Jess gave her nail technician a 450$ tip. The tip was 9% of the cost of the manicure. Write an equation to find b, the cost of the manicure.

Answer:

Step-by-step explanation:

3. parallel

4. neither

5. parallel

These are right. You can find the answer by plugging them into desmos. Good luck! Let me know if there is anything else I can help with :)

Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

The correct option is A. 20,000, as there are a total of 20,000 phone numbers available for the small town.

We know that the phone numbers of a small town either begin with 373 or 377. We are required to find out the number of phone numbers that are available. To solve this question, we need to count the number of phone numbers that are available for each prefix.

The prefix 373 can have numbers ranging from 3730000 to 3739999. Similarly, the prefix 377 can have numbers ranging from 3770000 to 3779999.

Therefore, the total number of phone numbers that are available is the sum of the phone numbers available for each prefix.

Total number of phone numbers = Number of phone numbers available for prefix 373 + Number of phone numbers available for prefix 377

Total number of phone numbers = 10000 + 10000

Total number of phone numbers = 20000

Therefore, The correct option is A. 20,000, as there are a total of 20,000 phone numbers available for the small town.

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The period of the given function is T = 2π

The period T of a function f(x) is such that:

f(x + T) = f(x).

In this case, our function is:

f(θ) = e^{iθ}

Remember that this can be written as:

f(θ) = cos(θ) + i*sin(θ)

So yes, this is in did a periodic function.

Then the period of the function f(θ) is the same as the period of the cosine and sine functions, which we know is T = 2π.

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The period of the considered function f(θ) = e^{iθ} is found to be P = 2π (assuming 'i' refers to 'iota' and 'e' refers to the base of the natural logarithm)

For any real value θ, we have:

\(e^{i\theta} = \cos(\theta) + i\sin(\theta)\)

where 'e' is the base of the natural logarithm, and 'i' is iota, the imaginary unit.

Functions which repeats their values after a fixed interval, are called periodic function.

For a function \(y = f(x)\), it is called periodic with period 'T' if we have:

\(y = f(x) = f(x + T) \: \forall x \in D(f)\)

where D(F) is the domain of the function f.

Suppose that, the period of the function \(f(\theta) = e^{i \theta}\) be P, then we get:
\(f(\theta + P) = f(\theta)\\\\e^{i(\theta)} = e^{i(\theta + P)}\\\\\cos(\theta) + i\sin(\theta) = \cos(\theta + P) + i\sin(\theta + P)\)

When two complex numbers are equal, then their real parts are equal and their imaginary parts are equal.

That means,

\(\cos(\theta) + i\sin(\theta) = \cos(\theta + P) + i\sin(\theta + P)\) implies that:

\(\cos(\theta) = \cos(\theta + P)\\\sin(\theta) = \sin(\theta + P)\)

Also, we know that the period of sine and cosine function is \(2\pi\)

Thus, we get:

\(P = 2\pi\)

Thus, the period of the function \(f(\theta) = e^{i \theta}\)  is P = 2π

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The function f(x) = (1/3)x³ - (1/2)x² - (199/6)x + (211/6).

To find f(x) based on the given information, we can use integration.

Given that f′′(x) = 2x² - x, integrating once gives:

f′(x) = (2/3)x³ - (1/2)x² + C₁

where C₁ is a constant of integration.

Using the given information that f′(2) = 163, we have:

f′(2) = (2/3)2³ - (1/2)2² + C₁ = 8/3 - 2 + C₁ = 163

Solving for C₁, we get:

C₁ = 163 + 2 - 8/3 = 521/3

Substituting this value of C₁, we get:

f′(x) = (2/3)x³ - (1/2)x²+ 521/3

Integrating f′(x) once more, we get:

f(x) = (1/2)x⁴ - (1/6)x³ + (521/3)x + C₂

where C₂ is a constant of integration.

Using the given information that f(1) = 3, we have:

f(1) = (1/2)1⁴ - (1/6)1³ + (521/3)1 + C₂ = 3

Solving for C₂, we get:

C₂ = 3 - (1/2) + (1/6) - (521/3) = -169/3

Substituting this value of C₂, we get the final expression for f(x):

f(x) = (1/2)x⁴ - (1/6)x³ + (521/3)x - 169/3

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Answer:

a) n less than or equal to 21

b) n greater than or equal to 5

c) n > 3/5

Step-by-step explanation:

i hope this helps!!

Answer:

A.) n ≤ 21

B.) n  ≥ 5

C.) n > 3/5

Step-by-step explanation:

For the first question it says that the number is no more than 21, so it could be equal to or less than 21

For the second question, it says that the number is at least 5, so it could be equal to or greater than 5

Finally, for the last question it says that the number is more than 3/5, so greater than would be the correct inequality symbol to use

Utilization is the percentage of actual output from a system in comparison to its design capacity. Given the following information, what would utilization be? Effective capacity = 20 units per day Design capacity = 60 units per day Actual output = 15 units per day.

The correct option is- C. 25%.

The utilization would be \(\frac{15}{60}\) = 0.25 or 25%.Therefore, the correct option is C. 25%. It was a definite and specific offer that could be accepted by anyone who met the requirements. It is an example of a unilateral offer since it was an open offer, anyone who agreed to the terms of the contract could have accepted it. Furthermore, it was a clear and unambiguous offer since it did not require any more clarification.

Shawna and Beatrice, by virtue of their status as the offerees, had the option of accepting or rejecting the offer. The acceptance must meet the requirements of a valid contract. The acceptance must be communicated clearly and immediately. In addition, the acceptance must conform to the offer's terms. In Hyde v Wrench (1840), the court held that an acceptance must be unconditional and absolute and that if the acceptance is not in line with the terms of the offer, it is a counteroffer that terminates the original offer. Since Shawna and Beatrice had not yet responded to the offer, there was no acceptance of the contract. Therefore, there was no legal agreement between the parties as a contract must have both an offer and an acceptance in order to be considered valid.

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Answer:

178/7

Step-by-step explanation:

4x-7+3x+9=180

4x+3x-7+9=180

7x-7+9=180

7x+2=180

7x=180-2

7x=178

x=178/7

Answer:

Please read the assumptions that lead to the proposed answer of options a, b, and e being correct.  Options c and d are easily rejected.  The question is ambiguous about the locations of the angles.

Step-by-step explanation:

Parallel lines have slopes that are identical.  Lines p and q have the same slopes.

It is difficult imagining what angles are represented by x, y, and z.  There are only 2 lines, and they do not intersect.  The locations of the angles are not identified.  The lack of an intersecting point means it is free range as to where we assign the angles.

The attached graph illustrates some possibilities for x, y, and z.  It uses two simple equations as examples, with the same slope to make them parallel.  Assinment of any angles requires the use of an imaginary line that intersects the two parallel lines.  Even then, there aren't many unique locations for the angles.  To illustrate the analysis, lets assign the angles x, y, and z to thelocations shown on the graph.  

Even with this huge step, there is limited information to be able to identify which of the answer options is correct.  We can say that:

x = z

x+y=180

y+z=180

The answer options (below) appear to have similar relationships, so let's agree that the use of the imaginary line, plus the locations of x, y, and z are valid.  Looking at the answer options, we can match choices a, b, and e to the conclusions above.  d makes no sense because it is not an equation.  c says that both lines must be perpendicular to the x axis, a limitation that is relatively immaterial to whether they are parallel.  The condition of being parallel depends on those two angles being the same (e.g., 45 and 45, 22 and 22, etc.) and not require that they both be 90.

Answer Options               Guarantee Parallel?

a. x = z                                     Yes

b. x + y = 180 degree              Yes

c. x + z = 180 degree              No

d. x + y                                     No

e. y + z = 180                           Yes

A jacket with an original cost of $82 is on sale. The cost of the deal is $74.50. The percentage change does the discount represent is 9%.

Percentage change = (amount of increase or decrease) / original amount

= original amount-new amount/ original amount

= (82.74.50)/82

=7.5/82

≈0.09

=9%

What is percentage change?

A quantity's percentage change is equal to the ratio of the difference between the quantity's current value and its starting value multiplied by 100. When a quantity's ultimate value is determined by increasing or decreasing a percentage of its original value, there is always a change in the quantity's percentage change (or percent change).

The difference that results from subtracting the old value from the new value, dividing by the old value, and multiplying the result by the old value is the percentage change. Typically, we multiply a fraction by 100 to create a percent.

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Answer:

17.4cm

Step-by-step explanation

17) In a triangle ABC, BC=8cm, AC=12cm and angle ABC=120

To get the length of AB, we will use the cosine rule

AB² = BC² + AC² - 2(BC)(AC) cos <ABC

AB² = 8² + 12² - 2(8)(12) cos 120

AB² = 64 + 144 - 192cos12

AB² = 208 - (-96)

AB² = 208 +96

AB² = 208 - (-96)

AB² = 304

AB² = 17.4cm

Hence the length of AB is 17.4cm

Question: 6z ^2 (7z^2 + 3z- 2)

Answer: 42z^4 + 18z^3-12z^2

(hope this helps) :)

The FIFO principle and enter the units with the lower unit cost first in the Cost of Goods Sold Unit Cost column and in the Inventory Unit Cost column.

To determine the cost of goods sold for each sale and the inventory balance after each sale using the first-in, first-out (FIFO) method, we need to follow these steps:

1. Identify the units sold and their respective costs:
  - Start with the units available for sale at the beginning of the year.
  - For each sale, allocate the units sold from the oldest inventory (first-in) at their corresponding cost.

2. Calculate the cost of goods sold (COGS) for each sale:
  - Multiply the number of units sold by their respective cost.
  - This will give you the cost of goods sold for each sale.

3. Update the inventory balance after each sale:
  - Subtract the units sold from the total units available for sale.
  - Multiply the remaining units by their respective cost to get the ending inventory value.

Remember to follow the FIFO principle and enter the units with the lower unit cost first in the Cost of Goods Sold Unit Cost column and in the Inventory Unit Cost column.

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The transformation that would produce an image with vertices B"(-2, 1), C"(3, 2), D"(0, -1) from the original vertices B(-3,0), C(2, -1), D(-1, 2) is the transformation (x,y) → (X + 1, y + 1).

By applying the transformation (x,y) → (X + 1, y + 1), each point's x-coordinate is shifted one unit to the right (X = x + 1), and each point's y-coordinate is shifted one unit upward (Y = y + 1). This results in the image with the given coordinates B"(-2, 1), C"(3, 2), D"(0, -1).

The other transformations listed do not match the given image coordinates and would not produce the desired result.

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Answer:

(x, y) → (x, −y) → (x + 1, y + 1)

Step-by-step explanation:

Reflect the vertices over the x-axis by applying the transformation (x, y) → (x, -y):

B'(-3, 0) → B'(-3, 0)

C(2, -1) → C(2, 1)

D(-1, 2) → D(-1, -2)

Translate the reflected vertices by (1, 1):

B'(-3, 0) → B″(-3 + 1, 0 + 1) → B″(-2, 1)

C(2, 1) → C″(2 + 1, 1 + 1) → C″(3, 2)

D(-1, -2) → D″(-1 + 1, -2 + 1) → D″(0, -1)

So, the correct sequence of transformations is:

(x, y) → (x, -y) → (x + 1, y + 1)

(Image provided for more proof)

To eliminate negative exponents the base is inverted by taking its reciprocal, and the exponent then becomes positive.

Given:

Eliminating negative exponents:

Example:

1)  \(x^{-5}\)

on reciprocal:

= 1/x^5

eliminated negative

2) \(x^{-7}y^{-4}\)

= x^-7*1/y^4

= 1/x^7y^4

Therefore To eliminate negative exponents the base is inverted by taking its reciprocal, and the exponent then becomes positive.

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Answer:

3x-x+2=4

Step-by-step explanation:

The given transfer function, |H(w)| = 1 for -81≤w≤B2 and |H(w)| = 0 for all other w, represents a Band pass filter.

A transfer function describes the relationship between the input and output signals of a filter. In this case, the transfer function |H(w)| = 1 for -81≤w≤B2 indicates that the filter allows frequencies within the range of -81 to B2 to pass through unaffected, while attenuating or blocking frequencies outside this range.

A low pass filter allows frequencies below a certain cutoff frequency to pass through, while attenuating higher frequencies. A high pass filter, on the other hand, allows frequencies above a certain cutoff frequency to pass through, while attenuating lower frequencies.

In this case, the transfer function does not exhibit the characteristics of a low pass or high pass filter since it does not specify a cutoff frequency. Instead, it specifies a range of frequencies (-81 to B2) where the magnitude of the transfer function is 1, indicating that these frequencies are allowed to pass through without attenuation. Frequencies outside this range have a magnitude of 0, indicating that they are attenuated or blocked.

Therefore, the given transfer function represents a band pass filter, as it allows a specific range of frequencies to pass through while blocking frequencies outside that range.

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The time that you will arrive at your destination, given the distance of the trip and the average speed, is 2 pm

To find the time of arrival by using the car going at 90 km /h, you need to find the time that the whole trip would take.

The time the trip would take is found by the formula:

= Distance of trip / Average speed

= 495 / 90

= 5 . 5 hours

0.5 hours is 30 minutes so this is 5 hours 30 minutes.

The time you will arrive is therefore:

= 8 : 30 + 5 hours 30 minutes

= 2 pm

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A stack of 35 cups would have a height of 30 units.

To determine the height of a stack of 35 cups using the equation S(n) = 0.5n + 12.5, we can substitute n = 35 into the equation and evaluate the function.

Given that S(n) represents the height of the stack and n represents the number of cups in the stack, we want to find S(35), which represents the height of the stack when there are 35 cups.

Substituting n = 35 into the equation S(n) = 0.5n + 12.5, we have:

S(35) = 0.5(35) + 12.5

Now we can perform the calculations:

S(35) = 17.5 + 12.5

S(35) = 30

Therefore, a stack of 35 cups would have a height of 30 units.

In the given equation S(n) = 0.5n + 12.5, the term 0.5n represents the contribution to the stack's height from the cups themselves, and 12.5 represents a constant height added to account for the base or any other additional height.

By substituting n = 35 into the equation, we calculate the height of the stack when there are 35 cups. In this case, the height is determined to be 30 units.

Understanding and utilizing function notation allows us to express mathematical relationships and evaluate them for specific values. It provides a concise and standardized way of representing mathematical functions and their corresponding outputs.

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The child who received more land if the land was divided evenly among them compared to the way the mother divided it is Sofia. Option (d) is correct.

A mother divided her land of 141/4 acres among her 5 adopted adult children such that Samuel received 11 acres, Sophia received 9 acres, Anthony received 8 acres, Jasmine received 5 acres, and Juan received 4 1/4 acres.

Among the given children, the child who received more land if the land was divided evenly among them compared to the way the mother divided it is Sofia.

To determine the land received by each child if the land was divided evenly among them, divide the total area by the number of children.

Therefore, each child would receive 141/4 ÷ 5 acres.

141/4 ÷ 5 = 113/20 ≈ 5.65 acres.

(to two decimal places)

Approximately, each child would receive 5.65 acres of land.

Which is not how the mother divided her land among the children.

Now, let's compare the area of land that each child received with the 5.65 acres they would have received if the land was divided evenly among them.Samuel received 11 acres.

11 > 5.65

So, Samuel received more land than they would have received if the land was divided evenly among them.Sophia received 9 acres.

9 < 5.65

So, Sophia received less land than they would have received if the land was divided evenly among them.

Anthony received 8 acres.

8 < 5.65

So,

Anthony received less land than they would have received if the land was divided evenly among them.

Jasmine received 5 acres.

5 = 5.65

So, Jasmine received the same land as they would have received if the land was divided evenly among them.

Juan received 4 1/4 acres.

21/4 = 5.25 and

5.25 < 5.65

So, Juan received less land than they would have received if the land was divided evenly among them.

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Answer:

1. The number of steps taken is correlated with the hate rate because a correlation coefficient of 0.88, shows a positive strong relationship.

2. her heart rate is dependent on the number of steps she takes, therefore, a number of steps taken causes her rate to change.

What is the Correlation Coefficient?

A correlation coefficient shows how correlated two variables are.

The correlation coefficient ranges from -1 to 1.

The closer the correlation coefficient is to -1 or 1, the stronger the correlation between the two variables.

1. The number of steps taken is correlated with the hate rate because a correlation coefficient of 0.88, shows a positive strong relationship.

2. her heart rate is dependent on the number of steps she takes, therefore, the number of steps taken causes her rate to change.

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Step-by-step explanation:

Answer: d2 = 15 cm

Step-by-step explanation:

The area of a kite with diagonald d1 and d2 is

A = 1/2(d1)(d2)

From the formula A = 1/2(d1)(d2) find d2.

d2 = 2A/d1

Substitute A = 120cm2 and d1 = 16 cm.

d2 = 2(120)/16

simplify.

d2 = 15 cm

Therefore, the length of d2 is 15 cm.

Answer:

c = 15

Step-by-step explanation:

a^2 + b^2 = c^2

This formula is the Pythagorean Theorem, which is used to find the length of one of the three sides to a right triangle. a and b are the two short sides, while c is the hypotenuse (long diagonal side).

Given a and b we are able to solve for c

c^2 = 9^2 + 12^2

c^2 = 81 + 144

c^2 = 225

Square root both sides to cancel the square

c = 15

Answer:

15

Step-by-step explanation:

Use this equation

a^2+b^2=c^2

so,

9 squared is 81 and 12 squared is 144.

81+144=225

The square root of 225 is 15.

Answer:

D. 160

Step-by-step explanation:

Options a, d, and e could describe a binary search tree while the rest doesn't.

In a binary search tree (BST), every element 'a' has certain properties regarding its position relative to other elements in the tree. Let's analyze it:

a. "Lesser than all elements in its left subtree": This statement would hold true in a BST. In a BST, the left subtree contains elements that are smaller than the current element.

b. "Greater than all elements in its left subtree": This statement would not hold true in a BST. In a BST, the left subtree contains elements that are smaller than the current element, so 'a' cannot be greater than all elements in its left subtree.

c. "Lesser than all elements in its right subtree": This statement would not hold true in a BST. In a BST, the right subtree contains elements that are greater than the current element, so 'a' cannot be lesser than all elements in its right subtree.

d. "Greater than all its descendants": This statement would hold true in a BST. In a BST, all elements in the left subtree are smaller than the current element, and all elements in the right subtree are greater. Therefore, 'a' would be greater than all its descendants.

e. "Greater than all elements in its right subtree": This statement would hold true in a BST. In a BST, the right subtree contains elements that are smaller than the current element, so 'a' can be greater than all elements in its right subtree.

In summary, options a, d, and e could describe a binary search tree, while options b and c would not accurately describe a binary search tree.

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Answer:

It's y-x= -4

Step-by-step explanation:

I drew the graph and figured out the points. Hope this helps.

Answer:

4

Step-by-step explanation:

\(\mathrm{-9 = 9, -5 = 5,\:because\:they\:are\:in\:absolute\:value}\\9 - 5 = 4\)

Answer:

-4

Step-by-step explanation:

−9 − (−5)

Multiply

−1 by −5.

−9 + 5

Add

−9 and 5.

you get...

−4

Maximum 8A/144 people are allowed to entire the park.

The entire space taken up by the surface of the park is called area.

If the park is rectangular shaped, then the area is the product of length and breadth. If it is square shaped, area can be determined by the square of the side length.

Given, length of unused space = 12 foot

    breadth of unused space = 12 foot

Area of unused space = 12 x 12 = 144 square feet

Maximum 8 people is allowed for every 144 squares feet space

Let, area of the entire park is A square feet

Now maximum number of people allowed = (8 × A)/ 144

hence, 8A/144 people is allowed.

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h(-1) is undefined in the real number system since the square root of a negative number is not a real number.

What is the real number?

Real numbers are a set of numbers that include all rational and irrational numbers. They can be represented on the number line and are often used to represent physical quantities such as distance, time, and temperature.

To find h(-1), we substitute -1 for x in the given equation for h(x) and simplify:

h(x) = (√x+5)/(6x-2)

h(-1) = (√(-1)+5)/(6(-1)-2) [Substitute x=-1]

= (√(-1) is not a real number, since the square root of a negative number is not real]

Therefore, h(-1) is undefined in the real number system since the square root of a negative number is not a real number.

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Answer:

7

Step-by-step explanation:

Answer:

answer B

Step-by-step explanation:

Hello,

(f+g)(-1) = f(-1) + g(-1) = (-1+3) + (-1+6) = 2 + 5 = 7

so the correct answer is B

hope this helps