An annual depreciation rate is the percent that the value of an item decreases each year. A company purchases technology for $5,000. The company uses the function $r=1-\sqrt[3]{\frac{S}{5000}}$

to relate the annual depreciation rate $r$ (in decimal form) and the value $S$ (in dollars) of the technology after 3 years. Find $S$ when $r=0.15$ .

Therefore, the coordinates of  [tex]S'[/tex] are  [tex](-2, -1)[/tex] .

A series of numbers called coordinates is used to describe a point's location in a two- or three-dimensional space.

Typically, coordinates in a two-dimensional space are expressed as a pair of integers (x, y), where x denotes the point's horizontal location (also known as the abscissa) and y denotes its vertical position (also known as the ordinate).

Coordinates are commonly expressed as a triplet of numbers (x, y, z) in a three-dimensional space, where x, y, and z stand for the locations along the x, y, and z axes, respectively.

In order to describe the location of objects or points in space, coordinates are often employed in a variety of disciplines, including mathematics, physics, engineering, and computer graphics.

To rotate a point 180° about the origin, we need to negate the x-coordinate and the y-coordinate of the point.

So to find the coordinates of S', we can apply this rule to the coordinates of S:

x-coordinate of   [tex]S' = -x-[/tex] coordinate of [tex]S = -(2) = -2[/tex]

y-coordinate of  [tex]S' = -y-[/tex]  coordinate of  [tex]S = -(1) = -1[/tex]

Therefore, the coordinates of S' are [tex](-2, -1).[/tex]

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Answer:

------------------

According to the problem, 2 laps make a difference of 10% as:

Hence the total distance in terms of laps is:

Find the total distance:

The value of proᵥᵥv is (-30/37)i + (42/37)j and the decomposed vector v into v₁ and v₂ are  6 + 6j and -5i + j - 6 respectively.

a. To find the projection of w onto v (proᵥᵥw), we can use the formula,

proᵥᵥw = (w · ȳ)ȳ where ȳ is the unit vector in the direction of v.

First, let's find the unit vector in the direction of v,

|v| = √((-5)² + 7²) = √(74)

ȳ = v/|v| = (-5/√(74))i + (7/√(74))j

Next, let's find the dot product of w and ȳ,

w · ȳ = (-1)(-5/√(74)) + (-1)(7/√(74))

w · ȳ  = 12/√(74)

Finally, we can find the projection of w onto v,

proᵥᵥw = (w · ȳ)ȳ = (12/√(74))((-5/√(74))i + (7/√(74))j)

(w · ȳ)ȳ = (-60/74)i + (84/74)j

(w · ȳ)ȳ = (-30/37)i + (42/37)j

Therefore, the projection of w onto v is (-30/37)i + (42/37)j.

b. v₁ = ((v · w)/|w|²)w

v₂ = v - v₁ where |w| is the magnitude of w. First, let's find |w|,

|w| = √((-1)² + (-1)²)

|w| = √(2)

Next, let's find v · w,

v · w = (-5)(-1) + (7)(-1)

v · w = -12

Using the formula, we can find v₁,

v₁ = ((v · w)/|w|²)w = (-12/2)(-1 - j)

v₁ = 6 + 6j

Now, finding v₂,

v₂ = v - v₁

v₂ = (-5i + 7j) - (6 + 6j)

v₂ = -5i + (7 - 6)j - 6

v₂ = -5i + j - 6

As a result, the vector v can be divided into two parts: v₁ = 6 + 6j and v₂ = -5i + j - 6, where v₁ is parallel to w and v₂ is orthogonal to w.

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Complete question - Given v = - 5i + 7j and w = - 1 - j.

a. Find proᵥᵥv

b. Decompose v into two vectors v₁ and v₂ where v₁ is parallel to w and v₂ is orthogonal to w.

the rate of interest is 11.25%.we can use simple interest formula get answer as above

what is simple interest ?

Simple interest is a type of interest that is calculated as a percentage of the principal amount of a loan or investment, and is based only on the original amount of money that was borrowed or invested.

In the given question,

We can use the formula for simple interest to solve for the rate:

Simple Interest = (Principal x Rate x Time) / 100

Substituting the given values, we get:

$900 = (400 x Rate x 20) / 100

Multiplying both sides by 100 and dividing by 400 x 20, we get:

Rate = $900 / (400 x 20) = 0.1125 or 11.25%

Therefore, the rate of interest is 11.25%.

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If house is purchased for $313,000 with a 15% down payment, the monthly payment for the mortgage is $1,906.33.

To find the monthly payment for a mortgage secured at 7% for 25 years on a house purchased for $313,000 with a 15% down payment, we can use the formula for calculating mortgage payments:

P = L[c(1 + c)ⁿ]/[(1 + c)ⁿ - 1]

Where P is the monthly payment,

L is the loan amount (which is the purchase price minus the down payment),

c is the monthly interest rate (which is the annual interest rate divided by 12),  

n is the total number of monthly payments (which is the number of years multiplied by 12).

Substituting the given values, we get:

L = $313,000 - 0.15($313,000) = $266,050

c = 0.07/12 = 0.00583

n = 25 x 12 = 300

Plugging these values into the formula, we get:

P = $266,050[0.00583(1 + 0.00583)³⁰⁰]/[(1 + 0.00583)³⁰⁰ - 1]

Simplifying the expression, we get:

P = $1,906.33

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The practical domain of the situation is [0, ∞].

The practical range of the situation is [0, 100].

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [0, ∞] or 0 ≤ x ≤ ∞.

Range = [0, 100] or 0 ≤ y ≤ 100.

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If the total distance available is 92.75 yards, and there is a sign 5 yards before the starting line, the actual distance available for the race is:

92.75 - 5 = 87.75 yards

Since there are 5 sections of the race, each section covers:

87.75 / 5 = 17.55 yards

Therefore, each section of the race is 17.55 yards long.

The table for the function y = f(x) - 5 is

x    f(x) - 5

5   -33

-3    -5

-2     2

0    21

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

x    f(x)

5   -28

-3    0

-2     7

0    26

To create a table for the function y = f(x) - 5, we subtract 5 from the values of f(x)

using the above as a guide, we have the following:

x    f(x) - 5

5   -28 - 5

-3    0 - 5

-2     7 - 5

0    26 - 5

Evaluate

x    f(x) - 5

5   -33

-3    -5

-2     2

0    21

This represents the table for the function y = f(x) - 5

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Answer:

B

Step-by-step explanation:

let the mid-point of DE be ( x , y )

x = (8+4)/2 = 6

y = (6+10)/2 = 8

the mid- point of DE is ( 6 , 8 )

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The thought is to utilize humor and creativity  to come up with reactions that are totally off-base but still somehow related to Mine-craft.

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Answer:

the formula: Speed = Distance / Time.

Let's break down the problem into two parts:

a) Find the average speed of the motorist.

Let's assume the average speed of the motorist is "v" km/h.

The distance the motorist traveled in 1 1/2 hours is given by: Distance = Speed × Time = v × (3/2) km.

The distance the cyclist traveled in 1 1/2 hours (opposite direction) is given by: Distance = Speed × Time = 45 × (3/2) km.

Since they passed each other, the sum of their distances should be equal to the distance between Town A and Town B.

So, we can set up the equation: v × (3/2) + 45 × (3/2) = Distance between Town A and Town B.

b) Find the distance between Town A and Town B.

When the motorist reached Town B 2 hours later, the cyclist was 30 km away from Town A.

We can set up the equation: Distance between Town A and Town B = v × 2 + 30.

Now, let's solve the equations:

v × (3/2) + 45 × (3/2) = v × 2 + 30.

Simplifying the equation, we have: (3v + 135)/2 = 2v + 30.

Multiplying both sides of the equation by 2 to eliminate the fraction, we get: 3v + 135 = 4v + 60.

Subtracting 3v from both sides of the equation, we have: v = 75.

Therefore, the average speed of the motorist is 75 km/h.

To find the distance between Town A and Town B, we substitute the value of v into the equation:

Distance between Town A and Town B = v × 2 + 30 = 75 × 2 + 30 = 150 + 30 = 180 km.

Therefore, the distance between Town A and Town B is 180 km.

The clear difference between an angle bisector and a segment bisector is that angle bisector passes through the apex of an angle while segment bisector passes through the midpoint of the line segment.

An angle bisector is defined as the line the divides an angle into two equal parts by passing through its apex.

A segment bisector is defined as the line that divides a segment at the midpoint into two parts.

The difference between angel bisector and segment bisector is that angle bisector passes through the apex of an angle while segment bisector passes through the midpoint of the line segment.

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Ilana ran a total distance of 23.725 miles during her first week of training for a half marathon.

Distance refers to the amount of space or physical separation between two points or objects. It is a measure of how far apart two objects or points are from each other.

Ilana will run 4.125 miles each day for the first three days, which gives a total distance of:

4.125 miles/day × 3 days = 12.375 miles

For the next two days, she will run 5.675 miles per day, which gives a total distance of:

5.675 miles/day × 2 days = 11.35 miles

To find the total distance that Ilana ran during her first training week, we simply add the distances from the first three days and the next two days:

12.375 miles + 11.35 miles = 23.725 miles

Therefore, Ilana ran a total of 23.725 miles during her first week of training.

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If you double the length and the width, you are quadrupling the area.

This is because 2 × 2 = 4.

Perimeter of new rectangle=   2 × perimeter of initial rectangle.

The perimeter will be double of if we double the length and breadth of rectangle

→ When doubling the dimensions of a rectangle, why the area is quadruple:

We know that :

Area of rectangle = l × b

where, l is length and b is breadth

A = L × W

This means area equals length times width.

if you double the length and you double the width, the formula becomes:

A = 2 × L × 2 × W

A = 2 × 2 × L × W

A = 4 × L × W

if you double the length and the width, you are quadrupling the area.

This is because 2 × 2 = 4.

→When doubling the dimensions of a rectangle, why the perimeter is doubles?

Let length be equal to ′l′

And breadth be equal to ′b′

Perimeter of rectangle = 2 (l + b) ____(equation i )

The perimeter if the length and breadth of the rectangle will increase by two, or will it double? So new parameters of rectangle when its length and breadth will get double on initial one.

Double length of rectangle of initial one= 2 × l=2l

Double breadth of rectangle of initial one = 2×b=2b

So the perimeter of new rectangle whose length and breadth are double of initial one are:

As we know that:

Perimeter of rectangle = 2 (l + b)

So,

Perimeter of new rectangle= 2(2l+2b),  (by taking 2 common)

Perimeter of new rectangle = 2×2(l + b) ____  equation (ii)

As from equation (i) perimeter of initial rectangle is = 2(l + b)

So from equation (i) and (ii)

Perimeter of new rectangle= 2 × 2(l + b)

Perimeter of new rectangle=   2 × perimeter of initial rectangle.

Hence, the perimeter will be double of if we double the length and breadth of rectangle.

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Answer:

[tex] {m}^{2} + 7m - 30 = [/tex]

[tex](m - 3)(m + 10)[/tex]

Answer:

C

Step-by-step explanation:

In the given diagram, the areas of the figures are as follows:

Area of the rectangle is 1/6 cm²

Area of the parallelogram is 12 m²

From the question, we are to calculate the areas of the given plane shapes

From the diagram, we have a rectangle and a parallelogram

The area of a rectangle is given by the formula

Area = l × w

Where l is the length

and w is the width

From the given information,

l = 1/2 cm

w = 1/3 cm

Thus,

Area = 1/2 cm × 1/3 cm

Area = 1/6 cm²

Hence, the area of the rectangle is 1/6 cm²

For the parallelogram

The area of a parallelogram is given by the formula

Area = b × h

Where b is the base length

and h is the perpendicular height

From the given information,

b = 6 m

h = 2 m

Thus,

Area = 6 m × 2 m

Area = 12 m²

Hence, the area of the parallelogram is 12 m²

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The correct answer is:

x = 0°, 30°, 150°, 180°

This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.

For the frequencies to be the same, we need to find values of n and m such that:

n = m

Solving for n and m, we get:

n = m = 2

So both functions complete two cycles in the interval [0, 2π).

We can find the times when this occurs by setting the angles in radians equal to multiples of 2π/2, or π:

2sin2x = sin x

2sin2x - sin x = 0

sin x (2sin x - 1) = 0

sin x = 0 or 2sin x - 1 = 0

sin x = 0 when x is an integer multiple of π.

2sin x - 1 = 0 when sin x = 1/2, which occurs when x = π/6 or x = 5π/6.

Therefore, the frequencies of the sound waves are the same at x = π/6, x = π/2, x = 5π/6, and x = 3π/2.

The correct answer is:

x = 0°, 30°, 150°, 180°

This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.

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Answer:

(r, y)=(10,-2)

Step-by-step explanation: Hope this helps :)

The events committee is surveying only 1.5% of the student population by asking the girls' basketball team about the school dance.

To calculate the percentage of the student population being surveyed, you can use the formula:

Percentage = (Number of students surveyed / Total number of students) * 100

In this case, the number of students surveyed is 15 (girls' basketball team), and the total number of students is 1,000.

Percentage = (15 / 1,000) * 100 = 1.5%

So, the events committee is surveying only 1.5% of the student population by asking the girls' basketball team about the school dance.

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The events committee wants to survey students about a school dance. The committee is

meeting in the gym, where the girls' basketball team is practicing. They survey the

players on the girls' basketball team.

If there are 1,000 students in the school, and the girls' basketball team has 15 players, what percentage of the student population is being surveyed by the events committee about the school dance?

Han has walked 3/5 km.

Distance is the length of space between two reference points. It is a scalar quantity, and it is measured in meters.

In the given question, we have that;

distance from Han's house to Priya's house = 4/5 km

Han has walked 3/4 of the way already.

Thus,

distance walked by Han = 3/4 of 4/5

                                         = 3/4 x 4/5

                                         = 12/ 20

                                         = 3/ 5

distance walked by Han is 3/5 km.

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Answer:

Step-by-step explanation:To solve this problem, we can use similar triangles. Let the side length of the cube be s, and let the midpoints of AB, AC, and BC be P, Q, and R, respectively. Then OP, OQ, and OR are the diagonals of the faces of the cube, and so they are equal to .Consider triangle AOB. By the Pythagorean theorem, we have , so . Since angle AOB is 90 degrees, we can use similarity to see that triangle OAP is similar to triangle OAB, so . Solving, we find that .Using similar triangles, we can find that . Since the sum of the squares of the lengths of the diagonals of a cube is equal to three times the square of the side length, we have

$$(0P2 + 0Q? + OR?) = 35388 Substituting the values we found for $OP$, $OQ$, and $OR$, we haveSimplifying and solving for , we find that . Thus, the side length of the cube inscribed in the tetrahedron is .

Answer:

√75 =8.66.

Step-by-step explanation:

The square root of 75 is an irrational number where the numbers after the decimal point go up to infinity. √75 = 8.660.√75 cannot be written in the form of p/q, hence it is an irrational number. irrational with never-ending digits.

Let's see how to find the square root of 75 by the long division method.

Step 1: Express 75 as 75.000000. We take the number in pairs from the right. Take 75 as the dividend.

Step 2: Now find a quotient which is the same as the divisor. Multiply quotient and the divisor and subtract the result from 75.

Step 3: Now double the quotient obtained in step 2. Here is 2 × 8 = 16. 160 becomes the new divisor.

Step 4: Apply decimal after quotient '8' and bring down two zeros. We have 1100 as the dividend now.

Step 5: We need to choose a number that while adding to 160 and multiplying the sum with the same number we get a number less than 1100. 160+ 6 = 166 and 166 × 6 = 996. Subtract 996 from 1100. We get 104

Step 6: Bring down two zeros again and place it after 104, so that it becomes 10400 which is the new dividend. Now multiply the number in the quotient by 2. Here it is 86. We get 172. Have it as 1720. Now find a number at the unit's place of 1720 multiplied by itself gives 10400 or less. We find that  1726  × 6 = = 10356. Find the remainder.

Step 7 : Repeat the process until we get the remainder equal to zero. The square root of 75 up to two places is obtained by the long division method. Thus √75 = 8.66

Florence was 0.16 m/s faster in the 100-meter race than in the 200-meter race

An equation is an expression that shows the relationship between numbers and variables using mathematical operators.

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

She completed the 100-meter race in 10.49 seconds and the 200-meter race in 21.34 seconds. Hence:

For 100 meters:

Speed = 100 m / 10.49 s = 9.53 m/s

For 200 meters:

Speed = 200 m / 21.34 s = 9.37 m/s

The speed difference = 9.53 m/s - 9.37 m/s = 0.16 m/s

Florence was 0.16 m/s faster

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Answer: To work out 2.1/0.7 without a calculator, you can use long division as follows:

0.7 | 2.1

    1.4   (3 times 0.7 is 2.1)

   -----

    0.7

    0.0   (there is no remainder)

Therefore, 2.1/0.7 = 3, which means that 2.1 is equal to 3 times 0.7.

Answer:

see below

Step-by-step explanation:

2.1

-----

.7

Multiply the top and bottom by 10 to get rid of the decimals.

2.1 *10 = 21

.7 * 10 = 7

21/7 = 3

Answer:

The polynomial has a unique zero in the interval [1,2] by using intermediate value theorem

The mixed fraction 1 and 1/4 is equal to 5/4 and the mixed fraction 1 and 1/2 is equal to 3/2.

Given first number = 1 and 1/4.

1 and 1/4 is a mixed fraction so, we can write it in the form as  [tex]1\frac{1}{4}[/tex] .

To find the value of  [tex]1\frac{1}{4}[/tex]  we have to multiply 4 with 1 and add the numerator part of the fraction which is 1 and then divide it by 4 which is the denominator. So,

 [tex]1\frac{1}{4}[/tex]  = ((4x1) + 1 )/4 = 5/4.

Similary, for 1 and 1/2,

[tex]1\frac{1}{2}[/tex] = ((2x1) + 1)/2 = 3/2.

From the above analysis, we can conclude that the value of 1 and 1/4 is 5/4 and the value of 1 and 1/2 is 3/2.

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The solutions for -2x²+2x+1 are x = 1 + √(3)/2 and x = 1 - √(3)/2.

To use the quadratic formula to solve -2x²+2x+1, we first identify the coefficients a, b, and c of the quadratic equation in standard form: ax²+bx+c=0. In this case, a=-2, b=2, and c=1. We then plug these values into the quadratic formula

x = (-b ± √(b²-4ac)) / 2a

Substituting the values, we get

x = (-2 ± √(2²-4(-2)(1))) / 2(-2)

Simplifying the expression inside the square root

x = (-2 ± √(4+8)) / (-4)

x = (-2 ± √12) / (-4)

Simplifying the radical

x = (-2 ± 2√3) / (-4)

Reducing the fraction

x = (1 ± √3/2)

Therefore, the two solutions are x = (1 + √3/2) and x = (1 - √3/2).

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The area of the shaded shape is 62.5cm^2.

To find the area of the shaded shape, we need to break it down into simpler shapes that we can calculate the area of. From the image, we can see that the shape is composed of a rectangle and two right-angled triangles.

First, we need to find the dimensions of the rectangle. Since the shape has vertical and horizontal lines of symmetry passing through its center, we know that the rectangle is divided into four equal parts.

Therefore, the length of the rectangle is twice the length of one of the triangles, which is 5cm. So, the length of the rectangle is 2 x 5cm = 10cm. The width of the rectangle is also 5cm.

Next, we need to find the area of each of the triangles. We know that the base of each triangle is 5cm, and the height is half of the width of the rectangle, which is 2.5cm. Therefore, the area of each triangle is:

0.5 x base x height = 0.5 x 5cm x 2.5cm = 6.25cm^2

So, the total area of the two triangles is 2 x 6.25cm^2 = 12.5cm^2.

Finally, we can find the area of the shaded shape by adding the area of the rectangle and the area of the triangles:

Area = rectangle area + triangle area = 10cm x 5cm + 12.5cm^2 = 62.5cm^2.

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The total is $24,947.06 plus $9,647.06 in compound interest.

One way to earn or pay interest on interest is through compound interest. It denotes that interest will be charged on both the main amount and the accrued interest in the subsequent period. Savings or investments can expand over time with the aid of compound interest.

We can use the following formula to determine compound future value:

FV = P * (r/n + 1)(n*t)

where P is the principal, r is the yearly interest rate, n is the number of times interest is compounded annually, and t is the amount of time in years.

Your values have led us to:

FV = 15300 * (1 + 0.08/4)²⁴

FV = $24,947.06

The total is $24,947.06 plus $9,647.06 in interest.

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