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Howie wants to get a car loan with 4% simple interest rate. If the car costs $25,000, how much would Howie need to pay back at the end of one year, including the interest?

Answers

Answer 1

Answer:

The amount Howie will pay back at the end of one year is $26000.00

The given parameters are:

$P =25000$ -- the principal amount

$R = 4\%$ -- the interest rate

$T=1$ --- the duration

The amount to pay back in this duration is then calculated using:

$A = P(1 + RT)$

So, we have:

$A = 25000(1 + 4\% * 1)$

$A = 25000(1 + 4\% )$

Express percentage as decimal

$A = 25000(1 + 0.04)$

$A = 25000(1 .04)\n$

Multiply

$A = 26000$

Hence, the amount to pay back is $26000.00

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HELP MEEEEEEEEEEEEEE PLEASE

Answers

Answer: The answer is A (32)

Step-by-step explanation:

you multiply 8 times 4 and you get 32.

In the figure, side AB is given by the expression (5x + 5)/(x + 3), and side BC is (3x + 9)/(2x - 4).The simplified expression for the area of rectangle ABCD is _______, and the restriction on x is ____.

Answers

Answer:

The simplified expression for the area of rectangle ABCD is $( 15(x + 1))/(2(x - 2))$ , and the restriction on x is x≠2 .

Step-by-step explanation:

Side AB = Width of rectangle = (5x + 5)/(x + 3)

Side BC = Length of rectangle = (3x + 9)/(2x - 4)

Area of Rectangle = Length * Width

Putting values:

$Area\,\,of\,\,rectangle =( (3x + 9))/((2x - 4)) * ((5x + 5))/((x + 3))$

Solving,

$Area\,\,of\,\,rectangle =( 3(x + 3))/((2x - 4)) * (5x + 5)/((x + 3)) \nArea\,\,of\,\,rectangle =( 3)/(2(x - 2)) * 5x + 5\nArea\,\,of\,\,rectangle =( 3(5x + 5))/(2x - 4)\nArea\,\,of\,\,rectangle =( 15x + 15)/(2x - 4)\nArea\,\,of\,\,rectangle =( 15(x + 1))/(2(x - 2))$

The restriction on x is that x ≠ 2, because if x =2 then denominator will be zero.

So, the answer is:

The simplified expression for the area of rectangle ABCD is $( 15(x + 1))/(2(x - 2))$ , and the restriction on x is x≠2 .

9. Mark drinks one cup of coffee everyday. He orders a coffee from Dunkin Donuts and it costs him $3.50 everyday. He is starting to think that he might buy a Keurig and k-cups instead. The Keurig is $150 and each k-cup costs $0.50. How many cups of coffee will it take for the cost at Dunkin Donuts to be the same as having a Keurig and k-cups?

Answers

Answer: 50 cups of coffee

Step-by-step explanation:

Let x represent the number of cups of coffee that it will take for the cost at Dunkin Donuts to be the same as having a Keurig and k-cups.

He orders a coffee from Dunkin Donuts and it costs him $3.50 everyday. It means that the cost of ordering x cups would be 3.5x.

The Keurig is $150 and each k-cup costs $0.50. It means that the cost of ordering x cups would be 150 + 0.5x.

For the ordering cost to be the same, it means that

3.5x = 150 + 0.5x

3.5x - 0.5x = 150

3x = 150

x = 150/3

x = 50

The time taken to build a house is inversely proportional to the number of builders.If there are 6 builders, it takes 80 days to complete the house.
How many builders must be employed to build the house in just 16 days?

Answers

Answer:

30 builders

Step-by-step explanation:

80÷5=16

6x5=30

HELP! i'll mark you brainliest . find y

Answers

Answer: Thanks for points by the way what grade are you in ???

Step-by-step explanation:

Sand is poured onto a surface at 13 cm3/sec, forming a conical pile whose base diameter is always equal to its altitude. How fast is the altitude of the pile increasing when the pile is 1 cm high? Note that the volume of a cone is 13πr2h where r is the radius of the base and h is the height of the cone.

Answers

Answer:

Altitude of the pile will increase by 16.56 cm per second.

Step-by-step explanation:

Sand is poured onto a surface at the rate = 13 cm³ per second

Or $(dV)/(dt)=13$

It forms a conical pile with a diameter d cm and height of the pile = h cm

Here d = h

Volume of the pile $V=(1)/(3)* \pi r^(2)h$ cm³per sec.

Since h = d = 2r [r is the radius of the circular base]

r = $(h)/(2)$

$V=(1)/(3)\pi ((h)/(2))^(2)h$

$V=(1)/(3)\pi ((h^(2)))/(4)(h)$

$V=(1)/(12)\pi h^(3)$

$(dV)/(dt)=(1)/(12)\pi * 3(h)^(2)(dh)/(dt)$

$(dV)/(dt)=(1)/(4)\pi * h^(2)* (dh)/(dt)$

Since $(dV)/(dt)=13$ cm³per sec.

13 = $(1)/(4)\pi (1)^(2)(dh)/(dt)$ [For h = 1 cm]

$(dh)/(dt)=(13*4)/(\pi )$

$(dh)/(dt)=(52)/(3.14)$

$(dh)/(dt)=16.56$ cm per second.

Therefore, altitude of the pile will increase by 16.56 cm per second.

Final answer:

To solve this problem, we first find the expression for the volume of the cone in terms of the height. We then differentiate this expression to get the relation between the rates of change of the volume and the height. By substituting the given values, we can find the rate of change of the height when the cone is 1 cm high.

Explanation:

The question is related to the application of calculus in Physics, specifically rates of change in the context of real-world problem involving a three dimensional geometric shape - a cone. The student asks how fast the altitude of a pile of sand is increasing at a given time if sand is being poured onto a surface at a constant rate and the pile forms a cone whose base diameter is always equal to its altitude.

We know that the volume of a cone is given by V = (1/3)πr²h, where r is the radius of the base and h is the altitude. Since in this problem the base diameter is always equal to its altitude, we have d = 2r = h, or r = h/2.

Replace r in the volume formula, yielding V = (1/3)π(h/2)²h = (1/12)πh³. Differentiate this expression with respect to time (t) to find the rate of change of V with respect to t, dV/dt = (1/4)πh² * dh/dt.

Given that sand is poured at a constant rate of 13 cm³/sec (that is, dV/dt = 13), we can solve for dh/dt when h = 1cm. Substituting the given values into the equation, 13 = (1/4)π(1)² * dh/dt, we find dh/dt = 13/(π/4) = 52/π cm/sec. Therefore, when the conical pile is 1 cm high, the altitude is increasing at a rate of 52/π cm/sec.

Learn more about Calculus in Physics here:

brainly.com/question/28688032

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