Sophie invested $92,000 in an account paying an interest rate of 6 1/8% compounded

continuously. Damian invested $92,000 in an account paying an interest rate of 6 5/8%

compounded monthly. After 14 years, how much more money would Damian have in

his account than Sophie, to the nearest dollar?

From the graphing utility, we get the value of the integral as, Integral = 0.7206 Comparing the values of the integrals obtained from Trapezoidal rule, Simpson's rule and graphing utility, we find that the integral value obtained from the graphing utility is closest to the Simpson's rule.

We are given the definite integral ∫31ln(x)dx and we are required to approximate the integral using the trapezoidal rule and Simpson's rule. Also, we are supposed to compare these results with the approximation of the integral using a graphing utility using n=4.Trapezoidal Rule. The trapezoidal rule for numerical integration is a method to approximate the definite integral using linear interpolation.

This rule approximates the definite integral by dividing the total area into trapezoids. The formula for trapezoidal rule is given by:(Image attached)Here, a = 3 and b = 1The value of h can be calculated as follows;h=(b−a)/nh=(3−1)/4=0.5We need to calculate the values of f(1), f(1.5), f(2), f(2.5), f(3) using n = 4(Image attached)The value of integral using the trapezoidal rule is,Integral = 0.7201.

Simpson's rule is used to approximate the value of definite integral. Simpson's rule involves approximating the integral under the curve using the parabolic shape. This is done by dividing the area under the curve into small sections and then approximating each section with a parabolic shape. The formula for Simpson's rule is given as:(Image attached)Here, a = 3 and b = 1

The value of h can be calculated as follows;h=(b−a)/nh=(3−1)/4=0.5We need to calculate the values of f(1), f(1.5), f(2), f(2.5), f(3) using n = 4(Image attached)The value of integral using the Simpson's rule is,Integral = 0.7200Comparing with Graphing UtilityIntegral = 0.7201 (from Trapezoidal rule)Integral = 0.7200 (from Simpson's rule).

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Answer:D

Step-by-step explanation:

The formula for sine is opposite/hypotenuse. This is the only formula that you can use with the given information.

Answer:

32.1m

Step-by-step explanation:

[tex]2\pi r*(\frac{x}{360})=[/tex] arc length of sector of a circle

2 radii + arc length of a sector of a circle= perimeter of the sector

x=90 degrees

r=9

substitute values to find the arc length

[tex]2(9)*\pi *(\frac{90}{360} )= arc length\\arclength=14.1\\[/tex][tex]14.1+2(9)=32.1[/tex]

The composite function -11-x^2 can be written in terms of the standard domain for the sine function as sin[−11−x2]. This function can be evaluated by substituting the value of x into the expression.

To do this, simply substitute the value of x into the equation:[tex]sin[-11-x^2][/tex]and evaluate the result. For example, if x=5, the equation would be sin[-11-5^2], which would evaluate to sin(-26).

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we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.

Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.

Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.

We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-

7800000-25000= 7775000m

hence, to make 7800000 from 25000 we have to add 7775000.

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3BE² + 3DF²- (2AC²- AB) is the answer of the following question

The calculation is as follows

Let E and F be the feet of the perpendiculars from B and D, respectively, to AC. We can use the fact that the area of a quadrilateral is equal to half the product of the diagonals multiplied by the sine of the angle between them to find the length of the diagonal BD.

Since ABCS is a quadrilateral, we have:

Area of ABCS = (1/2) * AC * BD * sin(angle between AC and BD)

Substituting the given values, we get:

924 = (1/2) * 33 * BD * sin(angle between AC and BD)

sin(angle between AC and BD) = 924 / (16.5 * BD)

Now, consider triangles ABC and ACD. Using the Pythagorean theorem, we can write:

AB² + BC² = AC² (1)

CD²+ BC² = AC² (2)

Adding equations (1) and (2), we get:

AB² + 2BC²+ CD²= 2AC²

Substituting AC = 33 and rearranging, we get:

BC² = (2AC²- AB² - CD²) / 2

We can also write:

BE²= AB²- AE² (3)

DF² = CD²- CF²(4)

Adding equations (3) and (4), we get:

BE² + DF²= AB²+ CD² - AE²- CF²

Substituting BC²from earlier, we get:

BE²+ DF² = 2AC² - BC²- AE²- CF²

We want to find BE + DF. Squaring both sides of equation (3), we get:

BE²= AB² - AE²

AE²= AB²- BE²

Similarly, squaring both sides of equation (4), we get:

DF²= CD²- CF²

CF²= CD² - DF²

Substituting these expressions into the equation for BE²+ DF², we get:

BE²+ DF² = 2AC² - BC² - (AB² - BE²) - (CD²- DF²)

Simplifying, we get:

BE² + DF²= 2AC² - BC²- AB²- CD² + 2BE² + 2DF²

Collecting like terms, we get:

BE²+ DF²- 2BE² - 2DF²= 2AC²- BC² - AB² - CD²

Simplifying, we get:

BE²- DF² = 2AC²- BC²- AB²- CD²- 2BE² - 2DF²

Substituting the values we know, we get:

BE²- DF²= 2(33)²- BC²- AB² - CD²- 2BE²- 2DF²

Rearranging, we get:

3BE²+ 3DF² - BC²- AB²- CD²= 2(33)² - 924

Substituting BC^2 from earlier, we get:

3BE²+ 3DF² - (2AC²- AB)

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In order to have an average speed of 4 mph for the entire trip, you would need to run at a speed of 7 mph for the next 0.5 hours after walking for 1.5 hours at 3 mph.

Let's begin by calculating the total distance covered during the entire trip, which is:

distance = (time walked) x (walking speed) + (time ran) x (running speed)

We know that the time walked is 1.5 hours and the walking speed is 3 mph, so the distance covered during walking is:

distance walked = (time walked) x (walking speed) = 1.5 x 3 = 4.5 miles

We also know that the average speed for the entire trip is 4 mph, and that the total time for the trip is 2 hours. Therefore, the distance covered during the entire trip is:

distance = (average speed) x (total time) = 4 x 2 = 8 miles

So the distance covered during running is:

distance ran = distance - distance walked = 8 - 4.5 = 3.5 miles

Now we can use the formula for average speed:

average speed = total distance / total time

To find the running speed, we need to solve for the running time, which is:

time ran = distance ran / running speed

Substituting this expression into the average speed formula, we get:

4 = (distance walked + distance ran) / (1.5 + time ran)

4 = (4.5 + 3.5) / (1.5 + distance ran / running speed)

Simplifying this expression, we get:

1.5 + distance ran / running speed = 2

distance ran / running speed = 0.5

Substituting the values we calculated, we get:

3.5 / running speed = 0.5

Solving for the running speed, we get:

running speed = 3.5 / 0.5 = 7 mph

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Answer:

(3480 - 600)/2 = 1440cm

Step-by-step explanation:

The sample size is 12 with an error calculation of 5 if 97% of the confidence interval is around a sample mean of 31. 3.

Percent confidence = 97

Sample mean =  31. 3

Standard deviation = 7. 6

Sample size = 40

Error calculation = 5

The formula for a confidence interval using the t-distribution is:

CI = x ± tα/2 * (s/√n)

CI = 31.3 ± 2.423 * (7.6/√40)

CI = 31.3 ± 3.940

CI = (27.36, 35.24)

The population mean with an error of 5,

n = (Zα/2 * σ / E)^2

Assuming a 95% confidence level, the sample size is,

n = (1.96 * 7.6 / 5)^2

n = 11.69

Therefore we can conclude that the sample size is 12 with an error calculation of 5.

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Answer:

Total number bags is 36

1:2:3 the answer

The number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is 4680.

Step by step explanation:
The number of positive integers with exactly four decimal digits between 1000 and 9999 inclusive can be obtained as follows:

Total number of four decimal digits = 9999 − 1000 + 1 = 9000
Numbers that are multiples of 5 are obtained by starting with 1000 and adding 5, 10, 15, 20, ..., 1995, that is, 5k, where k = 1, 2, 3, ..., 399.

Therefore, the number of positive integers with exactly four decimal digits that are multiples of 5 is 399.

Numbers that are multiples of 7 are obtained by starting with 1001 and adding 7, 14, 21, 28, ..., 1428, that is, 7m, where m = 1, 2, 3, ..., 204.

Therefore, the number of positive integers with exactly four decimal digits that are multiples of 7 is 204.

Note that some numbers in the interval [1000, 9999] are divisible by both 5 and 7. Since 5 and 7 are relatively prime, the product of any number of the form 5k by a number of the form 7m is a multiple of 5 × 7 = 35.

The numbers of the form 35n in the interval [1000, 9999] are

1035, 1070, 1105, 1140, ..., 9945, 9980.
We can check that there are 285 numbers of this form.

To find the number of positive integers with exactly four decimal digits that are not divisible by either 5 or 7, we will subtract the number of multiples of 5 and 7 and add the number of multiples of 35.

Therefore, the number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is

9000 - 399 - 204 + 285 = 4680.

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Answer:

[tex]{ \sf{a = { \blue{ \boxed{{53 \: \: \: \: \: \: \: \: }}}}} \: cm}[/tex]

Step-by-step explanation:

[tex] { \mathfrak{formular}}\dashrightarrow{ \rm{4 \times side \: length}}[/tex]

Each side has length of a?

[tex]{ \tt{perimeter = a + a + a + a}} \\ \dashrightarrow{ \tt{ \: 212 = 4a}} \\ \\ \dashrightarrow{ \tt{4a = 212}} \: \\ \\ \dashrightarrow{ \tt{a = \frac{212}{4} }} \: \: \\ \\ { \tt{a = 53 \: cm}}[/tex]

The star Proxima Centauri is 4.2 light-years away from Earth, making it the sun's nearest rival. The word "nearest" means "nearest" in Spanish.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

Hence, The star Proxima Centauri is 4.2 light-years away from Earth, making it the sun's nearest rival. The word "nearest" means "nearest" in Spanish.

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Answer:

we bought 12 $3 clearance mystery books and 5 $8 regular-priced science fiction books.

Step-by-step explanation:

You can make all four sides of each trapezoid different. Since a trapezoid has four sides, we can change the length of each of the remaining two sides to create different trapezoids. option B is correct.

A trapezoid is a four-sided polygon with two parallel sides and two non-parallel sides. It is sometimes called a trapezium outside of North America. The parallel sides of a trapezoid are called bases, while the non-parallel sides are called legs. The height of a trapezoid is the perpendicular distance between the bases. The area of a trapezoid is calculated by taking the average of the bases and multiplying it by the height. Trapezoids are commonly encountered in geometry and are used in many real-world applications, such as in construction and engineering.

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An interpretation of the IQR and median in the context of the data set include the following: D. The range of the middle 50% of the lengths of garter snakes is 4 inches.

Based on the information provided about the given box-and-whisker plot (see attachment), the five-number summary for the given data set include the following:

In Mathematics, the range of a data set can be calculated by using this mathematical expression;

Range = Highest number - Lowest number

Range = 30 - 10

Range = 20

Interquartile range (IQR) = Q₃ - Q₁

Interquartile range (IQR) = 29 - 24

Interquartile range (IQR) = 5

Middle 50% of the lengths = 20/5 = 4 inches.

In conclusion, the median is the middle of the data set and it means 50 percent of the lengths of the garter snakes are greater and 50 percent are less than 27 inches.

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Answer:

To solve the integral, we can use partial fractions and then integrate each term separately. The integrand can be written as:

[tex]\dfrac{x^4(1-x)^4}{1+x^2} = \dfrac{x^4(1-x)^4}{(x+i)(x-i)}[/tex]

Using partial fractions, we can write:

[tex]\dfrac{x^4(1-x)^4}{(x+i)(x-i)} = \dfrac{Ax+B}{x+i} + \dfrac{Cx+D}{x-i}[/tex]

Multiplying both sides by (x+i)(x-i), we get:

[tex]x^4(1-x)^4 = (Ax+B)(x-i) + (Cx+D)(x+i)[/tex]

Substituting x=i, we get:

[tex]i^4(1-i)^4 = (Ai+B)(i-i) + (Ci+D)(i+i)[/tex]

Simplifying, we get:

[tex]16 = 2Ci + 2B[/tex]

Substituting x=-i, we get:

tex^4(1+i)^4 = (Ci+D)(-i-i) + (Ai+B)(-i+i)[/tex]

Simplifying, we get:

[tex]16 = 2Ai + 2D[/tex]

Substituting x=0, we get:

[tex]0 = Bi + Di[/tex]

Substituting x=1, we get:

[tex]0 = A+B+C+D[/tex]

Solving these equations simultaneously, we get:

A = -22/7 + π

B = 0

C = 22/7 - π

D = -2/5

Therefore, the integral can be written as:

[tex]\int_0^1 \dfrac{x^4(1-x)^4}{1+x^2}dx = \int_0^1 \left[\dfrac{-22/7+\pi}{x+i} + \dfrac{22/7-\pi}{x-i} - \dfrac{2/5}{1+x^2}\right]dx[/tex]

Integrating each term separately, we get:

[tex]\int_0^1 \dfrac{-22/7+\pi}{x+i}dx = [-22/7+\pi]\ln(x+i) \bigg|_0^1 = [\pi-22/7]\ln\left(\dfrac{1+i}{i}\right)[/tex]

[tex]\int_0^1 \dfrac{22/7-\pi}{x-i}dx = [22/7-\pi]\ln(x-i) \bigg|_0^1 = [22/7-\pi]\ln\left(\dfrac{1-i}{-i}\right)[/tex]

[tex]\int_0^1 \dfrac{-2/5}{1+x^2}dx = -\frac{2}{5}\tan^{-1}(x)\bigg|_0^1 = -\frac{2}{5}\tan^{-1}(1) + \frac{2}{5}\tan^{-1}(0) = -\frac{2}{5}\tan^{-1}(1)[/tex]

Therefore, the correct options are:

A) [tex]\pi-\frac{22}{7}[/tex]

B) [tex]\frac{2}{105}[/tex]

C) 0

D) [tex]\frac{71}{15}-\frac{3\pi}{2}[/tex]

The point-slope form of the line equation that passes through the points (- 9, - 9) and (- 8, 1) is equals to the y= 10x + 81.

The standard equation of a line is, y = mx + b where m is the slope and b is the y-intercept. This is a very useful form of the linear equation when comparing lines. We have to determine the equation of the line that passes through the points (- 9, - 9) and (- 8, 1). First we determine the value of slope of line. The formula for slope of line that passing through the points (x₁,y₁),(x₂,y₂) is [tex]m = \frac{y_2 - y_1}{x_2- x_1} [/tex]

here, x₁ = -9, y₁ = -9 , x₂ = -8, y₂ = 1, so

[tex]m = \frac{1-(-9)}{-8-(-9)} = \frac{10}{1} = 10[/tex]

The point-slope form for line passing through points (x₁,y₁),(x₂,y₂) is y − y₁ = m(x − x₁)

=> y - (-9) = 10( x -(-9))

=> y + 9 = 10( x + 9)

=> y + 9 = 10x + 90

=> y = 10x + 81

Hence required equation is y = 10x + 81.

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0, which is less than 0.01.

Suppose that X is a uniformly distributed random variable, scaled so that it has zero mean and unit variance. (1) What is P{|X|> ox}? (2) What is P{[X] > 30x}? (3) Is X spiky? Be sure to consider both positive and negative values of X.

For a uniformly distributed random variable with mean 0 and variance 1, P{|X|> ox} is equal to 0.5. (2) For a uniformly distributed random variable with mean 0 and variance 1, P{[X] > 30x} is equal to 0. (3) X is not spiky since P{|X| > 30x}

0.000045, which is greater than 0.01.
Suppose that Y is a Laplacian random variable with a pdf given by: fy(u) 2 e 2 -Au-hel, -  Oy}? (2) What is P{İY| > 30y}? (3) Is Y spiky? Be sure to consider both positive and negative values of Y.
Answer: (1) For a Laplacian random variable with mean 0 and variance 1, P{|Y|> oy} is equal to 0.5. (2) For a Laplacian random variable with mean 0 and variance 1, P{[Y] > 30y} is equal to 0.000045. (3) Y is spiky since P{|Y| > 30y}

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The value of x= 10.2.

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

Hence, The value of x= 10.2.

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The probability of rolling one of these five numbers is 5/37.

Suppose you roll a special 37-sided die. The probability that one of the following numbers is rolled is as follows:

35 | 25 | 33 | 9 | 19.

The total number of sides of a die is 37. As a result, there are 37 numbers in the die.

Rolling one of the 5 given numbers implies that you can select either 35 or 25 or 33 or 9 or 19.

Therefore, the probability of rolling any of these numbers is:

1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 = 5 / 37

So, the probability of rolling one of these five numbers is 5/37.

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The width of the rectangle whose length of one side is 7.8 feet and the area enclosed is 5 feet is given as 40/7 feet.

Area refers to the field on the ground which is enclosed by the closed polygon. It is defined within the boundary of the closed polygon. Open polygons cannot have a deterministic area. In the given problem, the length of one side is 7/8 feet and the area of the rectangle is 5 feet.

It is known that area of rectangle is equal to the product of its length and its width.

∴Area of rectangle = Length × width

⇒ 5 = 7/8 × width

⇒ width = (5 × 8)÷7 = 40/7 feet

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The Answer: The first step is Rearranging the Equation

v=9

v=-5

Step-by-step explanation:

STEP

1

:

Rearrange this Absolute Value Equation

Absolute value equalitiy entered

     4|-v+2|-3 = 25

Another term is moved / added to the right hand side.

     4|-v+2| = 28

STEP

2

:

Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is 4|-v+2|

For the Negative case we'll use -4(-v+2)

For the Positive case we'll use 4(-v+2)

STEP

3

:

Solve the Negative Case

     -4(-v+2) = 28

    Multiply

     4v-8 = 28

    Rearrange and Add up

     4v = 36

    Divide both sides by 4

     v = 9

STEP

4

:

Solve the Positive Case

     4(-v+2) = 28

    Multiply

     -4v+8 = 28

    Rearrange and Add up

     -4v = 20

    Divide both sides by 4

     -v = 5

    Multiply both sides by (-1)

     v = -5

    Which is the solution for the Positive Case

STEP

5

:

Wrap up the solution

v=9

v=-5

The amount that each type would be 11.87 lbs of cashews and 15.13 lbs of brazil nuts

1. First, find the total cost of 27 lbs of the mixture: 27 lbs x $6.41/lb = $171.07.
2. Next, find the cost of cashews and brazil nuts in the mixture. Cashews cost $7.70/lb and brazil nuts cost $4.80/lb.
3. Subtract the cost of the brazil nuts from the total cost of the mixture: $171.07 - (27 lbs x $4.80/lb) = $105.27.
4. Divide the cost of the cashews ($105.27) by the cost of one pound of cashews ($7.70): $105.27/$7.70 = 13.66 lbs.
5. Subtract the number of pounds of cashews (13.66) from the total pounds of the mixture (27) to find the number of pounds of brazil nuts: 27 - 13.66 = 15.13 lbs.
6. Therefore, the mixture should contain 11.87 lbs of cashews and 15.13 lbs of brazil nuts.

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Answer:

112°

Step-by-step explanation:

Finding the unknown angle in a quadrilateral:

        Sum of all angles of a quadrilateral = 360

                                      a + 49 + 72 + 127 = 360

                                                     a + 248  = 360

                                                                a = 360 - 248

                                                                a = 112°

Each pair of children gets to bat for 7.5 minutes.

To find out how much time each pair gets to bat, we need to divide the total session time by the number of pairs of children who bat.

Number of pairs of children who bat = 6 groups x 1 pair/group = 6 pairs

Total time for the session = 45 minutes

Time per pair of children who bat = Total time / Number of pairs of children who bat

= 45 minutes / 6 pairs

= 7.5 minutes per pair

Therefore, each pair of children gets to bat for 7.5 minutes.

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well, we know the discount is just 30 - 21 = 9, so hmm if we take 30(origin amount) to be the 100%, what's 9 off of it in percentage?

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 30 & 100\\ 9& x \end{array} \implies \cfrac{30}{9}~~=~~\cfrac{100}{x} \\\\\\ 30x=900\implies x=\cfrac{900}{30}\implies x=30[/tex]