Find the first five non-zero terms of Maclaurin series (Taylor series centered at x=0) for the function below as well as radius of convergence.
f(x)=xe^x

Tom had 60 dollars as his pocket money initially.

Let's assume that Tom had x dollars as his pocket money.

He spent 2/3 of his pocket money on apples, which means he spent (2/3)x dollars on apples.

He had 1/3 of his pocket money left after buying the apples.

Out of the remaining money, he spent 1/4 on bananas, which means he spent (1/4)(1/3)x = (1/12)x dollars on bananas.

The total amount spent on apples and bananas is given as $45. So, we can write the equation:

(2/3)x + (1/12)x = 45

Multiplying both sides by 12 to get rid of the fractions:

8x + x = 540

Simplifying, we get:

9x = 540

Dividing both sides by 9:

x = $60

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Answer:

We can first write 3 3/4 as an improper fraction:3 3/4 = 15/4Then, using the distributive property, we get:12 • 3 3/4 = 12 • (3 + 3/4) = 12 • 3 + 12 • 3/4 = 36 + 9 = 45Therefore, 12 • 3 3/4 simplifies to 45.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathtt{12\times 3\dfrac{3}{4}}[/tex]

[tex]\mathtt{= 12 \times \dfrac{3\times4+3}{4}}[/tex]

[tex]\mathtt{= 12\times\dfrac{12 + 3}{4}}[/tex]

[tex]\mathtt{= 12\times\dfrac{15}{4}}[/tex]

[tex]\mathtt{= \dfrac{12}{1}\times\dfrac{15}{4}}[/tex]

[tex]\mathtt{= \dfrac{12\times15}{4\times1}}[/tex]

[tex]\mathtt{= \dfrac{180}{4}\rightarrow 180\div4 \rightarrow \bold{12(3 + \dfrac{3}{4}})\rightarrow 12(3) + 12(\dfrac{3}{4})\rightarrow 36 + 9}[/tex]

[tex]\mathtt{= 45}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathtt{12(3 + \dfrac{3}{4})\ which\ gives\ you\ \bf 45}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: The diameter of the drawing of the planet= 14 mm

Step-by-step explanation:

Given: In a drawing of the solar system the scale is 1 mm = 500 km

which means [tex]1 \ km=\frac{1}{500}mm[/tex] on the drawing.

The diameter of planet =7000 kilometers.

Then the diameter of the drawing of the planet [tex]=\frac{7000}{500}=14[/tex]

Therefore, the diameter of the drawing of the planet= 14 mm.

a. There are 1,000 different possible selections.  b. The probability of winning is 1/1,000, or 0.001.  c. If you win, your net profit is $476.05.  d. The expected value is $0.476.  e. The Pick 4 game is better.

a.  There are 1,000 different possible selections (000 to 999).

b.  The probability of winning is 1/1,000, or 0.001.

c.  If you win, your net profit is $476.05. This can be calculated by,

$477.38 - $1.33 = $476.05

d. The expected value is $0.476. This can be calculated by,

$476.05 * 0.001 = $0.476

e. The Pick 4 game is better.
The expected value of a Pick 3 bet is $0.476, while the expected value of a Pick 4 bet is $0.85. The Pick 4 bet is better because it has a higher expected value. This is because the Pick 4 game has more possible selections, meaning the odds of winning are lower than the Pick 3 game, but the prize is larger. So, the expected value for Pick 4 is larger than Pick 3. The expected value of a bet is the amount of money you can expect to win if you make the same bet over and over again, so a higher expected value means you have a better chance of making a profit in the long run.

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Answer:

z=1.20

Step-by-step explanation:

Just Took Test

The area of the parallelogram will equal to Area of the rectangle

The area of a parallelogram is given by the formula:

Where A is the area of the parallelogram,

b is the length of the base of the parallelogram,

h is the height of the parallelogram.

The area of a rectangle is given by the formula:

Where A is the area of the rectangle  

l is the length of the rectangle  

w is the width of the rectangle.

Here we have a Parallelogram    

Where the height of the parallelogram is 4.5 cm and the length is 7 cm  

Using the formula,

Area of parallelogram = 4.5 cm × 7 cm = 31.5 cm²

From the data,

The length of a rectangle is 7 cm and width is 4.5 cm

Using the formula,

Area of the rectangle = 7 cm × 4.5 cm = 31.5 cm²  

Therefore,

The area of the parallelogram will equal to Area of the rectangle

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There are 36 different outfits that can be created using six tops, three pants, and two jackets.

Combinations refer to the ways in which a set of objects or items can be arranged or chosen without regard to their order.

In mathematics, a combination is a selection of objects from a larger set, where the order of the selected objects does not matter.

Here we have

A designer has designed different tops, pants, and jackets to create outfits.  

Number of options for tops = 6

Number of options for pants = 3

Number of options for jackets = 2

Here,

The total number of different outfits that can be created = (No of options for tops) × (No of options for pants) × (No of options for jackets)  

= 6 × 3 × 2

Therefore,

There are 36 different outfits that can be created using six tops, three pants, and two jackets.

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Devon's height when he was in second grade was 312 feet 3 and 1 half feet.

The proper explanation of this answer is given below. Devon's height .

To arrive at this answer, we must subtract 116 feet from 423 feet, which is the height that Devon is currently measuring as a fifth grader. 423 feet - 116 feet = 307 feet. However, we know that his height was 312 feet 3 and 1 half feet, which is 5 feet more than 307 feet. Therefore, we can add 5 feet to 307 feet to get the answer, 312 feet 3 and 1 half feet.

The height that Devon is now measuring as a fifth grader is 423 feet, so we must subtract 116 feet from that measurement to get this answer. 307 feet Equals 423 feet minus 116 feet. Yet, we are aware of his height, which was 312 feet 3 and a half feet, or 5 feet taller than 307 feet. In order to obtain the solution, 312 feet 3 and a half feet, we can add 5 feet to 307 feet.

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The size of angle x is equal to 100°.

Based on the identical isosceles triangles ΔABD and ΔACD, we can logically deduce the following:

m∠DAB = 25°

AD = BD = CD

In triangle ΔABD, we have:

AD = BD (Given)

m∠DBA = ∠DAB (Angle opposite to equal sides are congruent)

m∠DBA = 25°.

Next, we would determine the measure of m∠ADB;

m∠DBA + m∠DAB + m∠ADB = 180° (Sum of angle in a triangle)

25° + 25° + m∠ADB = 180°

m∠ADB = 180° - 50°

m∠ADB = 130°.

Since ΔABD and ΔACD are two identical isosceles triangles, we have:

m∠DCA = m∠DBA

m∠DCA = 25°

Similarly, we have:

m∠DAC = m∠DAB = 25°

m∠ADC = m∠ADB = 130°

Generally speaking, we know that a complete revolution (circle) is equal to 360°:

m∠ADC + m∠ADB + m∠CDB = 360°

130° + 130° + x = 360°

x = 360° - 260°

x = 100°.

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A plane traveled 630 kilometers each way to Toronto and back. The trip there was with the wind. It took 7 hours. The trip back was into the wind. The trip back took 15 hours. The speed of the plane in still air is 66 km/h, and the speed of the wind is 24 km/h.

Let's use the following variables:

When the plane is flying with the wind, its effective speed is p + w. When it is flying against the wind, its effective speed is p - w.

We know that the distance to Toronto and back is 630 km each way, for a total of 1260 km. We also know that the time it took to fly to Toronto with the wind was 7 hours, and the time it took to fly back against the wind was 15 hours.

Using the formula distance = speed x time, we can set up the following equations:

630 = (p + w) x 7 (equation 1)

630 = (p - w) x 15 (equation 2)

We now have two equations with two unknowns. We can solve for either p or w in terms of the other variable. Let's solve for p in terms of w.

From equation 1, we get:

p + w = 90

From equation 2, we get:

p - w = 42

Adding the two equations, we get:

2p = 132

So,

p = 66 km/h

Now we can use either equation 1 or equation 2 to solve for w. Let's use equation 1:

630 = (66 + w) x 7

Simplifying this equation, we get:

90 = 66 + w

w = 24 km/h

Therefore, the speed of the plane in still air is 66 km/h, and the speed of the wind is 24 km/h.

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The equation of the line that is perpendicular to line m and passes through the point (3, 2) is y = (2/5)x + 4/5.

To find the equation of a line that is perpendicular to line m, we need to know the slope of line m.

The slope of line m can be found using the two given points on the line, (0, -3) and (-2, 2):

slope of line m = (change in y) / (change in x) = (2 - (-3)) / (-2 - 0) = 5 / (-2) = -5/2

A line perpendicular to m will have a slope that is the negative reciprocal of -5/2. The negative reciprocal is obtained by flipping the fraction and changing its sign.

slope of line perpendicular to m = -1 / (-5/2) = 2/5

Now we have the slope of the line perpendicular to m and a point that it passes through, (3, 2). We can use the point-slope form of the equation of a line to find its equation:

y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Substituting in the values we have:

y - 2 = (2/5)(x - 3)

Simplifying:

y - 2 = (2/5)x - (6/5)

y = (2/5)x - (6/5) + 2

y = (2/5)x + 4/5

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Answer:

x= 100

Step-by-step explanation:

x/5 = 20

multiply both the sides by 5 we get

5× x/5 = 20×5

x = 100

Answer:

x=2

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

Answer:

52.

Step-by-step explanation:

So 143 members represent 100% of the population of the problem. A ratio of 4:7 similarly represent 100%. First, you need to get the value of 4:7 in a representation of 100%. You can do that by adding the two (4+7=11) and then dividing it by each value of it. So 7 divided by 11 is .6363, or 63.63% of the whole. Then 4 divided by 11 is .3636, or 36.36% of the whole. After getting this, seeing that the ratio for union members to non union members is 4 union members to 7 nonunion members, and there are 143 employees in total, just get the value of 36.36% of 143; in this case, it's 51.99 - rounded off to 52 employees.

Answer:

52 members

Step-by-step explanation:

Proportional setup.

(4/11)=(x/143)

Answer:

28√2 units.

Step-by-step explanation:

Let's denote the length of a side of the square as "s". We know that the diagonal of the square is √2 times the length of a side, so we can write:

√2 s = 14

Solving for "s", we can divide both sides by √2:

s = 14 / √2

To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √2:

s = (14 / √2) x (√2 / √2) = 14√2 / 2 = 7√2

Now we can find the perimeter of the square by adding up the lengths of all four sides:

Perimeter = 4s = 4(7√2) = 28√2

Therefore, the perimeter of the square is 28√2 units.

Answer:

1 and -1

Step-by-step explanation:

[tex]5 - \sqrt[3]{( {x}^{2} - 9 } = 7[/tex]

[tex] - \sqrt[3]{( {x}^{2} - 9} = 7 - 5[/tex]

[tex]- \sqrt[3]{( {x}^{2} - 9} = 2[/tex]

[tex] \sqrt[3]{( {x}^{2} - 9} = - 2[/tex]

Cube both sides of the equation:

[tex] {x}^{2} - 9 = { - 2}^{3} [/tex]

[tex] {x}^{2} - 9 = - 8[/tex]

[tex] {x}^{2} = - 8 + 9[/tex]

[tex] {x}^{2} = 1[/tex]

[tex] {x}^{2} - 1 = 0[/tex]

[tex](x - 1)(x + 1) = 0[/tex]

[tex]x = 1 \: \: or \: \: x = - 1[/tex]

[tex]5-\sqrt[3]{x^2-9}=7\implies 5=\sqrt[3]{x^2-9}+7\implies -2=\sqrt[3]{x^2-9} \\\\\\ (-2)^3=(\sqrt[3]{x^2-9})^3\implies -8=x^2-9\implies 1=x^2 \\\\\\ \pm\sqrt{1}=x\implies \pm 1 = x[/tex]

Therefore, the measure of the area of rhombus EFGH is 252 square units.

A rhombus is a four-sided geometric shape that has the following properties:

All four sides are of equal length.

Opposite sides are parallel to each other.

The angles formed between adjacent sides are equal (i.e., they are all congruent).

The diagonals of a rhombus bisect each other at right angles, meaning they intersect at a 90-degree angle. Additionally, the length of one diagonal is equal to the product of the length of the other diagonal and the sine of one of the angles formed by adjacent sides.

by the question.

[tex]EK^2 = EG^2/4 + KH^2 (where KH is half the length of FH)EK^2 = 36^2/4 + (14/2)^2EK^2 = 324 + 49EK^2 = 373EK = sqrt(373)[/tex]

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The values of x = 17 and y = 0.

Define quadratic equation?

A quadratic equation is a second-degree polynomial equation in one variable of the form a + b + c = 0, where a, b, and c are constants and x is the variable. The term "quadratic" comes from the Latin word "quadratus", which means square.

Given:

[tex]x^{4} - 8x^{2} y^{2} +16y^{4} -289[/tex] equals to 0

[tex]x^{4} - 8x^{2} y^{2} +16y^{4} -289 = 0[/tex]

[tex]x^{4} - 8x^{2} y^{2} +16y^{4} =289[/tex]

We know that [tex](x-b)^{2} =x^{2} -2xy +y^{2}[/tex]

Compare it: [tex](x^{2} -4y^{2} )^{2} = x^{4} - 8x^{2} y^{2} +16y^{4}[/tex]

So, [tex](x^{2} -4y^{2} )^{2} = 289[/tex]

[tex](x^{2} -4y^{2} ) = 17[/tex]

We know that [tex](x^{2} -b^{2} ) = (x+y)(x-y)[/tex]

So, [tex](x +2y)(x-2y) =17[/tex]

If we solve two equations that is:

(x+2y) = 17 and  (x-2y) = 17

Simplification, x = 17 and y = 0

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1. An equation for Lin is y = 1/3x + 8.

2. An equation for Diego is y = 2/3x + 6.

3. The intersection point of the solution is (6, 10).

Let there have total number of balloons are y.

Lin fills her balloons at a rate of 1/3 ounce per second.

So she filled 1/3 x balloons.

She has already filled balloons with 8 ounces of water.

So the required equation is;

y = 1/3x + 8.................(1)

Diego fills her balloons at a rate of 2/3 ounce per second.

So he filled 2/3 x balloons.

He has already filled balloons with 6 ounces of water.

So the required equation is;

y = 2/3x + 6.................(2)

To determine the intersecting point we solve the both equation.

Subtract equation 1 and 2, we get

1/3x + 8 - 2/3x - 6 = 0

-1/3x + 2 = 0

Subtract 2 on both side, we get

-1/3x = -2

Multiply by -3 on both side, we get

x = 6

Now put the value of x in equation 1

y = 1/3 × 6 + 8

y = 10

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False. A data set of the heights of 12-year-old boys would not necessarily follow a normal distribution pattern as it may be skewed or not evenly distributed around the mean.

False. A normal distribution is a type of probability distribution that takes the shape of a bell curve. It is characterized by having an equal number of values on either side of the mean, with the values in the middle being more numerous than those on the outside. A data set of the heights of all 12-year-old boys who live on a given street in the city of Grand Rapids would not necessarily fit this pattern. It is possible that the data set may be skewed in one direction or the other, depending on the height of the tallest and shortest boys in the group. It is also likely that the data will not be evenly distributed around the mean, as some boys may be taller or shorter than others.

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The answer of the given question based on the following equations are  the order of the variables from least to greatest is c, a, b, since c = 18 is the smallest, followed by a = 36, and b = 72 is the largest.

A variable is  symbol or letter used to represent  value that can change or vary. Variables are commonly used in the algebra and other branches of mathematics to represent the unknown quantities, as well as in a scientific and engineering applications to represent the physical parameters and measurements.

In algebra, variables are typically represented by the letters such as x, y, z, a, b, c, etc.

To solve this problem, we first need to solve each equation for its respective variable, a, b, and c.

a - 5 = 31

Adding 5 to both sides, we get:

a = 36

1/2b - 5 = 31

Adding 5 to both sides and multiplying by 2, we get:

b = 2(31 + 5) = 72

2c - 5 = 31

Adding 5 to both sides and dividing by 2, we get:

c = (31 + 5)/2 = 18

Therefore, the order of the variables from least to greatest is c, a, b, since c = 18 is the smallest, followed by a = 36, and b = 72 is the largest.

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Yes, the triangles ∆AOR and ∆EOD are similar. By Angle-Angle similarity rule, triangle AOR is similar to triangle EOD.

See the above figure, it consists two triangles say ∆AOR and ∆EOD. Now, we check whether both of triangles are similar or not. Similar triangles are are the triangles that have corresponding sides in ratio to each other and corresponding angles equal to each other. It's time to check the similarity property in ∆AOR and ∆EOD.

In ∆AOR, measure of angle R = 105°

In ∆EOD, measure of angle D = 35°

measure of angle DOE = 40°

Sum of interior angles of triangle = 180°

so, measure of angle E = 180° - 35° - 40°

= 105°

Now, in ∆AOR and ∆EOD,

Measure of angle R = measure of angle E = 105° ( since equal angles)

Measure of angle AOR = measure of angle EOD ( corresponding angles)

Thus, two angles of triangle EOD are congruent or equal to the corresponding angles of another triangle, AOR. So, by Angle-Angle ( AA) congruence rule, ∆AOR is similar to the ∆EOD.

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Complete question:

See the above figure, Are the triangles similar? If yes, write a similarity statement and explain how you know they are similar.

the tax estimated to be collected by the government during the financial year 2020/21 is 666.9 billion rands.

why it is and what is a financial year?

The tax estimated to be collected by the government during the financial year 2020/21 is not explicitly given in the table. However, the total revenue collected by the government during the financial year 2020/21 is given, which is:

666.9 billion rands

Therefore, the tax estimated to be collected by the government during the financial year 2020/21 is 666.9 billion rands.

A financial year (also known as fiscal year) is a period of 12 months that a company or government uses for financial reporting and accounting purposes. It does not necessarily correspond to the calendar year, which is a period of 12 months starting on January 1st and ending on December 31st.

The financial year is important because it helps organizations to keep track of their financial performance over a consistent period of time, which facilitates comparison of financial results from year to year. The financial year is often chosen to align with a company's operational cycle, which may be seasonal or have other considerations that affect the timing of revenues and expenses.

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The 99% confidence interval for the average length (in inches) of all six-month-old boys is 27.74 in. to 27.98 in. The correct answer is E

This is calculated using the average length (27.6 in.) and standard deviation (0.28 in.) recorded by the pediatrician. To calculate the confidence interval, you need to calculate the margin of error. The margin of error is found using the following formula:

ME = (Critical Value) x (Standard Deviation/√Sample Size)

For a 99% confidence interval, the critical value is 2.58. Therefore, the margin of error for this sample is (2.58) x (0.28/√50) = 0.24 in. This means that the 99% confidence interval for the average length of all six-month-old boys is 27.6 in. ± 0.24 in., or 27.74 in. to 27.98 in. The correct answer is E

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Answer: $100,000

Step-by-step explanation:

$100,000. This is because the balance in the account varies jointly with principal, the annual interest rate, and time measured in years with a constant of proportionality of 1. Therefore, the balance in the account at the end of 50 years is 10,000 × 1 × (1 + 0.05)50, which is equal to $100,000.

Answer:

$35000

Step-by-step explanation:

account worth = deposit + simple interest

/ 100

 intrest = deposit x year x simple interest

10000×50×5/100=25000

account worth = deposit + simple interest

 = 10000 + 25000

 = $ 35000

To estimate the proportion of Hispanic customers in a particular state to within 0.04 accuracy and with 99% confidence, you need a sample size of 397 customers.

To accurately estimate the proportion of Hispanic customers in a particular state to within 0.04 accuracy and with 99% confidence, you will need a sample size of 397 customers. To calculate this, you will need to use the formula:
n = ( 2z × p* × q*) / e2
Where:
- n is the sample size
- z is the Z-score associated with the confidence level (in this case, it is 2.58 for 99%)
- p* is the planning value for the population proportion (in this case, it is not known, so it should be set to 0.5)
- q* is the compliment of p* (in this case, q* = 1 - 0.5 = 0.5)
- e is the desired accuracy (in this case, e = 0.04).
Substituting the values into the formula:
n = (2.582 × 0.5 × 0.5) / 0.042 = 397.

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The store will make a net profit of $1,111.25 from selling the plants.

The first step is to calculate the total revenue from selling the plants:

Next, we need to calculate the cost of buying the plants from the wholesaler:

Cost of plants = 500 x $2.49

Cost of plants = $1,245.00

The net profit is then the difference between the total revenue and the cost of buying the plants:

Net profit = Total revenue - Cost of plants

Net profit = $2,356.25 - $1,245.00

Net profit = $1,111.25

Therefore, the store will make a net profit of $1,111.25 from selling the plants.

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