You have $8.80 in pennies and nickels. You have twice as many nickels as pennies. Write a system of linear equations that models the situation. Be sure to state what x and y represent. Solve those equations algebraically to determine how many of each type of coin do you have. please help

Answer:

a

Step-by-step explanation:

The estimated market value of Citrus County's assets, with an average duration of 8 and a market value of $1 million, would be approximately $1,055,284 if the interest rate changes to 4%.

In this case, the assets have an average duration of 8. When the interest rate changes from 5% to 4%, the change in interest rates is 1%. By applying the duration formula, the estimated percentage change in the market value of the assets would be approximately -8% (negative duration multiplied by the change in interest rates).

To calculate the estimated market value, we need to multiply the estimated percentage change (-8%) by the current market value ($1 million) and add it to the current market value. Thus, the estimated market value would be approximately $1,055,284 (1,000,000 + (1,000,000 * -8%)).

Duration is a measure of the sensitivity of an asset's price to changes in interest rates. It provides an estimate of the percentage change in the market value of an asset for a given change in interest rates. The duration formula states that the percentage change in the market value of an asset is approximately equal to the negative duration multiplied by the change in interest rates.

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Numbers without fractions are referred to as "whole numbers," and they are made up of positive integers and zero. It is denoted by the letter "W," and its corresponding set of numbers are 0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12,..

A mathematical procedure called addition symbolizes adding objects t to a larger collection. The plus sign ( + ) is used to denote it.

Some examples of the addition of whole numbers is:

1 + 8 = 9

10 + 19 = 29

A mathematical operation known as subtraction symbolizes the process of determining the difference between two numbers or units. The negative sign is used to denote it ( - ).

An example of subtraction of whole numbers is:

10 - 2 = 8

40 - 25 = 15

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James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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Answer:

We have the equation of the line as : 4x+2y=12

Step-by-step explanation:

Now 4x+2y=12

=> 2y = 12 - 4x

=> y = 6 - 2x

A line with a slope m and y-intercept c can be written as y = mx + c

In the case of y = -2x -...

Step-by-step explanation:

I hope the picture is clear enough.

Answer:

Ron to Bill = 67 yd

Bill to John = 30 yd

Total number of yards = 97 yd

Step-by-step explanation:

See the figure below.

Use the Pythagorean theorem to find the distance from Ron to Bill.

a² + b² = c²

60² + 30² = c²

c² = 3600 + 900

c² = 4500

c = √4500

c = 67

Ron to Bill = 67 yd

Bill to John = 30 yd

Total number of yards = 97 yd

$ 410

hi there !

80% ................. $328

100% .................$ x

x = 100×328/80

= 32800/80

= $ 410

Good luck !

Answer:

I don't know the answer but all you have to do is multiply

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

The probability that a pupil uses neither pool nor gym is 11/70

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6.

Number of pupil that can use pool and gym = 28

Number of people that can use pool = 48

Number of people that can use gym = 39

Number of people that can use pool only = 48 - 28 which is 20

Number of people that can use gym only = 39 - 28 = 11

Total number of persons that can use either pool, gym or both = 20 + 11 + 28 which is 59

Number of people that cannot use either or both of the facilities = 70 - 59 which is 11.

Probability = required outcome / possible outcome

Required outcome = 11

possible outcome = 70

Probability = 11/70

In conclusion, the probability that a pupil uses neither swimming pool nor gym is 11/70

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Answer:

65

Step-by-step explanation:

The inside of a triangle is 180 degrees and the other two angles are the same so 50+65+65 =180. The answer is 65

Step-by-step explanation:

180-159= 21

21+112= 124

180-124= 56°

x = 56°

Angles in a triangle add up to 180°

Angles in a straight line add up to 180°

Hope this helped!

Another answer:

27°

(another answer has explained it, credits to them)

Answer:

The focus (or foci).

Step-by-step explanation:

The focus of a hyperbola are equidistant from the center of the hyperbola. They can be found with the formula c²= a² + b². The points for the foci being

(-c, y) and (c, y).

In this illustration, the foci are the points in blue.

The mean height of the hexagon is 21.33 in.

To find the length of the sides of a regular hexagon with a perimeter of 372 inches, you must divide the perimeter by 6. This gives you a result of 62 inches for the length of each side. The other steps are:

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To find the minimum value of n, iterate through values of n until the error term is less than 0.01. Then, use the Maclaurin series with this n to estimate e^(1.1).

To estimate e^(1.1) within 0.01 using a Taylor polynomial centered at x=0, we'll apply the Maclaurin series, which is a Taylor series expansion of a function at x=0. The Maclaurin series for e^x is given by:
e^x = 1 + x + (x^2)/2! + (x^3)/3! + ... + (x^n)/n! + ...
Now, we want to estimate e^(1.1) within 0.01. Let x = 1.1, and find the minimum value of n such that the remainder term (the error) is less than 0.01.
Using the Lagrange remainder formula, the maximum error is given by:
|e^(1.1) - P_n(1.1)| ≤ M*(1.1)^(n+1)/((n+1)!)
Here, M is the maximum value of the (n+1)th derivative of e^x on the interval [0, 1.1], which is just e^(1.1) since the derivatives of e^x are also e^x.
To find the minimum value of n, iterate through values of n until the error term is less than 0.01. Then, use the Maclaurin series with this n to estimate e^(1.1).

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Nicole would have $73,036.70 - $56,772.25 = $16,264.45 more money than Bentley after 14 years at the given interest rate.

Simple interest refers to an interest rate where the interest is just calculated on the principal sum of money. For the duration of the loan or investment, the interest rate is only applied once to the principal sum. On the other hand, compound interest is a type of interest where the interest is computed using both the principal and the interest from prior periods. After each compounding period, the interest rate is applied to the newly created balance.

The compound interest is given as:

\(A = P * e^{(rt)}\)

Substituting the given values:

\(A = 29000 * e^{(0.0541 * 14)} = $73,036.70\)

Now, after 14 years:

\(A = P * (1 + r/100)^t\)

Substituting the values:

\(A = 29000 * (1 + 0.04885)^{14} = $56,772.25\)

Hence, Nicole would have $73,036.70 - $56,772.25 = $16,264.45 more money than Bentley after 14 years

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The phenomena of hiding distribution characteristics in a system from applications and users is known as distribution transparency. Access transparency, location transparency are some examples.

Distributed databases have the attribute of distribution transparency, which keeps consumers from knowing the internal workings of the distribution.

Thus, access transparency, location transparency are some examples of the (distribution) transparency.

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Answer:

Y= 2x-28

Step-by-step explanation:

The present value of the payments is smaller than the amount of the loan, so you will not be able to pay off the loan.

The present value of the payments refers to the current value of the future payments, considering the time value of money. In this case, the payments are made over a period of 8 months, and each payment is listed. To determine if the payments will be enough to pay off the credit card, we need to calculate the present value of these payments and compare it to the initial loan amount of $5,000.

Since the interest rate on the credit card is 1.5% per month, we need to discount each payment back to its present value. By discounting the payments, we can see the equivalent value of these payments in today's dollars. If the present value of the payments is equal to or greater than $5,000, it would be enough to pay off the loan. However, if the present value is smaller than $5,000, it means the payments will not be sufficient to pay off the loan.

In this case, without specific information about the discount rate used to calculate the present value, we cannot make an exact determination. However, based on the given information, which states that the present value of the payments is smaller than the amount of the loan, it suggests that the payments will not be enough to pay off the credit card debt.

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Answer:

0.075

Step-by-step explanation:

To represent 7 1/2 as a decimal, it would be 0.075 since there are 7 hundredths and half a hundredth.

Answer: $62100

Step-by-step explanation:

The following can be deduced from the information given in the question:

Credit balance = $54000

Total revenues = $72,200

Total expenses = $48,300

Dividends = $15,800

Closing entry= Credit balance + Total revenues - (Total expenses + Dividends)

= $54000 + $72,200 - ($48300 + $15800)

= $126200 - $64100

= $62100

Answer:

$1.27

$9030.56

$2,210.34

Step-by-step explanation:

The formula for calculating future value:

FV = P (1 + r/n)^nm

FV = Future value  

P = Present value  

R = interest rate  

m = number of compounding

N = number of years  

1. 1( 1 + 0.24 /12)^12 = $1.27

2. 5000 ( 1 + 0.12 /4)^( 5 x 4) = $9030.56

the formula for calculating future value when there is continuous compounding is : A x e^r x N

A= amount e = 2.7182818 N = number of years r = interest rate

3. 1000 x e^0.1 x 2 = $2,210.34

Answer:

$72 is the retail price

Step-by-step explanation:

100 x (100-28)/100

The value of a should be 2 for the function to be composite.

What is composite function?

When two functions, f and g, are combined to create a third function, h, the result is such that h(x) = g(f(x)).

Main Body:

A commutative function means that when you insert one function in space of x in the other function, they will equal x. The equation is

f(g(x)) = g(f(x)) = x

So, 2(\(\frac{x+1}{a}\)) - 1 = \(\frac{(2x-1)+1}{a}\)

If you multiply both sides by a, you get   2a(\(\frac{x+1}{a}\)) - a = (2x-1)+1

Simplify it                                                   2a(\(\frac{x+1}{a}\)) - a = 2x

Add a to both sides                                    2a(\(\frac{x+1}{a}\))  = 2x +a

The two as on the left cancel out                   2(x+1)=2x+a

Distribute the 2:                                              2x+2=2x+a

Then subtract 2x from both sides                        2 = a

Therefore, a = 2

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Answer:

B. 2

Step-by-step explanation:

Right on Edge

Using trigonometry, it is found that:

1. Graph 2 shows an angle in which cos(θ) = -8/17 and sin (θ) is negative.

2. The angles are θ = 157.38º and θ = 202.62º, as shown in Graph 1.

3. Graph 3 shows an angle of θ = 315º.

In item 1, it asks for an angle in which both the sine and the cosine of the angle are negative. This happens in the third quadrant, hence Graph 2 shows an angle in which cos(θ) = -8/17 and sin (θ) is negative.

The secant of an angle is given by one divided by the cosine of the angle, that is:

sec(θ) = 1/cos(θ)

Considering the numeric value of the secant in this problem, we have that:

-13/12 = 1/cos(θ)

-13cos(θ) = 12

cos(θ) = -12/13

The cosine is negative in the second and the third quadrant, hence graph 1 shows these equivalent angles.

Applying the inverse cosine, the angles are given as follows:

θ = arccos(-12/13)

θ = 157.38º and θ = 202.62º. (two equivalent angles).

An angle of 315º is on the fourth quadrant of the unit circle, hence Graph 3 shows this angle.

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Therefore, the rate of the canoe in still water is 36 miles per hour.

Let's assume the rate of the canoe in still water is represented by r (miles per hour), and the rate of the current is represented by c (miles per hour).

When paddling with the current, the effective speed of the canoe is increased by the rate of the current, so the equation for the distance can be written as:

(r + c) * 4 = 64

When paddling against the current, the effective speed of the canoe is decreased by the rate of the current, so the equation for the distance can be written as:

(r - c) * 6 = (3/4) * 64

Simplifying the second equation:

6(r - c) = (3/4) * 64

6r - 6c = 48

Now we have a system of two equations:

(r + c) * 4 = 64

6r - 6c = 48

We can solve this system of equations to find the values of r and c.

Multiplying equation 1) by 6, we get:

6(r + c) = 6 * 64

6r + 6c = 384

Adding this equation to equation 2), the variable c will be eliminated:

6r + 6c + 6r - 6c = 384 + 48

12r = 432

Dividing both sides by 12, we find:

r = 36

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Answer:

100

Step-by-step explanation:

It is a rule that for two opposite arcs, with intersecting lines, between them, the average of the arcs is equivalent to the inside angle. Given this, we can say that:

(CF + ED)/2 = angle G

plug values in

(12x+9x+10)/2 = 110

multiply both sides by 2

21x + 10 = 220

subtract 10 from both sides

21x = 210

divide both sides by 21

x=10

Plug this into DE

10*9+10 = 100