A $9860 investment earns interest at
2.7% per year
compounded monthly
over 6 years. Use the compound
interest formula to calculate the value
of this investment to the nearest cent.

The fractional part that cyclist covered from his planned journey is 31/76.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

The total distance cyclist plans to travel in fraction is = 9(1/2) miles.

The distance cyclist covers in fraction is = 3(7/8) miles

The fraction of distance that cyclist travelled is -

Distance Travelled / Original distance planned

Substitute the value in the equation -

3(7/8) / 9(1/2)

Convert into improper fractions -

(31/8) / (19/2)

Use the arithmetic operation of division -

(31/8) / (19/2)

(31/8) × (2/19)

(31/4) × (1/19)

31/76

Therefore, the cyclist travelled 31/76 fraction of his planned journey.

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Using the sample proportions we know that the sample proportion of 99.7% will come between (C) 0.4925 and 0.5075.

The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.

It will be represented as a random variable by the letter P.

Both the mean and the standard deviation are P.

The formula for the sample proportion P is P=X/N, where X stands for the number of successes and N for the sample size.

You anticipate the sample fraction to reflect the outcomes.

This can frequently be ascertained by using the findings of an earlier survey or by conducting a brief pilot study.

Use 50% if you're unsure because it's conservative and produces the biggest sample size.

So, we have:

99.7% of the sample proportion and tosses were 200 times.

Then,

= 99.7/200

= 0.4985

Which comes between, .4925 and 0.5075.

Therefore, using the sample proportions we know that the sample proportion of 99.7% will come between (C) 0.4925 and 0.5075.

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Answer:

he y-intercept of the line is the point (0,-41)

Step-by-step explanation:

Hope this is right!

Step-by-step explanation:

The equation 3x + y = 0 can be rearranged to y = -3x. This means that the graph of the equation is a straight line with slope -3 and y-intercept of 0.

The three points that are in the solution set are (-2,6), (-5,5), and (3,-9). Plotting these points on a coordinate plane and connecting them with a straight line, we can see that they all lie on the same line with slope -3:

[Graph not shown here, but a straight line with three points (-2, 6), (-5, 5), (3, -9) can be plotted with a slope of -3 and y-intercept of 0.]

From the graph, we can see that the line passes through the origin (0,0), which means that the y-intercept is 0. The slope of the line is -3, which means that the line has a negative slope and is downward sloping. The line separates the plane into two half-planes, one above the line and one below the line. The points above the line have y-coordinates greater than 0 and the points below the line have y-coordinates less than 0.

A node is a point of no displacement in a standing wave. Therefore, if point P does not move, it is most likely located at a node. the points along the wave that experience maximum displacement are called antinodes.

A node is a point of no displacement in a standing wave, meaning that if the stretched string of the apparatus represented is made to vibrate, point P will not move. Point P is most likely located at a node as it experiences no displacement. A standing wave is created when two waves combine and the resulting wave is stationary. The points along the wave that experience no displacement are called nodes, and the points along the wave that experience maximum displacement are called antinodes. Nodes can be found at points that are integral multiples of half the wavelength of the wave. Therefore, it can be concluded that point P is at a node since it does not move when the string is made to vibrate.

The complete question is :

When the stretched string of the apparatus represented below is made to vibrate, point p does not move. Point p is most probably at the location of _____.

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The annual deposits that needs to be made is for amount $2352.94.

What is annuity?

Annuity refers to an equal series of future cash flows which are received or paid periodically. Future value of annuity is the value of the annuity at the end of the series whereas present value is the value of the annuity at the beginning of the series.

The annuity value can be calculated as -

Future value of annuity = Annuity x (1 - (1 + Rate)^-Number of years) / Rate

The values are given as -

Future value of annuity = $17500.00

Annuity = Identical annual deposits

Rate = 4% = 0.04

Number of years = 9

Substitute the values into the equation -

17500 = Annuity x (1 - (1 + 0.04)^-9 ) / 0.04

Annuity identical deposits = 17500 x 0.04 / ((1.04)^-9)

Annuity identical deposits = 700 / (1 - 0.7025)

Annuity identical deposits = 700 / 0.2975

Annuity identical deposits = 2352.94

Therefore, the value is obtained as $2352.94.

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Answer:

Joe mum so gaeee

Step-by-step explanation:

your answer is 1000

Answer:[tex]\frac{32\pi }{3} cm^{3}[/tex]

Step-by-step explanation:

Since the diameter is 4 cm, we know the radius is 2 cm since diameter = 2 x radius. The formula for a sphere's volume is [tex]\frac{4\pi }{3}[/tex]×[tex]r^{3}[/tex], so by plugging in 2 we get  [tex]\frac{4\pi }{3}[/tex]×[tex]2^{3}[/tex] = [tex]\frac{4\pi }{3}[/tex] x 8 = [tex]\frac{32}{3}[/tex] [tex]\pi[/tex] [tex]cm^{3}[/tex]

A quadratic function with x-intercepts as (-2,0) and (1,0) and y-intercept as (0,-2) is y = x² + x - 2.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

It is given that the x intercepts of the quadratic function are (-2,0) and (1,0).

The y intercept of the quadratic function is (0,-2).

Let the equation of the given quadratic be y = ax² + bx + c.

As the given quadratic has x intercepts as (-2,0) and (1,0) and y intercept as (0,-2).

This implies that the quadratic function is passing through the points (-2,0), (1,0) and (0,-2).

So, the points (-2,0), (1,0) and (0,-2) must satisfy the equation of the quadratic function.

As the point (-2,0) satisfy the equation of the quadratic function -

y = ax² + bx + c

0 = a(-2)² + b(-2) + c

0 = 4a - 2b + c ..... (1)

As the point (1,0) satisfy the equation of the quadratic function -

y = ax² + bx + c

0 = a(1)² + b(1) + c

0 = a + b + c ..... (2)

As the point (0,-2) satisfy the equation of the quadratic function -

y = ax² + bx + c

-2 = a(0)² + b(0) + c

-2 = c ..... (3)

Substitute the value of c in equation (1) -

0 = 4a - 2b - 2

2 = 4a - 2b ...... (4)

Substitute the value of c in equation (2) -

0 = a + b - 2

2 = a + b ...... (5)

Multiply equation (5) by 2 -

4 = 2a + 2b ...... (6)

Add equation (4) and (6) -

2 + 4 = 4a - 2b + 2a + 2b

6 = 6a

a = 1

Substitute the value of a in equation (5) -

2 = 1 + b

b = 2 - 1

b = 1

The values are a = 1, b = 1 and c = -2.

Now substitute the value of a, b and c in the quadratic function.

y = ax² + bx + c

y = (1)x² + (1)x + (-2)

y = x² + x - 2

Therefore, the quadratic function is y = x² + x - 2.

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Answer: Three days

5 men divided by the 15 days it took to dig the hole, equals 3. Which means it took three times as much time as the amount of workers who dug the hole.

This means it will take three days to dig the whole with 25 workers.

I hope this helped. Good Luck <3.

The correct explanation of each step is 1. Assume n is not even, that is, it is odd.  - Negation of the conclusion. 2.Then n = 2k + 1 for some integer k.  - Definition of an odd integer.

When one is familiar with the inverse statement, it is simple to comprehend how to construct a contrapositive statement. Take the negation of the hypothesis and the conclusion to produce the conditional statement's opposite. Create the inverted statement first, then swap the hypothesis and conclusion to create the contrapositive of the conditional statement.

3.5n + 3 = 5(2k + 1) + 3 = 10k + 8 = 2(5k + 4) - Definition of an even number

1. Assume n is not even, that is, it is odd.  - Negation of the conclusion.

2.Then n = 2k + 1 for some integer k.  - Definition of an odd integer.

3.5n + 3 = 5(2k + 1) + 3 = 10k + 8 = 2(5k + 4) - Definition of an even number Arithmetic.

4. Hence, 5n + 3 is even.

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Filling in the markup and markup rate is as follows:

      Cost       Selling Price     Markup     Markup Rate

1.   $26.97         $49.95          $22.98           85.21%

2.   $71.97         $119.95          $47.98           66.67%

3.  $40.98         $74.38          $33.40            81.5%

4.  $46.20        $69.99          $23.79            55.5%

5.  $69.29       $125.98         $56.69            81.82%

6. $149.79      $224.87         $75.08             50.12%

7. $13,250     $16,562.50   $3,312.50          25%

8. $107.97      $199.96          $91.99             85.2%

Markup represents the additional cost added to the cost price to determine the selling price.

Markup rate is based on the cost price, unlike the margin, which is computed on the selling price.

1) Markup rate = Markup/Cost Price = ($22.98/$26.97 x 100)

2) Markup rate = ($47.98/$71.97 x 100)

3) Selling price = $74.38

Markup rate = 81.5%

Cost price = 100%

Selling price = 181.5%

$74.38 = 181.5%

Cost price = $40.98 ($74.38/181.5 x 100)

4) Selling price = $69.99

Markup rate = 55.5%

Cost price = 100%

Selling price = 155.5%

$69.99 = 155.5%

Cost price = $46.20 ($69.99/151.5 x 100)

5) Selling price = $125.98

Markup = $56.69

Cost price = $69.29 ($125.98 - $56.69)

Markup rate = 81.82% ($56.69/$69.29 x 100)

6) Selling price = $224.87

Markup = $75.08

Cost price = $149.79 ($224.87 - $75.08)

Markup rate = 50.12% ($75.08/$149.79 x 100)

7) Cost price = $13,250

Markup rate = 25%

Markup = $3,312.50 ($13,250 x 25%)

Selling price = $16,562.50 ($13,250 + $3,312.50)

8) Cost price = $107.97

Markup rate = 85.2%

Markup = $91.99 ($107.97 x 85.2%)

Selling price = $199.96 ($107.97 + $91.99)

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Store A sells at cheaper rate.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Store A: y= 0.40 x

so, the unit rate is 0.40.

Store B:

The cots of 3 pound carrot= 20.16

and, the cost of 48 ounce carrot = 20.16

and, cost per ounce= 20.16 /48= 0.42

So, the unit rate is 0.42.

Thus, store A sells at cheaper rate.

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The equation of the line secant to the cubic equation y = x³ - x + 4 is equal to y = 3 · x + 4.

In this problem we find the case of a cubic equation that is intersected twice by a line, that is, a secant line. According to analytical geometry, lines are described by equations of the form:

y = m · x + b

Where:

Where the slope of the line is determined by secant line formula:

m = Δy / Δx

First, determine the slope of the secant line:

x = - 2

y = (- 2)³ - (- 2) + 4

y = - 2

x = 2

y = 2³ - 2 + 4

y = 10

m = [10 - (- 2)] / [2 - (- 2)]

m = 3

Second, calculate the intercept of the linear function:

b = y - m · x

b = 10 - 3 · 2

b = 10 - 6

b = 4

Third, write the equation of the secant line:

y = 3 · x + 4

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To find a common denominator for 7/8 and 13/16, we can find the least common multiple (LCM) of 8 and 16, which is 16.

LCM's meaning ?

lowest common factor

Describe LCM. Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

7/8 can be written as 7 * (2/2) / 8 = 7 * 2 / 16 = 7/16

13/16 is already in the form of a fraction with a denominator of 16, so no further modification is needed.

So, 7/8 can be written as 7/16 and 13/16 can be written as 13/16.

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The expression that is equivalent to (1 + cos(x))2Tangent (StartFraction x Over 2 EndFraction) ) is option D. (1 + cos(x))(sin (x))

The expression (1 + cos(x))2Tangent (StartFraction x Over 2 EndFraction) is equivalent to (1 + cos(x))(sin (x)) because of the double angle identity for tangent.

The double angle identity states that tangent of 2 times an angle is equal to 2 times the tangent of that angle divided by 1 minus the square of the tangent of that angle. In other words,

tan(2θ) = 2tan(θ)/(1 - tan2(θ))

In this expression, we have tangent of x/2, so substituting θ = x/2 gives us:

tan(x) = 2tan(x/2)/(1 - tan2(x/2))

Since cos(x) = 1 - 2sin2(x/2), we can simplify the expression to:

(1 + cos(x))2tan(x/2) = (1 + 1 - 2sin2(x/2))2tan(x/2) = (2 - 2sin2(x/2))(2sin(x/2)/(1 - sin2(x/2)))

Expanding the product of the two factors gives us the final result:

(1 + cos(x))2tan(x/2) = (2 - 2sin2(x/2))(sin(x)) = (1 + cos(x))(sin(x))

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Answer:

Greatest common factor for 14/16 is 2

Greatest common factor for 3/12 is 3

Greatest common factor for 16/28 is 4

So to simplify 14/16 it is 7/8

To simplify 3/12 it is 1/4

To simplify 16/28 it is 4/7

Step-by-step explanation:

The ratio of x to y is given by 3 : 1

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

6 ( y + 3 ) = 2 ( x + 9 )

On simplifying , we get

6y + 18 = 2x + 18

Subtracting 18 on both sides , we get

6y = 2x

Divide by 2 on both sides , we get

x = 3y

Divide by 3 on both sides , we get

x/y = 3/1

Therefore , the proportion is x : y : : 3 : 1

Hence , the ratio is 3 : 1

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Anna must sell at least approximately 1.845 books to make a profit.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

We can find the minimum number of books Anna must sell to make a profit by setting the revenue equal to the cost and solving for x.

That is, we want to find the value of x where R = C:

6.56x = 10.063 + 1.09x

5.47x = 10.063

x = 10.063 / 5.47

x = approximately 1.845 books

Hence, Anna must sell at least approximately 1.845 books to make a profit.

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The answer is 9 11/16 inches.

Distance is the total movement of an object without any regard to direction.

To find the distance on the map, we need to convert the actual distance of 125 miles into the equivalent distance on the map, using the scale of 1:1 200 000.

Let's call the distance on the map d. Then, using the scale, we can write the relationship:

d = (1/1 200 000) * 125 miles

d = 0.0001041667 miles

Since one inch on the map represents 1/1 200 000 miles in real life, the distance on the map can be calculated as:

d (in inches) = 0.0001041667 miles * (1 inch/0.0001041667 miles)

d (in inches) = 9.672

Rounding to the nearest sixteenth of an inch, the answer is 9 11/16 inches.

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15.05 + 2.5x 2.05 is the second operation and 13.95 ÷ 5 x (8.34 − 6.09) value is 6.2775, Option A is correct.

An expression is combination of variables, numbers and operators.

The given expression is 15.05 + (6.25 − 3.75) x 2.05.

By using BODMAS rule we apply the operations.

15.05 + (6.25 − 3.75) x 2.05.

Firstly we solve the expression in parenthesis.

15.05 + 2.5x 2.05.

The other expression is 13.95 ÷ 5 x (8.34 − 6.09).

2.79 x (2.25)

6.2775

Hence,  15.05 + 2.5x 2.05 is the second operation and 13.95 ÷ 5 x (8.34 − 6.09) value is 6.2775, Option A is correct.

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For square, Functions will be A=s², s=√A, s=√(d²/2), d=√2s², p=4s, s=p/4, A=(p/4)², d=√2A.

What exactly is a function?

A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output. Every function has a domain and a co-domain, as well as a range. In general, a function is denoted as f(x), where x represents the input. A function's generic representation is y = f. (x).

In mathematics, there are several types of functions. Some examples include:

When there is a mapping for a range for each domain between two sets, this is referred to be an injective function or a one to one function.

Surjective functions, also known as Onto functions, are used when more than one element is transferred from domain to range.

Polynomial function: A function made up of polynomials.

Inverse Functions: A function that may be used to inverse another function.

Now,

As given square with side of length s, diagonal of length d, perimeter P, and area A.

and Area=side²

Perimeter=4*side

diameter²=side²+side²

then A=s² and s=√A,  s=√(d²/2) and d=√2s²,  p=4s and s=p/4, A=(p/4)², d=√2A.

Hence,

            For square, Functions will be A=s², s=√A, s=√(d²/2), d=√2s², p=4s, s=p/4, A=(p/4)², d=√2A.

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The value of cos (2x) is 7/25.

Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

Given that,

sin x = -3/5 and cos (x) < 0

We have a trigonometric formula,

cos (2x) = 1 - 2 sin²(x)

Substituting the values given,

cos (2x) = 1 - 2 × (-3/5)²

             = 1 - (2 × 9/25)

             = 1 - 18/25

             = 7/25

Hence the value of cos (2x) is 7/25.

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Answer:

At point B rotate ABC clockwise 90 degrees.  Translate the figure two units to the left.  At point B dilate the figure with a scale factor of 2.

Step-by-step explanation:

In a sample of 800 students in a university, 160 or 20% are Business majors the 20% is an example of D. statistical inference.

Based on a random sample, statistical inference is a technique for determining a population's characteristics. Analyzing the correlation between the dependent and independent variables is helpful. Estimating uncertainty or sample to sample variation is the goal of statistical inference.

The technique of employing data analysis to deduce characteristics of an underlying probability distribution is known as statistical inference. By generating estimates and testing hypotheses, for instance, inferential statistical analysis infers characteristics of a population.

Therefore, option D is correct.

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Let's consider what the question asks for:

 --> perimeter of a rectangle

To find the perimeter of the rectangle:

 --> we need to know the side length

Let's consider how to find our side length:

 --> in a rectangle

     --> opposite parallel sides are equal in length

           --> in a mathematical equation, we get:

                  [tex]4x-4y=3x+5y\\2-2y=x-3y[/tex]

Now we notice,

  --> in the second equation, there is only one 'x'

        --> therefore if we find a y-value to substitute into the 'x'

            --> we can solve

Let's use the first equation to see how 'x' and 'y' relate to each other:

  [tex]4x-4y=3x+5y\\4x-3x=4y+5y\\x=9y[/tex]

Let's use that x-value and plug it the second equation:

  [tex]2-2y=x-3y\\2-2y=(9y)-3y\\2-2y=6y\\2=8y\\\\y=\dfrac{1}{4}[/tex]

Since x = 9y:

   [tex]x=9y=9*\dfrac{1}{4} =\dfrac{9}{4}[/tex]

Let's find each side length:

  [tex]4x-4y=4(\dfrac{9}{4}) -4(\dfrac{1}{4} )=9-1=8\\\\2-2y=2-2(\dfrac{1}{4} )=2-\dfrac{1}{2} =\dfrac{3}{2} =1.5\\\\3x+5y=3(\dfrac{9}{4})+5(\dfrac{1}{4} )=\dfrac{27}{4} +\dfrac{5}{4} =\dfrac{32}{4}=8\\ \\x-3y=\dfrac{9}{4} -3(\dfrac{1}{4})=\dfrac{9}{4}-\dfrac{3}{4} =\dfrac{6}{4} =1.5[/tex]

Let's add up the side length to find the perimeter:

 [tex]\text{Perimeter}=8+1.5+8+1.5=9.5+9.5=19[/tex]

Answer: 19

Answer: The markup percentage of 100% means the store added an amount equal to the original cost of the chair to its price, so the selling price of the chair before tax was 494.47 * 2 = $989.94.

The sales tax is calculated as 5.5% of the selling price before tax, which is 5.5/100 * 989.94 = $54.45.

The total amount paid by Sally for the leather chair, including tax, is 989.94 + 54.45 = $1044.39.

Step-by-step explanation:

The labor grew by 25% between 1980 and 1990. The answer is D) 56.25%

How to calculate the percentages?

Percentage is a way of representing a fraction of 100. To calculate the percentage of a certain quantity, you can use the following formula:

Percentage = (part / whole) x 100

Given the production function Y = A * K⁰ॱ⁵ * L⁰ॱ⁵, we can calculate the growth of labor (L) between 1980 and 1990 by using the information on real GDP (Y), total factor productivity (A), and capital (K).

We can rearrange the production function to find L:

L = (Y / A) / K⁰ॱ⁵

For 1980:

L = (400 / 1) / 25⁰ॱ⁵ = 2

For 1990:

L = (990 / 1.1) / 81⁰ॱ⁵ = 2.5⁰ॱ⁵

Now, we can find the percentage growth of labor between 1980 and 1990 by using the formula:

Percentage growth = (L1990 - L1980) / L1980 * 100

Percentage growth = (2.5 - 2) / 2 * 100 = 25%

So, the labor grew by 25% between 1980 and 1990. The answer is D) 56.25%

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