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Dividing Whole Numbers - Standard Algorithm - Item 92123
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Comparing with  y = ? x+ ?  this equation we get the first value is 2.50 and the second value is 8

What is equation?

An equation is a mathematical statement which is built by two expressions connected by an equal ('=') sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.

A bike rental costs $2.50 per hour plus a fee for renting a helmet, which is required. The total cost

of renting a bike for 2 hours (h) is $13.

If it rented for 2 hours then rental costs will be $(2×2.50)= $5

Let the number of hours be x

Then the equation will be

y= 2.50x+8 --------(1)

As the total cost is $13

c= 8 [as 13- 5 =8]

Hence, comparing with  y = ? x+ ? we get the first value is 2.50 and the second value is 8.

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Answer:

Step-by-step explanation:

Kaylee held 1000 shares after the split. The post-split price per share was $17.06.

Explanation:

Before the split, Kaylee held 500 shares of the stock, and each share was worth $34.12. So, her total investment was 500 x $34.12 = $17,060.

After the 2-for-1 split, each share is split into 2 shares. So, the total number of shares she holds becomes 500 x 2 = 1000.

To find the post-split price per share, we divide the pre-split price by 2.

Post-split price per share = $34.12 / 2 = $17.06.

The transformation rule used to create this image is (x, y) → (1/4x + 1, 3/8y + k)

A transformation in geometry is the process of altering a geometric shape or object's position, orientation, or size.

This transformation involves moving a shape from one place to another without altering its size, shape, or orientation. To put it another way, the entire shape is moved a specific amount in one direction

Here we have

A pre-image has coordinates B(8, 4), U(6, 10) and N(5, −2). The image has coordinates B’(2, 1), U’(1.5, 2.5) and N’(1.25, −0.5).

To find the transformation rule, identify the type of transformation that maps the pre-image coordinates to the image coordinates.

One way to do this is to find the changes in the x-coordinates and y-coordinates between the pre-image and image points.

Let's start with point B.

The x-coordinate has decreased from 8 to 2, and the y-coordinate has decreased from 4 to 1.5.

This implies that there has been horizontal compression and vertical compression.

Here the x-coordinate has been compressed by a factor of 2/8 = 1/4, and the y-coordinate has been compressed by a factor of 1.5/4 = 3/8.

So, the transformation rule for point B is:

=> B(x, y) → B'(1/4x, 3/8y)

Using the same method for points U and N, we can find the transformation rules for those points:

U(x, y) → U'(1/4x, 3/8y + 7/8)

N(x, y) → N'(1/4x + 1, 3/8y - 1/4)

So, the overall transformation rule is:

(x, y) → (1/4x + 1, 3/8y + k)

where k is a constant that depends on the particular point being transformed.  

Therefore,

The transformation rule used to create this image is

(x, y) → (1/4x + 1, 3/8y + k)

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Angle 1 and angle 3 are vertically opposite angles.

We know that :

▪︎ Vertically opposite angles are always equal.

Which means :

Angle 1 = Angle 3

Thus, the measure of angle 3 = 70°

▪︎Therefore, the correct option is (I) 70

The first four terms of the Taylor series for f(x) = 1/(x - 5) at a = 1 are:

[tex]-1/4 - 1/16(x - 1) + 1/64(x - 1)^2 - 3/512(x - 1)^3[/tex]

What is series?

In mathematics, a series is a sum of the terms of an infinite sequence of numbers. It is often represented by the symbol Σ (sigma) and written as an expression that adds up the terms of the sequence.

To find the Taylor series for the function f(x) = 1/(x - 5) at a = 1, we need to compute its derivatives at x = 1 and evaluate them at a = 1. We can use the formula for the Taylor series, which is given by:

[tex]f(x) = f(a) + f'(a)(x - a) + f''(a)(x - a)^2/2! + f'''(a)(x - a)^3/3! + ...[/tex]

We start by finding the derivatives of f(x):

[tex]f(x) = 1/(x - 5)\\\\f'(x) = -1/(x - 5)^2\\\\f''(x) = 2/(x - 5)^3\\\\f'''(x) = -6/(x - 5)^4[/tex]

Now, we can evaluate these derivatives at a = 1:

[tex]f(1) = 1/(1 - 5) = -1/4\\\\f'(1) = -1/(1 - 5)^2 = -1/16\\\\f''(1) = 2/(1 - 5)^3 = 1/32\\\\f'''(1) = -6/(1 - 5)^4 = -3/128[/tex]

Substituting these values into the formula for the Taylor series, we get:

[tex]f(x) = -1/4 - 1/16(x - 1) + 1/64(x - 1)^2 - 3/512(x - 1)^3 + ...[/tex]

Therefore, the first four terms of the Taylor series for f(x) = 1/(x - 5) at a = 1 are:

[tex]-1/4 - 1/16(x - 1) + 1/64(x - 1)^2 - 3/512(x - 1)^3[/tex]

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The interest rate needed for an investment of $5700 to double in 7 years if interest is compounded continuously is approximately 9.9%.

We have,

The formula for continuous compounding is:

A = Pe^(rt)

where A is the final amount, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

We want to find the interest rate needed for an investment of $5700 to double in 7 years, so:

2P = Pe^(rt)

Divide both sides by P:

2 = e^(rt)

Take the natural logarithm of both sides:

ln 2 = rt ln e

Since ln e = 1, we have:

ln 2 = rt

Solve for r:

r = ln 2 / t

r = ln 2 / 7

r ≈ 0.099

Thus,

The interest rate needed for an investment of $5700 to double in 7 years if interest is compounded continuously is approximately 9.9%.

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Answer:

A'B'C'D' will be smaller than ABCD.

Step-by-step explanation:

A is at (5, 10) so A' will be at (0.8*5, 0.8*10) = (4, 8).

By applying the same rule B' will be the point (8,8).

C' will be (8, 4) and D' (4, 4).

So the lengths of the new square will be 4 units so its smaller than ABCD.

(The sides of ABCD are 5 units long)

The elements using rooster-method:

A){3,4,5,6,7,8,9,10}

B){5,6,7,8,9,10,11,12,13,14}

What is rooster-method?

By listing the items of a set inside brackets, the roster method may be used to display the elements of a set. One of three ways to describe a set is in rooster form. The items of a set are listed in the roster form between curly or following brackets, with commas separating each element. When items repeat in the set, the roster approach actually has an issue. Because the elements do not follow a pattern or have a specific order, it is impossible to describe the elements in roster notation if the set has a significant number of elements or any repeated elements.

A)Set of natural odd numbers greater than 2 but less than 11:

Let us represent the set using symbol O:

O = {3,4,5,6,7,8,9,10}

B){x| x∈ N and 4<x<15}

Given that x is a natural number greater than 4 but less than 15.

X={5,6,7,8,9,10,11,12,13,14}

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There are campers y = 650(676/650)^x.

The number of campers, y, x years after the camp opens, can be modeled using an exponential equation with the form y = a(b)x. Let's use x = 0 for the first year the camp was open (last year), and x = 1 for this year.

Then, we have:

y = a(b)^0 = 650 (when x = 0)

y = a(b)^1 = 676 (when x = 1)

These two points can be used to find the values of a and b.

We will first use the first equation to find a:

a = 650

Next, we'll use the second equation to solve for b:

676 = 650(b)^1

676/650 = (b)^1

b = 676/650

To describe the number of campers, an exponential equation of the type y = a(b)^x is needed.

y = 650(676/650)^x

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You would need to purchase 16.67 to 20 pounds of Brussels sprouts to serve five trimmed 12 sprouts

If you want to serve five trimmed 12 sprouts to each of 200 guests, you would need a total of:

5 sprouts/guest x 200 guests = 1000 sprouts

Assuming that the sprouts are sold by weight, it can be difficult to estimate the exact amount to purchase, as the weight of a given number of sprouts can vary depending on their size and density.

However, as a rough estimate, you can assume that 1 pound of Brussels sprouts contains approximately 50-60 sprouts.

Therefore, to serve 1000 sprouts, you would need approximately:

1000 sprouts / 50 sprouts/pound = 20 pounds of Brussels sprouts

or

1000 sprouts / 60 sprouts/pound = 16.67 pounds of Brussels sprouts

So, you would need to purchase approximately 16.67 to 20 pounds of Brussels sprouts to serve five trimmed 12 sprouts to each of 200 guests, depending on the size and density of the sprouts.

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Answer:

≈ 63,4°

Step-by-step explanation:

Given:

A right triangle

AB = 2

BC = 1

Find: ∠C - ?

Use trigonometry:

[tex] \tan(∠c) = \frac{ab}{bc} [/tex]

[tex] \tan(∠c) = \frac{2}{1} = 2[/tex]

[tex] {tan}^{ - 1} (2) ≈63.4°[/tex]

Answer:

The answer is approximately √3/2

Step-by-step explanation:

cos 0=4√3

cos0=cos(4√3)

cos0≈√3/2

Considering the information, the mean number of books read is approximately 3.06 books.

We need to calculate the sum of the number of books read by each student and divide it by the total number of students:

Therefore, mean, also known as the average, is a measure of central tendency that represents the sum of a set of values divided by the total number of values. In this case, we have a sample of 33 students, and we want to find the mean number of books they read. We can conclude that the mean number of books read is approximately 3.06 books.

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The pattern that is formed that makes it always true is that the patterns were formed from triangles that are upside down as well as the use of Sierpiński triangle and lastly, with the use of black and white fillings.

The pattern of the Sierpiński triangle is one that comes up as a result of repeatedly removing certain triangles from an original equilateral triangle.

The Sierpiński triangle is known to be a kind of self-similar fractal equilateral triangle that is known to be made up of smaller equilateral triangles.

Note that It is a basic example of a mathematically generated pattern that can be reproduced at any magnification. It was named after Polish mathematician Wacław Sierpiński, but pre-dates his work as a decorative pattern.

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Answer:

After writing the values of x and y in terms of z , and substituting them in the third equation we get:

x=-1/5

y=11/5

z=-2

Answer:

Chart A is represented by the graph.

Step-by-step explanation:

The first input - output ratio of 5 cars to 25 dollars represented in the graph rules out charts B and D.

Chart C is ruled out by the 30 input, $175 is not even represented by the y-axis of the graph.

This means that the only chart left is chart A.

Answer:

in the first worksheet in number (3) we are asked to factorize certain equations (mainly quadratics)

so in number one we have the quadratic equation as 4x²-12x+9. so this is an expression not equation and so therefore it is represented as the formula ax²+bx²+c

[tex]therefore \: a = 4 \\ \: \: \: \: b = - 12 \\ \: \: \: c = 9 \\ [/tex]

therefore 4 multiplied by 9 equals 36.

then we find a number that is a factor of 36 but can add to get -12. that number is -6 therefore substitute in the eqn

[tex]4 x^{2} - 6x - 6x + 9[/tex]

then factorize to get an answer of

[tex](2x - 3)(2x - 3)[/tex]

The surface area of the remaining solid is 20 square centimeters.

To find the surface area of the remaining solid, we need to subtract the surface area of the square hole from the surface area of the cube.

The surface area of the cube is given by the formula:

SA_cube = 6[tex]s^{2}[/tex]

where s is the length of one side of the cube. In this case, s = 2 cm, so:

SA_cube = 6[tex](2)^{2}[/tex] = 24 [tex]cm^{2}[/tex]

The surface area of the square hole can be found by calculating the area of the square face that has been removed. Since the side of the square hole is 2 cm, its area is:

SA_hole = [tex](2 cm)^{2}[/tex] = 4 [tex]cm^{2}[/tex]

Therefore, the surface area of the remaining solid is:

SA_remaining = SA_cube - SA_hole = 24 [tex]cm^{2}[/tex] - 4 [tex]cm^{2}[/tex]= 20 [tex]cm^{2}[/tex]

So the surface area of the remaining solid is 20 square centimeters.

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Answer:

The answer for a is 100 and b is still 200

because 200-200 =0 the when you multiple it by 200 you get 200 still and same applies to a

The vector translation of kite A to kite B and kite B to kite C indicates;

a. The coordinates of the vertices of the kite B are; (4, 10), (3, 4), (3, 3), and (5, 2)

Please find attached the drawing of the kite B created with MS Excel

b. The location of the coordinates of the vertices of the kite C are; (-2, 1), (-3, 1), (-3, 0), (-1, -1)

Please find attached the diagram of the location of the kite C created with MS Excel

c. The vector is [tex]\binom{-2}{4}[/tex]

d. The vector is; [tex]\binom{2}{-4}[/tex]

A translation transformation is a transformation in which involves the displacement of the figure to a new location.

a. The vector translation [tex]\binom{4 }{7}[/tex] indicates that the kite is translated 4 units to the right and 7 units upwards

The coordinates of the vertices of the kite A are; (0, -3), (-1, -3), (-1, -4), and (1, -5)

The coordinates of the vertices of the kite B are therefore;

b. The coordinates of the vertices of the kite C obtained from the translation of the kite B by the vector [tex]\binom{-6 }{-3}[/tex] are;

(-2, 1), (-3, 1), (-3, 0), (-1, -1)

c. The vector translation that maps kite A onto kite C is therefore;

Translation to the right of kite A with respect to kite C = -2 - 0 = -2

Translation upwards from kite A to kite C = 1 - (-3) = 4

The translation that maps kite A onto kite C is; [tex]\binom{-2 }{4}[/tex]

d) The vector translation that maps kite C onto kite A can be found as follows;

Translation to the right of kite C with respect to kite A = 0 - (-2) = 2

Translation upwards from kite C to kite A = -3 - 1 = -4

The vector translation that maps kite C onto kite A is; [tex]\binom{2}{-4}[/tex]

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In summary a) sine(0°) = 0, cosine(0°) = 1, tangent(0°) = 0/1 = 0, b) sine(360°) = 0, cosine(360°) = 1, tangent(360°) = 0/1 = 0, c) sine(450°) = 1, cosine(450°) = 0, tangent(450°) is undefined

Why is it?

In the unit circle, a 0° angle lies on the positive x-axis, while a 360° angle completes one full revolution and returns to the same point on the unit circle as 0°. Similarly, a 450° angle completes 1 full revolution and moves an additional 90° counterclockwise.

Here are the sine, cosine, and tangent values for these angles:

For 0° and 360°, the values are the same since they lie on the positive x-axis:

sine(0°) = 0

cosine(0°) = 1

tangent(0°) = 0/1 = 0

For 450°, we can subtract 360° to get an equivalent angle:

sine(450°) = sine(450° - 360°) = sine(90°) = 1

cosine(450°) = cosine(450° - 360°) = cosine(90°) = 0

tangent(450°) = tangent(450° - 360°) = tangent(90°) is undefined (since cosine(90°) = 0)

Therefore, the values for the sine, cosine, and tangent functions of the angles a) 0°, b) 360°, and c) 450° are:

a) sine(0°) = 0, cosine(0°) = 1, tangent(0°) = 0/1 = 0

b) sine(360°) = 0, cosine(360°) = 1, tangent(360°) = 0/1 = 0

c) sine(450°) = 1, cosine(450°) = 0, tangent(450°) is undefined

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The solution to the equation [tex]COS^ {X}[/tex]-SINX=1/4 is: X ≈ 1.911 radians

What is Radian?

A radian is a unit of measurement for angles, used in mathematics and physics. It is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. One radian is equivalent to approximately 57.3 degrees.

Rearrange the equation to get [tex]COS^ {X}[/tex] = SINX + 1/4.

Square both sides of the equation to eliminate the square root:

[tex]COS^ {2X}[/tex]= [tex]SIN^ {2X}[/tex] + 1/2*SIN(X) + 1/16

Use the identity [tex]COS^ {2X}[/tex]+ [tex]SIN^ {2X}[/tex]= 1 to substitute for [tex]COS^ {2X}[/tex]

1 - SIN^2(X) = SIN^2(X) + 1/2*SIN(X) + 1/16

Simplify the equation and rearrange terms:

SIN^2(X) + SIN(X) - 15/16 = 0

Solve for SIN(X) using the quadratic formula:

SIN(X) = (-1 ± sqrt(1 + 120/16))/4

Simplify the expression under the square root and evaluate both solutions:

SIN(X) = (-1 ± sqrt(129))/4

Since the range of SIN(X) is [-1, 1], only the positive solution is valid:

SIN(X) = (-1 + sqrt(129))/4

Use the identity[tex]COS^ {2X}[/tex] + [tex]SIN^ {2X}[/tex] = 1 to find the corresponding value of COS(X):

COS(X) = sqrt(1 - [tex]SIN^ {2X}[/tex])

= sqrt(1 - (-1 + sqrt(129))^2/16)

Therefore, the solution to the equation C[tex]COS^ {X}[/tex]-SINX=1/4 is:

X ≈ 1.911 radians (or approximately 109.49 degrees)

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The calculated previous population of the city was 42,500.

Let's denote the previous population as "x".

According to the problem, the current population is 28% less than the previous population, which can be represented as:

x - 0.28x = 30,600

Simplifying and solving for x, we have:

0.72x = 30,600

Divide by 0.72

x = 30,600 / 0.72

x = 42,500

Therefore, the previous population was 42,500.

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Answer:

log5[x^2z^9w√(x^4-81)]

Using the properties of logarithms, we can rewrite the given expression as a sum and/or difference of logarithms as follows:

log5[x^2z^9w√(x^4-81)] = 2log5(x) + 9log5(z) + log5(w) + 0.5log5(x^4-81)

Note that the square root (√) can be expressed as a exponent of 0.5, and we can use the properties of logarithms to split the logarithm of a product into a sum of logarithms of individual factors.

Step-by-step explanation:

Answer:

The answer is 1054ft³

Step-by-step explanation:

Volume of rectangular prism =1/3LWH

V=1/3×31/2×51/3×12

V=1054ft³

The graph of the inequalities is attached

Graphing a nonlinear inequality involves following a similar process as graphing a linear inequality, but with some additional considerations:

Simplify the inequality as much as possible to get it into a standard form.

Identify the shape of the inequality. Is it a parabola, a circle, a hyperbola, or some other shape?

Determine the direction of the inequality. Is it "greater than" or "less than" the given value?

Plot the curve that represents the boundary of the inequality, using the shape and standard form of the inequality.

Determine whether the inequality is "strict" (i.e., greater than or less than) or "non-strict" (i.e., greater than or equal to, or less than or equal to). the situation in the problem is strict

Shade the area of the graph that satisfies the inequality, based on the direction of the inequality and whether it is strict or non-strict.

The graph is attached

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An equation of the lines that pass through this pair of points (3,-5) and (2, -1) is equal to y = -4x + 7.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-1 + 5)/(2 - 3)

Slope (m) = 4/-1

Slope (m) = -4.

At data point (2, -1) and a slope of -4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-1) = -4(x - 2)  

y + 1 = -4x + 8

y = -4x + 7

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[tex]~~~~~~ \stackrel{ \textit{\LARGE semiannually} }{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &2 \end{cases}[/tex]

[tex]A = 10000\left(1+\frac{0.08}{2}\right)^{2\cdot 2} \implies A\approx 11698.59\hspace{5em}\underset{ interest }{\stackrel{11698.59~~ - ~~10000 }{\approx \text{\LARGE 1698.59}}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{ \textit{\LARGE quaterly} }{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quaterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}[/tex]

[tex]A = 10000\left(1+\frac{0.08}{4}\right)^{4\cdot 2} \implies A \approx 11716.59\hspace{5em}\underset{ interest }{\stackrel{ 11716.59~~ - ~~10000 }{\approx\text{\LARGE 1716.59}}} \\\\[-0.35em] ~\dotfill\\\\ 1716.59~~ - ~~1698.59 ~~ \approx ~~ \text{\LARGE 18}[/tex]

The inverse of the function f(x) = 9x^2 - 12, x≥0 is q(x) = (√[x + 12])/3

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

f(x) = 9x^2 - 12, x≥0

Replace f(x) with y

So, we have

y = 9x^2 - 12

Swap x and y

x = 9y^2 - 12

So, we have

9y^2 = x + 12

Divide by 9

y^2 = (x + 12)/9

Take the square roots of both sides

y = (√[x + 12])/3

Hence, the inverse function is

q(x) = (√[x + 12])/3

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Complete question

if the domain of the function,f, is restricted to x≥0, which function is the inverse of f? the function is f(x) = 9x^2 - 12, x≥0. A. p(x)=√z-12/9 B. q(x)=√x+12/9. C. h(x)=√x-12/3. D. g(x)=√x+12/3