplifying, we have the solution:

W^0.4 = 3(12t + (5/3)(2^0.4))/5

To solve for W, we raise both sides to the power of 2.5:

W = [3(12t + (5/3)(2^0.4))/5]^2.5

This is the solution to the given initial value problem satisfying W(0) = 2 ounces.

To check if our solution satisfies the differential equation, we can differentiate W with respect to t and substitute it into the given differential equation dw/dt = 12W^0.6.

Differentiating W, we have:

dW/dt = [2.5(3(12t + (5/3)(2^0.4))/5)^1.5] * 3(12) = 12(12t + (5/3)(2^0.4))^1.5

Now we substitute dW/dt and W into the differential equation:

12(12t + (5/3)(2^0.4))^1.5 = 12(12t + (5/3)(2^0.4))^0.6

Both sides of the equation are equal, confirming that our solution satisfies the given differential equation.

Now, let's move on to the second part of the question regarding the population interaction between reef sharks (S) and butterfly fish (M).

To create a slope field for the differential equation ds/dm = S(0.25M-0.75)/M(1-0.5s), we can choose different values of S and M and calculate the corresponding slopes at various points on the S-M plane.

We need to pay close attention to the domains of the variables S

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Answer:

The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator

Your welcome

Solution:

The number of footballs given is

The equation for basketball will be

The equation for baseball will be

The equation for softball will be

Part 2:

The table will be used to solve part 2

The chores overshadowed the joy of our Reunion, learned a valuable lesson about managing time and prioritizing obligations

Embarking on a bike ride to visit a friend who lives 3 miles away, little did I know that a looming sense of forgotten chores would soon disrupt my plans. Determined to fulfill my obligations, I mustered the strength to continue riding towards my friend's house, albeit with a heavy heart.

I pedaled towards my destination, the weight of my impending chores grew heavier with each passing moment. Thoughts of unfinished tasks occupied my mind, and I knew that I couldn't stay for long once I reached my friend's place. However, in my haste, a newfound urgency propelled me forward, and I found myself pedaling at a speed 5 mph faster than my initial journey.

With this increased velocity, the return trip promised to be swifter, yet time was slipping away. My mind raced as I calculated the implications of my predicament. The total round trip, comprising both the journey to my friend's house and the hurried return, needed to be accomplished within a tight time frame of 30 minutes.

As I approached my friend's house, I realized that I had no choice but to deliver my news swiftly and immediately turn back around. The momentary joy of reunion would be overshadowed by the pressing chores that awaited me. Regrettably, I bid my friend a hasty farewell, explaining the circumstances that compelled my premature departure.

Once on my bike again, I kicked up the pace, utilizing the extra speed to my advantage. The wind rushed past my face as I hurriedly retraced my path, pushing myself to complete the return trip as swiftly as possible. The seconds ticked away relentlessly, as the pressure mounted to make it back within the allocated timeframe.

In a flurry of determination, I managed to reach home just in the nick of time, fulfilling my duties and responsibilities. Exhausted but relieved, I contemplated the whirlwind of events that had transpired within the span of this half-hour adventure.

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Note the question be like :

A company is hosting a team-building event and has allocated a total of 4 hours for various activities. If Activity A takes 1 hour, Activity B takes 2 hours, and Activity C takes 45 minutes, what is the maximum amount of time that can be dedicated to Activity D while still staying within the allocated 4-hour timeframe?

Answer:

0.125 miles

Explanation:

1/4 of a mile is 440 yards and 1/8 of a mile is 220. 440-220=220.

The equation that represents this situation is p = 4 + 5d

Algebraic expressions are known as mathematical expressions made up of:

From the information given, we have that:

The equation this represents is:

p = 4 + 5d

Thus, the equation that represents this situation is p = 4 + 5d

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This means the Probability of drawing a star is now 4/8 or 1/2, which is equal to the probability of drawing a card without a star. Thus, the game is now fair.

To make the game fair, we need to ensure that the probability of drawing a card with a star is the same as the probability of drawing a card without a star.

Currently, there are 4 cards with stars and 6 cards without stars, which means the probability of drawing a star is 4/10 or 2/5, while the probability of drawing a card without a star is 6/10 or 3/5.

To make the game fair, we need to adjust the number of cards with stars and without stars so that the probabilities are equal.

Option A is not correct because the game is not currently fair.

Option B is not correct because adding 2 cards with stars will increase the probability of drawing a star to 6/12 or 1/2, which is not equal to the probability of drawing a card without a star.

Option C is also not correct because adding a star to 1 of the blank cards will still result in a probability of drawing a star that is not equal to the probability of drawing a card without a star.

Therefore, the correct answer is option D: take away 2 blank cards. If we remove 2 blank cards, we are left with 4 cards with stars and 4 cards without stars. This means the probability of drawing a star is now 4/8 or 1/2, which is equal to the probability of drawing a card without a star. Thus, the game is now fair.

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Answer: -1/16

Step-by-step explanation:

3/8  --->  6/16

5/16 - 6/16 = (-1/16)

The bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.

What are scientific notations?

Scientific notations are a way of representing either a very small or a very large number in the powers of 10. Scientific notations comprise digits from 1 to 9 with powers of 10.

Calculation of the amount by which a bacterial cell is smaller than the amoeba cell

Given the length of amoeba cell in scientific notations is 3.5 × 10^(- 4)

The length of a bacterial cell in scientific notations is 5 × 10^(- 6)

To obtain how small the bacterial cell is from the amoeba cell, we need to divide both the lengths i.e.

= 3.5 × 10^(- 4) / 5 × 10^(- 6)

= 0.7 × 10^(2)

= 7 × 10^(1)

Hence, the bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.

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Answer:

50mph

Step-by-step explanation:

Given the following :

Distance (d) of journey = 20 miles

Wind speed = 30mph head wind in one way, 30mph tail wind in the other direction

Return trip = 45 minutes (45/60 = 0.75 hour) less Than the outbound journey

Speed of plane in still air

Outbound trip :

Velocity = Distance / time

Time = distance / velocity

Velocity = (v - 30) due to head wind

Return Velocity (V +30) due to tail wind

Outbound time = return distance

20 / (v - 30) = 20 / (v +30) + 0.75

20v + 600 = 20v + 0.75v^2 + 22.5v - 600-22.5v-675

600 = 0.75v^2 - 1275

0.75v^2 = 1875

v^2 = 1875/ 0.75

v^2 = 2500

v = sqrt(2500)

v = 50mph

Since the terms of the series approach zero, the series converges.

To determine whether the series converges or diverges, we need to examine the behavior of the terms as n approaches infinity.

The series is given by:

1/(5n + 4)

As n approaches infinity, the denominator (5n + 4) grows without bound. To determine the behavior of the series, we consider the limit of the terms as n approaches infinity:

lim (n→∞) 1/(5n + 4)

To simplify this expression, we divide both the numerator and denominator by n:

lim (n→∞) (1/n) / (5 + 4/n)

As n approaches infinity, the term 1/n approaches zero, and the term 4/n approaches zero. Thus, the limit becomes:

lim (n→∞) 0 / (5 + 0)

Since the denominator is a constant, the limit evaluates to:

lim (n→∞) 0 / 5 = 0

The limit of the terms of the series as n approaches infinity is zero.

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Answer:

4 meters

Step-by-step explanation:

Given a quadratic equation in which the coefficient of \(x^2\) is negative, the parabola opens up and has a maximum point. This maximum point occurs at the line of symmetry.

Since the divers height, y is modeled by the equation

\(y= -x^2 + 2x + 3\)

Step 1: Determine the equation of symmetry

In the equation above, a=-1, b=2, c=3

Equation of symmetry, \(x=-\dfrac{b}{2a}\)

\(x=-\dfrac{2}{2*-1}\\x=1\)

Step 2: Find the value of y at the point of symmetry

That is, we substitute x obtained above into the y and solve.

\(y(1)= -1^2 + 2(1) + 3=-1+2+3=4m\)

The maximum height of the diver is therefore 4 meters.

Mean 4.9 letters and standard deviation 1.5 letters are best estimates of the population parameters . So, the correct option is (C)

The estimated mean of the sampling distribution is 4.9 letters, which is a good estimate of the population mean word length. The estimated standard deviation of the sampling distribution is 0.15 letter, which is the standard error of the mean.

The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size. Since the sample size is 100 and the standard error is 0.15 letter, we can estimate the population standard deviation as follows:

population standard deviation = standard error x sqrt(sample size)

= 0.15 x sqrt(100)

= 1.5 letters

Therefore, the best estimates of the population parameters are:

Mean = 4.9 letters (same as the estimated mean of the sampling distribution)

Standard deviation = 1.5 letters

So, the correct option is (C) Mean 4.9 letters and standard deviation 1.5 letters.

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The volume of the solid obtained by rotating the region enclosed by the graphs y = x² and y = \(x^{(1/2)\) about the line x = -5 is -45π/14 cubic units.

To find the volume of the solid obtained by rotating the region enclosed by the graphs y = x² and y = \(x^{(1/2)\) about the line x = -5, we can use the method of cylindrical shells.

The idea is to slice the region into thin vertical strips, rotate each strip about the given axis (x = -5), and then sum up the volumes of these cylindrical shells.

Let's proceed step by step:

Determine the limits of integration:

To find the boundaries of the region, we need to solve the equations y = x² and y = \(x^{(1/2)\) to find their points of intersection.

Setting the two equations equal to each other, we have:

x² =\(x^{(1/2)\)

\(x^{(3/2)\) - \(x^{(1/2)\) = 0

Factoring out \(x^{(1/2)\), we get:

\(x^{(1/2)\)(x - 1) = 0

This gives us two points of intersection: x = 0 and x = 1.

Therefore, the limits of integration for x are from 0 to 1.

Set up the integral for the volume:

We need to find the volume of each cylindrical shell and integrate it over the given range of x.

The radius of each shell is the distance from the axis of rotation (x = -5) to the corresponding x-value on the curve.

The height of each shell is the difference between the upper and lower curves at that x-value.

The volume of each cylindrical shell is given by:

dV = 2πrh dx

where r is the radius and h is the height.

The radius, r, is the distance from the axis of rotation (x = -5) to the x-value on the curve:

r = x + 5

The height, h, is the difference between the upper and lower curves:

h = x² - \(x^{(1/2)\)

Therefore, the integral for the volume becomes:

V = ∫(0 to 1) 2π(x + 5)(x² - \(x^{(1/2)\)) dx

Evaluate the integral:

Integrate the expression 2π(x + 5)(x² - \(x^{(1/2)\)) with respect to x over the range (0 to 1).

This step involves simplifying the integrand and performing the integration.

V = ∫(0 to 1) 2π(x³ - \(x^{(5/2)\) + 5x² - 5\(x^{(1/2)\)) dx

Evaluate each term separately:

V = 2π(∫(0 to 1) x³ dx - ∫(0 to 1) \(x^{(5/2)\) dx + ∫(0 to 1) 5x² dx - ∫(0 to 1) 5\(x^{(1/2)\) dx)

Evaluate each integral:

V = 2π(\(x^{4/4\) - 2\(x^{(7/2)/7\) + 5\(x^{3/3\) - 10\(x^{(3/2)/3)\) |(0 to 1)

Substituting the limits of integration:

V = 2π[(1/4 - 2/7 + 5/3 - 10/3) - (0)]

V = 2π[(21/84 - 16/84 + 140/84 - 280/84)]

V = 2π[-135/84]

V = -135π/42

Simplifying the fraction, we have:

V = -45π/14

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The resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2

Quadratic equation are equations that has a leading degree of 2. Most quadratic equations have 3 terms.

Given the quadratic equation x^2-19x-39 = 0

Add 39 to both sides to have:

x^2 - 19x - 39 + 39 = 0 + 39

x^2 -19x = 39

Complete the square of the resulting

x^2-19x+(19/2)^2 = 39 + (19/2)^2
(x+19/2)^2 = 39 + (19/2)^2

x + 19/2 = ±√39 + (19/2)^2

x = ±√39 + (19/2)^2 - 19/2

Hence the resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2

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Answer: 8 inches by 6 inches

Step-by-step explanation:

The width of each class interval from the given grouped frequency distribution table is 9.

In a frequency distribution, the numerical width of a class is referred to as the class interval. Data is organised into classes in a grouped frequency distribution. The class interval is determined by the difference between the upper and lower class limits.

The give class intervals are 20-29, 30-39, 40-49 and 50-59.

The size, or width, of a class interval is the difference between the lower and upper class boundaries and is also referred to as the class width, class size, or class length.

So, class width = Upper class - Lower class

29-20=9

39-30=9

Therefore, the width of each class interval is 9.

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Answer:

x=15

Step-by-step explanation:

79-15=64

94-30=64

The value of x for which r || s will be 15.

What are Parallel lines?

Parallel lines are those lines that are equidistance from each other and never intersect each other.

Given that;

Lines r and s are parallel to each other.

m ∠1 = 79 - x

m ∠2 = 94 - 2x

Since, Two lines r and s are parallel to each other.

Then, By definition of alternate angles of parallel lines;

m ∠1 = m ∠2

Now, Substitute the given values we get;

m ∠1 = m ∠2

79 - x = 94 - 2x

Subtract 79 both side,

79 - x - 79 = 94 - 2x - 79

- x = 15 - 2x

Add 2x both side,

- x + 2x = 15 - 2x + 2x

x = 15

Thus, The value of x is 15 for which r || s.

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The following are the incorrect versions of theorems proved in class with their correct statements:

a) If a sequence of continuous functions fn converges pointwise to a continuous function f, then the convergence is uniform.

FALSE CORRECTION: If a sequence of continuous functions fn converges uniformly to a continuous function f, then the convergence is pointwise. (This statement is known as the Weierstrass M-test.)

b) If a power series has radius of convergence R > 0, then it converges uniformly for * ∈ [-R, R].

FALSE CORRECTION: If a power series has radius of convergence R > 0, then it converges uniformly for x ∈ [a + r, b - r], where (a + r, b - r) is a subinterval of the interval of convergence. (This statement is known as the Weierstrass M-test.)

c) Any rearrangement of a convergent series converges to the same sum.

FALSE CORRECTION: A convergent series is absolutely convergent if and only if any rearrangement of its terms converges to the same sum.

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