Find the Zeros of each quadratic equation below by graphing

Identify the best deal for each item

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The velocity v = ds/dt in terms of t and the position s is: [tex]v = 15t^{(3/2)} - 8t^{(1/2)} + 6[/tex] and [tex]s = 5t^{(5/2)} - 16t^{(3/2)} + 6t + 27[/tex] respectively.

To find the velocity v = ds/dt in terms of t and the position s, we first need to integrate the acceleration equation with respect to time to get the velocity equation:

d²s/dt² = 30 sqrt(t) – 12/ sqrt(t)

Integrating both sides with respect to t, we get:

ds/dt = 30/2 * t^(3/2) - 12 * 2/3 * t^(1/2) + C₁

where C₁ is the constant of integration.

Using the condition ds/dt = 12 when t = 1, we can solve for C₁:

12 = 30/2 * 1^(3/2) - 12 * 2/3 * 1^(1/2) + C₁

C₁ = 6

Substituting this value of C₁ back into the velocity equation, we get:

ds/dt = 15t^(3/2) - 8t^(1/2) + 6

Now, we can integrate the velocity equation to get the position equation:

s = 5t^(5/2) - 16t^(3/2) + 6t + C₂

where C₂ is the constant of integration.

Using the condition s = 16 when t = 1, we can solve for C₂:

16 = 51^(5/2) - 161^(3/2) + 6*1 + C₂

C₂ = 27

Substituting this value of C₂ back into the position equation, we get:

s = 5t^(5/2) - 16t^(3/2) + 6t + 27

Therefore, the velocity v = ds/dt in terms of t and the position s is: v = 15t^(3/2) - 8t^(1/2) + 6 and s = 5t^(5/2) - 16t^(3/2) + 6t + 27 respectively.

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The maximum walking speed of a giraffe with a leg of 6 feet is approximately 1.41 times greater than that of a hippopotamus with a leg of 3 feet.

The equation given in the problem, S= square root of gL, represents the maximum walking speed S of an animal with a leg of length L. To find the ratio of the maximum walking speed of a giraffe with a leg of 6 feet to that of a hippopotamus with a leg of 3 feet, we can plug in the values of g and L for each animal and calculate the ratio.

For the giraffe: S = √(g6) = √(326) ≈ 9.8 ft/sec

For the hippopotamus: S = √(g3) = √(323) ≈ 5.7 ft/sec

So the ratio of the maximum walking speed of a giraffe with a leg of 6 feet to that of a hippopotamus with a leg of 3 feet is approximately 9.8/5.7 ≈ 1.72 or 1.41 to the nearest hundredth.

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The FICA tax will be $3595.5 on an income of $47,000.

Given that the principal amount = $47,000

Given that the FICA is taxed at the percentage of 7.65%

To findout the FICA tax we have to findout the 7.65% of money from the principal money $47,000.

The formula for finding the Y% of money from Z amount is = [tex]\frac{y}{100}[/tex] * Z

From the above formula, we can find the FICA tax.

FICA tax = [tex]\frac{7.65}{100}[/tex] * 47000 = 0.0765 * 47000 = 3595.5.

From the above solution, we can conclude that the FICA tax on an income of $47,000 is $3595.5

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The factorization of the given algebraic expression will give us:

4πr²(1 + ¹/₃r)

In order for us to factorize an algebraic expression, the highest common factors of the terms of the given algebraic expression would first be found and then we will group the terms accordingly. In simple terms, the reverse process of expansion of an algebraic expression is referred to as  its factorization.

We are given the algebraic expression as:

4πr² + ⁴/₃πr³

Now, we want to factor 4πr² from both terms and this will give us:

4πr²(1 + ¹/₃r)

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Answer:

Subtract 1 from both sides.

Answer:

subtract 1 from both sides. because taking out the 1 from 1 and 1 from 17 will equal 16. which leaves t/4=16

Choice D is correct: This situation satisfies each of the conditions for a binomial variable, so X has a binomial distribution.

A random variable X is said to have a binomial distribution if it satisfies the following conditions:

The variable X represents the number of successes in a fixed number of independent trials.

Each trial has only two possible outcomes: success or failure.

The probability of success is constant for each trial.

The trials are independent.

In this case, Yoshi attempts the same three-point shot until he makes the shot, so the number of attempts is not fixed. However, each attempt can be classified as a success (if he makes the shot) or a failure (if he misses the shot), so the variable X represents the number of successes in a sequence of independent trials with only two possible outcomes. Also, the probability of success is constant for each attempt, and the attempts are independent, so all four conditions for a binomial distribution are satisfied. Therefore, X is a binomial variable.

Choice D is correct: This situation satisfies each of the conditions for a binomial variable, so X has a binomial distribution.

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Part A: In the given scenario, the expression (32 + 2x) represents the rental price charged by the equipment rental business after x price increases of $2 each. The initial rental price is $32, and for every $2 increase in rental price, the rental price is raised by 2 units. The expression (24 – x) represents the number of rentals the equipment rental business can expect to make after x price increases. As the rental price increases, the number of customers is expected to decrease by one rental for every $2 increase in rental price.

Part B: To find the revenue after 3 rental price increases, we need to calculate f(3), where f(x) = (32 + 2x)(24 – x).

Substituting x = 3, we get:

f(3) = (32 + 2(3))(24 – 3) = (32 + 6)(21) = 38 × 21 = $798

Therefore, the revenue after 3 rental price increases is $798.

Part C: To find the rental price that would give the maximum revenue for the company, we need to find the value of x that maximizes the function f(x) = (32 + 2x)(24 – x). We can do this by finding the critical points of the function, which occur when the derivative of the function is equal to zero:

f'(x) = (32 + 2x)(-1) + (24 - x)(2) = -32 + 16x + 48 - 2x = 14x + 16

Setting f'(x) = 0 and solving for x, we get:

14x + 16 = 0

[tex]x = \frac{-16}{14} = \frac{-8}{7}[/tex]

However, [tex]x = \frac{-8}{7}[/tex] is not a valid solution since it represents a negative number of rental price increases, which is not possible in this scenario. Therefore, we need to test the endpoints of the interval [0, 6], since x represents the number of rental price increases and cannot exceed 6 (which would result in a rental price of $44, the maximum price in this scenario).

f(0) = (32 + 2(0))(24 - 0) = 32 × 24 = $768

f(6) = (32 + 2(6))(24 - 6) = 44 × 18 = $792

Comparing the values of f(0), f(3), and f(6), we see that f(6) gives the maximum revenue of $792. Therefore, the rental price that would give the maximum revenue for the company is $44, which is the rental price after 6 price increases of $2 each.

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a = 5

b = 4

c= 0

Therefore, the equation for graph C is Y = a ^b + c

Y = 5 ^4 + 0

A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Graphs are a popular tool for graphically illuminating data relationships.

A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.

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56 Sundays Maths Ice Cream Shop can serve with 7 cups of sprinkles using one-eighth (1/8) cup of sprinkles per Sunday.

Converting the cups of sprinkles into eighths:

  7 cups × 8 eighths/cup

= 56 eighths

Dividing the total eighths by the eighths used per Sunday:

  56 eighths / (1/8 cup per Sunday)

= 56 Sundays

So, Maths Ice Cream Shop can serve for 56 Sundays using 7 cups of sprinkles with each Sunday serving one-eighth cup of sprinkles.

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The volume of the rectangular prism is 31.5 in³.

From the diagram, we know that the height of the rectangular prism is 9 cubes. We can see the length is 7 cubes and the width is 4 cubes. Each cube is half an inch. Therefore we multiply every side by 1/2.

Height = 9 × (1/2)

Height = 4.5 inches

Length = 7 × (1/2)

Length = 3.5 inches

Width = 4 × (1/2)

Width = 2 inches

Volume = L × W × H

Volume = 3.5 × 2 × 4.5

Volume = 31.5 inches³

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Therefore, the correct sequence of transformations is:

Dilation by a scale factor of 2, centered at the origin.

Translation of 7 units to the left.

This is equivalent to option D.

To move AABC onto ADEF, we need to perform a sequence of transformations that will map each point of AABC onto the corresponding point of ADEF. Let's first label the vertices of AABC and ADEF as shown:

We can see that A and D have the same coordinates, so we only need to map B, C, and A' to E, F, and D', respectively.

Option A suggests a dilation by a scale factor of 2, centered at the origin, followed by a reflection over the y-axis. This transformation will map B to E, but it will also map C to C' which is not the same as F. Moreover, A' will be mapped to a point that is reflected over the y-axis and does not coincide with D. Therefore, option A is not the correct answer.

Option B suggests a translation of 7 units to the right, followed by a dilation by a scale factor of 2 centered at the origin. This transformation will not map B to E, but it will map A' to D', and C to a point that is 7 units to the right of F. Therefore, option B is not the correct answer either.

Option C suggests a dilation by a scale factor of 2, centered at the origin, followed by a translation of 7 units to the right. This transformation will map A' to D', and B to a point that is 7 units to the right of E. However, it will also map C to a point that is 7 units to the right of F, which is not the same as F. Therefore, option C is not the correct answer.

Option D suggests a dilation by a scale factor of 2, centered at the origin, followed by a translation of 7 units to the left. This transformation will map B to E, and A' to D', but it will also map C to a point that is 7 units to the left of F. However, if we reflect the resulting figure over the y-axis, we obtain the desired result.

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The chances of success in cycling across the United States is higher on the central route because more than half of the people who started on this route finished it (52%), while on the other routes the chances of successful completion is lower (route north (0%) south (0.02%).

According to the above, to find the probability of success in crossing the United States from coast to coast, we must divide the number of successful attempts by the total number of attempts as shown below:

North Route

0 ÷ 2 = 0

Center Route

10 ÷ 19 = 0.52

South Route

1 ÷ 39 = 0.025

According to the above, the highest probability of success is found in the central route with 0.52, that is to say that more than half of those who tried this route finished.

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The probability of being assigned all hardback books is approximately 0.33 or 33%.

This can be done by combination formula C(n,r) = n!/(r!(n-r)!)

The total number of ways to choose three books from a list of 14 books is given by the combination formula,

C(14,3) =14!/(3!(14-3)!) =  (141312) / (321) = 364.

To find the probability of selecting all hardback books, we need to determine the number of ways to select 3 books from the 10 hardback books. This is given by the combination formula,

C(10,3) = 10!/(3!(10-3)!) = 1098 / (321) = 120.

Therefore, the probability of selecting all hardback books is:

P(all hardback) = C(10,3) / C(14,3) = 120/364 = 0.3297

So, the probability of being assigned all hardback books is approximately 0.33 or 33%. This means that out of all possible combinations of 3 books, about 33% will consist of only hardback books.

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The area of the playground include the following: 900 square yards.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = base area × height

Area of playground, A = 45 × 20

Area of a playground, A = 900 square yards.

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Answer:

12

Step-by-step explanation:

multiply 4x18 then divide by 6

The value of a is -16

If α and β are zeroes of the quadratic equation x²-6x+a, then we know that:

α + β = 6

α * β = a

We are also given that 3α + 2β = 20.

3α + 2β = 20

3(α + β) - α = 20

3(6) - α = 20

18 -α = 20

18 - 20 = α

α = -2

Substituting α = -2 into the equation α + β = 6, we get:

- 2 + β = 6

beta = 8

Therefore, α = -2 and β = 8, and we can find a using the equation α * β = a:

a = α * β

= - 2 * 8

= 16

Therefore, the value of a is -16

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The situation represents exponential decay.

The rate of growth or decay, r, is equal to 0.02.

So the depth of the lake each year is 0.98 times the depth in the previous year.

It will take between 11 and 12 years for the depth of the lake to reach 26. 7 meters.

The situation represents exponential decay, as the depth of the lake decreases by a constant percentage each year. The rate of decay is 2% per year, so the rate of growth or decay, r, is equal to 0.98 (1 - 0.02). This means that the depth of the lake each year is 0.98 times the depth in the previous year.

To find the number of years it will take for the depth of the lake to reach 26.7 meters, we can use the formula for exponential decay:\

D = D₀ *[tex]e^{(-rt)[/tex]

where D is the current depth, D₀ is the initial depth, r is the rate of decay, and t is the number of years.

Substituting the given values, we get:

26.7 = 30 * [tex]e^{(-0.02t)[/tex]

Solving for t, we get:

t = ln(26.7/30) / (-0.02) ≈ 11.33

Therefore, it will take between 11 and 12 years for the depth of the lake to reach 26.7 meters.

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The probability of choosing a vowel from the word PROBABILITY, expressed as a decimal, is approximately 0.364.

To find the probability of choosing a vowel from the word PROBABILITY, you'll need to follow these steps:

1. Identify the total number of letters in the word: There are 11 letters in the word PROBABILITY.
2. Identify the number of vowels in the word: There are 4 vowels (O, A, I, and I).
3. Calculate the probability by dividing the number of vowels by the total number of letters: Probability = (number of vowels) / (total number of letters) = 4/11.

A decimal indication that the probability of selecting a vowel from the word PROBABILITY is roughly 0.364.

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Answer:

United States medals to Soviet Union medals:

Fraction: 1211/1010

Decimal: 1.198

Percent: 119.8%

Soviet Union medals to Great Britain medals:

Fraction: 1010/867

Decimal: 1.165

Percent: 116.5%

United States medals to Great Britain medals:

Fraction: 1211/867

Decimal: 1.397

Percent: 139.7%

The number of countries that have won between 2,250 and 2,499 total medals to the number of countries that have won between 0 and 249 total medals:

Fraction: 2/1

Decimal: 2

Percent: 200%

Only one country participating in the Summer Olympics has never won a medal. Write a comparison of the number of countries that have never won a medal to the number of participating countries:

Fraction: 1/205

Decimal: 0.00488

Percent: 0.488%

Step-by-step explanation =

United States medals to Soviet Union medals:

The fraction represents the ratio of medals won by the United States to those won by the Soviet Union. To find it, you can divide the number of medals won by the United States (1,211) by the number of medals won by the Soviet Union (1,010): 1211/1010.

To convert this fraction to a decimal, divide the numerator (1211) by the denominator (1010): 1.198.

To convert the decimal to a percent, multiply it by 100: 119.8%.

Soviet Union medals to Great Britain medals:

The fraction represents the ratio of medals won by the Soviet Union to those won by Great Britain. To find it, you can divide the number of medals won by the Soviet Union (1,010) by the number of medals won by Great Britain (867): 1010/867.

To convert this fraction to a decimal, divide the numerator (1010) by the denominator (867): 1.165.

To convert the decimal to a percent, multiply it by 100: 116.5%.

United States medals to Great Britain medals:

The fraction represents the ratio of medals won by the United States to those won by Great Britain. To find it, you can divide the number of medals won by the United States (1,211) by the number of medals won by Great Britain (867): 1211/867.

To convert this fraction to a decimal, divide the numerator (1211) by the denominator (867): 1.397.

To convert the decimal to a percent, multiply it by 100: 139.7%.

The number of countries that have won between 2,250 and 2,499 total medals to the number of countries that have won between 0 and 249 total medals:

The fractions represent the ratios of the number of countries that have won between two ranges of total medals. To find these fractions, you need to count the number of countries that fall into each range, and then divide one by the other. According to the information provided, there are 2 countries that have won between 2,250 and 2,499 total medals, and 1 country that has won between 0 and 249 total medals. So the fraction is 2/1.

To convert this fraction to a decimal, divide the numerator (2) by the denominator (1): 2.

To convert the decimal to a percent, multiply it by 100: 200%.

Only one country participating in the Summer Olympics has never won a medal. Write a comparison of the number of countries that have never won a medal to the number of participating countries:

The fraction represents the ratio of the number of countries that have never won a medal to the total number of participating countries. According to the information provided, only one country has never won a medal, and there are 205 participating countries. So the fraction is 1/205.

To convert this fraction to a decimal, divide the numerator (1) by the denominator (205): 0.00488.

To convert the decimal to a percent, multiply it by 100: 0.488%.

Answer:

[tex] \frac{7 \sqrt{39} }{5} [/tex]

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]( {11.2})^{2} - { {7} }^{2} = 76.44 > 0[/tex]

The missing side is equal to:

[tex] \sqrt{76.44} = \frac{7 \sqrt{39} }{5} [/tex]

Riley and her family move from the Midwest all the way to San Francisco. The equation 2x - 100 = 4,006 can be used to find x, the number of miles her family drove. Riley's family drove 2,053 miles from the Midwest to San Francisco.

Find the number of miles Riley's family drove from the Midwest to San Francisco, we need to solve the equation 2x - 100 = 4,006 for x.
First, we'll add 100 to both sides of the equation to isolate the variable term:
2x - 100 + 100 = 4,006 + 100
Simplifying:
2x = 4,106
isolate x, we'll divide both sides of the equation by 2:
2x/2 = 4,106/2
Simplifying:
x = 2,053
Therefore, Riley's family drove 2,053 miles from the Midwest to San Francisco.

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The measure of arc AB is 120 degrees.

What is meant by an arc?

An arc refers to a portion of the circumference of a circle or an ellipse. It is measured in degrees and can be used to calculate the length of the curve.

What is the term measure?

The term "measure" refers to the size or circumference of a geometric object, such as length, area, or volume. It is a numerical value that quantifies the measured property.

According to the given information

Let O be the centre of the circle. Since AB is parallel to CD, we have angles ACD and ADC that are equal since they are alternate interior angles. Therefore, the angle ACD is also 42 degrees.

Let x be the measure of arc AB, and then the measure of arc CD is 2x. Since the sum of the measures of arcs AB and CD is equal to the total circumference of the circle, we have:

x + 2x = 360 degrees

3x = 360 degrees

x = 120 degrees

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To find the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective, we can use the geometric distribution. The probability of not curing the disease is 1 - 0.70 = 0.30.

Let X be the number of patients needed to find one patient on whom the medicine would not be effective. Then X follows a geometric distribution with p = 0.30. The probability that it will take at least five patients to find one patient on whom the medicine would not be effective is:

P(X ≥ 5) = (1 - p)^(5-1) = 0.7^4 ≈ 0.2401

Therefore, the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is approximately 0.2401.

To find the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients, we can use the binomial distribution. Let X be the number of patients out of four who are cured by the medicine. Then X follows a binomial distribution with n = 4 and p = 0.70. The probability that the medicine will be effective on exactly three out of four randomly selected patients is:

P(X = 3) = (4 choose 3) * (0.70)^3 * (1 - 0.70)^(4-3) = 4 * 0.343 * 0.3^1 ≈ 0.4116

Therefore, the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is approximately 0.4116.

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The value of angle LQ in the intersected arc is 34 degrees.

If two secants intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.

Therefore, let's find the arc angle LQ as follows:

let

x = arc angle LQ

m∠U = 1 / 2 (108 - x)

37 = 54 - 0.5x

subtract 54 from both sides of the equation

37 = 54 - 0.5x

37 - 54 = 54 - 54 - 0.5x

-17 = -0.5x

divide both sides by -0.5

x = -17 / -0.5

x = 34 degrees

Therefore,

arc angle LQ = 34 degrees

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The percent of error in the measurement is 8%. This means that the measured value of 5.52 miles is 8% less than the actual distance of 6 miles.

To find the percent of error, we need to calculate the difference between the measured value and the actual value, divide that by the actual value, and then multiply by 100 to convert to a percentage.

Actual distance around the neighborhood = 6 miles

Measured distance around the neighborhood = 5.52 miles

Difference = Actual distance - Measured distance

Difference = 6 miles - 5.52 miles

Difference = 0.48 miles

Percent of error = (|Difference| / Actual distance) x 100%

Percent of error = (|0.48| / 6) x 100%

Percent of error = 0.08 x 100%

Percent of error = 8%

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Answer: 2

Step-by-step explanation:

Answer:

[tex] \frac{dy}{dx} = \frac{4}{9} [/tex]

Step-by-step explanation:

sol,

2x+3y-6x+6y=0

f(x,y)=2x+3y-6x+6y

f(X,-y)=2x+3y-6y,fx=?

f(x-y)=2x+3y-6y,fy=?

fx=-4

fy=9

[tex] \frac{d}{y} = \frac{ - 4}{9} [/tex]

now,

[tex] \frac{dy}{dx} = \frac{4}{9} [/tex]

To maintain the same ratio of Fuji apple trees to Gala apple trees, the owners of Hillsdale Orchard should: plant 12 new Fuji apple trees when they plant 30 new Gala apple trees.

To find the number of new Fuji apple trees that the owners of Hillsdale Orchard should plant to maintain the same ratio of Fuji apple trees to Gala apple trees, we need to use a ratio table.

First, we need to determine the ratio of Fuji apple trees to Gala apple trees before the new trees are planted. Let's assume that there are currently 40 Fuji apple trees and 100 Gala apple trees. The ratio of Fuji apple trees to Gala apple trees is therefore 40:100, which can be simplified to 2:5.

Next, we need to use this ratio to determine the number of new Fuji apple trees that need to be planted. Since the owners are planting 30 new Gala apple trees, we can use the ratio of 2:5 to find the corresponding number of new Fuji apple trees.

To do this, we need to divide the number of new Gala apple trees by the denominator of the ratio (which represents the number of units of the ratio). In this case, the denominator is 5.

30 (new Gala apple trees) ÷ 5 (denominator) = 6

This means that for every 5 new Gala apple trees, the owners should plant 2 new Fuji apple trees. Therefore, the owners should plant 12 new Fuji apple trees (2 trees for every 5 new Gala apple trees, multiplied by the 30 new Gala apple trees being planted).

In summary, to maintain the same ratio of Fuji apple trees to Gala apple trees, the owners of Hillsdale Orchard should plant 12 new Fuji apple trees when they plant 30 new Gala apple trees.

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The second derivative yⁿ (y'') is 48x² - 6, and the third derivative yᵐ (y''') is 96x.

To calculate the second and third derivatives of the function y = 4x^4 - 3x² + 7x:

1. First, calculate the first derivative, y':
y' = dy/dx = (d/dx)(4x^4 - 3x² + 7x)
Using the power rule for derivatives, we get:
y' = 16x³ - 6x + 7

2. Now, calculate the second derivative, y'' (also denoted as yⁿ when n=2):
y'' = d²y/dx² = (d/dx)(16x³ - 6x + 7)
Applying the power rule again:
y'' = 48x² - 6

3. Finally, calculate the third derivative, y''' (also denoted as yᵐ when m=3):
y''' = d³y/dx³ = (d/dx)(48x² - 6)
Using the power rule one more time:
y''' = 96x

So, the second derivative yⁿ (y'') is 48x² - 6, and the third derivative yᵐ (y''') is 96x.

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La probabilidad de sacar un producto defectuoso al azar de las tres cajas es aproximadamente 0.0917, o un 9.17%.

La probabilidad de sacar un producto defectuoso al azar de las tres cajas se puede calcular utilizando la fórmula de la probabilidad.

Primero, calculemos la probabilidad de sacar un producto defectuoso de cada caja:

1. En la primera caja, hay 3 productos defectuosos entre 20 productos en total. La probabilidad es 3/20.

2. En la segunda caja, hay 2 productos defectuosos entre 16 productos en total. La probabilidad es 2/16.

3. En la tercera caja, no hay productos defectuosos entre 10 productos en total. La probabilidad es 0/10.

Para encontrar la probabilidad total, sumamos las probabilidades de cada caja y luego dividimos por el número total de cajas:

(3/20 + 2/16 + 0/10) / 3 ≈ (0.15 + 0.125 + 0) / 3 ≈ 0.0917

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