A student is graduating from college in 12 months but will need a loan in the amount of $11,985 for the last two semesters. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are:

Unsubsidized Stafford Loan: annual interest rate of 3.85%, compounded monthly, and a grace period of six months from time of graduation

PLUS loan: annual interest rate of 4.15%, compounded monthly, with a balance of $12,491.95 at the time of repayment

Which loan will have a higher balance, and by how much at the time of repayment?

The PLUS loan will have a higher balance by $37.30 at the time of repayment.
The Stafford loan will have a higher balance by $37.30 at the time of repayment.
The PLUS loan will have a higher balance by $204.39 at the time of repayment.
The Stafford loan will have a higher balance by $204.39 at the time of repayment.

solution of the linear equation is x = (2a - 16)/ 3 and y = - (a+16)/ 9

An algebraic expression that shows a relationship between two variables   that have only first order term. One of the main criteria for linear equation is that we get a straight line when plot this equation in a coordinate system.

.

we are given, two linear equations x - a -3y = 0

and a - 2x -3y - 16 =0

from the first equation, x = a + 3y

we put the value of x in the second equation, a - 2(a +3y) - 3y -16= 0

                                                                     a - 2a - 6y - 3y -16 = 0

                                                          - a - 9y -16 =0

                                                   - (a + 16) = 9y

                                              y = - (a+16) / 9

now we put the value of y in the equation, x = a + 3y

                                    get, x = a+ 3 [ - (a+16)] / 9

                                      x = a + [ - (a+16)] / 3

                                          x = (3a - a -16) / 3

                              x = (2a - 16)/ 3

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Answer:

The price per cup would be 0.41 cents.

Step-by step explaination:

Answer:

$0.41

Step-by-step explanation:

To find the price per cup of milk, we first need to know how many cups are in a 3-quart carton.

1 quart is equivalent to 4 cups, so a 3-quart carton contains:

\(\sf 3\;quarts=3 \times 4 \;cups= 12\;cups\)

Now, we can calculate the price per cup by dividing the total price by the number of cups:

\(\begin{aligned}\textsf{Price per cup} &= \dfrac{\textsf{Total price}}{\textsf{Number of cups}} \\\\&=\sf \dfrac{\$4.92}{12}\\\\&=\sf \$0.41\end{aligned}\)

Therefore, the price per cup of milk is $0.41.

Si alquilas el auto por un día y recorres 50 kilómetros, el precio del alquiler es de $400

Si rentas un auto por un día y recorres 50 kilómetros, el precio de renta será

$300 por día + $2 por kilómetro recorrido * 50 kilómetros

= $300 + $100 = $400.

La función que relaciona el precio de renta con los kilómetros recorridos se puede expresar como

P = 300 + 2K,

donde P es el precio de renta en dólares y K es la cantidad de kilómetros recorridos.

Si rentas un auto por un día y deseas que el precio de renta sea de $500, podemos utilizar la función determinada en el punto 2 para calcular la cantidad de kilómetros que puedes recorrer.

Reemplazando P = 500 en la función, tenemos

500 = 300 + 2K, entonces 200 = 2K, entonces K = 100.

Por lo tanto, puedes recorrer 100 kilómetros si deseas que el precio de renta sea de $500.

La función determinada en el punto 2 es lineal, ya que relaciona una variable dependiente (el precio de renta) con una variable independiente (los kilómetros recorridos) de manera lineal. Por lo tanto, la respuesta es is Lineal.

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The width of the lawn must be 13 ft. The result is obtained by using the area of the factory as a quadratic equation.

On a lot measuring 78 ft by 104 ft, a factory surrounded with the lawn is to be build. Tha lawn has uniform width and the area of the lawn is equal to the area of the factory building.

Find the width of the lawn that must be build!

Let's say:

The dimension of the factory:

See the illustration picture in the attachment!

The total area is

A = 78 ft × 104 ft

A = 8,112 sq ft

Since the factory area is equal to lawn area, the factory area is

A₀ = 8,112/2 = 4,056 sq ft

Use the area of the factory arranged as a quadratic equation to find x!

Width × Length = A₀

(78 - 2x) × (104 - 2x) = 4,056

8,112 - 156x - 208x + 4x² = 4,056

4x² - 364x + 4,056 = 0

x² - 91x + 1014 = 0

(x - 13) (x - 78) = 0

x = 13 or x = 78

Since the width of the lot is 78 ft, the width of the lawn must be less than that. So, the solution that makes sense is x = 13 ft.

Hence, the width of the lawn surrounding the factory is 13 ft.

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Given that the correlation between two variables is r=0.23. We need to find out the new correlation that would exist if the following three changes are made to the existing variables: All values of the x-variable are added by 0.14. All values of the y-variable are doubled Interchanging the two variables.  the correct option is B. 0.37.

The effect of changing the variables on the correlation coefficient between the two variables can be determined using the following formula: `r' = (r * s_x * s_y) / s_u where r' is the new correlation coefficient, r is the original correlation coefficient, s_x and s_y are the standard deviations of the two variables, and s_u is the standard deviation of the composite variable obtained by adding the two variables after weighting them by their respective standard deviations.

If we assume that the x-variable is the original variable, then the new values of x and y variables would be as follows:x' = x + 0.14 (since all values of the x-variable are added by 0.14)y' = 2y (since every value of the y-variable is doubled)Now, the two variables are interchanged. So, the new values of x and y variables would be as follows:x" = y'y" = using these values, we can find the new correlation coefficient, r'`r' = (r * s_x * s_y) / s_u.

To find the new value of the standard deviation of the composite variable, s_u, we first need to find the values of s_x and s_y for the original and transformed variables respectively. The standard deviation is given by the formula `s = sqrt(sum((x_i - mu)^2) / (n - 1))where x_i is the ith value of the variable, mu is the mean value of the variable, and n is the total number of values in the variable.

For the original variables, we have:r = 0.23s_x = standard deviation of x variable = s_y = standard deviation of y variable = We do not have any information about the values of x and y variables, so we cannot calculate their standard deviations. For the transformed variables, we have:x' = x + 0.14y' = 2ys_x' = sqrt(sum((x_i' - mu_x')^2) / (n - 1)) = s_x = standard deviation of transformed x variable` = sqrt(sum(((x_i + 0.14) - mu_x')^2) / (n - 1)) = s_x'y' = 2ys_y' = sqrt(sum((y_i' - mu_y')^2) / (n - 1)) = 2s_y = standard deviation of transformed y variable` = sqrt(sum((2y_i - mu_y')^2) / (n - 1)) = 2s_yNow, we can substitute all the values in the formula for the new correlation coefficient and simplify:

r' = (r * s_x * s_y) / s_ur' = (0.23 * s_x' * s_y') / sqrt(s_x'^2 + s_y'^2)r' = (0.23 * s_x * 2s_y) / sqrt((s_x^2 + 2 * 0.14 * s_x + 0.14^2) + (4 * s_y^2))r' = (0.46 * s_x * s_y) / sqrt(s_x^2 + 0.0396 + 4 * s_y^2)Now, we can substitute the value of s_x = s_y = in the above formula:r' = (0.46 * * ) / sqrt( + 0.0396 + 4 * )r' = (0.46 * ) / sqrt( + 0.1584 + )r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = r' = Therefore, the new correlation coefficient, r', would be approximately equal to.

Hence, the correct option is B. 0.37.

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Answer:

The larger number could be 9 or -10.

Step-by-step explanation:

Hi there!

Let the larger number be equal to a.

Let the smaller number to be equal to b.

We're given that their difference is 4:

\(a-b=4\)

We're also given that the sum of the smaller number and the square of the larger number is 86:

\(b+a^2=86\)

Rearrange the first equation to isolate a:

\(a=4+b\)

Substitute the first equation into the second:

\(b+(4+b)^2=86\\b+(16+8b+b^2)=86\\b+16+8b+b^2=86\\16+9b+b^2=86\\b^2+9b-70=0\)

Factor:

\(b^2+14b-5b-70=0\\b(b+14)-5(b+14)=0\\(b-5)(b+14)=0\)

The zero-product property tells us that when multiple terms have a product of 0, then at least one of the terms is equal to 0:

\(b-5=0\\b=5\)

Or

\(b+14=0\\b=-14\)

Therefore, b, or the smaller number, could be either 5 or -14.

Now, use b to solve for a:

\(a-5=4\\a=9\)

Therefore, the larger number is 9 if the smaller number is 5.

\(a+14=4\\a=-10\)

Therefore, the larger number is -10 if the smaller number is -14.

I hope this helps!

To maximize profits, the firm should produce a quantity of goods x = 5 and y = 10, based on the cost function and price constraints.

To maximize profits, the firm needs to find the quantities of goods x and y that will yield the highest profit. The profit function can be defined as the revenue minus the cost. Revenue is calculated by multiplying the quantity of each good produced with their respective prices, while the cost function is given as C(x, y) = 10x + xy + 10y.

The firm is committed to delivering a total of 15 units, which can be expressed as x + y = 15. To determine the optimal production quantities, we need to maximize the profit function subject to this constraint.

By substituting the price expressions Ps = 50 - x + y and Py = 50 - x + y into the profit function, we obtain the profit equation. To find the maximum profit, we can take the partial derivatives of the profit equation with respect to x and y, set them equal to zero, and solve the resulting system of equations.

Solving the equations, we find that the optimal production quantities are x = 5 and y = 10, which maximize the firm's profits.

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Answer:

3x-6+1

Step-by-step explanation:

I know algebraaaaaa

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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Using mathematical operations to evaluate the equations, the only equation that fits is m/10 + 4.7 = 3.7

An expression is an algebraic statement that is made up of constant, variables etc. An equation on the other hand is two equal expression often times, there's are unknown variables which the values makes them equal to one another.

In this problem, we have to plug the value of m = 10 in all equations and see which fits, or we can simply just solve for m

a) 5m + 5 = -40

5m = -40 - 5

5m = -45

m = -9

This does not fit

b) m/10 + 4.7 = 3.7

multiply through by 10

m + 47 = 37

m = 37 - 47

m = -10

The equation is true.

c)  m / 2 + 21 = 15

collect like terms

m / 2 = 15 - 21

m / 2 = -6

m = -12

This is false

d)

-49 + 3m = 72

3m = 72 + 49

3m = 121

m = 40.3

This is not true

Only m /10 + 4.7 = 3.7 is true for m = -10

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Answer:

96.5 or 97

Step-by-step explanation:

To break the numbers down, 96.5% of all the Earth's water is contained within the oceans as salt water, while the remaining 3.5% is freshwater lakes and frozen water locked up in glaciers and the polar ice caps. Of that fresh water, almost all of it takes the form of ice: 69% of it, to be exact.

Answer:

97 percent

Step-by-step explanation:

I'm wrote your notes

There could be x 21 tables with two people at them in the restaurant. Inequality caused by 2-seat tables is thus 21 or higher.

A connection that compares two numbers in an unfair manner is known as an inequality in mathematics. It is most typically used to compare the sizes of two numbers on a number line.

In mathematics, larger than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol are the five symbols used to represent inequality ().

Rule 1: When the same quantity is added to or withdrawn from both sides of an inequality, the inequality sign is unaffected. Rule 2: Divide or multiply both sides by a positive integer while leaving the inequality symbol alone.

The quantity of 2-seat tables in the restaurant will be denoted by the letter "x". The restaurant has 8 chairs plus 2 more seats. We can write the inequality to ensure that there are enough tables to fit at least 50 people:

8 + 2x ≥ 50

To solve for x, we can subtract 8 from both sides:

2x ≥ 42

And finally, we can divide both sides by 2:

x ≥ 21

So, the possible number of 2-seat tables in the restaurant is x ≥ 21

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Answer:

Answer:

C) \(\theta\approx\{0.3218,1.249,3.463,4.3908\}\)

Step-by-step explanation:

\(5\sin2\theta=3;\: 0\leq\theta\leq 2\pi\\\\\sin2\theta=\frac{3}{5}\\ \\2\theta\approx\{0.6436,2.498,6.926,8.7816\}\\\\\theta\approx\{0.3218,1.249,3.463,4.3908\}\)

Answer:

https://quizlet.com/71025324/ch-6-simple-interest-flash-cards/

Step-by-step explanation:

that has all your questions

Compound amount = $8867.39

compound interest = $1867.39

EXPLANATION

Given:

Principal(p) = $7000 Rate(r) = 0.12 Time(t) = 2 n= 4

We can calculate the compound amount(A) using the formula below:

Substitute the values and evaluate.

Hence, the compound amount = $8867.39

We proceed to find the compound interest.

A = P + I

⇒ I = A - P

= 8867.39 - 7000

=1867. 39

Therefore, the compound interest = $1867.39

Answer:

hope it help u sorry for dirty handwriting

Answer:

Zeroes: (-1.45, 0) and (3.45, 0)

Step-by-step explanation:

I plugged the equation into a graphing calc and located the x-values when graphing.

If a bungee jumper free falls for 4 seconds, they will fall approximately 257.6 feet during that time.

The terms given are "time in seconds," "t," "bungee jumper," "free fall," "function," "distance," "object falls," "feet," "4 seconds," and "how far."

When a bungee jumper experiences free fall, the amount of time in seconds, t, is related to the distance they fall, d, in feet. This relationship can be represented by a function that describes the motion of the jumper. In this case, we can use the free-fall equation d = 1/2 * g * t^2, where g is the acceleration due to gravity (approximately 32.2 feet per second squared).

Given that the bungee jumper free falls for 4 seconds, we can determine how far the jumper falls by plugging t = 4 into the function. Doing so, we get:

d = 1/2 * 32.2 * (4^2)

d = 16.1 * 16

d = 257.6 feet

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Answer:

1. Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: \(\mathbf{5^3a^2b^4c}\)

5.  \(x^-6 = \frac{1}{x^6}\)

6. \(5^{-3}.3^{-1}=\frac{1}{5^3.3^1}\)

7. \(a^{-3}b^0c^4=\frac{c^4}{a^3}\)

Step-by-step explanation:

Question 1:

We need to rewrite the expression using exponents

5.a.b.b.5.c.a.b.5.b

We will first combine the like terms

5.5.5.a.a.b.b.b.b.c

Now, if we have 5.5.5 we can write it in exponent as: \(=5^{1+1+1}=5^3\)

a.a as \(a^{1+1}=a^2\)

b.b.b.b as: \(b^{1+1+1+1}=b^4\)

So, our result will be:

\(5^3a^2b^4c\)

Rewriting the expression 5.a.b.b.5.c.a.b.5.b using exponents we get: \(\mathbf{5^3a^2b^4c}\)

Question:

Rewrite using positive exponent:

The rule used here will be: \(a^{-1}=\frac{1}{a^1}\) which states that if we need to make exponent positive, we will take it to the denominator.

Applying thee above rule for getting the answers:

5) \(x^{-6} = \frac{1}{x^6}\)

6) \(5^{-3}.3^{-1}=\frac{1}{5^3.3^1}\)

7) \(a^{-3}b^0c^4=\frac{b^0c^4}{a^3}\)

We know that \(b^0=1\) so, we get

\(a^{-3}b^0c^4=\frac{b^0c^4}{a^3}=\frac{c^4}{a^3}\)

Answer:

x = 3

Step-by-step explanation:

First, distribute the -3 to each term in the parentheses. Now, you have

-6x + 24 = 2x. Add 6x to both sides, and now you have 24= 8x. Divide both sides by 8, and now you get x=3.

For given number 100

the exponent form = 10²

the word form = One Hundred

For given question,

The area of a closet is 100 square feet.

We need to write the number in exponent form and word form.

First we write given number in exponent form

⇒ 100 = 10 × 10

⇒ 100 = 10²

So, the exponent form given number 100 is 10²

And the word form of given number is : One Hundred

Therefore, for given number 100

the exponent form = 10²

the word form = One Hundred

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Answer:6

Step-by-step explanation:

when x is -1 y is 6. input -1 as x in the equation and solve, otherwise graph.

Answer:

Step-by-step explana

Answer:

D (70)

Step-by-step explanation:

The interior angles of a triangle has to add up to 180

Answer:

You would go 45 miles.

Step-by-Step Explanation:

If you are going 60 mph you would be going 1 mile per minute