(Student Loans LC) A student is graduating from college in 18 months but will need a loan in the amount of $7,855 for the three remaining semesters. The student may either receive an unsubsidized or subsidized Stafford Loan. The terms of each loan are: Unsubsidized Stafford Loan: annual interest rate of 3.7%, compounded monthly Subsidized Stafford Loan: annual interest rate of 4.7%, compounded monthly What is the difference in the balance of the two loans at the time of graduation?

- 427.60
- 302.57
- 890.95
- 447.57

Answer:

Add parentheses ( ) to make the equation true:

11 x 6 ÷ (8 + 3) = 6

Solve for y

4y + (16 - 7) = 25

y = 4

9 x (8 - 5)

= 27

3. {[3 x (9 + 7)] - 8}

Sorry, can't figure this one out.

5. Mable saved $10 of her lemonade stand money. She then made 7 times as much as the money she had saved. Mable's friend gave her $12. How much money does Mable now have in all?

Mable has $82 all together.

Step-by-step explanation:

You're welcome.

The equivalent exponential expressions are 625 · 5ˣ and [tex]a^{4 + x}[/tex].

Exponents are a short way of representing repeated multiplication. The exponent, or power, indicates the number of times the base is multiplied by itself.

An exponent is a small number written to the right and above the base number, indicating how many times the base number should be multiplied by itself.

By the rule of exponents,

Here we have

Exponents 5⁴· 5ˣ  

We can rewrite the above expression as follows

Since 5⁴ = 625

=> 5⁴· 5ˣ  = 625 · 5ˣ

By using the Rules of exponents,

=> 5⁴ + 5ˣ =  [tex]a^{4 + x}[/tex]

Therefore,

The equivalent exponential expressions are 625 · 5ˣ and [tex]a^{4 + x}[/tex].

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Burt saves $1,500 from each pay check.

What is the percentage?

A percentage is a way of expressing a number or quantity as a fraction of 100. It is commonly used to express the proportion of one quantity relative to another or the amount of change between two quantities.

For example, if you received a score of 80 out of 100 on a test, you can express that score as a percentage by dividing 80 by 100 and multiplying by 100. The result is 80%, which means you scored 80% of the total possible points.

Percentages are often used in finance, such as when calculating interest rates, taxes, and discounts. They are also used in statistics to express the probability or likelihood of an event occurring.

Understanding percentages are important in everyday life, as they are commonly used to compare and evaluate different quantities and values.

Burt earns a semi-monthly income of $3,250, which means he earns $6,500 per month.

He spends 24% of his income on his mortgage, which is:

0.24 x $6,500 = $1,560

He spends 6.5% of his income on utilities, which is:

0.065 x $6,500 = $422.50

He spends 15% of his income on food, which is:

0.15 x $6,500 = $975

He spends 8% of his income on miscellaneous items, which is:

0.08 x $6,500 = $520

Therefore, his total expenses are:

$1,560 + $422.50 + $975 + $520 = $3,477.50

To find out how much he saves from each paycheck, we need to subtract his total expenses from his monthly income:

$6,500 - $3,477.50 = $3,022.50

Since he gets paid semi-monthly, he saves half of this amount from each paycheck:

$3,022.50 / 2 = $1,511.25

Rounding this amount to the nearest $100, we get:

$1,500

Therefore, Burt saves $1,500 from each paycheck.

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Derek bought a house for £140,000 and sold it for £145,500. To work out Derek's percentage profit, we need to use the formula:

Profit percentage = (Profit / Cost price) x 100%

Where:

In this case, Derek's profit is:

Substitute the values into the formula:

Therefore, Derek's percentage profit is 3.93%.

~ Zeph

The optimal amounts of Gatorade and cookies to buy are 4 bottles of Gatorade and 4 boxes of cookies, which gives a total cost of 4(1) + 4(2) = 12, the maximum possible utility for this budget

To find the optimal amounts of Gatorade and cookies to buy in order to maximize utility with a budget of $12, we can use the method of Lagrange multipliers.

Let x be the number of bottles of Gatorade to buy, and let y be the number of boxes of cookies to buy. We want to maximize the utility function:

U(x,y) = xy

Subject to the budget constraint:

1x + 2y = 12

To apply the method of Lagrange multipliers, we form the Lagrangian function:

L(x,y,λ) = xy - λ(1x + 2y - 12)

Taking partial derivatives of L with respect to x, y, and λ and setting them equal to zero, we get:

δL/δx = y - λ= 0

δL/δλ  = x - 2λ= 0

δL/δλ = 1x + 2y - 12 = 0

Solving these equations simultaneously, we get:

x = 4

y = 4

λ = 2

Hence, the optimal amounts of Gatorade and cookies to buy are 4 bottles of Gatorade and 4 boxes of cookies.

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Answer: $119.90

Step-by-step explanation:

Answer:

ED = 57 , AB = 19

Step-by-step explanation:

the midsegment FC is half the sum of the parallel bases , that is

[tex]\frac{AB+ED}{2}[/tex] = FC

[tex]\frac{4x+3+18x-15}{2}[/tex] = 38 ( multiply both sides by 2 )

22x - 12 = 76 ( add 12 to both sides )

22x = 88 ( divide both side by 22 )

x = 4

then

ED = 18x - 15 = 18(4) - 15 = 72 - 15 = 57

AB = 4x + 3 = 4(4) + 3 = 16 + 3 = 19

Answer:

The roots of the equation
[tex]x^{3}-10x^{2}+31 x-30 = 0[/tex]

correspond to the x-intercepts of the function graph

Step-by-step explanation:

The roots of the equation
[tex]x^{3}-10x^{2}+31 x-30 = 0[/tex]

are x = 2, x = 3, x = 5

which are located at points (2, 0), (3, 0), (5,0)

These points are the x-intercepts of the graph of the equation
So the x-intercepts of the equation are the roots of the equation

I have graphed this using Geogebra which I am familiar with. You should probably use Desmos as per the instructions

A continuous variable is a variable that can take on any value within a certain range, and often takes the form of real numbers but a discrete variable is a variable that can only take on specific values within a certain range, and often takes the form of integers

Continuous and discrete variables are two types of quantitative variables in statistics.

A continuous variable is a variable that can take on any value within a certain range, and often takes the form of real numbers. Examples of continuous variables include height, weight, time, temperature, and distance. These variables can be measured using instruments with varying degrees of precision, but they can theoretically take on an infinite number of values.

On the other hand, a discrete variable is a variable that can only take on specific values within a certain range, and often takes the form of integers. Examples of discrete variables include the number of siblings a person has, the number of cars in a parking lot, and the number of points a basketball team scores in a game. These variables can only take on a limited number of values, and often represent counts or whole numbers.

The main difference between continuous and discrete variables is the way they can be measured and the number of possible values they can take. Continuous variables can take on an infinite number of values and can be measured with varying degrees of precision, while discrete variables can only take on specific values and are often measured with exact precision.

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At 7 a.m., the temperature was 2°.

Temperature is a measure of the average kinetic energy of particles in a system, measured in degrees on a specific scale (such as Celsius or Fahrenheit). The higher the temperature, the faster the particles move. Temperature is also related to heat, which is the transfer of energy between two systems at different temperatures. Heat always flows from a higher temperature system to a lower temperature system. In addition, temperature is related to pressure, which is the force exerted by the particles in a system. When the temperature of a system increases, so does the pressure.

At 7 a.m., the temperature was 2°. This is because temperatures dropped by 2° per hour until 2 o'clock in the morning. In the 6 hours (from 2 a.m. to 8 a.m.) there were 12° of decrease in temperature (2° per hour x 6 hours). This means that the temperature at 7 a.m. was -6° (2° - 12° = -6°).

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Answer:

371.5 square units.

Step-by-step explanation:

the shaded region is a ring-shaped region between the two concentric circles, we can find the area of the shaded region as follows:

The area of the large circle is given by:

Area of large circle = π × r^2

where r is the radius of the large circle, which is 13.5.

Area of large circle = 22/7× (13.5)^2

Area of large circle ≈ 572.78

The area of the small circle is given by:

Area of small circle = π × r^2

where r is the radius of the small circle, which is 8.

Area of small circle = 22/7× (8)^2

Area of small circle ≈ 201.14

The area of the shaded region is the difference between the area of the large circle and the area of the small circle:

Area of shaded region = Area of large circle - Area of small circle

Area of shaded region ≈ 572.78 - 201.14

Area of shaded region ≈ 371.5

Therefore, the approximate area of the shaded region is 371.5square units.

Answer:

The area of the shaded region is 371.5 square units to the nearest tenth.

Step-by-step explanation:

To find the area of the shaded region of two concentric circles with a common center, subtract the area of the smaller circle from the area of the larger circle.

The formula for the area of a circle is A = πr², where r is the radius of the circle.

From inspection of the given diagram:

Therefore, the area of the shaded region is:

[tex]\begin{aligned}\textsf{Area of shaded region}&=\textsf{Area of larger circle}-\textsf{Area of smaller circle}\\&=\pi (13.5)^2-\pi (8)^2\\&=182.25 \pi - 64 \pi\\&=118.25 \pi\\&=371.493331...\\&=371.5\; \sf unit^2\;\;(nearest\;tenth)\end{aligned}[/tex]

The area of the shaded region is 371.5 square units to the nearest tenth.

The value of length 8inch into cm is 20.32 cm.

8inch can be converted into centimeters (cm) using the conversion factor of 1 inch equals 2.54 centimeters.  it's essential to use the appropriate conversion factor and ensure that the units cancel out correctly to arrive at the desired result.

Since 8 is a unit of inches, we can simply multiply 8 by the conversion factor of 2.54 cm/inch to get the equivalent measurement in centimeters.

So, the conversion can be done as follows:

8 inches x 2.54 cm/inch = 20.32 cm

Therefore, 8 inches is equal to 20.32 centimeters.

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_____The given question is incomplete, the complete question is given below:

How to convert 8 inches into cm.

The value of ∫[1/(x² - 25)^3/2]dx when x = 5 secθ using integral by substitution, the answer is (1/2)[(x/5)^2 - 1]^-1/2 + C

To solve this problem, we simply need to use integration by substitution.

∫[1/(x² - 25)^3/2]dx when x = 5 secθ

We can start by making the substitution x = 5 secθ, which implies that dx/dθ = 5 secθ tanθ.

Substituting these expressions into the integral, we get:

∫[1/(x² - 25)^3/2]dx = ∫[1/(25sec²θ - 25)^3/2] (5 secθ tanθ)dθ

Simplifying the denominator inside the integral:

25sec²θ - 25 = 25(sec²θ - 1) = 25tan²θ

Substituting this back into the integral:

∫[1/(25tan²θ)^3/2] (5 secθ tanθ)dθ = ∫(5/125)tanθ/cos³θ dθ = ∫tanθ/cos³θ dθ

We can simplify this using the substitution u = cosθ, which implies that du/dθ = -sinθ and, therefore, -du = sinθdθ.

Substituting these expressions back into the integral, we get:

∫tanθ/cos³θ dθ = -∫(1/u³) du = u^-2/2 + C

Substituting back u = cosθ, we get:

u^-2/2 + C = cos^-2θ/2 + C

Therefore, the final answer in terms of x is:

cos^-2θ/2 + C = (1/2)[(x/5)^2 - 1]^-1/2 + C

Since the solution is not in the option, the answer is none of these

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The length seen in the miscroscope is 3.3 inches

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

Scale factor = 10

Object length = 0.33 in

This means that the length of the object seen through the microscope is 10 times the actual length.

So, we have

Length = 10 * Actual length

The actual length is 0.33 inches, so the length seen through the microscope is:

Length = 10 * 0.33

Length = 3,3

Hence, it would appear to be 3.3 inches long when viewed through Sam's microscope.

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The range for the function y = x + 5, when the domain is {-2, 2}, is {7, 3}.

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

y = x + 5

Domain {-2, 2}

Substitute the known values in the above equation, so, we have the following representation

When x = 2, y = 2 + 5 = 7

When x = -2, y = -2 + 5 = 3

Hence, the range for the relation y = x + 5 is {7, 3}.

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Complete question

find the range of the following function when the domain is -2 and 2

y = x + 5

15 members of the club voted in the election.

To find out how many members voted, we can start by calculating 30% of the total number of club members:

30% of 50 = (30/100) * 50 = 15

So 15 members of the club voted in the election.

Based on the given conditions, formulate:

Reduce the fraction: (30/100)

Multiply a number to both the numerator and the denominator:

(30/100) * 50

Write as a single fraction: 0.3 * 50

Calculate the product or quotient: 15

Rewrite a fraction with denominator equals 100 to a percentage:

Answer: 15

The French club held elections to elect new board members. 50 club members, or 30% of them, cast ballots. So, 15 members casted the most votes.

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When computing the correlation​ coefficient, the effect of changing the order of the variables on​ r is option (A) It has no effect on r

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables.

Changing the order of the variables has no effect on the correlation coefficient, It has no effect on r.

This is because the correlation coefficient measures the degree of association between two variables, regardless of which variable is designated as the dependent variable or independent variable. The formula for the correlation coefficient is symmetrical, meaning that it yields the same result regardless of the order in which the variables are entered into the formula.

Therefore, the correct option is (A)  It has no effect on r

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The required value of h(t)=-20+11t at t=11 is , h(11)=101.

The word PEMDAS is primarily used in the US, although we refer to it as BODMAS in India and the UK. Yet, there is no distinction between them. For both the rule and brackets, addition, subtraction, multiplication, and division are performed in the same order.

The following is the full form of PEMDAS:

P – Parentheses  [{()}]

E – Exponents (Powers and Roots)

MD- Multiplication and Division (left to right) (× and ÷)

AS –A= Addition  and S= Subtraction (left to right) (+ and -)

whereas the full form of BODMAS is – Brackets Order Division Multiplication Addition and Subtraction.

If h(t)=-20+11t and you wish to evaluate h(11):

h(11)=-20+11(11)

h(11)=-20+121

h(11)=101

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Answer:

B and E

Step-by-step explanation:

Information we need to know:

Like terms - a set of number which variables are the same

In the question we can see that there are two numbers that have the variable y and two numbers that have the variable of 0 (meaning that they are regular numbers)

Hence our options would be B and E

Hope this helps, have a lovely day! :)

Answer:

If ABCD is a square, all sides are 11 and all angles are 90 degrees, so:

BC = AD = 11

AC = BD = 11√2

EC = AC - AE = 11√2 - 11 = 11(√2 - 1)

mDAB = 90 degrees

mAEB = 180 - mDAB = 90 degrees

mCBD = 90 degrees

mBAC = 45 degrees

Step-by-step explanation:

The mode would remain the same because 24 is already a part of the set.

Mode is a measure of central tendency, or an average, in a set of numerical data. It is the most frequently occurring value in a set of data.

For example, consider the following set of numbers: 1, 2, 2, 3, 3, 3, 4, 4, 5. In this set, 3 is the mode since it appears most often. It occurs three times, while the other numbers occur fewer times.

Mode can be used with both continuous and discrete data. Continuous data can be divided into classes, and the mode is the most frequent class. For example, if the numbers above were in the following classes: 1-2, 3-4, 5-6, then 3-4 would be the mode since it occurs the most often.

Mode can also be used with categorical data. In this case, the mode is the most frequent category.

For example, if the data set consists of the categories blue, green, and red, and blue occurs most often, then blue is the mode.

24 is the most frequently occurring number in the set of 24, 58, 24, 24 53. So it is the mode. It appears 3 times, which is more than any other number.

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A U.S. dollar bill is approximately 6.14 inches (15.6 cm) long, 2.61 inches (6.6 cm) wide, and 0.0043 inches (0.11 mm) thick.

A United States dollar bill is a rectangular piece of paper currency that is approximately 6.14 inches (15.6 cm) long, 2.61 inches (6.6 cm) wide, and 0.0043 inches (0.11 mm) thick. It is standardized by the U.S. government and has a green and black design featuring images of historical figures such as George Washington and Benjamin Franklin.

The front of the bill displays a portrait of a U.S. president, while the back showcases symbols and images related to U.S. history and culture. The U.S. dollar bill is the most widely used form of currency in the world and is accepted as a means of payment in many countries outside the United States.

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Generally, the main five functions of consumer protection agencies includes:

Consumer protection agencies are organizations that work to protect consumers from unfair and deceptive business practices. These agencies perform a variety of functions to promote fair and ethical business practices and ensure that consumers are able to make informed decisions when purchasing goods and services.

The list of the consumer protection agencies we have in U.S. are:

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The Laplace Transform Method can be used to solve all of these equations except for equation (e).

a.) Yes, the Laplace Transform Method can be used to solve this third-order linear differential equation with constant coefficients and a nonhomogeneous term.

b.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with constant coefficients.

c.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.

d.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with variable coefficients.

e.) No, the Laplace Transform Method cannot be used to solve this first-order nonlinear differential equation.

f.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.

g.) Yes, the Laplace Transform Method can be used to solve this first-order nonlinear differential equation.

h.) Yes, the Laplace Transform Method can be used to solve this first-order linear differential equation with constant coefficients and a nonhomogeneous term.

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Answer:

300

Step-by-step explanation:

you have to do 3,000 times 10% then you will get 300 that’s what I have learned for example if you do 30,000 of 10% it would be 3,000.

So the reason for the discrepancy between the calculated result and the result obtained by hand is due to how the remainder is being handled.

By hand, the remainder is kept as a separate value, whereas a calculator may display the result as a decimal instead of showing the remainder.

When dividing 587 by 187 by hand, the result would indeed be 0 with a remainder of 16:

3 | 5 8 7

  - 5 6 1

  -------

    2 7 6

    2 8 1

    -----

      9 6

Therefore, the quotient is 0 with a remainder of 16, which can also be written as 0.085 by dividing the remainder (16) by the divisor (187).

However, when using a calculator, it may display the result as a decimal instead of showing the remainder. In this case, the calculator would compute 587 divided by 187 as 3.136, which can be rounded to 0.357 if the result is being displayed to three decimal places.

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Answer:

32

Step-by-step explanation:

The standard form of the polynomial f( x ) = ( x + 4 )² - 18 is f( x ) = x² + 8 - 2.

The standard form of a polynomial is expressed as;

ax² + bx + c

To write a polynomial in its standard form, we simplify and arrange the terms in descending order.

Given the function in the question;

f( x ) = ( x + 4 )² - 18

First, simplify using FOIL Method

f( x ) = ( x + 4 )( x + 4 ) - 18

f( x ) = x( x + 4 ) + 4( x + 4 ) - 18

f( x ) = x² + 4x + 4x + 16 - 18

Add like terms

f( x ) = x² + 4x + 4x + 16 - 18

f( x ) = x² + 8 - 2

Therefore, the standard form is f( x ) = x² + 8 - 2.

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The Evaluate the expression (12)2•(3•5−3)+13 is [tex]{7\frac{1}{2}[/tex]

Multiply the numerator by the reciprocal of the denominator:

[tex]5(\frac{3}{2} )[/tex]

Multiply [tex]5(\frac{3}{2} )[/tex]:

Combine [tex]5[/tex] and [tex]\frac{3}{2}[/tex]:

[tex]\frac{5⋅3}{2}[/tex]

Multiply [tex]5[/tex] by [tex]3[/tex]:

[tex]\frac{15}{2}[/tex]

The result can be shown in multiple forms.

Exact Form:

[tex]\frac{15}{2}[/tex]

Decimal Form:

[tex]7.5[/tex]

Mixed Number Form:

[tex]{7\frac{1}{2}[/tex]

Hence, The Evaluate the expression (12)2•(3•5−3)+13 is [tex]{7\frac{1}{2}[/tex]

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Answer:

Step-by-step explanation:

66666