A vacuum cleaner sells for a sale price of $130. This price represents a
25% discount from the original price. What is the ORIGINAL PRICE of the
vacuum cleaner?

9514 1404 393

Answer:

  14.2 years

Step-by-step explanation:

The value is described by the exponential function ...

  y = (initial value)·(decay factor)^x

where y is the value after x years.

The decay factor is (1 - annual depreciation) = 1 - 0.0925 = 0.9075, so we want to find x when ...

  6000 = 23900·0.9075^x

  6000/23900 = 0.9075^x . . . . . . . . . . . . . . divide by 23900

  log(6000/23900) = x·log(0.9075) . . . . . . . take logarithms

  x = log(6000/23900)/log(0.9075) ≈ 14.2396

It will be about 14.2 years until the value of the car is $6000.

Answer:

14.2

Step-by-step explanation:

Answer:B

y=13cos(1/13x)+13

Step-by-step explanation:

The cosine equation to model the height of the red spot over a distance you ride is y = 13 cos (x/13) + 13. Then the correct option is B.

It is a function that repeats itself in a particular time interval.

You ride through some wet paint on your bike, creating a red spot on the tire.

Write a cosine equation to model the height of the red spot over the distance you ride.

Your bike tire has a radius (r) of 13 inches.

The period is the circumference of the tire (2πr).

The cosine equation is given as

y = A cos (Bx + C) + D

Where

A = the amplitude

B = time period

C = phase difference

D = shifting of central line

Then we have the diagram

A = 13

B = 1/13

C = 0

D = 13

Then the equation will be

\(\rm y = 13 \cos (\dfrac{1}{13}x - 0 ) + 13\\\\y = 13 \cos (\dfrac{x}{13} ) + 13\)

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Answer:

its A.56

Step-by-step explanation:

In mathematics, the place value chart is a tool that helps students understand the value of digits in a number. It is a visual representation of how digits are grouped and arranged to represent numbers. The place value chart is arranged in columns, with each column representing a different place value.

The place value chart starts with the ones place, also called units place. This is the rightmost column and it represents the ones digit in a number. The next column is the tens place, which represents the tens digit in a number. The hundredth place represents the hundreds digit and so on. Each column is ten times larger than the previous one.

A place value chart can be used to understand the value of a digit in a number.

Place value chart also helps to understand decimal numbers, which are numbers that have a decimal point. The decimal point separates the whole numbers from the fractional numbers. Each place to the right of the decimal point represents a smaller value.

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Answer:

lines NP and OP are intersecting

Step-by-step explanation:

they touch at point P

The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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Here are the matching pairs for the given question:

1. The smallest multiple that two or more given numbers have in common multiple

2. A number resulting from multiplying a given number by an integer solution

3. The least common multiple of two or more denominators Solve

4. The value(s) of a variable that will make an algebraic sentence true Least common denominator

5. The process for finding the solution(s) to an algebraic equation Least common multiple

1. Common Multiple - The smallest multiple that two or more given numbers have in common is known as the common multiple of those numbers.

2. Multiple - A number that results from multiplying a given number by an integer solution is known as a multiple.

3. Least Common Multiple - The least common multiple of two or more denominators is the smallest number that is a multiple of each denominator.

4. Least Common Denominator - The smallest common multiple of the denominators of two or more fractions is known as the least common denominator.

5. Least Common Multiple - The process for finding the solution(s) to an algebraic equation is known as the least common multiple.

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The value of the constant k is 12.

By Vieta's formulas, the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, and the product of the roots is c/a. Therefore, we have:

m + (m-1) = 7 (sum of the roots)

m(m-1) = k (product of the roots)

Expanding the first equation, we get:

2m - 1 = 7

Solving for m, we get:

m = 4

Substituting m = 4 into the second equation, we get:

4(4-1) = k

Simplifying, we get:

12 = k

Therefore, the constant k is equal to 12.

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Answer:

sry need points

Step-by-step explanation:

Answer:

sorry um i forgot :(

Step-by-step explanation:

16733

Answer:

2700

Step-by-step explanation:

10% * 27,000 = 2700

Because the point (-5, 3) in the pre-image and its corresponding position (5, 3) in the picture are both at the same distance from the y-axis. The pre-point image's (-3, 5) is mirrored to the image's point (3, 5).

The x-axis is the horizontal axis and the y-axis is the vertical axis in two-dimensional space. As seen in the image below, they are represented by two number lines that perpendicularly connect at (0, 0).

This is a reflection of the pre-image that was provided over the y-axis:

Segment

10 9 8 7 6 5 -5 -6 -7 -8 -9 -10

Because the point (-5, 3) in the pre-image and its corresponding position (5, 3) in the picture are both at the same distance from the y-axis, they are reflected to one another.

Similar to this, the pre-point image's (-3, 5) is reflected to the image's point (3, 5).

The x-coordinates of all other locations in the pre-image are negated in the image because they have corresponding points there that are equally spaced from the y-axis.

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Answer: 12

The answer to your geometry question is 12, I hope this helps.

The coordinates of the matrix m=[337−6] with respect to the standard basis of the space of 2x2 matrices, b={[1000],[0100],[0010],[0001]}, are [337, -6, 0, 0].

To find the coordinates of a matrix m=[a b; c d] with respect to the standard basis b, we need to express m as a linear combination of the basis vectors.

So we have to solve the equation

m = x[1000] + y[0100] + z[0010] + w[0001]

where [1000], [0100], [0010], and [0001] are the standard basis vectors.

Expanding the equation gives

[a b; c d] = x[1 0; 0 0] + y[0 1; 0 0] + z[0 0; 1 0] + w[0 0; 0 1]

Equating the corresponding entries of the matrices gives

a = x

b = y

c = z

d = w

Therefore, the coordinates of the matrix m=[337 -6] with respect to the standard basis are

x = 337

y = -6

z = 0

w = 0

So the coordinates of m are (337, -6, 0, 0) with respect to the standard basis.

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Answer: You write the latitude first, followed by a comma, and then the longitude.

Step-by-step explanation:

x = 147 / 0.5446 ≈ 270.2 ft

To find the length of the guy wire for a radio transmission tower, trigonometry concepts are applied. Given a tower height of 160 feet, with the wire attached 13 feet from the top and making an angle of 29° with the ground, we can solve for the length of the guy wire, represented by x.

Using the Pythagorean theorem and considering the right triangle formed by the tower height, the wire attachment point, and the ground, we can set up the equation:

x = √((160 - 13)² + x²)

Next, we apply the tangent function to the given angle:

tan(29°) = (160 - 13) / x

Simplifying, we have:

0.5446 = 147 / x

To solve for x, we rearrange the equation:

x = 147 / 0.5446 ≈ 270.2 ft

Rounding to the nearest tenth of a foot, the length of the guy wire required is approximately 270.2 feet. This wire is attached 13 feet from the top of the tower and makes a 29° angle with the ground.

Trigonometry plays a crucial role in solving real-world problems involving angles and distances. It provides a mathematical framework for calculating unknown values based on known information, enabling accurate measurements and constructions.

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Answer:

Step-by-step explanation:

A

The measure of SP is 80°, therefore, option (B) is correct.

The center angle that creates the intercepted arc is what is known as the arc measure, which is measured in degrees.

Given that, mKN= 20° and m∠T = 30°.

The formula for the measure of angle ∠T is:

\(m\angle{T}= \frac{mSP - mKN}{2}\\30^{\circ} = \frac{mSP - 20^{\circ}}{2}\)

60° = mSP - 20°

mSP = 60° + 20°

mSP = 80°

Hence, the measure of SP is 80°, therefore, option (B) is correct.

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Answer: 44 cm

Step-by-step explanation:

area of circle = πr²

1520 cm² = πr²

r is approximately 22 cm (21.996159369...)

so D (diameter) would be 44

The price paid by school district for each typewriter after applying 18% quantify discount is equal to  $106.56.

Regular selling price of each typewriter = $129.95

Number of typewriter required by school district  = 50

Total cost of 50 type writers = $129.95 × 50

                                               = $6497.5

Discount percent on whole quantity = 18%

18% of $6497.5

= ( 18 / 100 ) × $6497.5

= $1169.55

Total price paid by school district for 50 typewriters

= $6497.5 - $1169.55

= $5327.95

Price paid by school district for 1 typewriters

= $5327.95 / 50

= $106.559

= $106.56

Therefore, the price paid school district for each typewriter is equal to

$106.56.

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Answer:

(3/4)  /  (7/8)     invert the second fraction and multiply

(3/4) * (8/7) =

24/28 =

6/7

Step-by-step explanation:

Explanation: There's a little trick to help you if you have to divide two fractions.

3/4 divided by 7/8 is the same as (3/4)/(7/8) and maybe you've already realised that multiplying by half is the same as dividing by two (easiest example for this). If you need a moment to think about why that is take that moment and continue reading when it makes sense to you. Continuing with that logic multiplying by 1/4 is the same as dividing by 4 and multiplying by 1/8, 1/9 or 1/10 is the same as dividing by 8,9 or 10. Actually multiplying by a certain number is always the same as dividing by its 'reciprocal'. The reciprocal of a number is defined as the number one divided by that number.

So the reciprocal of 8 is 1/8, the reciprocal of 5 is 1/5 and so on...

If you've understood why that is you're holding a new power in your hands because now you can derive from that that (3/4) / (7/8) is the same as (3/4) * (8/7) and if you now imagine this as being written as fractions with the numbers under and above a line you can simply multiply together 3*8 and 4*7 to get 24/28 which can be simplified to 6/7.

The volume of the block after cutting the smaller cubes is:

volume = 56/125 \(cm^{3}\)

What is volume?

Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies.

The formula to calculate the volume of the cube is given by:

Volume = \(a^{3}\), where a is the length of its sides or edges

Length of solid wooden cube= \(\frac{4}{5} cm\)

Length of smaller wooden cube= \(\frac{1}{3} cm\)

Volume of the large cube = \((\frac{4}{3} )^{3}\)

Volume of the large cube = \(\frac{64}{125} cm^{3}\)

Volume of the small cube = \(\frac{1}{5} cm^{3}\)

Volume of the small cube = \(\frac{1}{125} cm^{3}\)

Volume of block after cutting out the smaller cubes is

                = \(\frac{64}{125} -\frac{(8)(1)}{125}\)

                = \(\frac{64-8}{125}\)

                =\(\frac{56}{125}\)\(cm^{3}\)

Hence, the volume of the block after cutting the smaller cubes is:

volume = 56/125 \(cm^{3}\)

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Answer:

linear

y = 2.75x

Step-by-step explanation:

Price: $2.75/lb

Let y = cost.

Let x = number of pounds.

equation:

y = 2.75x

Linear equation

This is a direct proportion, so it is a linear equation.

For equal changes in x, you get equal changes in y.

Answer:360

Step-by-step explanation:

Answer:

6x+10-3x=55

6x-3x=10+55

3x=65

65÷3=21.6

The probability of ordering a caramel macchiato or a muffin is 82%.

Let us denote the Probability of ordering a caramel Macchiato as P(C), the Probability of ordering a muffin as P(M), the probability of ordering both a caramel macchiato and a muffin as P(C ∩ M), and the probability of ordering a caramel macchiato or a muffin P(C ∪  M).

It is given that:

P(C)=72%

P(M)=32%

P(C ∩ M)=22%

We need to find P(C ∪  M).

According to the Union Law of probability, the probability of the union of two events A and B is equal to the sum of their individual probabilities minus the probability of their intersection.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

In this case:

P(C ∪ M)=P(C)+P(M)-P(C ∩ M)

Upon substituting the given values;

P(C ∪ M)=72%+32%-22%=82%

Hence, the probability of ordering a caramel macchiato or a muffin =

P(C ∪  M) is 82%.

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Answer:

its b 34

Step-by-step explanation:

Answer:

the actual answer is 37. I have the assignement and 37 was correct.

Step-by-step explanation:

Answer: 570 total calories

Step-by-step explanation:

450 calories in 50 grams of fat

120 calories in 30 grams of protein

120 + 450= 570

Answer:

1.12x14=208

Step-by-step explanation:

base X height

Answer:

Slope is 3/1

Rise is 3

run is 1

hope this helps