Question 3

CLASS PRESIDENT In a poll for senior class president, 68 of the 145 male students said they planned to vote for Santiago. Out of 139

female students, 89 planned to vote for his opponent, Measha.

Construct a conditional relative frequency table based on voter preference. Show your calculations on a separate sheet of paper. Round to

the nearest whole percent if necessary

Solving a direct variation equation to find n gives n = -1

From the question, we have the following parameters that can be used in our computation:

A direct variation includes the points (2, –10) and (n,5).

This means that

(2, –10) = (n,5)

Express as an equation

So, we have

-2/10 = n/5

Multiply both sides of the equation by 5

So, we have the following representation

n = -2/10 * 5

Evaluate the product

n = -1

Hence, the value of n in the equation is -1

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The cost of a croissant before the increase was $0.75, the cost of a cup of coffee was $0.75, and the cost of a fruit bowl was $2.25.

Let's start by assigning variables to the cost of each item before the price increase. Let x be the cost of a croissant, y be the cost of a cup of coffee, and z be the cost of a fruit bowl.

From the problem statement, we know that:

x + y + z = 5.25 (total cost before price increase)

z = 3x (fruit bowl costs 3 times as much as a croissant)

Substituting z = 3x into the first equation, we get:

x + y + 3x = 5.25

4x + y = 5.25

Now we need to solve for x and y. We don't have an equation directly relating the price increase to the new prices, but we can use the percentage increase to write:

New croissant price = x + 0.15x = 1.15x

New coffee price = y + 0.4y = 1.4y

The new total cost will be:

1.15x + 1.4y + z

Substituting z = 3x, we get:

1.15x + 1.4y + 3x

Simplifying this expression and using the equation 4x + y = 5.25 to eliminate y, we get:

1.15x + 1.4y + 3x = 4.15x + 1.4(5.25 - 4x)

4.15x + 1.4(4x - 5.25) = 4.55x - 5.85

Therefore, the new total cost will be $4.55x - $5.85. To find the cost of each item before the increase, we can solve the system of equations:

4x + y = 5.25

z = 3x

Substituting z = 3x into the first equation, we get:

4x + y + 3x = 5.25

7x + y = 5.25

Solving for y in terms of x, we get:

y = 5.25 - 7x

Substituting this expression into the equation for the new total cost, we get:

4.55x - 5.85 = 1.15x + 1.4(5.25 - 4x) + 3x

Simplifying and solving for x, we get:

x = 0.75

Substituting this value of x into the equation for y, we get:

y = 5.25 - 7(0.75) = 0.75

Substituting x and z = 3x into the equation for the total cost before the increase, we get:

0.75 + 0.75 + 3(0.75) = 3.75

Therefore, the cost of a croissant before the increase was $0.75, the cost of a cup of coffee was $0.75, and the cost of a fruit bowl was $2.25.

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x is approximately 20.5 degrees when rounded to the nearest degree. Therefore, x ≈ 21 degrees.

General process of solving for an unknown angle.

1. Determine the type of angle: Determine whether the angle is a right angle (90 degrees), acute (less than 90 degrees), or obtuse (greater than 90 degrees).

2. Use geometric properties: If there are geometric properties or relationships given in the problem, such as angles formed by parallel lines or within a triangle, apply those properties to find the value of x.

3. Apply trigonometric functions: If the problem involves trigonometry, use sine, cosine, or tangent functions along with the given information to solve for x.

4. Apply algebraic equations: If there is an algebraic equation involving x, set up the equation and solve for x by isolating it on one side of the equation.

To find the value of x in the given triangle, we can use the inverse tangent function, which is tan^-1.

tan(x) = opposite/adjacent

tan(x) = 5/14

To isolate x, we take the inverse tangent of both sides:

x = tan^-1(5/14)

Using a calculator, we can find that x is approximately 20.5 degrees when rounded to the nearest degree. Therefore, x ≈ 21 degrees.

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Answer:

11.17, my answer needs to be 20+ characters soooooooo

The critical points of the given function f(x) = ** + 5x/ (10x-60) are x = 6 and x = -6/5. The function is decreasing on (-∞, -6/5) and increasing on (-6/5, 6) and (6, ∞). The First Derivative Test shows that x = -6/5 is a local maximum and x = 6 is a local minimum.

To find the critical points, we need to first find the derivative of the function. Using the quotient rule, we get:

f'(x) = (10x - 60)(**)' - **(10x - 60)' / (10x - 60)²

Simplifying, we get:

f'(x) = 50 / (10x - 60)²

The critical points occur where the derivative is zero or undefined. Here, the derivative is never undefined, so we only need to find where it is zero:

50 / (10x - 60)² = 0

This occurs when x = 6 and x = -6/5.

Next, we need to determine the intervals on which the function is increasing or decreasing. To do this, we can use the first derivative test. We test a value in each interval of interest to see if the derivative is positive or negative:

For x < -6/5, we choose x = -2:

f'(-2) = 50 / (10(-2) - 60)² = -5/81 < 0

Therefore, the function is decreasing on (-∞, -6/5).

For -6/5 < x < 6, we choose x = 0:

f'(0) = 50 / (10(0) - 60)² = 5/9 > 0

Therefore, the function is increasing on (-6/5, 6).

For x > 6, we choose x = 10:

f'(10) = 50 / (10(10) - 60)² = 5/81 > 0

Therefore, the function is increasing on (6, ∞).

Finally, we can use the First Derivative Test to determine the nature of the critical points.

For x = -6/5:

f'(-6/5 - ε) < 0 and f'(-6/5 + ε) > 0, for small values of ε.

Therefore, x = -6/5 is a local maximum.

For x = 6:

f'(6 - ε) < 0 and f'(6 + ε) > 0, for small values of ε.

Therefore, x = 6 is a local minimum.

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Both Nori and her brother Sean made the same amount in interest, $100, assuming that their investments lasted 1 year.

The interest refers to the income or payment received or made for giving or taking credit from a lender.

The interest is usually depicted using a rate, which is expressed over 100.

Nori's Investment = $5,000

Interest rate = 2%

Interest amount = $100 ($5,000 x 2%)

Sean's investment = $10,000

Interest rate = 1%

Interest amount = $100 ($10,000 x 1%)

Thus, Nori and Sean equally made $100 in interest from their investments.

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Andrew and his mother will have wrapped the same number of candy pieces in 21.6 minutes.

We need to find out how many minutes (s) Andrew and his mother wrapped the same number of candy pieces.

Given data:

The number of pieces that Andrew’s mother can wrap is y = 73.

Andrew wraps at a rate of y = 3x + 8.

To find the number of minutes (s) at which Andrew and his mother have wrapped the same number of candy pieces, we need to equate both equations and then find the value of x the equation is given as,

73 = 3x + 8

65 = 3x

x = 21.6

Therefore, Andrew and his mother will have wrapped the same number of candy pieces after 21.6 minutes.

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The domain and range that represents this situation is: B Domain All real numbers greater than or equal to 0; Range: All real numbers greater than or equal to 46.

In the given situation, the number of giraffes in the San Antonio Zoo is represented by the function y = 46(1.08)ˣ To determine the domain and range that represent this situation, we must consider the context and the variables involved.

The domain represents the possible values of x, which corresponds to the number of years. Since time cannot be negative in this context, the domain includes all real numbers greater than or equal to 0.

The range represents the possible values of y, which corresponds to the number of giraffes. The initial number of giraffes is 46, and the population is increasing each year. Therefore, the range includes all real numbers greater than or equal to 46.

Based on this information, the correct answer is B: Domain: All real numbers greater than or equal to 0; Range: All real numbers greater than or equal to 46.

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Complete question:

There are 46 giraffes in the San Antonio Zoo. The population increases at a rate of 8% each year. The function y = 46(1.08)* can be used to determine y, the number of giraffes

at the zoo after x years. What is the domain and range that represents this situation?

A Domain: All real numbers less than or equal to 46

Range: All real numbers

B Domain: All real numbers greater than or equal to 0

Range: All real numbers greater than or equal to 46

C Domain: All real numbers greater than or equal to 1.08

Range: All real numbers greater than 0

D Domain: All real numbers

Range: All real numbers greater than or equal to 0

It will take 32 days for all 24 gallons to leak out of the bucket at a rate of 3 gallons every 4 days.

If water is leaking out of a bucket at a rate of 3 gallons every 4 days, then the rate of leakage is 3/4 gallons per day.

Let x be the number of days it takes for all 24 gallons to leak out. To explain this situation, we can construct an equation.

24=3/4*x

To solve for x, we can cross-multiply.

24*4=3x

3x=96

x=96/3

x = 32

Therefore, it will take 32 days for all 24 gallons to leak out of the bucket at a rate of 3 gallons every 4 days.

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Possible options for z could be:

1) z = -6

2) z = -7

These are two possible options for z that satisfy the given inequality.

Given that the opposite of z is greater than 5, we can write this as an inequality:

-z > 5

To find the possible options for z, we can follow these steps:

Step 1: Multiply both sides of the inequality by -1 to solve for z. Remember to flip the inequality sign when multiplying by a negative number:

z < -5

Step 2: Choose two values for z that satisfy the inequality z < -5.

Possible options for z could be:

1) z = -6
2) z = -7

These are two possible options for z that satisfy the given inequality.

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The actual measure of major arc JML is approximately 289.33°, which is closest to 287°.

We know that minor arc KL is supplementary to major arc JML. So,

m∠KL = 180° - m∠JML

Substituting the given values, we get:

8x - 6 = 180 - (25x - 13)

Solving for x, we get:

33x = 193

x = 193/33

Substituting this value of x in the expression for m∠JML, we get:

m∠JML = 25(193/33) - 13

m∠JML = 1468/3

m∠JML ≈ 489.33°

However, since lines KL and JM appear tangent, we know that minor arc KL and major arc JML share the same endpoint and thus are part of the same circle. So, the actual measure of major arc JML is:

m(arc JML) = 360° - m(arc KL)

We can find m(arc KL) by subtracting m∠KLM from 180°:

m(arc KL) = 180° - m∠KLM

m(arc KL) = 180° - (8(193/33) - 6)

m(arc KL) ≈ 70.67°

Substituting in the formula for m(arc JML), we get:

m(arc JML) = 360° - 70.67°

m(arc JML) ≈ 289.33°

Therefore, the actual measure of major arc JML is approximately 289.33°, which is closest to option (b) 287°.

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a. The down payment is $22,500.

b. The mortgage is $202,500.

c. The monthly mortgage payment is $1,027.

a. The down payment is 10% of the home price, which is $225,000 x 0.1 = $22,500.

b. The mortgage is the remaining amount that you need to pay, which is $225,000 - $22,500 = $202,500.

c. The monthly mortgage payment can be calculated using the formula for a fixed-rate mortgage:

Monthly Payment = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

where P is the principal amount (the mortgage), i is the monthly interest rate (4.5% / 12 = 0.375%), and n is the total number of monthly payments (30 years x 12 months/year = 360).

Plugging in the values, we get:

Monthly Payment = $202,500 [ 0.00375(1 + 0.00375)^360 ] / [ (1 + 0.00375)^360 – 1] = $1,027.

Therefore, your monthly mortgage payment will be $1,027.

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Let's evaluate the limit using l'Hôpital's Rule when it is convenient and applicable:

The evaluated limit using l'Hôpital's Rule is 5.

Given limit,

lim (x -> 0) (sin(5x) / x)

Since both the numerator and denominator approach 0 as x approaches 0,

we can apply l'Hôpital's Rule.

Step 1: Differentiate the numerator and the denominator with respect to x.
- Derivative of sin(5x) with respect to x: 5*cos(5x)
- Derivative of x with respect to x: 1

Step 2: Apply l'Hôpital's Rule:
lim (x -> 0) (5*cos(5x) / 1)

Step 3: Evaluate the limit:
As x approaches 0, cos(5x) approaches cos(0) = 1.

Therefore, the limit is: 5*1 = 5

So, the evaluated limit using l'Hôpital's Rule is 5

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Step-by-step explanation:

-3x - 2x - 5 = -7

-5x - 5 = -7

-5x = -7 + 5

-5x = -2

x = 2/5

The quotient of 1.892×10^8 and 4.3×10^3 expressed in scientific notation is 4.4×10^4.

The quotient is determined by dividing any two numbers. In this case, the two numbers are 1.892×10^8 and 4.3×10^3. In order to calculate the quotient here, we will divide 1.892×10^8 by 4.3×10^3. Hence,

1. Divide the coefficients: 1.892 ÷ 4.3 = 0.44

2. Subtract the exponents: (10^8) ÷ (10^3) = 10^(8-3) = 10^5

3. Combine the results: 0.44 × 10^5

To express this answer in scientific notation, we need to move the decimal point one place to the left and adjust the exponent accordingly:

0.44 × 10^5 = 4.4×10^4

Therefore, the quotient expressed in scientific notation is 4.4×10^4.

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The probability of Shayla winning the $200 prize with 10 lottery tickets is approximately 0.2753%.

In a probability context, an event refers to an outcome or set of outcomes of an experiment or process. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of winning the lottery can be calculated using the formula:

Probability of winning = 1 / odds

Here, the odds of winning are given as 1-in-3,598. So, the probability of winning is:

Probability of winning = 1 / 3,598

= 0.000278

= 0.0278%

Shayla has bought 10 lottery tickets. So, the probability of winning the $200 prize with at least one ticket can be calculated as the complement of the probability of not winning with any of the tickets. That is:

Probability of winning with at least one ticket = 1 - Probability of not winning with any ticket

The probability of not winning with a single ticket is 1 - 0.000278 = 0.999722. So, the probability of not winning with all 10 tickets is:

Probability of not winning with all 10 tickets = (0.999722)¹⁰

= 0.997247

Therefore, the probability of winning with at least one ticket is:

Probability of winning with at least one ticket = 1 - Probability of not winning with all tickets

= 1 - 0.997247

= 0.002753

= 0.2753% (approx)

So, the probability of Shayla winning the $200 prize with 10 lottery tickets is approximately 0.2753%.

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Shayla's probability of winning the $200 prize with 10 lottery tickets are at 0.2753%.

An event in the context of probability is a result, or series of results, of an experiment or procedure. By dividing the number of favourable outcomes by the total number of possible outcomes, the probability of an event is determined.

The following formula can be used to determine the likelihood of winning the lottery:

Probability of winning = 1 / odds

The odds of winning in this case are 1 in 3,598. Therefore, the likelihood of winning is:

Probability of winning = 1 / 3,598

= 0.000278

= 0.0278%

Shayla purchased ten lottery tickets. As a result, the likelihood that at least one ticket will win the $200 reward can be computed as the complement of the likelihood that none of the tickets will win. Which is:

winning chances with at least one ticket = 1 - likelihood of failing to win with any ticket

The likelihood that a single ticket won't be the winner is 1 - 0.000278 = 0.999722. Consequently, the likelihood of not winning with all ten

tickets is:

with all ten tickets, what is the likelihood of not winning = (0.999722)¹⁰

= 0.997247

Consequently, the following is the likelihood of winning with at least one ticket:

winning chances with at least one ticket = 1 - likelihood of failing to win with any ticket

= 1 - 0.997247

= 0.002753

= 0.2753% (approx)

Shayla's chances of winning the $200 prize with 10 lottery tickets are at 0.2753%.

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Answer:

38

Step-by-step explanation:

Formula

Inscribed angle = Central angle/2

Here

Inscribed angle = x

Central angle = 76

x = 76/2

x = 38

When the value of pp=95 the value of qq will be equal to 6.

It is given that pp varies inversely with qq, so we can write that

pp=k/qq

where k is the proportionality constant.

here we can find the value of k by substituting the value of pp and qq with 19 and 30 in the relation that is given above, we get:

30=k/19

k=30*19

k=570

we the value of k to be 570 after putting the values in the relation.

Now if pp is changed to 95, and k is equal to 570 we can get the value of qq by putting the known values in the same relation.

pp=k/qq

qq=570/95

qq=6.

Therefore, when the value of pp is 95 the value for qq will be equal to 6.

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a. The teacher's age in seconds can be written in scientific notation as 1.5 × [tex]10^{9}[/tex] seconds.

b. A more reasonable unit of measurement for this situation could be years, as it is a common unit used to express human age.

c. To convert the teacher's age from seconds to years, we can divide the number of seconds by the number of seconds in a year. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and approximately 365 days in a year. So,

1.5 × [tex]10^{9}[/tex] seconds ÷ (60 seconds/minute × 60 minutes/hour × 24 hours/day × 365 days/year) = approximately 47.5 years

Therefore, the teacher is approximately 47.5 years old when using the more reasonable unit of measurement.

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The number of engines that must be made to minimize the unit cost are 180

From the question, we have the following parameters that can be used in our computation:

C(x) = −0.5x² + 180x + 25,609.

Differentiate the above equation

So, we have the following representation

C'(x) = -x + 180

Set the equation to 0

So, we have the following representation

-x + 180 = 0

This gives

x = 180

Substitute x = 180 in the above equation, so, we have the following representation

C(180) = −0.5(180)² + 180(180) + 25,609

Evaluate

C(180) = 41809

Hence, the engines that must be made to minimize the unit cost are 180

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The ordered pairs of the linear expression y = 4x - 9 is (0, -9)

From the question, we have the following parameters that can be used in our computation:

The linear expression y = 4x - 9

To determine the ordered pairs of the linear expression, we set x to any value say x = 0 and then calculate the value of y

Using the above as a guide, we have the following:

y = 4(0) - 9

Evauate

y = -9

Divide both sides by 1

y = -9

This means that the value of y is equal to -9

So, we have (0, -9)

Hence, the ordered pairs of the linear expression is (0, -9)

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There are 56 servings in a 28 pound bag of dog food.

We have the information from the question is:

Fei Yen dog eats 8 ounces of dog food each day.

Fei Yen bought a 28 pound of dog food.

To find the how many 8 ounces servings are in a 28 pound bag of dog food?

Each day Fei yen's dog eat dog food = 8 ounces

Fei yen bought a 28 pound bag of dog food.

Now, Firstly convert the pounds into ounces.

We know that:

1 pound = 16 ounces

Then, 28 pounds = 28 × 16 = 448 ounces

The number of 8 ounces servings are in a 28 pound bag of dog food:

=> [tex]\frac{448}{8} =56[/tex]

Hence, there are 56 servings in a 28 pound bag of dog food.

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The required values on the graph, the solution is approximate x = -0.33.

We can begin by combining like terms on the left-hand side:

3x² - 6x - 4 - 2/x + 3 + 1 = 0

3x² - 6x - 2/x = -3

Next, we can factor out the x term:

x(3x - 2) - 2(3x - 2) = -3

(x - 2)(3x - 2) = -3

Since the equation is equal to -3, we can add 3 to both sides to get:

(x - 2)(3x - 2) + 3 = 0

We can then factor the left-hand side to get:

(x - 2)(3x - 2 + 3) = 0

(x - 2)(3x - 2 + 3) = (x - 2)(3x + 1) = 0

This equation has two solutions: x = 2 and x = -1/3.

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Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

The volume of the pyramid with a square base of side length 16.6 meters and a height of 9.1 meters is approximately 836.6 cubic meters.

To find the volume of a pyramid with a square base, you'll need to know the side length of the base and the height of the pyramid. In this case, the side length of the square base is 16.6 meters, and the height of the pyramid is 9.1 meters. Here's a step-by-step explanation to calculate the volume:

1. Find the area of the square base: Since the base is a square, you'll need to multiply the side length by itself.
Area = side_length × side_length
Area = 16.6 m × 16.6 m
Area ≈ 275.56 m²

2. Calculate the volume of the pyramid: To find the volume, you'll multiply the area of the base by the height of the pyramid and divide the result by 3.
Volume = (Area × Height) / 3
Volume ≈ (275.56 m² × 9.1 m) / 3
Volume ≈ 836.626 m³

3. Round the answer to the nearest tenth of a cubic meter:
Volume ≈ 836.6 m³

So, the volume of the pyramid with a square base of side length 16.6 meters and a height of 9.1 meters is approximately 836.6 cubic meters.

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The value of f(3) is 172.

The problem provides us with the linear approximation of a function at a given point. In this case, we are given the linear approximation at x=3.5 as L(x) = 121(x-3) + 172. We are asked to find the value of the original function f(3). Since 3 is to the left of the given point 3.5, we need to use the left-hand side of the linear approximation.

To find the value of f(3), we substitute x=3 in the linear approximation:

L(3) = 121(3-3.5) + 172

= 121(-0.5) + 172

= -60.5 + 172

= 111.5

Therefore, the value of f(3) is 172.

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Answer:

I guess you need the value of (x) if that's so then

x= -4

Step-by-step explanation:

Therefore, the trader should sell the article for GHC 4440.00 to make a profit of 48%.

Percent is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred". Percentages are usually denoted by the symbol %, which is placed after the numerical value. Percentages are used in many fields, including finance, science, and everyday life, to represent proportions, rates, and changes in quantities.

Here,

Let's call the original cost of the article "C".

We know that the trader made a profit of 24%, which means that he sold the article for 100% + 24% = 124% of its cost:

124% of C = GHC 3720.00

To find C, we can divide both sides by 1.24:

C = GHC 3720.00 / 1.24

C = GHC 3000.00

So the trader originally purchased the article for GHC 3000.00.

Now we want to know how much the trader should sell the article for to make a profit of 48%. This means that he wants to sell the article for 100% + 48% = 148% of its cost:

148% of C = ?

Substituting C = GHC 3000.00, we get:

148% of GHC 3000.00 = (148/100) x GHC 3000.00

= GHC 4440.00

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When 7 gallons an hour is converted to cups per minute it would be = 1.9 cups /min.

To convert gallons per hour to cups per minute the following is carried out.

The constitution of a gallon when measured in cups = 16 cups.

Therefore if 1 gallon = 16 cups

7 gallons = X cups

Make X the subject of formula;

X = 16×7

= 112 cups

This means that , 112 cups = 1 hour(60 mins)

y cups = 1 min

make y the subject of formula;

y = 112/60

= 1.9 cups /min

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The Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 for 0 ≤ x ≤ 0.9 is approximately 0.000129.

To find the Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0, we need to find the maximum value of the fifth derivative of [tex]e^x[/tex] on the interval [0, 0.9].

Since the nth derivative of [tex]e^x[/tex] is [tex]e^x[/tex] for all n, the fifth derivative is also [tex]e^x[/tex]. To find the maximum value of[tex]e^x[/tex]on the interval [0, 0.9].

We evaluate [tex]e^x[/tex] at the endpoints and at the critical point x = 0.45, which is the midpoint of the interval:

[tex]e^0[/tex] = 1

[tex]e^0.9[/tex]≈ 2.4596

[tex]e^0.45[/tex] ≈ 1.5684

The maximum value of [tex]e^x[/tex] on the interval [0, 0.9] is approximately 2.4596.

The Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 is given by:

E₄(x) ≤ (M/5!)[tex]|x-0|^5[/tex]

where M is the maximum value of the fifth derivative of [tex]e^x[/tex] on the interval [0, 0.9].

So, we have:

E₄(x) ≤ (2.4596/5!) [tex]|x|^5[/tex] for 0 ≤ x ≤ 0.9

Substituting x = 0.9 into this inequality, we get:

E₄(0.9) ≤ (2.4596/5!)[tex](0.9)^5[/tex] ≈ 0.000129

Therefore, the Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 for 0 ≤ x ≤ 0.9 is approximately 0.000129.

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