A sale at a store is 15%. If the sale price after
the discount is $35.70. What was the original
price of the sweatshirt (S)?

Answer:

Step-by-step explanation:

It is possible that after an elastic collision a moving mass (1) strikes a stationary mass (2) and the two objects will have exactly the same final speed.

During an elastic collision, the momentum and kinetic energy are both conserved. Since one of the object is a stationary object, its velocity will be zero hence the other moving object will collide with the stationary object and cause both of them to move with a common velocity. The expression for their common velocity can be derived using the law of conservation of energy.

Law of conservation of energy states that the sum of momentum of bodies before collision is equal to the sum of momentum of the bodies after  collision.

Since momentum = mass*velocity

Before collision

Momentum of body of mass m1 and velocity u1  = m1u1

Momentum of body of mass m2 and velocity u2  = m2u2

Since the second body is stationary, u2 = 0m/s

Momentum of body of mass m2 and velocity u2  = m1(0) = 0kgm/s

Sum of their momentum before collision = m1u1+0 = m1u1 ... 1

After collision

Momentum of body of mass m1 and velocity vf  = m1vf

Momentum of body of mass m2 and velocity vf  = m2vf

vf is their common velocity.

Sum of their momentum before collision = m1vf+m2vf ... 2

Equating 1 and 2 according to the law;

m1u1 = m1vf+m2vf

m1u1 = (m1+m2)vf

vf = m1u1/m1+m2

vf s their common velocity after collision. This shows that there is possibility that they have the same velocity after collision.

Answer:

68 degrees.

Step-by-step explanation:

Angle A is congruent to C, or they are the same. Angles B and D would also be congruent because they are facing each other.

A1 = 9 × 1 - 6 = 3

A2 = 18 - 6 = 12

A3 = 27 - 6 = 21

A4 = 36 - 6 = 30.

Step-by-step explanation:

Σ ( 9n - 6 ) , n = 1

An = general term.

let Σ (An) = Σ (9n-6)

An = 9n-6

to determine the terms, plug in the value of n into the general term(An)

If you're asked for the 1st term then n = 1

if you're asked for the 2nd term then n = 2. and so forth.

To find the 1st 4 terms, just plug in 1 up to 4 into n bit by bit.

An = 9n - 6

A1 = 9 × 1 - 6 = 3

A2 = 18 - 6 = 12

A3 = 27 - 6 = 21

A4 = 36 - 6 = 30. done.

write the terms from 1 to 4 like this :

{ A1, A2, A3, A4 } = { 3, 12, 21, 30 }.

Answer:

It's the first one: 7 to the fourth over 3 to the tenth.

Step-by-step explanation:

Answer:

I think it is the first one

Step-by-step explanation:

Applying the Chain Rule, the derivatives are given as follows:

The function Z is defined as follows:

z = x^7y^7.

The variables x and y are functions of variables s and t, as follows:

Hence the derivative of z as a function of s is given as follows:

∂z/∂s = (dz/dx)(dx/ds) + (dz/dy)(dy/ds).

Hence, applying the derivative rules for the exponents, and for the exponents, we have that:

\(\frac{\partial z}{\partial s} = 7x^6y^7\cos{(t)} + 7y^6x^7\sin{(t)} = 7x^6y^6(y\cos{t} + x\sin{t})\)

Replacing the values of x and y, we have that:

\(\frac{\partial z}{\partial s} = 7(s\cos{t})^6(s\sin(t))^6(y\cos{t} + x\sin{t})\)

We follow the same logic as above, only that now the inside derivatives, that is, the derivatives of x and y, are as function of t and not of s, hence:

∂z/∂t = (dz/dx)(dx/dt) + (dz/dy)(dy/dt).

Then:

\(\frac{\partial z}{\partial t} = -7x^6y^7s\sin{(t)} + 7y^6x^7s\cos{(t)} = 7sx^6y^6(-y\sin{t} + x\cos{t})\)

Then, replacing x and y as functions of s and t, we have that:

\(\frac{\partial z}{\partial t} = -7x^6y^7s\sin{(t)} + 7y^6x^7s\cos{(t)} = 7s(s\cos{t})^6(s\sin{t})^6(-y\sin{t} + x\cos{t})\)

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Answer:

Our range is within [0,2π]

We cant exceed that.

tan∆ + 1=0

tan∆= -1

∆=tan-¹(-1)

∆=-45°

Now it has 3 Solutions within the given interval

-45° x π/180 = -π/4

So For the second quadrant... 180-∆ = 180-45 =135°

It is true for tan(135) Which is also equal to -1

135xπ/180 = 3π/4

then

360-45 = 315

This is also true because tan(315)=-1

315° x π/180 = 7π/4

This is where we stop so we dont exceed the given range.

Based on the cross-price elasticity of Demand, we can conclude that good X and good Y are substitutes.

Let's calculate the cross-price elasticity of demand using the given information:

a. Find the percentage change in quantity demanded of good Y:

Percentage Change in Quantity Demanded of Good Y = (New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded * 100

Percentage Change in Quantity Demanded of Good Y = (6250 - 5000) / 5000 * 100 = 25%

b. Find the percentage change in the price of good X:

Percentage Change in Price of Good X = (New Price - Initial Price) / Initial Price * 100

Percentage Change in Price of Good X = (5 - 4) / 4 * 100 = 25%

Now, we can calculate the cross-price elasticity of demand:

Cross-Price Elasticity of Demand = Percentage Change in Quantity Demanded of Good Y / Percentage Change in Price of Good X

Cross-Price Elasticity of Demand = 25% / 25% = 1

b. Based on the calculated cross-price elasticity of demand, we can determine the types of goods:

If the cross-price elasticity of demand is positive (as in this case, where it is 1), it indicates that the two goods are substitutes. This means that when the price of good X increases, the quantity demanded of good Y also increases, suggesting that consumers view these goods as alternatives to each other.

Therefore, based on the cross-price elasticity of demand, we can conclude that good X and good Y are substitutes.

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Answer:

Step-by-step explanation:

Answer: Changing the radius of an object by a given amount has a greater effect on the volume than changing the height by the same amount. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. If we change the radius by a given amount, say x, the new radius would be r+x. Hence, the new volume would be V' = π(r+x)²h = π(r²+2rx+x²)h = V + 2πrxh + πx²h. We can see that the volume change equals 2πrxh + πx²h. The first term is proportional to both the radius and the height, whereas the second term is proportional to the square of the radius and the height. Assuming that the height change is also x, the new volume would be V'' = πr²(h+x) = V + πr²x. We can see that the volume change is proportional to the radius squared and the change in height. Therefore, changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount.

Answer:

1.12

Step-by-step explanation:

Answer:

1.12

Step-by-step explanation:

Answer:

1. 0.33

2. the cost per ounce

3. that everytime you go up an ounce, it will cost 0.33 more

4. y = 0.33x + 0.33

Step-by-step explanation:

If Frank spends $90 on his $1800 monthly income, then 95 percent of monthly check does not go toward food.

Let's say Frank spends $90 on food and has a monthly income of $1800. We can calculate the percentage of his monthly check that does not go towards food as follows:

Percentage = (Total Income - Food Expenses) / Total Income

Percentage = (1800 - 90) / 1800

Percentage = 0.95 = 95%

Therefore, 95% of Frank's monthly check does not go towards food.

Here are the steps in detail:

Subtract the food expenses from the total income to get the amount of money that is not spent on food.

Divide the amount of money that is not spent on food by the total income to get the percentage.

In this case, the amount of money that is not spent on food is $1800 - $90 = $1710. The percentage of the monthly check that is not spent on food is $1710 / $1800 = 0.95 = 95%.

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Answer:

86 is is figurative language

Answer:

2. 20 oranges

3. 18 yellow tulips

4. 23 students

\(\boxed{A}\\\\ U=5(2n+22)+2\left( n+\cfrac{3}{2} \right) \\\\\\ U=10n+110+2n+3 \implies U=12n+113 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\hspace{5em}\textit{in 2009, that's 9 years after 2000, n = 9}\\\\ U(9)=12(9)+113\implies U(9)=221 ~~ millions\)

The proof demonstrates that given a well-ordered set W, an isomorphic ordinal can be found using the function F. The uniqueness of this ordinal is established using the Replacement Axioms. The set F(W) is shown to exist for each x in W, and if the least F(W) exists, it serves as an isomorphism of VV onto -y.

Lemma 2.7: This is a previously stated lemma that is referenced in the proof. Unfortunately, without the specific details of Lemma 2.7, it's difficult to provide further explanation for its role in the proof.

Well-ordered set W: A well-ordered set is a set where every non-empty subset has a least element. In this proof, W is assumed to be a well-ordered set.

Isomorphic ordinal: An ordinal is a mathematical concept that extends the notion of natural numbers to represent order and magnitude. An isomorphic ordinal refers to an ordinal that has a one-to-one correspondence or mapping with another ordinal, preserving their order and magnitude properties.

Function F: The function F is defined to assign an ordinal o to each element x in W. This means that for every x in W, there is a corresponding ordinal o.

Existence and uniqueness: The proof asserts that if there exists an ordinal o that is isomorphic to a specific initial segment of the ordinal VV (the set of all ordinals), then this ordinal o is unique. In other words, there is only one ordinal that can be mapped to the initial segment of VV given by x.

Replacement Axioms: The Replacement Axioms are principles in set theory that allow the construction of new sets based on existing ones. In this case, the Replacement Axioms are used to assert that the set F(W) exists, which is the collection of all ordinals that can be assigned to elements of W.

For each x in W: The proof states that for every x in W, there exists an ordinal o that can be assigned to it. If there is no such ordinal, the proof suggests considering the least x for which such an ordinal does not exist.

The least F(W): The proof introduces the concept of the least element in the set F(W), denoted as the least F(W). If this least element exists, it serves as an isomorphism (a one-to-one mapping) of the set of all ordinals VV onto the ordinal -y.

Overall, the proof outlines the existence and uniqueness of an isomorphic ordinal that can be obtained from a well-ordered set W using the function F, and it relies on the Replacement Axioms and the concept of least element to establish this result.

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The solution of the system is then given by:

x = t[1 -1 1 0.5 0.5 0.33] + s[0 -2 1 1 -2 1]

This is the general solution of the system in the form of a sum of scalar multiples of fixed column vectors.

The system of linear equations can be written in matrix form as:

[1 0 1 2 1 3 | 1]

[2 1 2 4 0 10| 5]

[3 1 3 6 6 15| 8]

where the augmented matrix is [A | B].

To solve the system using the method of specifying appropriate free variables, we first convert the coefficient matrix into reduced row echelon form using Gaussian elimination.

In reduced row echelon form, the first non-zero element of each row (known as the leading entry) is 1, and the leading entries of lower rows are to the right of the leading entries of higher rows.

Applying Gaussian elimination to the coefficient matrix, we get:

[1 0 1 2 1 3 | 1]

[0 1 0 2 -2 7| 0]

[0 0 0 0 0 0| 0]

We can see that there are two non-zero rows, indicating that the system has two independent equations.

We can choose two of the variables to be free variables, and express the other variables in terms of the free ones.

Let's choose x1 and x3 as the free variables.

We can find x2 as follows:

x2 = -x1 - 2x3 + 7

And we can find x4, x5 and x6 as follows:

x4 = (1 - x1 - x3)/2

x5 = 1 - x1 - 2x3 + 2x4

x6 = (1 - x1 - x3 - 2x4)/3

So the general solution of the system can be expressed as a sum of scalar multiples of fixed column vectors:

x1 = t

x2 = -t - 2s + 7

x3 = s

x4 = (1 - t - s)/2

x5 = 1 - t - 2s + (1 - t - s)/2

x6 = (1 - t - s)/3

where t and s are scalars.

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Answer:

8.604 in.

Step-by-step explanation:

We can use the formula for compound interest to find the height of domino #9:

A = P(1 + r)^n

where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).

Substituting the given values:

A = 3.00 in * (1 + 0.15)^9

Simplifying:

A = 3.00 in * 2.86797199

A ≈ 8.604 in

Therefore, the height of domino #9 is approximately 8.604 inches.

Answer:

Four times the difference of a number and 5 means equates to: 4(x-5), with x being the unknown number. You also know that this equation is equal to the number, x, increased by 4. So you now know that 4(x+5) is equal to (x+4

Answer:

Step-by-step explanation:

If divided: 0.38461538461

If percent: 38.4615%.

Brainliest rn:D

The odds of winning the game is \(\frac{8}{13}\).

Probability is the measure of happening and non-happening of the outcomes of a random experiment.

The sum of all the probabilities of all the elementary events of an experiment is always 1.

According to the given question.

We have

The probability of losing the game is \(\frac{5}{13}\)

Since, we know that the sum of all the probabilities of all elementary events of an experiment is always 1.

Therefore,

Probability of winning the game + Probability of losing the game = 1

⇒ Probability of winning the game + \(\frac{5}{13} =1\)

⇒ Probability of winning the game = \(1 - \frac{5}{13}\)

⇒ Probability of winning the game = \(\frac{13-5}{13}\)

⇒ Probability of winning the game = \(\frac{8}{13}\)

Hence, the odds of winning the game is \(\frac{8}{13}\).

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Answer:

z = 3(-6x + 4y + 3)/6y and + 1

Step-by-step explanation:

z = 9 - 3x × 2 - 3y × 2 and z - 6x × 2 + 6y × 2

z = 9 - 3 × 2x - 3 × 2y and z - 6 × 2x + 6 × 2y

z = 9 - 6x - 6y and z - 12x + 12y

z = 3(-6x + 4y + 3)/6y and + 1

Answer:

13.6

Step-by-step explanation:

The quotient is the outcome of a division problem so it is what 41 divided by  3 equals. Which it equals 13.666 in short 13.6

Answer:

A cone

Step-by-step explanation:

It volume it 42.411

The smaller number is 6 .

The larger number is 22

Let's let x be the smaller number and y be the larger number.

From the problem, we know that one number is eight less than five times the other, so we can write:

y = 5x - 8

We also know that the sum of the two numbers is 28, so we can write:

x + y = 28

Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.

Let's solve the first equation for x

x = (y + 8)/5

Now we can substitute this expression for x into the second equation:

(y + 8)/5 + y = 28

Multiplying both sides by 5 to eliminate the fraction, we get:

y + 8 + 5y = 140

Combining like terms, we get:

6y + 8 = 140

Subtracting 8 from both sides, we get:

6y = 132

Dividing both sides by 6, we get:

y = 22

Now we can use the equation y = 5x - 8 to solve for x:

22 = 5x - 8

Adding 8 to both sides, we get:

30 = 5x

Dividing both sides by 5, we get:

x = 6

Therefore, the smaller number is 6 and the larger number is 22.

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Answer:

The equation is;

S = 18 - 1.5t  

Step-by-step explanation:

From the question, we are made to know that the depth of the snow is S and the time taken to melt in hours is t

After 4 hours of melting, the snow depth is 12 inches  

Now, recall that the rate of melting is 1.5 inches/ hour  

So in the 4 hours, the amount of snow melted will be 1.5 * 4 = 6 inches  

So the total depth of the snow initially will be 6 + 12 = 18 inches  

So let’s write the equation;

S = 18 - 1.5t  

Where S is the depth of the snow after a particular number of hours t

Step-by-step explanation:

The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.

The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).

Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).

Function of graph:
By playing around in a graphing calculator, I got the equation to be

2 (cos (x + pi/2)).

the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.

By taking the product between the combinations of possible groups fo men and women we will see that the number of different committees is:

392

For a set of N elements, the number of different sets of K elements that can be formed is:

C(N, K) = N!/(K!*(N - K)!)

Here we have 8 men and 7 women, and we want to make a committee of 5 men and 6 women

Then the total number of different committees is given by the product between the different sets of 5 men and the different sets of 6 women, these are:

for men:

C(8, 5) = 8!/( 5!*(8 - 5)!) = (8*7*6)/(3*2*1) = 56

for women:

C(7, 6) = 7!/(6!*(7 - 6)!) = 7

Then the total number of different committees is:

C = 56*7 = 392

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Answer:

x = - 1

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

P is undefined when x = - 1

A: The linear equations are x + y = 125 and x = y + 45.

B: Everyday Angela spends 40 minutes in playing golf.

C: No, it is not possible for Angela to spend 80 minutes playing soccer every day.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Part A:

Let x be the number of minutes Angela plays soccer every day

Let y be the number of minutes Angela plays golf every day

According to the problem statement the linear equations are -

x + y = 125 (total time playing both sports is 125 minutes)

x = y + 45 (Angela plays 45 more minutes of soccer than golf)

Part B:

Substitute x = y + 45 into the first equation -

(y + 45) + y = 125

Use the addition operation -

2y + 45 = 125

2y = 80

y = 40

Angela spends 40 minutes playing golf every day.

Part C:

If Angela spends 80 minutes playing soccer every day, then

x = 80

y + 45 = 80 (using the equation x = y + 45)

y = 35

But this would mean that she plays golf for 35 minutes and soccer for 80 minutes, which adds up to a total of 115 minutes.

This is not possible since the problem states that Angela plays both sports for a total of 125 minutes every day.

Therefore, it is not possible for Angela to have spent 80 minutes playing soccer every day.

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Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - \(\frac{3}{2}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = \(\frac{0-3}{0-(-2)}\) = \(\frac{-3}{0+2}\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 )

0 = - \(\frac{3}{2}\) (0) + c = 0 + c , so

c = 0

y = - \(\frac{3}{2}\) x + 0 , that is

y = - \(\frac{3}{2}\) x