Penny attended a four year state college. she took out a student loan to pay for her tuition and room & board for the four years she was attending the college. her tuition fees were $6,970 per year, and the cost of her room and board was $11,320 per year. now that she has graduated, she will have to start paying back her loan. fortunately, penny has a grace period of one year before she has to start paying back the loan. her loan details are as follows: there is a fixed-rate interest of 4.5% and the interest compounds each month. during her one year grace period, interest will accrue on the loan, so that when she has to start paying the loan back she will owe more than what she owes now. her goal is to be able to payoff the loan in 10 years. what is the new loan amount after the one-year grace period (remember that interest will accrue on the loan during this initial 12-month period that she is not paying anything back on the loan)? this is the amount that she will be responsible for paying back. (round your answer to the nearest whole dollar)

A. There are 297,920 possible 4-card hands with exactly 2 Aces.

B. The probability of getting a 4-card hand of just clubs is approximately 0.0665 or 6.65%.

Explanation for A:

To find the number of 4-card hands with exactly 2 Aces, we can use the combination formula. There are 4 choose 2 ways to select the 2 Aces from a deck of 52 cards, and 48 choose 2 ways to select the other 2 cards from the remaining 48 cards in the deck. Therefore, the total number of possible 4-card hands with exactly 2 Aces is:

(4 choose 2) * (48 choose 2) = 6 * 1,128 = 6,768

Explanation for B:

There are 13 clubs in a deck of 52 cards. To find the probability of getting a 4-card hand of just clubs, we can use the formula for a combination of 4 clubs divided by the total number of possible 4-card hands:

(13 choose 4) / (52 choose 4) ≈ 0.0665 or 6.65%

Therefore, the probability of getting a 4-card hand of just clubs is approximately 0.0665 or 6.65%.

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The length of side RQ is 13.00 ft.

Given that a triangle RPQ, with sides RP = 8 ft, PQ = 13 ft and angle P between these sides equal to 71°, we need to find the length of side RQ which is opposite to the angle P,

To find the length of side RQ using the cosine rule, we can use the formula:

RQ² = RP² + PQ² - 2 RP PQ Cos(P)

Let's plug in the given values:

RP = 8 ft

PQ = 13 ft

angle P = 71°

Now we can calculate RQ:

RQ² = 8² + 13² - 2 × 8 × 13 × cos(71°)

Using a calculator, we can evaluate the cosine term:

RQ² = 64 + 169 - 208 × cos(71°)

RQ² ≈ 64 + 169 - 208 × 0.3072

RQ² ≈ 64 + 169 - 63.9936

RQ² ≈ 169.0064

Taking the square root of both sides:

RQ ≈ √169.0064

RQ ≈ 13.00 ft (rounded to two decimal places)

Therefore, the length of side RQ is 13.00 ft.

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Kate will need 3/8 cup of sugar.

Fractions represent the parts of a whole or collection of objects.

A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.

Now it is given that,

Cups of sugar needed for a recipe= 3/4

Now Kate only wants to make half of the recipe

Cups of sugar needed for a half of the recipe = Cups of sugar needed for a recipe / 2

⇒ Cups of sugar needed for a half of the recipe = 3/4 ÷ 2

⇒ Cups of sugar needed for a half of the recipe = 3/8

Thus, Kate will need 3/8 cup of sugar.

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Answer:

0.012

Step-by-step explanation:

Have a good day.

Answer:

.01

Step-by-step explanation:

Change the percent to decimal form

.04% = .0004

.0004 *30

.012

Round to the nearest hundredth

.01

The property illustrated in (2 + 1) + (6 + 5) = (6 +5) +(2 + 1) is the commutative property of addition

From the question, we have the following parameters that can be used in our computation:

(2 + 1) + (6 + 5) = (6 +5) +(2 + 1)

In the above expression, we can see that

The terms of the expression are swapped

This can be illustrated as

if a + b = b + a

The name of the property is the commutative property of addition

Hence, the name of the property illustrated in (2 + 1) + (6 + 5) = (6 +5) +(2 + 1) is the commutative property of addition

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Answer:

if im correct the answer is 70

Step-by-step explanation:

A circle has a 360 degree angle so what I did is i added 85+80+125 and i got 290. 360-290=70

System sequence diagram is the best model to use to document the inputs and the outputs to a system.

In the realm of software engineering, a sequence diagram, also known as a system sequence diagram (SSD), depicts process interactions grouped in chronological order. It illustrates the processes involved and the order in which messages must be exchanged for the processes to provide the functionality. In the 4+1 architectural perspective model of the system under development, sequence diagrams are often connected to use case realizations. Event diagrams and event scenarios are other names for sequence diagrams.

The diagrams display the events that external actors produce, their order, and any potential inter-system events for a given scenario of a use case. [1] The diagram emphasizes events that cross the system boundary from actors to systems and treats all systems as black boxes. The main success scenario of the use case, as well as frequent or complex alternate situations, should be represented using a system sequence diagram.

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Answer: 3024

Step-by-step explanation:

mutiply 18x 168

Answer: -4

Step-by-step explanation:

-2+3-5=-4

I HOPE THIS HELPS!!!!

The solution to the composite function operation is:

(f + g)(x) = 1/x + x² + 2x - 5

Composite functions are defined as when the output of one function is to be used as the input of another. If we have a function f and another function g, then we can say that the function  f of g of x, is the composition of the two functions.

The two functions are given as:

f(x) = 1/x

g(x) =  x² + 2x - 5

Thus, the operation (f + g)(x) is:

(f + g)(x) = (1/x) + x² + 2x - 5

(f + g)(x) = 1/x + x² + 2x - 5

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Answer:

274.75 in²

Step-by-step explanation:

Area of a circle = πr² = (3.14)(20/2)² = 314 in²

(314 in²)(1/8) = 39.25 in²

Pizza remaining = 314 - 39.25 = 274.75 in²

Answer: 274.75

Step-by-step explanation:

Diameter=20

r= 20/2=10

A= π\(r^{2}\)

   = 3.14*10*10

   = 314 square inches

1/8 of 314 = 39.25

So, are of remaining pizza = 314-39.25

                                              = 274.75 square inches

Step-by-step explanation:

According to given table we have pairs of points:

The rate of change is:

or

It is 2.25 and the meaning is:

Answer:A+B+C=180=30

Step-by-step explanation:

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Marc's current marginal tax rate can be determined by referring to the U.S. tax rate schedule for the year 2021 based on his taxable income.

To calculate Marc's current marginal tax rate, we need to look at the U.S. tax rate schedule for the year 2021. The tax rate schedule consists of several tax brackets, each with its corresponding tax rate. As taxable income increases, individuals move into higher tax brackets and are subject to higher tax rates. Based on Marc's taxable income of $260,000, we would need to refer to the tax rate schedule to determine his marginal tax rate. As the exact tax rates within the brackets can vary, it's important to consult the specific tax rate schedule for the given year.

By locating the corresponding tax bracket for $260,000 in taxable income, we can identify the applicable tax rate. Marc's current marginal tax rate would be the tax rate associated with the bracket that includes his interest.

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the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

Here we have the quadratic equation:

f(x) = (x + 3)*(x + 5)

The first claim is: "The y-intercept is at (15, 0)."

This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.

The second claim is:

"The x-intercepts are at (–3, 0) and (5, 0)"

This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.

Third claim:

"The vertex is at (-4, -1)"

The middle value between the zeros is:

(-3 + (-5))/2 = -4

Evaluating the function in x = -4 we get the y-value of the vertex:

f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1

So the vertex is at (-4, -1), this claim is true.

The fourth claim is:

"The midpoint between the x-intercepts is at (4, 0)."

Which is false, we already saw that the midpoint between the x-intercepts is at x = -4

Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

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Answer: $271.15

Step-by-step explanation:

$5.80 × 40 = 232

Time and a half = $8.70  

Overtime is 4.5 hours

$8.70 × 4.5 = 39.15

$232 + 39.15 = 271.15

The Laplace transform of f(t) is f(s) = (1/(s-2)) - 8 e^(-4s).

We can split the function into two parts:

f(t) = e^(2t) - 8h(t-4)

Taking the Laplace transform of each part separately, we get:

L{e^(2t)} = ∫_0^∞ e^(-st) e^(2t) dt = ∫_0^∞ e^(t(2-s)) dt = 1/(s-2) (by using the Laplace transform formula for e^(at))

L{8h(t-4)} = 8 e^(-4s) (by using the formula for the Laplace transform of the unit step function h(t-a))

Thus, the Laplace transform of f(t) is:

f(s) = L{f(t)} = L{e^(2t)} - L{8h(t-4)} = 1/(s-2) - 8 e^(-4s)

Therefore, the Laplace transform of f(t) is f(s) = (1/(s-2)) - 8 e^(-4s).

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The length of the line ed according to the description of the cube is; 8.5.

First, since the shape is a cube, it follows that the diagonal of the top face can be used to determine the length of the sides of the top face.

Therefore , we have; length of each side of the top face;

ag = ge = ef = fa = √288/2 = 6√2.

Also, the diagonal of a to d is; √432 = 12√3.

Hence, the length of ed in the group as evident from the length of sides of the cube's top face in which case,

Consequently, the length of line ed is;√432 × 8.5.

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Answer:

The steepness of any incline can be measured as the ratio of the vertical change to the horizontal change. For example, a  5 % incline can be written as  5100 , which means that for every  100  feet forward, the height increases  5  feet.Figure  4.4.1 In mathematics incline of a line the slope and use the letter  m  to denote it. The vertical change is called the rise and the horizontal change is called the run.Slopem=vertical changehorizontal change=riserun(4.4.1)The rise and the run can be positive or negative. A positive rise corresponds to a vertical change up and a negative rise corresponds to a vertical change down. A positive run denotes a horizontal change to the right and a negative run corresponds to a horizontal change to the left. Given the graph, we can calculate the slope by determining the vertical and horizontal changes between any two points.Example  4.4.1 Figure  4.4.2 From the given points on the graph, count  3  units down and  4  units right.m=riserun=−3units4units=−34 the Answer is.m=−34 .

Step-by-step explanation:

Answer:

To do this, just do 12 divided by 4.80 = 2.5 dollars per can at Corner Grocery, and at Max's Market 15 divided by 5.25 = 2.85 per can. So the Corner Grocery has a better unit price by 35 cents.

Thanks for your question.

Answer:

i dont know

Step-by-step explanation:

i dont know

Answer: 76 in

in the comment i explained it

Answer:

45 yards and 176 yards

Step-by-step explanation:

Perimeter of a rectangular playing field = 2(Length + width)

P = 2(L+W)..................... Equation 1

From the question,

Let the width of the rectangular playing field = x yards,

The the Length = 4x-4 yards.

Given: P = 442 yards.

Substitute these values into equation 1

442 = 2(4x-4+x)

442/2 = 5x-4

221 = 5x-4

5x = 221+4

5x = 225

x = 225/5

x = 45 yards.

Width = 45 yards.

Length = (45×4)-4 yards = 176 yards

Hence the dimensions of the playing field are, 45 yards and 176 yards