Lisa bought CDs that were each the same price. Including sales tax, she paid a total of . Each CD had a tax of . What was the price of each CD before tax?

Answer:

Equation- p-6= -14

Answer- p=-8

Step-by-step explanation:

Step-by-step explanation:

To find the value of x, we need to solve the equation:

5x - (x + 3) = 3(2 - 2x) + x

Expanding the right-side expression:

5x - (x + 3) = 6 - 6x + x

Combining like terms on both sides:

6x - 3 = 6 - 5x

Adding 5x and 3 to both sides:

11x = 9

Dividing both sides by 11:

x = 9/11

So the value of x is approximately 0.818181818.

Answer:

138.86

Step-by-step explanation:

Multiply the radius by 2 to get the diameter.

Multiply the result by π, or 3.14 for an estimation.

That's it; you found the circumference of the circle.

The solution to the given differential equation is L⁻¹{Y(s)} = (b³ t sin 2t) / (2 (sin bt - bt cos bt))

To solve the differential equation using the convolution theorem, we'll follow these steps:

Take the Laplace transform of both sides of the differential equation.

Use the convolution theorem to simplify the resulting expression.

Take the inverse Laplace transform to obtain the solution in the time domain.

Let's start with step 1:

Given differential equation: d²y/dt² - 4y = t cos 2t

Taking the Laplace transform of both sides, we get:

s²Y(s) - sy(0) - y'(0) - 4Y(s) = L{t cos 2t}

Where Y(s) represents the Laplace transform of y(t), y(0) is the initial condition for y(t) at t = 0, and y'(0) is the initial condition for dy/dt at t = 0.

The Laplace transform of t cos 2t can be found using the Laplace transform table:

L{t cos 2t} = -Im{d/ds[1 / (s² - (2i)²)]}

= -Im{d/ds[1 / (s² + 4)]}

= -Im{(-2s) / [(s² + 4)²]}

= 2Im{(s) / [(s² + 4)²]}

Now let's simplify the expression using the convolution theorem:

The Laplace transform of the convolution of two functions, f(t) and g(t), is given by the product of their individual Laplace transforms:

L{f * g} = F(s) G(s)

In our case, f(t) = y(t) and g(t) = 2Im{(s) / [(s² + 4)²]}.

Therefore, F(s) = Y(s) and G(s) = 2Im{(s) / [(s² + 4)²]}.

Multiplying F(s) and G(s), we get:

Y(s) G(s) = Y(s) 2Im{(s) / [(s² + 4)²]}

Now, we can rewrite the left-hand side of the equation using the convolution theorem:

Y(s) * 2Im{(s) / [(s² + 4)²]} = L{t cos 2t}

Taking the inverse Laplace transform of both sides, we have:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = L⁻¹{L{t cos 2t}}

Simplifying the right-hand side using the inverse Laplace transform table, we get:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = t sin 2t / 4

Now, we can apply the convolution theorem to the left-hand side of the equation:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = L⁻¹{Y(s)} * L⁻¹{2Im{(s) / [(s² + 4)²]}}

The inverse Laplace transform of 2Im{(s) / [(s² + 4)²]} can be found using the inverse Laplace transform table:

L⁻¹{2Im{(s) / [(s² + 4)²]}} = 1 / 2b³ (sin bt - bt cos bt)

Therefore, we have:

L⁻¹{Y(s)} * 1 / 2b³ (sin bt - bt cos bt) = t sin 2t / 4

From this, we can deduce the inverse Laplace transform of Y(s):

L⁻¹{Y(s)} = (t sin 2t / 4) / (1 / 2b³ (sin bt - bt cos bt))

Simplifying further:

L⁻¹{Y(s)} = (b³ t sin 2t) / (2 (sin bt - bt cos bt))

This is the solution to the given differential equation.

Know more about Convolution theorem here:

brainly.com/question/32608612

#SPJ11

The area of Unnex is 7,640 square miles, and the area of Biron is 14,320 square miles.

Let's denote the area of Unnex as "U" and the area of Biron as "B."

According to the given information, Nonlief initially had an area of 36,200 square miles. After Unnex seceded, Nonlief's area reduced to 28,560 square miles. This means that the area of Unnex is the difference between the initial area of Nonlief and the area remaining after Unnex seceded:

U = Initial area of Nonlief - Area remaining after Unnex seceded

U = 36,200 - 28,560

U = 7,640 square miles

Next, we are told that after Biron seceded, Nonlief was left with an area of 21,880 square miles. To find the area of Biron, we need to subtract the remaining area from the area before Biron seceded:

B = Area before Biron seceded - Remaining area after Biron seceded

B = 36,200 - 21,880

B = 14,320 square miles

Unnex therefore has an area of 7,640 square miles, while Biron has an area of 14,320 square miles.

for such more question on area

https://brainly.com/question/15822332

#SPJ8

a. The area of the mirror = 6,644.24 cm²; Circumference of the mirror = 288.88 cm

b. The area would be needed; c. circumference would be needed.

To find the circumference of a circle, you can use the formula C = 2πr, where C is the circumference, π (pi) is approximately equal to 3.14, and r is the radius

To find the area of a circle, you can use the formula A = πr², where A is the area, π (pi) =3.14, and r is the radius of the circle.

a. Area of the mirror = πr² = 3.14 * 46²

= 6,644.24 cm²

Circumference of the mirror = πr² = 2 * 3.14 * 46

= 288.88 cm

b. To find the amount of glass needed, the measure that would be used is the area.

c. To find the amount of wire needed, the measure that would be used is the circumference.

Learn more about circumference of a circle on:

https://brainly.com/question/29504171

#SPJ1

a. The area of the mirror = 6,644.24 cm²; Circumference of the mirror = 288.88 cm

b. The area would be needed; c. circumference would be needed.

To find the circumference of a circle, you can use the formula C = 2πr, where C is the circumference, π (pi) is approximately equal to 3.14, and r is the radius

To find the area of a circle, you can use the formula A = πr², where A is the area, π (pi) =3.14, and r is the radius of the circle.

a. Area of the mirror = πr² = 3.14 * 46²

= 6,644.24 cm²

Circumference of the mirror = πr² = 2 * 3.14 * 46

= 288.88 cm

b. To find the amount of glass needed, the measure that would be used is the area.

c. To find the amount of wire needed, the measure that would be used is the circumference.

Learn more about circumference of a circle on:

https://brainly.com/question/29504171

#SPJ1

The statements about the graph of function that are true include:

From the information given, f(0) = 4(0) - 15

= 0 - 15

= -15

Therefore, the graph crosses the y-axis at (0,-15) is true.

Also, the graph has a point of discontinuity at x=-2 and the graph is increasing over the interval (4,inf).

Learn more about function on:

https://brainly.com/question/2833285

#SPJ1

Answer:

(10, 5)

Step-by-step explanation:

The circle is located at (10, 5)

Answer:

7

Step-by-step explanation:

0+3=3-5=-2+9=7

Answer:

p = 3

Step-by-step explanation:

Given

4(2 + px) = 12x

If the coefficient of the x- term is the same on both sides of the equation, it will have no solution.

Distributing gives

8 + 4px = 12x ( equate the coefficients of the x- term )

4p = 12 ( divide both sides by 4 )

p = 3

The value of p when the equation has no solution will be 3. Then the correct option is B.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

4(2 + px) = 12x

8 + 4px = 12x

If the coefficient of the x-term is the same on both sides of the equation, it will have no solution.

4p = 12

p = 3

The value of p when the equation has no solution will be 3. Then the correct option is B.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2

Answer:

196 miles

Step-by-step explanation:

To find the distance that the bus drives, we can use the formula:

distance = rate x time

where rate is the average speed and time is the duration of the trip.

In this case, the average speed of the bus is 56 mph and the duration of the trip is 3 1/2 hours. However, it is easier to work with time in terms of a single unit, so let's convert 3 1/2 hours to 7/2 hours:

3 1/2 hours = (2 x 3) + 1/2 hours = 7/2 hours

Now we can plug in the values into the formula:

distance = rate x time

distance = 56 mph x 7/2 hours

We can simplify by multiplying 56 by 7 and then dividing by 2:

distance = (56 x 7) / 2 = 196 miles

Answer:

-4 cot (-45)

Step-by-step explanation:

cos (390)

sin (330)

Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

Answer:

112,5°

Step-by-step explanation:

angle of WXZ + angle of ZXY = 180

180 / 8 = 22,5

5 × 22.5 = 112,5 = angle of WXZ

There you go, hoped it helped!

Answer:

smaller number - 7

greater number - 8

Step-by-step explanation:

let a = smaller number

a + 1 = greater number

the following equation can be derived from the question

(5 x a) = 3 + 4(a + 1)

5a = 3 + 4a + 4

5a = 7 + 4a

5a - 4a = 7

a = 7 = smaller number

a + 1 = 7 + 1 = 8 = greater number

There are 10,000 possible code combinations for a 4-digit code on a standard keypad with digits 0 through 9.

To calculate the number of possible code combinations for a 4-digit code on a standard keypad with digits 0 through 9, we need to use the fundamental counting principle.

The fundamental counting principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together. This principle can be extended to any number of tasks.

For a 4-digit code, each digit can be chosen independently from the other digits, and there are 10 possible digits to choose from (0-9). Therefore, using the fundamental counting principle, we can calculate the number of possible code combinations as follows:

Number of possible code combinations = number of choices for the first digit x number of choices for the second digit x number of choices for the third digit x number of choices for the fourth digit

Number of possible code combinations = 10 x 10 x 10 x 10 = 10,000

This means that the chances of guessing the correct code by random chance are 1 in 10,000.

To learn more about combinations click on,

https://brainly.com/question/29574610

#SPJ4

Answer:

£481.02

Step-by-step explanation:

To calculate, you can multiply the original cost by the increase percentage (expressed as a decimal) and add that to the original cost:

£466.98 * 1.032 = £480.9936

£480.9936 + £466.98 = £481.02

Rounding to 2 decimal places, the answer is £481.02.

Null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the appropriate parameter (μ or p) is;

H0: μ ≤ 34, and also Ha: μ > 34

When a hypothesis testing is conducted, the null hypothesis (H0) and the alternative hypothesis (Ha) are set.

We will state the null hypothesis, and also the alternative hypothesis, w.r.t of the appropriate parameter.

The appropriate parameter for the given statement is the population mean (μ).

Americans works with an average years of 34 before retiring.

Null hypothesis (H0):

The population mean is less than or equal to 34.

H0: μ ≤ 34

Alternative hypothesis (Ha):

The population mean is greater than 34.

Ha: μ > 34

This hypothesis test is a two-tailed test because we are interested in testing whether the population mean is significantly different from 34, without specifying the direction of the difference.

Learn more about alternative hypothesis.

brainly.com/question/27335001

#SPJ11

Answer:

The equation H(x) = (-4x-5)(-x+5) can be simplified to H(x) = 4x^2 + 25.

The lesser value for x is -5, and the greater value for x is 5.

Answer:

3/2

Step-by-step explanation:

move all the variables to the left 0=2x-3

divide both sides -2x=-3

then your answer is 3/2

In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle

The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems

The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system

Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

Learn more about data life cycle here

brainly.com/question/28039445

#SPJ4

Answer:

$3,799.20

Step-by-step explanation:

We presume your formula is intended to be ...

M = Pm(1 + m)^(na)/((1 + m)^(na) - 1)

where M is the monthly payment, m is the monthly interest rate, n is 12, and a is the number of years.

This formula gives written below:

M = 3500·(.08/12)·(1 + (.08/12))^(12·2)/((1 + (.08/12))^(12·2) -1) ≈ 158.30

The total payback will be the sum of 24 of these payments is written below;

payback = 24×$158.30 = $3,799.20

The acceleration for each section of the graph can be found using slope as :

A : 1.5 m/s², B : 0, C : 6 m/s² and D : 0.5 m/s².

Given a graph which has time  marked on the X axis and velocity marked on the Y axis.

Acceleration is the slope of the velocity-time graph.

At sections A,

Consider two points (0, 0) and (2, 3).

Slope = (3 - 0) / (2 - 0) = 3/2 = 1.5

Acceleration = 1.5 m/s²

At section B,

velocity is constant, so graph is a straight line parallel to X axis.

So slope = 0

Acceleration = 0

At section C,

Consider two points (4, 3) and (5, 9).

Slope = (9 - 3) / (5 - 4) = 6

Acceleration = 6 m/s²

At section D,

Consider two points (5, 9) and (9, 11).

Slope = (11 - 9) / (9 - 5) = 2/4 = 0.5

Acceleration = 0.5 m/s²

Hence the accelerations are found using slope.

Learn more about Slope here :

https://brainly.com/question/31220734

#SPJ1

The probability of getting a return of 200% or more in a single year is approximately 0.0000317 or 0.00317%.

Assuming that the returns from holding small-company stocks are normally distributed, the probability of doubling or tripling your money in a single year can be estimated using the normal distribution formula.

To calculate the probability of doubling your money, you need to find the number of standard deviations away from the mean that represents a return of 100%. If we assume that the average return for small-company stocks is 10% per year with a standard deviation of 20%, we can use the formula:

Z = (100% - 10%) / 20% = 4.5

Using a normal distribution table or calculator, we can find that the probability of getting a return of 100% or more in a single year is approximately 0.0000317 or 0.00317%.

Similarly, to calculate the probability of tripling your money, you need to find the number of standard deviations away from the mean that represents a return of 200%. Using the same formula as above, we get:

Z = (200% - 10%) / 20% = 9.5

Using a normal distribution table or calculator, we can find that the probability of getting a return of 200% or more in a single year is approximately 0.000000002 or 0.0000002%.

It's important to note that these calculations are based on assumptions and estimates, and actual returns may vary significantly. Investing in small-company stocks involves significant risks, and investors should carefully consider their investment goals, risk tolerance, and overall financial situation before making any investment decisions.

To know more about probability, refer to the link below:

https://brainly.com/question/14188451#

#SPJ11

Given

find the number by determining part and whole

3/5 of a number is 6​

Procedure

The answer is 10

The speed of red light in crown glass is approximately 1.99 x \(10^8\) m/s.

a. The speed of violet light in crown glass can be calculated using the formula:

v = c/n

Where,

v is the speed of light in the material,

c is the speed of light in vacuum and

n is the index of refraction of the material for violet light.

Plugging in the values given, we get:

violet light speed in crown glass = c/n

violet light speed in crown glass = c/1.53

Using the value for the speed of light in vacuum,

c = 3.00 x \(10^8\) m/s,

We can calculate the speed of violet light in crown glass as:

violet light speed in crown glass = (3.00 x \(10^8\) m/s) / 1.53

= 1.96 x \(10^8\) m/s

Therefore, the speed of violet light in crown glass is approximately 1.96 x \(10^8\) m/s.

b. Similarly, the speed of red light in crown glass can be calculated using the same formula, but with the index of refraction for red light:

red light speed in crown glass = c/n = c/1.51

Using the same value for the speed of light in vacuum and plugging in the value for the index of refraction for red light, we get:

The red light speed in crown glass = (3.00 x \(10^8\) m/s) / 1.51 = 1.99 x 10^8 m/s

For similar question on speed:

https://brainly.com/question/28224010

#SPJ11

The length of the value x in the right triangle is 20.7 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum angles in a triangle is 180 degrees.

Therefore, the side of a right triangle can be found using trigonometric ratios as follows:

Hence,

cos 34° = adjacent / hypotenuse

Therefore,

adjacent side = x

hypotenuse side = 25

Hence,

cos 34 = x  /25

cross multiply

x = 25 cos 34

x = 25 × 0.82903757255

x = 20.7259393139

Therefore,

x = 20.7 units

learn more on right triangle here: https://brainly.com/question/29157263

#SPJ1

Answer: 0.4

Step-by-step explanation: I just did the quiz

Using the given radius we know that the area of the given shaded region is 61.5cm².

A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of such line segments.

The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."

The diameter of a circle is the distance measured through its center.

The radius of a circle is the distance from the center to any point on the edge.

The radius is equal to the diameter in half, or 2r=d2 r=d. A chord is a line segment that connects two points on a circle.

So, the area of the shaded region would be:

Area of shaded portion = Area of the square - Area of a circle

Length of the side of the square = 10cm

Area of square = (side)²

= (10cm)²

= 100cm²

Then,

Radius of Circle = 3.5cm

Area of Circle = πr²

= 22/7 × (35/10)²

= 22/7 × 1225/100

= 22 × 175/100

= 22 × 1.75

= 38.5cm²

Now,

Area of shaded portion = Area of the square - Area of a circle

Area of shaded portion = 100cm² - 38.5cm²

= 61.5cm²

Therefore, using the given radius we know that the area of the given shaded region is 61.5cm².

Know more about Radius here:

https://brainly.com/question/24375372

#SPJ1

Answer:

d (or V in the picture) = 16

Step-by-step explanation:

Because the two triangle are similar, the ratios of each of the side lengths should be equal.  Therefore, 8/1 should be equal to d/2.

1.) Set up equality of ratios: 8/1 = d/2

2.) Cross multiply: 8*2 = d*1

3.) 16 = d