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39) The balance in the account after 6 years is $4,073.62.

40) The balance in the account after 6 years is $4,134.83

What is the formula for compound interest?

[tex]A = P(1 + \frac{r}{n} )^{(nt) }[/tex]

Here P is the principal,A is the balance, r is the annual interest rate, n is the number of times the interest is compounded per year, t is the time in years.

39) Here given that P = $3500, r = 2.16% = 0.0216, n = compounded quarterly = 4 and t = 6.

So, [tex]A = 3500(1 + \frac{0.0216}{4})^{(4 \times 6)} = 4,073.62[/tex]

Therefore, the balance in the account after 6 years is $4,073.62.

40)Here given,P = $3500, r = 2.29% = 0.0229, n = 12 (compounded monthly), and t = 6.

[tex]A = 3500(1 + \frac{0.0229}{12})^{(12 \times 6)} = 4,134.83[/tex]

Therefore, the balance in the account after 6 years is $4,134.83.

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Hence, 7, 22, 37, and 52 are the first four terms in the arithmetic series with initial term 7 and common difference 15.

Algebraic progression is a series of numbers where each term following the first is derived by multiplying the previous president by a constant known as the common difference (d). An arithmetic progression often takes the form: A, A+D, A+2D, A+3D,... where "a" stands for the initial keyword and "d" for the common distinction.

given

The sequence's initial term is 7, and the shared discrepancy is 15. We can continuously add 15 to the preceding word to find the next terms.

As a result, the arithmetic sequence's first four terms are:

Initial term = 7

Term two: 7 plus 15 equals 22

Third term = 22 plus 15 equals 37

Fourth term: 37 plus 15 equals 52

Hence, 7, 22, 37, and 52 are the first four terms in the arithmetic series with initial term 7 and common difference 15.

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The area of the triangle is 87.6 cm².

The area of the triangle can be found as follows:

Therefore,

area of a triangle = 1 / 2 bh

where

Therefore,

b = 17 cm

h = 10.3 cm

Hence,

area of a triangle = 1 / 2 × 17 × 10.3

area of a triangle = 1 / 2 × 175.1

area of a triangle = 87.55

area of a triangle = 87.6 cm²

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according to the given information we can say that the fraction of the area of the circle that is shaded is 1/4 or 0.25.

Every point in a horizontal surface that is a certain distance above another point forms a circle (centre). It is a circle made out of point that are separated from each other in a horizontal direction as a result. At all angles, it is rotating symmetric about the centre. In the closed, two-dimensional plane of a circle, each pair of points is evenly separated from the "centre." A line that pierces the circle creates a specular symmetrical line. At all angles, it rotates symmetrically about the centre.

given,

If the circle is divided into two equal parts and one of them is shaded, then the shaded area is half of the total area of the circle. So the fraction of the area of the circle that is shaded is 1/2 or 0.5.

If the circle is divided into four equal parts and one of them is shaded, then the shaded area is one-fourth of the total area of the circle. So the fraction of the area of the circle that is shaded is 1/4 or 0.25.

Therefore, the answer depends on how many equal parts the circle is divided into and the number of shaded parts.

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The amount after 5 years with a principal of $5000 compounded quarterly at an interest rate of 2.25% annually is $5593.60 approximately.

Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment but also on any accumulated interest from previous periods. In other words, it's the interest earned on the principal amount plus any interest earned previously.

To calculate the amount after 5 years, we need to use the formula for compound interest:

A = P × {1 + r ÷ (n × 100)} ∧ (n × t)

where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $5000, r = 2.25% , n = 4 (since interest is compounded quarterly), and t = 5.

After applying these values, we get:

A = $5000 x (1 + 2.25/400) ⁴ ˣ ⁵

A = $5000 x (1.005625) ²⁰

A = $5000 x 1.1871955

A = $5593.60 (rounded off to 2 decimals)

Therefore, the amount after 5 years with a principal of $5000 compounded quarterly at an interest rate of 2.25% annually is $5593.60 approximately.

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The equation that represents the relationship between the distances each girl has run is: Marcia = -3/4 * k + 6.5

Let x be the distance run by Tamara in kilometers.

Since Tamara has completed 3/4 of the race, then x = 3/4 * k.

Since Tamara is 2.5 kilometers ahead of Marcia, then x - 2.5 = 4 - Marcia.

Substituting the first equation into the second equation, we get:

3/4 * k - 2.5 = 4 - Marcia

Multiplying both sides by -1, we get:

Marcia - 4 = -3/4 * k + 2.5

Adding 4 to both sides, we get:

Marcia = -3/4 * k + 6.5

Therefore, the equation that represents the relationship between the distances each girl has run is:

Marcia = -3/4 * k + 6.5

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Answer:

The party opposed to expanding slavery in the United States was the Republican Party. It was actually formed to go against slavery.  

The length of the arc is 1 unit.

The distance that runs through the curved line of the circle making up the arc is known as the arc length.

length of an arc is expressed as;

l = tetha/360 ×2πr

the circumference of circle is expressed as ;

C = 2πr

6 = 2×3.14 × r

r = 6/6.28

r = 0.955 units

Therefore length of the arc

= 60/360 × 6

since 2πr is the circumference,

l = 360/360 = 1 unit

therefore the length of the arc is 1 unit.

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According to the given information, the value of the surface integral is 8/3.

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface integral of a vector field F over a surface S is given by:

∬S F ⋅ dS = ∬R (F ⋅ ru × rv) dA

where R is the parameter domain of the surface S, ru and rv are the partial derivatives of the position vector r(u,v) with respect to u and v, and dA = ||ru × rv|| dudv is the area element on the surface.

In this case, we want to evaluate the surface integral:

∫∫H 4y dA

where H is the helicoid given by the vector parametric equation:

r(u,v) = <u cos(v), u sin(v), v>, 0 ≤ u ≤ 1, 0 ≤ v ≤ 9π.

The position vector r(u,v) has partial derivatives with respect to u and v given by:

ru = <cos(v), sin(v), 0>

rv = <-u sin(v), u cos(v), 1>

The area element is given by:

dA = ||ru × rv|| dudv = ||<cos(v), sin(v), u>| dudv = u dudv

Therefore, the surface integral can be written as:

[tex]$\int\int_H 4y dA = \int_0^{9\pi} \int_0^1 4(u\sin v)u dudv$\\$= \int_0^{9\pi} \sin v \int_0^1 4u^2 du dv$[/tex]

[tex]$= \int_0^{9\pi} \sin v \left(\frac{4}{3}\right) dv$\\$= \left[-\frac{4}{3} \cos v\right]_0^{9\pi}$[/tex]

= 8/3

Hence, According to the given information the value of the surface integral is 8/3.

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Answer:

[tex]tringle = \frac{1}{2} \times base \times hieght[/tex]

1/2 × 8×5

0.5×40

=20m

George sold 18, 22, 26, 12, 25, 20, and 19 cars per month over the past seven months.

George's first mistake was in Step 1 where he tried to find the total number of cars he needs to sell in the next month to have a mean number of sales per month of 24. To find this value, George should have multiplied the desired mean number of sales per month (24) by the total number of months (7) to get the total number of cars needed to have a mean of 24 over 7 months. However, it seems that George skipped this step and directly assumed that the total number of cars needed for a mean of 24 in the next month is simply 24.

Let's go through each step to explain

Step 1 Find the total cars needed to have a mean of 24

To find the total number of cars George needs to sell over the next 7 months to have a mean of 24 cars sold per month, he should multiply the desired mean (24) by the number of months (7)

Total cars needed = 24 * 7 = 168

Step 2  Find the total cars sold

To find the total number of cars George sold over the past 7 months, he should add up the individual sales for each month:

Total cars sold = 18 + 22 + 26 + 12 + 25 + 20 + 19 = 142

Step 3 Subtract the total cars sold from the total cars needed

To find the number of cars George needs to sell in the next month to meet his target mean of 24 cars sold per month over the past 8 months, he should subtract the total number of cars sold from the total cars needed

Cars needed in the next month = Total cars needed - Total cars sold

Cars needed in the next month = 168 - 142 = 26

Step 4 State the answer

George needs to sell 26 cars next month to have a mean of 24 cars sold per month over the past 8 months.

Therefore, George's mistake was in Step 1 where he did not correctly calculate the total number of cars he needs to sell over the next 7 months to have a mean of 24 cars sold per month.

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Answer:-by-step explanation:

the function has the x-intercept of (-2, 0)

the function has the y-intercept of (0, -8)

the function has the x-intercept of (4, 0)

Answer: 1.8

Let's put our whole number and fraction side by side so we can visualize the problem we're trying to solve:

3 ÷

5

3

The trick to working out 3 divided by 5/3 is similar to the method we use to work out dividing a fraction by a whole number.

All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator. Let's write this down visually:

3 x 3

5

=

9

5

So, the answer to the question "what is 3 divided by 5/3?" is:

9

5

Sometimes, after calculating the answer we can simplify the resulting fraction down to lower terms. In this example though 9/5 is already in it's lowest possible form.

If you made it this far you must really love your fractions and dividing whole numbers by them. Hopefully this simple guide was easy for you to follow along and you can now go forth and divide more whole numbers by as many fractions as your heart desires.

Convert 3 divided by 5/3 to Decimal

One last little calculation before you go. It's common to want to express your result as a decimal and, to do that, all you need to do is divide your numerator by your denominator:

9

5

= 1.8

Step-by-step explanation:

Rate UP stream =  ( s - w) = 106 km / 2 hr  

                                               (  where s = boat speed       w = current speed )

                              (s-w) = 53  km/hr

Rate DOWNstream = ( s+w) = 142 / 2 = 71 kmhr

( s-w) + ( s+w) = 53  + 71   km/hr

2s = 124  

s = 62 km /hr      then   s+w = 71   shows w = 9 km/hr

The slope-intercept form of the equation is y = 18x.

To find the function in slope-intercept form, we have to write the general form below as;

y = mx + c

m = slope

c = y-intercept

To find the slope, we need to take two points from the table given;

slope (m) = y2 - y1 / x2 - x1

m = 720 - 450 / 40- 25

m = 18

The slope of the line is 18

we can use this with any point to find the y - intercept

y = mx + c

720 = 18(40) + c

720 = 720 + c

c = 720 - 720

c = 0

The equation of the line in slope-intercept form is y = 18x

b. To determine how far he travelled with 55 gallons of gas

y = 18x

y = 18(55)

y = 990 miles

c. How many gallons will be required to cover 630 miles

y = 18x

630 = 18x

x = 630 / 18

x = 35 gallons

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Answer:

Step-by-step explanation:

7.3 is the anwser

Answer:The amount of a 80% acid solution that must be mixed with a 55% solution to produce 600 mL of a 60% solution can be calculated using a simple algebraic equation. Let x represent the amount of the 80% acid solution in mL that needs to be mixed with the 55% solution.

The equation can be set up as follows:

0.80x + 0.55(600 - x) = 0.60(600)

Step-by-step explanation: The left-hand side of the equation represents the total amount of acid in the mixture. The first term, 0.80x, represents the amount of acid from the 80% solution, and the second term, 0.55(600 - x), represents the amount of acid from the 55% solution. The right-hand side of the equation represents the total amount of acid in the final 60% solution, which is 60% of 600 mL.

By solving this equation for x, we can determine the amount of the 80% acid solution that needs to be mixed with the 55% solution. Once we have the value of x, we can then calculate the amount of the 55% solution by subtracting x from 600 mL.

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Let x=amount of 80% solution needed

Then 600-x=amount of 30% solution needed

Now we know that the pure acid in the 80% solution (0.80x) plus the amount of pure acid in the 30% solution ((0.30)(600-x)) has to equal the amount of pure acid in the final mixture(0.40*600), so our equation to solve is:

0.80x+0.30(600-x)=0.40*600 get rid of parens

0.80x+180-0.30x=240 subtract 180 from each side

0.80x+180-180-0.30x=240-180 collect like terms

0.50x=60 divide each side by 0.50

x=120 ml---------------------amount of 80% solution needed

600-x=600-120=480 ml---------------amount of 30% solution needed

CK

120*0.80+480*0.30=0.40*600

96+144=240

240=240

The value of 5 cubic cm in liters, can be converted to be

To convert cubic centimeters (cm³) to liters (L), we can use the following conversion factor:

1 L = 1000 cm³

This means that 1 liter is equal to 1000 cubic centimeters. To convert cubic centimeters to liters, we can divide the number of cubic centimeters by 1000.

For example, to convert 5 cubic cm to liters:

5 cm³ ÷ 1000 = 0.005 L

Therefore, 5 cubic cm is equal to 0.005 liters (or 5 mL).

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Full question:

5 cubic cm to Liters

The correct answer is C. The circumference of a circle varies directly as the radius.

It is calculated by multiplying the diameter of a circle by pi, or by measuring the length of a curved line that encloses the shape.

The relationship between the circumference of a circle and its radius is a linear equation, where the circumference is equal to two times pi times the radius, or C = 2πr.

The circumference of a circle varies directly as the radius, meaning that if the radius of a circle is doubled, the circumference will also double.

This linear relationship can be used to approximate the value of pi, which is a constant ratio between the circumference and the diameter of any circle.

Therefore, the statement that justifies why the measurements of the circumference and radii of circles with different areas can be used to approximate the value of pi is that the circumference of a circle varies directly as the radius.

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 [tex]1.[/tex] The answers are given below

   Equation: [tex]6xt +4yz -3 +10a = 1[/tex]

   Number of terms: [tex]4[/tex]

  Coefficients: [tex]6,4,10[/tex]

   Constants: [tex]-3,1[/tex]

 [tex]2.[/tex] Expression: [tex]25abc -2b +3ac -6bc +25[/tex]

    Number of terms: [tex]5[/tex]

    Coefficients: [tex]25,-2,3,-6[/tex]

    Constants: [tex]25[/tex]

  [tex]3.[/tex] Equation: [tex]25y -3xy+5x = 100[/tex]

     Number of terms: [tex]3[/tex]

     Coefficients: [tex]25,-3,5[/tex]

      Constants: [tex]100[/tex]

To break down each equation or expression and identify the number of terms, coefficients, and constants.

[tex]1.[/tex] Equation: [tex]6xt +4yz -3 +10a = 1[/tex]

   Number of terms: 4. There are four terms in this equation separated     by addition and subtraction operators.

Coefficients: [tex]6,4,10[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (xt, yz, a) in each term.

 Constants: [tex]-3,1[/tex]. These are the constants, which are the numerical values without any variables that are added or subtracted in the equation.

[tex]2.[/tex]  Expression:[tex]25abc -2b +3ac -6bc +25[/tex]

   Number of terms: [tex]5[/tex] There are five terms in this expression separated by addition and subtraction operators.

  Coefficients: [tex]25,-2,3,-6[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (abc, b, ac, bc) in each term.

  Constants: [tex]25[/tex]. This is the constant, which is the numerical value without any variables that is added in the expression.

[tex]3.[/tex]  Equation: [tex]25y -3xy+5x = 100[/tex]

    Number of terms:[tex]3[/tex]. There are three terms in this equation separated by addition and subtraction operators.

    Coefficients: [tex]25,-3,5[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (y, xy, x) in each term.

   Constants: [tex]100[/tex]. This is the constant, which is the numerical value without any variables on the right-hand side of the equation.

Therefore,   [tex]1.[/tex] The answers are given below

   Equation: [tex]6xt +4yz -3 +10a = 1[/tex]

   Number of terms: [tex]4[/tex]

   Coefficients: [tex]6,4,10[/tex]

   Constants: [tex]-3,1[/tex]

 [tex]2.[/tex] Expression: [tex]25abc -2b +3ac -6bc +25[/tex]

    Number of terms: [tex]5[/tex]

    Coefficients: [tex]25,-2,3,-6[/tex]

    Constants: [tex]25[/tex]

  [tex]3.[/tex] Equation: [tex]25y -3xy+5x = 100[/tex]

     Number of terms: [tex]3[/tex]

     Coefficients: [tex]25,-3,5[/tex]

      Constants: [tex]100[/tex]

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according to the question, the PLUS Loan will have a higher balance due at the time of repayment by $233.80 ($11,966.11 - $11,732.31).

Divide the principal times the interest rates, the length of time, and various other factors to arrive at simple interest. Simple return = principle + interest + hours is the marketing formula. The easiest way to compute interest is with this method. The most typical technique to figure out interest is to use a portion of the principal sum. He is only going to pay his share of the 100% interest, for example, if he loans $100 form a friend then agrees to pay it off with 5% interest. $100 (0.05) corresponds to $5. Interest must be paid as you borrow money and must be added to any loans you make. Interest is often determined as a yearly proportion of the loan total. The interest on the loan is this percentage.

given,

To compare the two loans, we need to calculate the total balance due for each loan at the time of repayment. We can start by calculating the balance due for the Unsubsidized Stafford Loan:

Principal: $10,720

Interest rate: 5.95% per year, compounded monthly

Time: 6 months grace period + 6 months repayment = 1 year

Number of periods: 12 months x 1/12 month per period = 12 periods

Using the formula for compound interest, the balance due on the Unsubsidized Stafford Loan after 1 year is:

B = P(1 + r/n)^(nt) + I [(1 + r/n)^(nt) - 1]/(r/n)

where B is the balance due, P is the principal, r is the annual interest rate, n is the number of times per year the interest is compounded, t is the time in years, and I is the monthly payment.

Plugging in the numbers, we get:

B = $10,720(1 + 0.0595/12)^(121) + $0 [(1 + 0.0595/12)^(121) - 1]/(0.0595/12)

B = $11,732.31

Now, let's calculate the balance due for the PLUS Loan:

Principal: $11,443.63

Interest rate: 6.55% per year, compounded monthly

Time: 6 months repayment

Number of periods: 6 periods

Using the same formula for compound interest, the balance due on the PLUS Loan after 6 months is:

B = $11,443.63(1 + 0.0655/12)^(120.5) + $0 [(1 + 0.0655/12)^(120.5) - 1]/(0.0655/12)

B = $11,966.11

Therefore, the PLUS Loan will have a higher balance due at the time of repayment by $233.80 ($11,966.11 - $11,732.31). Thus, the Unsubsidized Stafford Loan will have a lower balance due at the time of repayment compared to the PLUS Loan.

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The equations that will make a linear function are

A linear equation, also referred to as a linear function in mathematics, is used to identify relationships between variables that can be plotted on a straight line.

This class of polynomial functions have a degree of 1, indicating that the highest power of the variable within the formula cannot exceed 1.

It takes on the standardized form:

y = mx + b

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Clara's and Stefan's pizzas did not have the same ratio of pepperoni pieces to ham pieces.

For Clara,

The number of pepperoni pieces = 4

The number of ham pieces = 6

The ratio = 4:6 = 2:3

For Stefan,

The number of pepperoni piece = 6

The number of ham piece = 10

The ratio = 6:10 = 3:5

Therefore the ratio of Clara's and Stefan's pizzas is not the same.

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