Given the functions f(x) = x³ ln(1 – 4x²) and g(x) = sin(In x), find the Taylor series of f about x = 0 and its radius of convergence and the interval of convergence.

To estimate the number of sandwiches the deli manager should anticipate selling when 178 customers visit the deli, we can analyze the given data and approximate it using a linear function.

By observing the table, we notice that the number of sandwiches sold varies with the number of customers. This indicates a relationship between the two variables.

To estimate the number of sandwiches, we can fit a line to the data points and use the linear function to make predictions. Using a statistical software or a spreadsheet, we can perform linear regression analysis to find the equation of the best-fit line. However, since we are limited to text-based interaction, I will provide a general approach.

Let's assume the number of customers is the independent variable (x) and the number of sandwiches is the dependent variable (y). Using the given data points, we can calculate the equation of the line.

After calculating the linear equation, we can substitute the value of 178 for the number of customers (x) into the equation to estimate the number of sandwiches (y).

Please provide the data points for the number of sandwiches sold corresponding to each number of customers so that I can perform the linear regression analysis and provide a more accurate estimate for you.

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The probability of randomly drawing seven cards from a deck of cards and getting three Jacks and two Kings is approximately 0.00000027 or 2.7 in 10 million.

To compute the probability of randomly drawing seven cards from a deck of cards and getting three Jacks and two Kings, we can use the formula for hypergeometric probability.

The number of ways to draw three Jacks and two Kings from a deck of cards is given by:

(4 choose 3) * (4 choose 2) = 6 * 6 = 36

where (n choose k) represents the number of ways to choose k items from a set of n items.

The total number of ways to draw seven cards from a deck of cards is given by:

(52 choose 7) = 133,784,560.

So the probability of getting three Jacks and two Kings when drawing seven cards from a deck of cards is:

36 / 133,784,560 ≈ 0.00000027.

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Answer: -∞<x<∞

Explanation: The function has no undefined points or domain constraints.

Hi there!

Angles in a triangle sum up to 180°, so:

180° = 110° + 5x° + 2x°

Simplify:

180° = 110° + 7x°

Subtract both sides by 110:

70° = 7x°

Divide both sides by 7:

x = 10°

Plug in to solve for the other angles:

5x = 5(10) = 50°

2x = 2(2) = 20°

Answer:

4/75

Step-by-step explanation:

1/5 ÷15/4

1/5 ×4/15 = 4/75

1/5 divided by 15/4 equals 4/75.

Given that, we need to solve, 1/5 divided by 15/4

Division of fractions, is a mathematical process called fraction division involves multiplying one fraction by another.

To divide a fraction, multiply the first fraction by the second fraction's reciprocal.

A fraction's reciprocal is created by switching the numerator and denominator.

In order to divide 1/5 by 15/4, we multiply 1/5 by 15/4's inverse:

(1/5) ÷ (15/4) = (1/5) × (4/15)

The denominators and numerators can now be multiplied:

(1 × 4) / (5 × 15) = 4/75

1/5 divided by 15/4 equals 4/75 as a result.

Hence 1/5 divided by 15/4 equals 4/75.

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Answer:

0.00007494

Step-by-step explanation:

Answer:

416, I believe this is the answer.

Step-by-step explanation:

483 - 67 = 416

Foram vendidos 416 hambúrgueres na quinta-feira

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Initial investment= $8,800

Percentage decrease= 26.5%

To calculate the money Maya lost, we need to use the following formula:

Decrease on dollars= 8,800*0.265

Decrease in dollars= $2,332

At the end of the years she has:

Money left= 8,800 - 2,332

Money left= $6,468

2x²+5y²

= 2×(-4)²+5×3²

=2×16+5×9

= 32+45

=77

Answer:

Step-by-step explanation:

This is your position equation:

There's a whole lot of information in that equation, but what we are concerned about right now is the height of the ball after t = 3 seconds.  If this is the position of the ball at any time t, we will sub in 3 for t to find out where the ball is at 3 seconds.

which simplifies to

s(3) = -44.1 + 54 + 10 which is

s(3) = 19.9 meters

That's how high the ball is in the air at 3 seconds.

Step-by-step explanation:

the correct answer is 1/7

When a positive integer is raised to a negative power, we can evaluate it by taking the reciprocal of the positive integer raised to the absolute value of the negative power.

if we have a positive integer a raised to a negative power n, we can evaluate it as:

a^(-n) = 1 / a^n

For example, if we have 2^(-3), we can evaluate it as:

2^(-3) = 1 / 2^3 = 1/8

Similarly, if we have 5^(-2), we can evaluate it as:

5^(-2) = 1 / 5^2 = 1/25

Note that this rule applies only to positive integers raised to negative powers. When we have negative numbers raised to negative powers or fractions raised to negative powers, we need to use different rules for evaluation

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The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%. Albinism and hemophilia are both recessive genetic conditions, meaning that both parents must have the recessive gene in order for a child to be born with either condition. Since neither Clara nor Charles have either condition, the probability that their first child will be a boy with both albinism and hemophilia is 0%.

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.

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Answer:

The value of \(x\):

\(x = -2\)

Step-by-step explanation:

Find the value of \(x\):

\(-9x + 1 = -x + 17\)

-Add both sides by \(x\):

\(-9x + 1 + x = -x + x + 17\)

\(-8x + 1 = 17\)

-Subtract both sides by \(1\):

\(-8x + 1 - 1 = 17 - 1\)

\(-8x = 16\)

Divide both sides by \(-8\):

\(\frac{-8x}{-8} = \frac{16}{-8}\)

\(x = -2\)

So, the final answer would be \(x = -2\) .

Answer:

x=−2

Step-by-step explanation:

−9x+1=−x+17

Add x to both sides.

−9x+1+x=−x+17+x

−8x+1=17

Subtract 1 from both sides.

−8x+1−1=17−1

−8x=16

Divide both sides by -8.

−8x/-8 = 16/-8

Answer:

x=−2

Answer:

i believe it is c

Step-by-step explanation:

The answer is:

\(\large\textbf{They aren't equivalent.}}\)

In-depth explanation:

To determine the answer to this problem, we will use one of the exponent properties:

\(\sf{x^{-m}=\dfrac{1}{x^m}}\)

And

\(\sf{\dfrac{1}{x^{-m}}=x^m}\)

Now we apply this to the problem.

What is 4⁻³ equal to? Well according to the property, it's equal to:

\(\sf{4^{-3}=\dfrac{1}{4^3}}\)

And this question asks us if 4⁻³ is the same as 1/4⁻3.

Well according to the calculations performed above, they're not equivalent.

Answer:

2.5 inches

Step-by-step explanation:

Remember:

Big to small, multiply it all

Small to big, divide the pig

Since feet is bigger than inches we're dividing 25 by 10 which is 2.5

Answer:

1:2

Step-by-step explanation:

Answer:

1:2

Step-by-step explanation:

The two numbers whose sum is 52 and the product is maximum are 26 and 26.

Finding the least common multiples of the denominator expressions can help. Then using the similar method as we use in the sum of fractions would give the sum of algebraic fractions.

We need to find the two numbers whose sum is 52 and the product is maximum.

So, the multiples of 52 are

2, 26, 4, 13,

So, here we can see that the sum of 26 to itself would be equal to 52.

26 + 26 = 52

The product is also maximum compared to others.

26 x 26 = 676

Therefore, the two numbers are 26 and 26.

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1) The maximum height of the ball is: 144 ft

2) The number of seconds it will take to hit the ground is: 5 seconds

We are given the equation that models the ball's height about the ground as:

h(t) = -16t² + 64t + 80

This is a parabola that opens downward, max is at vertex;

The maximum height will be the value of t at the vertex. Thus:

t = -b/2a

t = -64/(2 * -16)

t = 2 seconds

Thus:

h_max = -16(2)² + 64(2) + 80

h_max = -64 + 128 + 80

h_max = 144 feet

The number of seconds it will take to reach the ground is when h(t) = 0. Thus:

-16t² + 64t + 80 = 0

Using quadratic calculator, we have:

t = 5 seconds

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Answer:

y = -4

x = 6

Solution:

7x + 11y = -2 [1]

7x + 3y = 30 [2]

[1] - [2],

8y = -32

y = -4

(use substitution method to find x)

substitute y = -4 into [2],

7x + 3y = 30

7x + 3(-4) = 30

7x - 12 = 30

7x = 30 +12

7x = 42

x = 6

Answer:

Step-by-step explanation:

Let's solve each problem one by one:

1. Adam has $2 and is saving $2 each day. Brodie has $8 and is spending $1 each day. After how many days will each person have the same amount of money?

Let's assume the number of days is represented by 'x'.

Adam's money after 'x' days = $2 + $2x

Brodie's money after 'x' days = $8 - $1x

To find the number of days when they have the same amount of money, we set up an equation:

$2 + $2x = $8 - $1x

Simplifying the equation:

$2x + $1x = $8 - $2

$3x = $6

x = $6 / $3

x = 2

Therefore, after 2 days, Adam and Brodie will have the same amount of money.

Answer: A. 5x + 4 = 3x - 2 (incorrect)

2. A number increased by 8 is equal to twice the same number increased by 7.

Let's represent the number by 'x'.

Equation: x + 8 = 2x + 7

Solving the equation:

x - 2x = 7 - 8

-x = -1

x = 1

Therefore, the number is 1.

Answer: D. x + 8 = 2x + 7 (correct)

3. Spot weighs 6 pounds and gains one pound each week. Buddy weighs 2 pounds and gains 2 pounds each week. After how many weeks will the puppies weigh the same?

Let's represent the number of weeks by 'x'.

Spot's weight after 'x' weeks = 6 + 1x

Buddy's weight after 'x' weeks = 2 + 2x

To find the number of weeks when they weigh the same, we set up an equation:

6 + 1x = 2 + 2x

Simplifying the equation:

x - 2x = 2 - 6

-x = -4

x = 4

Therefore, after 4 weeks, Spot and Buddy will weigh the same.

Answer: A. x + 6 = 2x + 2 (incorrect)

4. Five less than two times a number is equal to 4 less than the same number.

Let's represent the number by 'x'.

Equation: 2x - 5 = x - 4

Solving the equation:

2x - x = -4 + 5

x = 1

Therefore, the number is 1.

Answer: B. 2x - 5 = x - 4 (correct)

5. Ann has an empty cup and adds 1 ounce of water per second. Bob has 12 ounces of water and drinks 2 ounces per second. After how many seconds will they have the same amount of water?

Let's represent the number of seconds by 'x'.

Ann's water after 'x' seconds = 1x ounces

Bob's water after 'x' seconds = 12 - 2x ounces

To find the number of seconds when they have the same amount of water, we set up an equation:

1x = 12 - 2x

Simplifying the equation:

1x + 2x = 12

3x = 12

x = 12 / 3

x = 4

Therefore, after 4 seconds, Ann and Bob will have the same amount of water.

Answer: A. -2x + 12 = -x + 6 (incorrect)

6. Tom has

12 candies and eats 2 each minute. Sue has 6 candies and eats 1 every minute. After how many minutes will they have the same number of candies?

Let's represent the number of minutes by 'x'.

Tom's candies after 'x' minutes = 12 - 2x

Sue's candies after 'x' minutes = 6 - 1x

To find the number of minutes when they have the same number of candies, we set up an equation:

12 - 2x = 6 - 1x

Simplifying the equation:

-2x + 1x = 6 - 12

-x = -6

x = 6

Therefore, after 6 minutes, Tom and Sue will have the same number of candies.

Answer: A. -2x + 12 = -x + 6 (correct)

the perimeter of the pentagon greater than 26 centimeters is given by

23.51

Given that a pentagon with 5  sides of equal length and 5 interior angles of equal measure is inscribed in a circle

The circle has area of 16 pi sq cm.

Hence radius of circle = 4 cm

The pengagon each side would be a chord of equal length subtending angle 72 at the centre.

visualize the triangle made by one side of pentagon with centre.  This is isosceles with angles 72, 54 and 54

Use sine angle for this triangle.

, where R = radius =4 and s = side of pentagon.

s= 4.702

Perimeter = 5s = 23.5114 cm

Perimeter not greater than 26 cm.

If origin is at the centre then two vertices would be (4,0) (4cos 72, 4sin72),(4cos 144, 4 sin 144) and so on.

Longest diagonal = distance between (4,0) and (4cos 144, 4 sin 144)

= (-3.236, 2.351) and (4,0)

=7.608

Yes greater than 8 cm

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Answer:

Rr = 51 : 68

Step-by-step explanation:

Answer:

the median should be 2.5

Answer:

2.5

Step-by-step explanation:

By taking the dots ploted on the graph we can take those as actual numbers and put them on a line.

0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5

Now you will take off the numbers until you get to the middle number

0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5

Because the middle two numbers are 2 and 3, you take the mean of the two numbers.

(2 + 3) / 2

= 2.5

The vectors is perpendicular to (-4,2) will be (b) (-1,-2)

The dot product of two vectors is found by multiplying the corresponding components of the vectors and adding the results. which is, if the two vectors are (a, b) and (c, d), their dot product is ac + bd.

To calculate the dot product of (-4, 2) with each of the given vectors:

a) (-3.6):

(-4)(-3.6) + (2)(-3.6) = 14.4 - 7.2 = 7.2

b) (-1, -2):

(-4)(-1) + (2)(-2) = 4 - 4 = 0

c) (2, -3):

(-4)(2) + (2)(-3) = -8 - 6 = -14

d) (4, -8):

(-4)(4) + (2)(-8) = -16 - 16 = -32

Therefore, the vector that is perpendicular to (-4, 2) is option (b) (-1,-2).

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Rounding this value to the nearest tenth, the volume of the cone-shaped lampshade is approximately 81.7 cubic inches.

The volume of a cone-shaped lampshade, you can use the formula:

Volume = (1/3) × π × r² × h,

where π is a mathematical constant approximately equal to 3.14159, r is the radius of the cone, and h is the height of the cone.

Given that the diameter of the lampshade is 5 inches the radius (r) can be calculated by dividing the diameter by 2:

r = 5 inches / 2 = 2.5 inches.

The height of the lampshade is given as 6.5 inches.

Now we can substitute the values into the volume formula:

Volume = (1/3) × 3.14159 × (2.5 inches)² × 6.5 inches.

Calculating this expression, we get:

Volume ≈ 1/3 × 3.14159 × 6.25 inches² × 6.5 inches.

Volume ≈ 81.6816 cubic inches.

The following formula can be used to determine a lampshade's volume:

Volume is equal to (1/3) r2 h, where r is the cone's radius and h is its height. The mathematical constant is roughly equivalent to 3.14159.

If the lampshade has a diameter of 5 inches, the radius (r) may be found by multiplying the diameter by two:

2.5 inches is equal to r = 5 inches / 2.

The lampshade's height is listed as 6.5 inches.

We can now enter the values into the volume formula as follows:

Volume equals 1/3 of 3.14159 inches, 2.5 inches, and 6.5 inches.

When we compute this equation, we obtain:

Volume 1/3 3.14159 inches, 6.25 inches6.5 x 2 inches.

81.6816 cubic inches of volume.

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The Area of Trapezium is 50, 267 mm².

We have,

base 1 = 224 mm

base 2 = 77 mm

Height = 334 mm

Now, Area of Trapezium

= 1/2 (Sum of parallel side) x height

= 1/2 (224 + 77) x 334

= 1/2 x 301 x 334

= 50, 267 mm²

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Answer:

50

Step-by-step explanation:

Sum of angles in a circle is 360,

145 + 165 + x = 360

310 + x = 360

x = 360 - 310

x = 50