All hats are on sale for 22.5% off the original price.
Abrien is buying a hat that is originally priced at h.
Sales tax is 8.875%.
Part A: Which expression would calculate the final price
of a hat?
Part B: If the original price of a hat is $42, what is the
final price of buying four hats after the discount and
sales tax? (round your answer to the nearest dollar) Untitled Title
A. Part A: h(0.225)(0.08875)
Part B: 41
B. Part A: 4h(0.775)(1.08875)
Part B: $142
C. Part A: h(0.775)(1.08875)
Part B: $142
D. Part A: h(0.775)(0.08875)
Part B: $156

Option C, y = e^(x+y) + x^2 + 3x - 2, requires the use of implicit differentiation to find dy/dx.

The expression that requires the use of implicit differentiation to find dy/dx is option C: y = e^(x+y) + x^2 + 3x - 2.

Implicit differentiation is a technique used to differentiate equations where the dependent variable y is not explicitly expressed as a function of x. It involves differentiating both sides of the equation with respect to x, treating y as an implicit function of x.

Let's apply implicit differentiation to option C:

Starting with the equation: y = e^(x+y) + x^2 + 3x - 2

To find dy/dx, we differentiate both sides of the equation with respect to x:

d/dx(y) = d/dx(e^(x+y) + x^2 + 3x - 2)

Using the chain rule on the right side of the equation, we get:

dy/dx = d/dx(e^(x+y)) + d/dx(x^2) + d/dx(3x) - d/dx(2)

The derivative of e^(x+y) with respect to x requires the use of implicit differentiation. We treat y as an implicit function of x and apply the chain rule:

d/dx(e^(x+y)) = e^(x+y) * (1 + dy/dx)

The derivatives of the remaining terms on the right side are straightforward:

d/dx(x^2) = 2x

d/dx(3x) = 3

d/dx(2) = 0

Substituting these derivatives back into the equation, we have:

dy/dx = e^(x+y) * (1 + dy/dx) + 2x + 3

Next, we isolate dy/dx on one side of the equation by moving the term involving dy/dx to the left side:

dy/dx - e^(x+y) * dy/dx = e^(x+y) + 2x + 3

Factoring out dy/dx, we get:

(1 - e^(x+y)) * dy/dx = e^(x+y) + 2x + 3

Finally, we solve for dy/dx:

dy/dx = (e^(x+y) + 2x + 3) / (1 - e^(x+y))

Learn more about differentiation at: brainly.com/question/24062595

#SPJ11

Answer:

x = - 4/3

Step-by-step explanation:

6x +4 = 3x

-3x -3x

6x-3x = 3x

3x +4 = 0

-4 -4

3x = -4

_ _

3 3

x = -4/3

1. First we need to combine like terms, so we subtract 3x to both sides.

2. Then we combine the like terms

3. next move the 4 to the other side by subtracting. This will help keep the ex by itself.

4. now we divide 3 to both sides, leaving you with x = -4/3 as your answer.

1) 6x + 4 = 3x

______________

6x + 4 = 3x

6x = 3x - 4

6x = 3x - 4 - 3x

3x = -4

3x/3 = -4/3

x = - 4/3 ☑

Answer:

b= -8

Step-by-step explanation:

Answer:

1/12 + 3/12 = 4/12 (or 1/3)

Step-by-step explanation:

we want to express

1/12 + 1/4 as 1/12 + something / 12

1/12 + 1/4 = 1/12 + something/12

we already have the 1/12 part, so we're left with

1/4 = something / 12

first, we can calculate (denominator we want) / (denominator we have) = 12/4 = 3

then, we want to multiply our current value (1/4) by our result of the multiplication divided by itself.

3/3 = 1

1/4 = 1/4 * 1 = 1/4 * 3/3 = 3/12

thus, our second value is 3/12

we then have 1/12 + 3/12

if we have the same denominators, we can simply add the numerators up

1/12 + 3/12 = (1+3)/12 = 4/12

The steady-state solution of the heat conduction equation refers to the temperature distribution that remains constant over time. This occurs when the heat flow into a system is balanced by the heat flow out of the system.

To find the steady-state solution of the heat conduction equation, follow these steps:

1. Set up the heat conduction equation: The heat conduction equation describes how heat flows through a medium and is typically given by the formula:

  q = -k * A * dT/dx,

  where q represents the heat flow, k is the thermal conductivity of the material, A is the cross-sectional area through which heat flows, and dT/dx is the temperature gradient in the direction of heat flow.

2. Assume steady-state conditions: In the steady-state, the temperature does not change with time, which means dT/dt = 0.

3. Simplify the heat conduction equation: Since dT/dt = 0, the equation becomes:

  q = -k * A * dT/dx = 0.

4. Apply boundary conditions: Boundary conditions specify the temperature at certain points or surfaces. These conditions are essential to solve the equation. For example, you might be given the temperature at two ends of a rod or the temperature at the surface of an object.

5. Solve for the steady-state temperature distribution: Depending on the specific problem, you may need to solve the heat conduction equation analytically or numerically. Analytical solutions involve techniques like separation of variables or Fourier series expansion. Numerical methods, such as finite difference or finite element methods, can be used to approximate the solution.

It's important to note that the exact method for solving the heat conduction equation depends on the specific problem and the boundary conditions given. However, the general approach is to set up the heat conduction equation, assume steady-state conditions, simplify the equation, apply the boundary conditions, and solve for the steady-state temperature distribution.

Know more about steady-state solution here:

https://brainly.com/question/15073499

#SPJ11

."Proportion of variance accounted for" is also referred to as all of the following EXCEPT chi-squared.

"Proportion of variance accounted for" is commonly referred to as R^2 (pronounced R-squared), the correlation ratio, or eta-squared. These terms are used in different statistical contexts to describe the amount of variability in one variable that can be explained or predicted by another variable. R^2 is widely used in regression analysis to assess the goodness of fit of a model. The correlation ratio, also known as eta-squared, is used in analysis of variance (ANOVA) to measure the proportion of variance in a dependent variable that can be attributed to the group differences. Both R^2 and eta-squared indicate the strength of the relationship between variables or the amount of variance explained.

Know more about chi-squared here:

https://brainly.com/question/31871685

#SPJ11

(i) The remainder is -12.

(ii) Concluded that x - 3 is a factor of p(x).

(iii) It can be express p(x) as (x - 3)(x² - x + 1).

c) The equation x(x - 2)² = 3 has only one real root, which is x = 3.

(i) To find the remainder when p(x) = x³ - 4x² + 4x - 3 is divided by x + 1, we can use synthetic division, which is shown in the attached image.

Here, the remainder is -12.

(ii) According to the Factor Theorem, if (x - a) is a factor of a polynomial p(x), then p(a) = 0.

Substitute x = 3 into p(x) to verify if x - 3 is a factor:

p(3) = 3³ - 4(3)² + 4(3) - 3

= 27 - 36 + 12 - 3

= 0

Since p(3) = 0, we can conclude that x - 3 is a factor of p(x).

(iii) Using the factor we found in part (ii), we can divide p(x) by (x - 3) using long division or synthetic division:

We obtain a quotient of x² - x + 1 and no remainder.

Therefore, we can express p(x) as (x - 3)(x² - x + 1).

(c) Now let's consider the original equation x(x - 2)² = 3.

We know that x = 3 is a root of p(x) = x³ - 4x² + 4x - 3, which means it satisfies the equation p(x) = 0.

Hence, x = 3 is a solution to the equation x(x - 2)² = 3.

Since (x - 3) is a factor of p(x) and the quadratic factor (x² - x + 1) does not have any real roots, the equation x(x - 2)² = 3 has only one real root, which is x = 3.

Learn more about the polynomial long division here:

https://brainly.com/question/29718477

#SPJ4

Answer:d. 6500

Step-by-step explanation:

Answer: D)$6500

Step-by-step explanation: took the quiz

a) The area of a circle is given by the formula:

Where A is the area, π=3.14 and d is the diameter=8 ft.

By replacing values:

b) The circumference of a circle is given by:

Where C is the circumference, π=3.14 and d is the diameter=8 ft.

By replacing values:

Among these expressions, (4+1)x(12-6) has a total value of 30.

To determine which expression has a total value of 30, let's evaluate each expression one by one:

4+1x12-6

Following the order of operations (PEMDAS/BODMAS), we first do the multiplication:

4 + (1x12) - 6 = 4 + 12 - 6

Now, we do the addition and subtraction from left to right:

16 - 6 = 10

(4+1x12-6)

This expression has the same operations as the first one, so its total value is also 10.

(4+1)x(12-6)

First, we evaluate the expressions within the parentheses:

(5)x(6)

Now, we do the multiplication:

5 x 6 = 30

(4+1)x12-6

First, we evaluate the expression within the parentheses:

(5)x12 - 6

Now, we do the multiplication:

60 - 6

Finally, we do the subtraction:

54
for such more question on  total value

https://brainly.com/question/15337121

#SPJ11

Answer:

Step-by-step explanation:

its 212123s\

1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

Learn more about distributed here:

https://brainly.com/question/29664127

#SPJ11

If you download 45.54 gb at the same speed of 4.4 gb every 30 minutes, it will take about 12 hours and 18 minutes.

First, calculate the rate of download for 4.4 gb in 30 minutes:

4.4 gb/30 minutes = 0.147 gb/minute

Then, calculate the amount of time needed to download 45.54 gb:

45.54 gb/0.147 gb/minute = 310.2 minutes = 5 hours and 10.2 minutes

Finally, round up to the nearest minute:

5 hours and 10 minutes = 310 minutes = 12 hours and 10 minutes

To calculate the amount of time needed to download 45.54 gb, we first need to calculate the rate of download for 4.4 gb in 30 minutes. This can be done by dividing 4.4 gb by 30 minutes, which gives us 0.147 gb/minute. Then, we can calculate the amount of time needed to download 45.54 gb by dividing 45.54 gb by 0.147 gb/minute, which gives us 310.2 minutes. Finally, we can round up to the nearest minute, which gives us 12 hours and 10 minutes. Therefore, 45.54 gb will take about 12 hours and 18 minutes to download at the same rate of 4.4 gb in 30 minutes.

Learn more about minutes here

https://brainly.com/question/15600126

#SPJ4

In backtracking with conflict-directed back-jumping, the search for a solution to a problem is performed using a depth-first search algorithm. The variable order you mentioned, (a1, h, a4, f1, a2, f2, a3, t), represents the sequence in which variables are assigned values during the search. The value order, (red, green, blue), indicates the order in which the algorithm will try assigning different values to the variables.

Conflict-directed back-jumping is an improvement over basic backtracking, as it helps reduce the search space by identifying and jumping over irrelevant parts of the search tree. When a conflict (i.e., an unsolvable assignment) is encountered, the algorithm doesn't simply backtrack to the previous variable but rather identifies the cause of the conflict and jumps back to the most recent variable responsible for the conflict. This allows the algorithm to skip parts of the search tree that are guaranteed not to yield a solution.

In summary, backtracking with conflict-directed back-jumping is an efficient search technique that uses a specific variable and value order to assign values during the search. It improves upon basic backtracking by identifying the cause of conflicts and jumping back to the most recent relevant variable, thus reducing the search space and time complexity.

for such more questions on algorithms

https://brainly.com/question/13800096

#SPJ11

Answer:

The answer is less than one

Step-by-step explanation:

Because 1/2= less than 3

1 1/2= 3 and is less than 9

2 1/2= 5 not 15

This relationship is a function because the plant body can be of only one particular height at a time.

A function can be defined as a relationship between a set of inputs having only one output each. In other words, a function is basically a relationship between inputs and outputs; where each input is related to only one output at a time. Functions are said to occur when the recorded value of x is varied each time. Since we know that the height of the plant (the x-value) varies by each day, Therefore it is a function.

thus we can conclude that the correct option for the relationship between the height of the plant and the number of days is option D, which tells that this relationship is a function because the plant body can only be of one particular height at a time.

To learn more about functions

visit; https://brainly.com/question/12431044

#SPJ1

The angle ZFD = 57°

Given that:

arc FZ = 66"

FD is the diameter ·Because passing through, Centre.

Angle formed arc FZ at centre = 66°

Angle formed the arc FZ at Circumference at Circle ¹/₂ x66 = 33°

FD is diameter

∠Z= 90°.

∠ZFD = ∠ in Δ FZD

∠ZFD + ∠FZD + ∠FDZ = 180°

∠ZFD + 90° + 33° = 180°

∠ZFD = 180° - 90° - 33° = 57°

Hence the ∠ZFD = 57°

Therefore, angle ZFD is 57°

learn more about measure of the arc or angle: https://brainly.com/question/31034732

#SPJ1

Answer:

8 cm

Step-by-step explanation:

:)

Answer:

11.7

Step-by-step explanation:

use the distance formula known as pythagorem theorem and plug in the x and y values.

The sum of the first 30 terms of the arithmetic progression is 4125

An arithmetic progression is a sequence where the differences between every two consecutive terms are constant. And we use (n/2)[2(a) + (n - 1)d] to calculate for the sum of n-terms of an AP; where n = the number of terms, a = the first term and d = the common difference

We have the first 3 terms of the AP: 7, 16 and 25

16 - 7 = 9

25 - 16 = 9

so, the common difference between each term is 9

The sum of first 30 terms is calculated as follows:

n = 30, a = 7 and d = 9

Hence, by substitution, we will get;

30/2[2(7) + (30 - 1)9]

30/2[14 + (29)9]

30/2[14 + 261]

(30/2)(275) {divide 0 by 2}

15 × 275

4125

Hence, the sum of the first 30 terms of the AP by application of the formula for calculating the sum of a given number of terms is 4125.

Know more about arithmetic progression (AP) here:https://brainly.com/question/24205483

#SPJ1

Answer:

x=3

Step-by-step explanation:

the steps are on the picture

Answer:

\(x=3\)

Step-by-step explanation:

\(4x-5x+9=5x-9\)

\(\mathrm{Combine\:like\:terms:}\:4x-5x=-x\)

\(-x+9=5x-9\)

\(\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\)

\(-x+9-9=5x-9-9\)

\(=-x=5x-18\)

\(\mathrm{Subtract\:}5x\mathrm{\:from\:both\:sides}\)

\(-x-5x=5x-18-5x\)

\(=-6x=-18\)

\(\mathrm{Divide\:both\:sides\:by\:}-6\)

\(\frac{-6x}{-6}=\frac{-18}{-6}\)

\(x=3\)

Answer:

List from least to greatest:-16,-10,-3,5

List from closest to zero to the very far:-3,5,-10,16

Step-by-step explanation:

In order to know if the answer is accurate,draw a number line of directed numbers...the very far negative numbers,are said to be the least than the numbers almost close to zero...

Answer:

Step-by-step explanation:

1) The function f(x) = x is a straight line rising to the right and passing through the origin at an angle of 45 degrees This means this it passes though the points  .....   (-2, -2),  (-1, -1),  (1, 1),  (2, 2) .......

If g(x) = f(x) + 4 then g(x) will be a straight line parallel to f(x) where each point on g(x) is   4 units vertically up from each point on f(x). Its a translation of f(x) up 4 units.

The slope of both graphs is 1.

2) This line (g)x passes through the origin but has slope 1/3.

Answer:

t = 1

Step-by-step explanation:

Bring the like term together.

16 - 9 = 5t + 2t

7 = 7t

t = 1

Answer:

t=1

Refer to the attachment

hope it helps

Answer:

7π over 3

Step-by-step explanation:

Convert from degrees to radians using the ratio π over 180.

The 90% confidence interval for the population mean number of days it takes to find a job using the website's service is approximately 77.09 to 82.91 days.

To calculate a 90% confidence interval for the population mean number of days it takes to find a job using the website's service, follow these steps:

1. Identify the sample mean (X), sample size (n), and population standard deviation (σ). In this case, X = 80 days, n = 32, and σ = 10 days.

2. Determine the desired confidence level. Here, it's 90%.

3. Find the critical value (z) associated with the 90% confidence level. You can look this up in a standard normal distribution table or use a calculator that provides this functionality. For a 90% confidence interval, the critical value is approximately 1.645.

4. Calculate the standard error (SE) by dividing the population standard deviation (σ) by the square root of the sample size (n). In this case, SE = σ/√n = 10/√32 ≈ 1.77.

5. Multiply the critical value (z) by the standard error (SE) to obtain the margin of error (MOE): MOE = z * SE = 1.645 * 1.77 ≈ 2.91.

6. Calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error (MOE) from the sample mean (X). In this case, the lower bound = 80 - 2.91 ≈ 77.09, and the upper bound = 80 + 2.91 ≈ 82.91.

Thus, the 90% confidence interval for the population mean number of days it takes to find a job using the website's service is approximately 77.09 to 82.91 days.

Learn more about "confidence interval":

https://brainly.com/question/15712887

#SPJ11

Answer:

y = 1/2x - 8

Step-by-step explanation:

(4, -6) & (8, -4)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-4 - (-6)) / (8 - 4)

Simplify the parentheses.

= (2) / (4)

Simplify the fraction.

2/4

= 1/2

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 1/2x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (8, -4). Plug in the x and y values into the x and y of the standard equation.

-4 = 1/2(8) + b

To find b, multiply the slope and the input of x(8)

-4 = 4 + b

Now, subtract 4 from both sides to isolate b.

-8 = b

Plug this into your standard equation.

y = 1/2x - 8

This is your equation.

Check this by plugging in the other point you have not checked yet (4, -6).

y = 1/2x - 8

-6 = 1/2(4) - 8

-6 = 2 - 8

-6 = -6

Your equation is correct.

Hope this helps!

Answer:

Y = -X + 9

Step-by-step explanation:

yeah-ya....... right?