Taylor bought a watch onsale for 60% off the originalprice, and another 10% off thediscounted price. If the watchoriginally cost $82, what wasthe final sale price?

Step 1: Simplify both sides of the equation.

Step 2: Subtract 1/3x from both sides.

Step 3: Add 7 to both sides.

Step 4: Multiply both sides by 6.

Answer:

x=18

Answer:

v=20

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(v−15)=15

(3)(v)+(3)(−15)=15(Distribute)

3v+−45=15

3v−45=15

Step 2: Add 45 to both sides.

3v−45+45=15+45

3v=60

Step 3: Divide both sides by 3.

3v /3   =   60 /3

v=20

(a) To show that the problem RELATED = {〈M1, M2〉 | h(M1) ∩ h(M2) 6= ∅} is Turing recognizable, we need to construct a Turing machine that recognizes this language.

We can design a Turing machine T that takes as input the description of two Turing machines, M1 and M2. T simulates the computation of both M1 and M2 on all possible inputs in parallel. If it finds an input w on which both M1 and M2 halt, it accepts the input 〈M1, M2〉; otherwise, it continues simulating indefinitely.

Since the computation of T will eventually halt and accept if 〈M1, M2〉 is in RELATED, and it may run indefinitely if 〈M1, M2〉 is not in RELATED, the language RELATED is Turing recognizable.

(b) To show that the problem RELATED is undecidable, we can reduce the halting problem H to RELATED. We assume that H is undecidable, which means there is no Turing machine that can decide whether an arbitrary Turing machine halts on a given input.

We define a mapping reduction f from H to RELATED as follows:

Given an input 〈M, w〉 for the halting problem H, we construct an input 〈M', M〉 for the RELATED problem, where M' is a new Turing machine defined as follows:

M' = "On input x:

Simulate M on w.

If M halts on w, accept."

We can see that if M halts on w, then M' halts on all inputs, and therefore, h(M') is the set of all possible inputs. If M does not halt on w, then M' does not halt on any input. Thus, h(M') = ∅.

Now, we can see that 〈M, w〉 is in H if and only if 〈M', M〉 is in RELATED, as the intersection of h(M') and h(M) is non-empty if and only if M halts on w.

Therefore, by constructing the mapping reduction f from H to RELATED, we have shown that if RELATED were decidable, then H would also be decidable, which contradicts the assumption that H is undecidable. Hence, RELATED is undecidable.

(c) In this context, A represents the halting problem H, which is the problem of determining whether a Turing machine halts on a given input. B represents the problem RELATED, which is the problem of determining whether two Turing machines have a non-empty intersection in terms of the inputs on which they halt.

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Answer:2.131

Step-by-step explanation:

What is the predicted value for accidents per 1000 licenses for a city that has 13% of its licensed drivers under age 21, according to the estimated regression equation? Answer: 2.131 The p -value for "Percent under 21" in the regression output is p = 0.0000.

Answer:

y=x+5

Step-by-step explanation:

bc each time its increasing by 5

Answer:

4x+5

Step-by-step explanation:

10x + 7 - 6x - 2

4x +5

hope this helps

Answer: no I think the correct answer is 4x+5

Step-by-step explanation:

The equilibrium price for Toyota vehicles is OMR 2050, and the equilibrium quantity is 2400 vehicles. The choke price, or the price at which the quantity supplied falls to zero, is OMR 433.

To find the equilibrium price and quantity, we set the quantity demanded (Qd) equal to the quantity supplied (Qs):

5500 - (2p/5) = 3p - 1300

Simplifying the equation, we get:

5500 - (2p/5) = 3p - 1300

-2p/5 - 3p = -1300 - 5500

-2p - 15p/5 = -6800

-2p - 3p = -6800

-5p = -6800

p = (-6800)/(-5)

p = 1360

Substituting the value of p back into either the demand or supply equation, we can find the equilibrium quantity:

Qd = 5500 - 2(1360)/5

Qd = 5500 - 2720/5

Qd = 5500 - 544

Qd = 4956

Therefore, the equilibrium price is OMR 2050 and the equilibrium quantity is 2400 vehicles.

To find the choke price, we set the quantity supplied (Qs) equal to zero:

0 = 3p - 1300

3p = 1300

p = 1300/3

p ≈ 433

Hence, the choke price for Toyota vehicles in Oman is approximately OMR 433.

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The mean score of 90, and percentile of Bob's score of 80, gives Bob's exam score as approximately 92.5%

The Z-Score of the 80th percentile is 0.8416

The formula for Z-Score is presented as follows;

\(z = \frac{x - \mu}{ \sigma} \)

Where;

\( \sigma = The \: standard \: deviation\)

\( \mu = The \: mean = 90\%\)

x = The given score

Taking the mean as a proportion, we have;

\( \sigma = \sqrt{\frac{\mu \cdot (1-\mu)}{n}}\)

Which gives;

\( \sigma = \sqrt{\frac{0.9 \times (1-0.9)}{100}}= 0.03\)

Therefore, when z = 0.8416, gives;

\(0.8416 = \frac{x - 0.9}{ 0.03} \)

x = 0.8416 × 0.03 + 0.9 ≈ 0.925

Therefore;

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Answer:

None

Step-by-step explanation:

Distribute the 2 to the parentheses:

2(2x + 3) = 4x + 7

4x + 6 = 4x + 7

Subtract 4x from both sides:

6 = 7

6 \(\neq\) 7

This not true, since 6 can never be equal to 7.

This means there are no solutions

Answer: No solution

Step-by-step explanation: 2(2+3)=4+7/ has no proper input.

For the vector field 2.7.6, i=r+x-x, for various values of r, the potential function is V(x) = rx. The equilibrium points are x = 0, and its stability can be determined by examining the slope of the potential function at this point.

For the vector field 2.7.1, x = x(1-x), the potential function is V(x) = x^2/2 - x^3/3. The equilibrium points are x = 0 and x = 1, and their stability can be determined by examining the slope of the potential function at each point.

For the vector field 2.7.2, =3, the potential function is V(x) = 3x. The equilibrium point is x = 0, and it is stable since the slope of the potential function at this point is zero.

For the vector field 2.7.3, x = sinx, the potential function is V(x) = -cos x. The equilibrium points are x = 0, pi, 2pi, etc., and their stability can be determined by examining the slope of the potential function at each point.

For the vector field 2.7.4.1, =2+ sin x, the potential function is V(x) = 2x + cos x. The equilibrium points are x = 0, pi, 2pi, etc., and their stability can be determined by examining the slope of the potential function at each point.

For the vector field 2.7.5, x = -sinhx, the potential function is V(x) = -cosh x. The equilibrium points are x = 0, pi, 2pi, etc., and their stability can be determined by examining the slope of the potential function at each point.

For the vector field 2.7.6, i=r+x-x, for various values of r, the potential function is V(x) = rx. The equilibrium points are x = 0, and its stability can be determined by examining the slope of the potential function at this point.


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The system of linear equations is found to be inconsistent when k = √3 or k = -√3.

The given system of linear equations is:

kx + ky = 1 (1 k)

x+ ky = 3

Using Cramer's rule to solve the system of linear equations:

x = Dx/Dy,

y = Dy/Dx

Where,

Dx = |1 k|

           |3 k|

          = (1 x k) (3 x k) - (k x k)

           = 3 - k²

Dy = |1 k|

          |1 k|

         = (1 x k) - (k x 1)

            = k - 1

Substituting Dx and Dy in the formula,

x = Dx/Dy

= (3 - k²)/(k - 1),

y = Dy/Dx

= (k - 1)/(3 - k²)

The condition(s) on k such that the system is inconsistent is/are:

When k² = 3, then the denominator of x is 0.

Hence, the system of linear equations is inconsistent when k = √3 or k = -√3.

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Answer:

40

Step-by-step explanation:

A=5

mhdyudpsitsyooatost

The integral is convergent. To evaluate it, we use the formula for the integral of e^x, which is e^x + C. So, integrating e^-6p gives us (-1/6)e^-6p. Evaluating this from 0 to infinity, we get: (-1/6)e^-6(infinity) - (-1/6)e^0.

Since e^-6(infinity) approaches 0 as p approaches infinity, the first term becomes 0. Therefore, the integral evaluates to: (-1/6)e^0 = -1/6, So the quantity converges to -1/6.To determine whether the given integral is convergent or divergent, we need to analyze the integral: ∫[2, ∞] e^(-6p) dp.

To evaluate this integral, we first apply the Fundamental Theorem of Calculus. We find the antiderivative of e^(-6p) with respect to p, which is (-1/6)e^(-6p). Now, we need to evaluate the limit: lim (b → ∞) [(-1/6)e^(-6p)] [2, b].

When we take the limit as b approaches infinity, e^(-6p) approaches 0 because the exponent becomes increasingly negative. Thus, the integral is convergent.

To find the value of the convergent integral, we can calculate: ((-1/6)e^(-6*2)) - ((-1/6)e^(-6*∞)) = (-1/6)e^(-12) - 0 = (-1/6)e^(-12), So, the integral is convergent, and its value is (-1/6)e^(-12).

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The student has to plug y=2x+4 into 3x+y=9 to solve for the system of equations

Answer:

Step-by-step explanation:

The friend solved

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

Step-by-step explanation:

Horizontal shift of f(x) is f(x + a)

The shift is right if a < 0 and left if a > 0

The given function y = 3√x, will shift left if y = f(x + 2), which is:

Correct choice is B

The rate of change is $7 per one square feet.

In order to determine the rate of change, the difference between each successive cost would be divided by the difference in each successive size.

Rate of change = change in cost /change in size

(980 - 840) / (140 - 120)

140 / 20

= $7

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Answer:

98°

Step-by-step explanation:

x = 53° + 45° { exterior angle of a triangle is equal to the sum of two opposite interior angles }

x = 98°

In the graph of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

The simple linear regression equation represents a linear relationship between a dependent variable and an independent variable. It can be written as y = ß0 + ß1x, where ß0 is the intercept and ß1 is the slope of the regression line.

The slope (ß1) determines the rate of change in the dependent variable (y) for each unit change in the independent variable (x). It represents the steepness or inclination of the regression line. The sign of ß1 indicates whether the line has a positive or negative slope, indicating the direction of the relationship between the variables.

Thus, in the context of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

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The length of the line segment AB is 4.8 units

To find the length of the line segment AB in the convex quadrilateral ABCD with given information, we can use the following steps:

Step 1: Identify the given information
We are given that \(AT = 3 units\) , \(TD = 6 units,\)  \(TC=10 units\) and angle sum is 180 degrees.

Step 2: Utilize the Angle Bisector Theorem
Since lines AB and CD intersect in point T, we can apply the Angle Bisector Theorem to triangle ATC, with TD being the angle bisector. The theorem states that the ratio of the lengths of AT to TB is equal to the ratio of the lengths of CT to TD:

\(\frac{AT}{TB} = \frac{CT}{TD}\)


Step 3: Plug in the given values and solve for TB
Using the given values, we can set up the equation:

\(\frac{3}{TB} = \frac{10}{6}\)

To solve for TB, we can cross-multiply:

\(3(6)=10(TB)\\18=10(TB)\)

Now, divide both sides by 10:

Step 4: Find the length of line segment AB
To find the length of AB, we simply add the lengths of AT and TB:
\(AB = AT + TB\)

\(AB = 3 + 1.8\)

\(AB = 4.8 units\)

So, the length of the line segment AB is 4.8 units.

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Answer:

5+4x=21

Step-by-step explanation:

Let's say the "number" is x.

"more than" indicates addition, and "times" indicates multiplication.

5+4x=21

The answer is 77520.

How many different (ordered) playlists are possible?

Number of possible playlists = 77520

Explanation:

Total number of songs = 20

Songs in the playlist = 7

So, we need to select 7 songs out of 20. This can be done using combinations.

n = 20 , r=7

C( n , r ) = ?

C( n , r ) = C (20 , 7)

              = 20! / ( 7! (20-7)!)

              =  20! / ( 7! × 13! )

              = 77520

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Answer:

6 hours

Step-by-step explanation:

-3-2.5-2.5-2.5-2.5-2.5-2.5=18

srry if I took too long

Answer:

6 HOURS

Step-by-step explanation:

The correct answer would be 6 hours or A!

Hope this helps! Have a great day! :))

Answer:

x = -15 so, 15 ÷ -15 = 0

Step-by-step explanation:

Hope this helps!

Answer:

3 with multiplicity 4 and –6 with multiplicity 2

Step-by-step explanation:

Set equal to zero and solve for

x

. The multiplicity of a root is the number of times the root appears.

x=3(Multiplicity of 4)

x=−6(Multiplicity of 2)

Answer:D

Step-by-step explanation: I think this is the answer on edge

The approximate perimeter of quadrilateral WXYZ is 14.5 units and the approximate length of segment WX, XY and YZ are 4 units, 2  units and 4 units respectively.

From the given graph, W(3, 1), X(7, -1), Y(7, -3) and  Z(3, -3).

Length of WX is WX=√[(7-3)²+(-1-1)²]

= √20

WX = 4.5 units

The Approximate length of segment WX is 4.5 Units

Therefore, option C is the correct answer.

Length of XY is XY=√[(7-7)²+(-3+1)²]

XY = 2 units

The Approximate length of segment XY is 2 Units

Therefore, option A is the correct answer.

Length of YZ is YZ=√[(3-7)²+(-3+3)²]

YZ= 4 units

The Approximate length of segment YZ is 4 Units

Therefore, option B is the correct answer.

The Approximate length of segment WZ is 4 Units

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

Now, perimeter= WX+XY+YZ+WZ

= 4.5+2+4+4

Perimeter = 14.5 units

Therefore, option B is the correct answer.

Therefore, the approximate perimeter of quadrilateral WXYZ is 14.5 units and the approximate length of segment WX, XY and YZ are 4 units, 2  units and 4 units respectively.

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Thomas can pack the items into a maximum of 20 bags, with each bag containing 24 items after calculated with greatest common divisor.

To find the maximum number of bags Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192. The GCD will represent the maximum number of items that can be packed into each bag.

To find the GCD, we can use the Euclidean algorithm. First, we find the GCD of 120 and 168:

168 = 1 * 120 + 48

120 = 2 * 48 + 24

48 = 2 * 24 + 0

Therefore, the GCD of 120 and 168 is 24.

Next, we find the GCD of 24 and 192:192 = 8 * 24 + 0

Therefore, the GCD of 120, 168, and 192 is 24.

So, Thomas can pack 24 items into each bag. To find the maximum number of bags he can get, we divide the total number of items by 24:

Total number of items = 120 + 168 + 192 = 480

Number of bags = 480 / 24 = 20

Therefore, Thomas can get a maximum of 20 bags.

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Answer:

C

Step-by-step explanation:

khanacademy :)