Calculate the total cost of an item bought at a negotiated price of $14,380, a $2,700 trade-in allowance, a sales tax of 7.2 percent, and a $79 registration fee.$14266.08

$13,689.35

$12,794.36

$12,599.96

Answers

Answer 1
Answer:

The total cost of an item bought at a negotiated price of $14,380 is $12495.36.

Item bought at a negotiated price of $14,380, a $2,700 trade-in allowance,

A sales tax of 7.2 percent, and a $79  registration fee.

Let us find the cost of the item after 7.2% of sales tax.

What is the cost?

A cost is an expenditure required to produce or sell a product or get an asset ready for normal use.

The cost of an item after 7.2% of sales tax will be equal to 15640 plus 7.2% of 15640.

The cost of items after sales tax

=14,380+((7.2)/(100)* 14,380)

=14,380+(0.072 * 14,380)

=15415.36

Therefore the cost of an item after 7.2% of sales tax will be 15415.36

Now let us add the registration fee to the cost of the item.

The cost after registration fees is to the cost of items

=15415.36+79

=15495.36

Now let us subtract $2700 trade allowance to find the total cost of the item.

=15495.36- 2700

=12795.36

Therefore the total cost is $12495.36.

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Answer 2
Answer:

Answer:

The answer to this is option C: $12,794.36

Step-by-step explanation:

I just completed the test and this was the corrected answer.


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QuestionEnter the exponential function using t (for time) as the independent variable to model the situation. Thenfind the value of the function after the given amount of time.A new savings account is opened with $400 and gains 3.5% yearly for 5 years.The exponential function that models the situation is y = MyAfter 5 years, the savings account has $

Answers

Since, it is an exponential function, thus this is a compound interest problem;

Where; the function is given as;

\begin{gathered} A(t)=P(1+r)^t \n \text{Where A(t)= amount in the savings account at a time t} \n P=ca\text{ pital invested} \n r=\text{rate } \n t=\text{ time} \end{gathered}

Thus, the function required is;

\begin{gathered} A(t)=400(1+(3.5)/(100))^t \n A(t)=400(1.035)^t \end{gathered}\begin{gathered} y=400(1.035)^t \n \text{Where t is the time} \end{gathered}

After 5 years,

\begin{gathered} A(5)=400(1.035)^5 \n A(5)=400(1.1877) \n A(5)=475.07 \end{gathered}

The amount in the savings account after five years is $475.07

Suppose f(x,y)=xy, P=(−4,−4) and v=2i+3j. A. Find the gradient of f. ∇f= i+ j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (∇f)(P)= i+ j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf= Note: Your answer should be a number D. Find the maximum rate of change of f at P. Note: Your answer should be a number E. Find the (unit) direction vector in which the maximum rate of change occurs at P. u= i+ j Note: Your answers should be numbers

Answers

Answers:

  • Gradient of f:    \nabla f =  y\hat{i} + x\hat{j}
  • Gradient of f at point p: \nabla f = -4\hat{i} -4\hat{j}
  • Directional derivative of f and P in direction of v: \nabla f(P)v = -20\n
  • The maximum rate of change of f at P:  | \nabla f(P)| =  4√(2)
  • The (unit) direction vector in which the maximum rate of change occurs at P is:  v =  -(1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}

Step by step solutions:

Given that:

  • f(x,y) = xy
  • P = (-4,4)\n
  • v = 2i + 3j

A: Gradient of f

\nabla f = ((\partial f)/(\partial x), (\partial f)/(\partial y)) = (y,x) = y\hat{i} + x\hat{j}

B: Gradient of f at point P:

Just put the coordinates of p in above formula:

\nabla f = -4\hat{i} -4\hat{j}

C: The directional derivative of f and P in direction of v:

The directional derivative is found by dot product of \nabla f(P) \: \rm and \: \rm  v:

\nabla f(P)v = [-4,4][2,3]^T = -20\n

D: The maximum rate of change of f at P is calculated by evaluating the magnitude of gradient vector at P:

| \nabla f(P)| = √((-4)^2 + (-4)^2) = 4√(2)

E: The (unit) direction vector in which the maximum rate of change occurs at P is:

v = ((-4)/(4√(2)), (-4)/(4√(2))) = -(1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}

That vector v is the needed unit vector in this case.

we divided by 4√(2) to make that vector as of unit length.

Learn more about vectors here:

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Answer:

a) The gradient of a function is the vector of partial derivatives. Then

\nabla f=((\partial f)/(\partial x), (\partial f)/(\partial y))=(y,x)=y\hat{i} + x\hat{j}

b) It's enough evaluate P in the gradient.

\nabla f(P)=(-4,-4)=-4\hat{i} - 4 \hat{j}

c) The directional derivative of f at P in direction of V is the dot produtc of \nabla f(P) and v.

\nabla f(P) v=(-4,-4)\left[\begin{array}{ccc}2\n3\end{array}\right] =(-4)2+(-4)3=-20

d) The maximum rate of change of f at P is the magnitude of the gradient vector at P.

||\nabla f(P)||=√((-4)^2+(-4)^2)=√(32)=4√(2)

e) The maximum rate of change occurs in the direction of the gradient. Then

v=(1)/(4√(2))(-4,-4)=((-1)/(√(2)),(-1)/(√(2)))= (-1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}

is the direction vector in which the maximum rate of change occurs at P.

If a number is increased by 20% then the number is 24 find the number

Answers

Answer:

20

Step-by-step explanation:

  • x+20%=24
  • x+x*20/100=24
  • x+0.2x=24
  • 1.2x=24
  • x=24/1.2
  • x=20

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the ​P-value.

Answers

Answer:

hello your question has some missing parts below is the missing part

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean.

Identify the p-value.

Source DF SS MS F p

Factor 3 13.500 4.500 5.17 0.011

Error 16 13.925 0.870

Total 19 27.425

A) 0.011 B) 4.500 C) 5.17 D) 0.870

answer :  p-value = 0.011 ( A )

Step-by-step explanation:

using this information

Source DF SS MS F P

Factor 3 13.500 4.500 5.17 0.011

Error 16 13.925 0.870

Total 19 27.425

significance level = 0.05

given that the significance level = 0.05

and

F statistics are given as :  F = 5.17 , F critical = 3.25

hence the p-value = 0.011

from the analysis the p-value is less than the significance level is lower than the significance level

Final answer:

The p-value in a Minitab analysis of variance (ANOVA) test helps determine whether to reject or accept the null hypothesis that the samples all come from populations with the same mean. You would reject the null hypothesis if your p-value is less than the significance level (α = 0.05). Please refer back to your Minitab results to find this p-value.

Explanation:

In the context of your Minitab analysis of variance (ANOVA) results, the p-value that you should be looking at to determine the null hypothesis is not explicitly mentioned in your question. However, based on your description, you want to test the hypothesis that the different samples come from populations with the same mean (null hypothesis).

The p-value represents the probability that you would obtain your observed data (or data more extreme) if the null hypothesis were true. Therefore, if the p-value is less than the significance level (α = 0.05), you would reject the null hypothesis, suggesting that the samples do not all come from populations with the same mean. Conversely, if the p-value is larger than 0.05, you would fail to reject the null hypothesis, suggesting that the samples could come from populations with the same mean.

Please refer back to your Minitab results to find this p-value. Usually, it's labeled in the ANOVA table output as 'P' or 'Prob > F'.

Learn more about p-value here:

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An oil company fills 1/12 of a tank in 1/3 hour. At this rate, which expression can be used to determine how long will it take for the tank to fill completely? a. 1/12 x 3 hours
b. 1/3 x 12 hours
c. 1/3 x 1/12 hour
d. 3 x 12 hours

Answers

Selection B is appropriate.

_____
It takes 12 times as long to fill the whole tank as it does to fill 1/12 of the tank.
.. 12 * (1/3 hour) = (1/3)*12 hour

Answer: b . (1)/(3)*12 hours

Step-by-step explanation:

Given : A oil company fills (1)/(12) of a tank in (1)/(3) hour.

i.e. Time taken to fill (1)/(12) of a tank=  (1)/(3) hour.

By using the Unitary method, we multiply 12 on bith the sides of the above expression we get

Time taken to fill (1)/(12)*12  tank=  (1)/(3)*12 hour.

⇒ Time taken to fill 1 tank=  (1)/(3)*12=4 hour.

Hence, it will take (1)/(3)*12 hours or 4 hours for the tank to fill completely.

Thus , the correct answer is b . (1)/(3)*12 hours

*8. Consider a LTI system with unit impulse response, h(t) = e-3tu(t). Using direct integration technique for finding convolution, find its zero-state response due to an input, x(t) = u(t) (which is called unit step response of the system). Also, from your answer above, write down its response due to an input of the form, x(t) = 2δ(t) – 4u(t). [Hint: Use principle of superposition]

Answers

Answer:

Step-by-step explanation:

Check the attachment for solution