A student is graduating from college in 12 months but will need a loan in the amount of $10,720 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 5.95%, compounded monthly, and a payment grace period of six months from time of graduation PLUS loan: annual interest rate of 6.55%, compounded monthly, with a balance of $11,443.63 at graduation Which loan will have a lower balance, and by how much, at the time of repayment? The Stafford loan will have a lower balance by $485.06 at the time of repayment. The PLUS loan will have a lower balance by $485.06 at the time of repayment. The Stafford loan will have a lower balance by $274.54 at the time of repayment. The PLUS loan will have a lower balance by $274.54 at the time of repayment.

Answer: the population density is approximately 121.75 people/km^2.

Step-by-step explanation: Assuming a scenario whereby the island in question is entirely populated and encompasses a total expanse of 100 square kilometers, it follows that the resulting population density would be as follows:

The formula for population density can be expressed as the ratio of total population to a given geographic area. Mathematically, it is written as Population density = Population / Area.

The metric for measuring population density yields a value of 121.75 individuals per hectare.

The metric expressing the number of individuals residing in a given geographic area is referred to as population density. In this specific instance, the population density is calculated to be 121.75 persons per square kilometer.

Assuming a complete occupancy of the island and a cumulative surface area of 100 square kilometers, it can be posited that...

only the equation y=1/x shows an indirect proportional relationship, while the other three equations show either a direct proportional or a linear relationship.

How to solve the question?

The mathematical term "indirectly proportional" refers to a relationship in which two variables are related in such a way that when one increases, the other decreases, and vice versa. In other words, the two variables vary in opposite directions.

Out of the four equations given, only one shows an indirect proportional relationship. This equation is:

y=1/x

In this equation, y and x are indirectly proportional. As x increases, the value of 1/x decreases, and therefore, the value of y decreases as well. Similarly, as x decreases, the value of 1/x increases, and the value of y increases as well. This relationship is commonly known as an inverse relationship, where the two variables vary in opposite directions.

On the other hand, the other three equations do not show an indirect proportional relationship. The equation y=5x shows a direct proportional relationship, where y increases as x increases and vice versa. The equation y=-2x+1 is a linear equation with a negative slope, where y decreases as x increases, and y increases as x decreases. Lastly, the equation y=3x+5 is also a linear equation with a positive slope, where y increases as x increases, and y decreases as x decreases.

In summary, only the equation y=1/x shows an indirect proportional relationship, while the other three equations show either a direct proportional or a linear relationship.

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The simplified form of the expression (⅓m - 2/x) ÷ (9-y²) ÷ (2x²m-12x) ÷ (9x+3xy) is (x-3m)/(4mx (mx-6) (3-y)).

Mathematical expression is a mathematical statement involving numerical values, mathematical operations, variables, power of variables and combination of that.

The expression is = (⅓m-2/x)÷(9-y²) ÷(2x²m-12x)÷(9x+3xy)

We have to simplify the expression.

Simplifying the expression we get,

(1/3m - 2/x) ÷ (9 -y²) ÷ (2x²m -12x) ÷ (9x +3xy)

= ((x-3m) / 6mx)*(1 / (3²-y²)) ÷ ((2x (mx-6)) / (3x (3+y)))

= ((x-3m) / 6mx (3+y) (3-y)) * (3x (3+y) /2x (mx-6)) [Since, a²- b² = (a+b)(a-b)]

= (x-3m)/(4mx (mx-6) (3-y))

Hence the simplified expression is = (x-3m)/(4mx(mx-6)(3-y)).

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Yes, it is possible for the range of a data set of positive data values to be less than the mean of that data set.

The range of a data set is the difference between the maximum and minimum values in the data set, while the mean (also known as the average) of a data set is the sum of all the values divided by the total number of values.

For example, consider the following data set of positive values: {2, 3, 5, 7, 9}. The range of this data set is 9 - 2 = 7, while the mean is (2 + 3 + 5 + 7 + 9)/5 = 26/5 = 5.2. In this case, the range (7) is less than the mean (5.2).

This can occur when the data set has a relatively small range, meaning that the difference between the maximum and minimum values is not very large compared to the mean.

the distribution of the data set and the specific values within it can affect the relationship between the range and the mean.

It's important to note that range and mean are just two measures of central tendency and variability, and other measures such as median, mode, and standard deviation can provide additional insights into the characteristics of a data set.

therefore, Yes, it is possible for the range of a data set of positive data values to be less than the mean of that data set.

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What percentage of 1.23 is 2.17?  The amount over 100% will be the increase:

[tex]2.17 = \huge \text(\dfrac{x}{100}\huge \text )(1.23)[/tex]

[tex]x =\dfrac{ 2.17(100)}{1.23}[/tex]

[tex]x = 176.4\%[/tex]

The increase is 76.4%

The factored form of the trinomial 9b² + 13b + 4 is ( 9b + 4 )( b + 1 ).

Given the trinomial in the question:

9b² + 13b + 4

To factor the trinomial 9b² + 13b + 4, we need to find two binomials whose product equals 9b² + 13b + 4.

We can start by looking for two numbers that multiply to 9 × 4 = 36 and add up to 13. Those numbers are 9 and 4.

Now we need to use these numbers to factor the trinomial.

9b² + 4b  + 9b + 4

Factor out the greatest common factor from each group

9b² + 9b  + 4b + 4

9b( b + 1 ) + 4( b + 1 )

( 9b + 4 )( b + 1 )

Therefore, the factored form is ( 9b + 4 )( b + 1 ).

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Okay so Jack started with 50 chocolates, and ended with 2.

The simple way to calculate it would be by realizing that Jack only distributed 48 chocolates. We can find how many times 3 fits into 48 by dividing [tex]48\div3=16[/tex].

Using algebra, we substitute the value we want to find with [tex]x[/tex]. Here what we want to find is the number of friends that were at Jack's party.

We know that he started with 50 chocolates, then distributed [tex]3\times[/tex] the number of friends present (which is [tex]x[/tex]).

We write that down as [tex]50-3x[/tex]

(It's minus because when chocolates are distributed, Jack is taking away from what he has.)

We know that after this, there were only 2 chocolates left, so it's

[tex]\underline{\bold{50-3x=2}}[/tex]

Then we proceed by moving all the numbers to the right until only [tex]x[/tex] is left:

[tex]-3x=2-50[/tex]

[tex]-3x=-48[/tex]

[tex]x=\dfrac{-48}{-3}[/tex]

[tex]\boxed{\bold{x=16}}[/tex]

Conclusion: The number of people that attended the party was 16.

A graph which is that of the inequality shown include the following: D. Graph D.

In order to to graph the solution to the given linear inequality on a coordinate plane, we would use an online graphing calculator to plot the given linear inequality and then take note of the points that lie on its line;

y ≥ -3x + 1

Next, we would use an online graphing calculator to plot the given linear inequality as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that a possible solution for the linear equation is the ordered pairs (0, 1) and (1, -2), with a solid line that is shaded above to indicate the solution, and this must be represented with the greater than or equal to (>) inequality symbol.

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Answer:

Step-by-step explanation:

i wish i knew so i dont really know but i have heard that its 2 inches

The mass of the watermelons is 24 kg and the mass of the mangoes is 8 kg.

A physical quantity is mass. The unit of mass measurement is the body's weight. Normal mass units like grammes, kilogrammes, and pounds can be used to measure it.

We are informed of the following:

T + W = 27 (total mass of trolley and watermelons is 27 kg)

T + M = 11 (total mass of trolley and mangoes is 11 kg)

W = 3M (mass of watermelons is three times the mass of mangoes)

Elimination or substitution can be used to solve this set of equations. Substitutions made

We can enter W = 3M into the first equation in place of the third equation to obtain:

T + 3M = 27

From the second equation, we can substitute T = 11 - M into this equation to get:

(11 - M) + 3M = 27

Simplifying this equation, we get:

2M = 16

So, M = 8 kg. This means that the mass of the mangoes is 8 kg.

We can substitute this value of M back into the second equation to get:

T + 8 = 11

So, T = 3 kg. This means that the mass of the trolley is 3 kg.

Finally, we can substitute these values of T and M into the first equation to get:

3 + W = 27

So, W = 24 kg. This means that the mass of the watermelons is 24 kg.

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The probability that a congressman selected at random supports Bill A or Bill B is 0.83.

The probability that a congressman selected at random supports Bill A but not Bill B is 0.21.

The probability that a congressman selected at random supports neither Bill A nor Bill B is 0.17.

P(Bill A or Bill B) = P(Bill A) + P(Bill B) - P(Bill A and Bill B) = 0.35 + 0.62 - 0.14 = 0.83

ii. The probability that a congressman selected at random supports Bill A but not Bill B is the probability in the Bill A circle that is not in the overlap:

P(Bill A but not Bill B) = P(Bill A) - P(Bill A and Bill B) = 0.35 - 0.14 = 0.21

iii. P(neither Bill A nor Bill B) = P(not Bill A and not Bill B) = 0.17

Therefore, the probability that a congressman selected at random supports neither Bill A nor Bill B is 0.17.

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The remaining amount that Jackson has is $5.

The cost of 5 books at $7 each is:

5 books * $7/book = $35

To find the amount of change Jackson got from $40, we need to subtract the cost of the books from $40:

$40 - $35 = $5

Therefore, Jackson got $5 in change.

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Answer:

A., D.

Step-by-step explanation:

A. 0.5x

B. 2

C. 12

D. x

Answer: A., D.

the answer is (a) 30.To find the first term that appears in both sequences, we can simply compare the terms in each sequence until we find a match

what is sequence ?

In mathematics, a sequence is a set of numbers, called terms, arranged in a specific order. Each term in the sequence is obtained by applying a certain rule or formula to the preceding term(s) in the sequence.

In the given question,

Using Rule 1, we can create the first sequence:

10, 30, 90, 270, 810

Using Rule 2, we can create the second sequence:

58, 51, 44, 37, 30

To find the first term that appears in both sequences, we can simply compare the terms in each sequence until we find a match.

We see that the number 30 appears in both sequences as the fifth term of the second sequence and the second term of the first sequence.

Therefore, the answer is (a) 30.

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The number 369.964 in expanded form as 369.964 = 300 + 60 + 9 + 0.9 + 0.06 + 0.004

To express 369.964 in expanded form, we must break down the number by its place value. The digits to the left of the decimal point represent whole numbers, while the digits to the right represent fractions or decimals.

So let's start with the whole number part, 369. We can express this in expanded form by breaking it down into its component parts according to its place value. The digit 3 is in the hundreds place, which means it has a value of 300. The digit 6 is in the tens place, which means it has a value of 60. The digit 9 is in the ones place, which means it has a value of 9. Therefore, we can write 369 in expanded form as:

369 = 300 + 60 + 9

Now let's move on to the decimal part, 0.964. The digit 9 is in the tenths place, which means it has a value of 0.9. The digit 6 is in the hundredths place, which means it has a value of 0.06. The digit 4 is in the thousandths place, which means it has a value of 0.004. Therefore, we can write 0.964 in expanded form as:

0.964 = 0.9 + 0.06 + 0.004

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The axis of symmetry for y = (x - 1)² - 4 is x = 1.

Given the equation in the question;

y = (x - 1)² - 4

The axis of symmetry for a parabola in standard form is expressed as:

y = a(x - h)² + k is the vertical line passing through the vertex (h, k).

Comparing y = (x - 1)² - 4 to the standard form

We can see that h = 1 and k = -4.

Therefore, the vertex is (1, -4).

Since the axis of symmetry is the vertical line passing through the vertex, the equation of the axis of symmetry is

x = 1.

Therefore, the axis of symmetry is x = 1.

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Answer:

Step-by-step explanation:

the fewer jumps=the jumps Ronaldo did - the jumps Ahanu did

                          = 1080-1050

                          = 30

Answer:

The number series 2, 4, 6, 8, 10, 12, . . . . , 80. Therefore, 1640 is the sum of first 40 even numbers.......Sep 23, 2018

PLS MARK BRAINLIEST

Step-by-step explanation:

In circle L in which secant lines TQ and SQ intersect at point Q outside the circle value of x = 54°, m ST = 143°, m PR = 79°

∠PQR = 1/2( ST - PR)

∠PQR = 32°

m ST = (3x - 19)°

m PR = (x + 25)°

Putting the value in the equation we get

32 = 1/2( 3x - 19 - (x + 25) )

32 × 2 = 3x -19 -x -25

64 = 2x - 44

64 + 44 = 2x

108 = 2x

x = 54°

m ST = (3x - 19)°

m ST = 3(54) -19

m ST = 162 - 19

m ST = 143°

m PR = (x + 25)°

m PR = 54 + 25

m PR = 79°

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Answer:

It'd be 4300 mililiters

Step-by-step explanation:

3.8× 100= 3800

3800+500=4300

The scale factor in scale drawing from figutre A to figure B is 4

In a scale drawing, the scale factor represents the ratio of the size of an object in the drawing to the size of the corresponding object in real life.

In the given scale drawing, the object is scaled up from 7 cm to 28 cm.

Therefore, the scale factor can be calculated as follows:

scale factor = size of object in drawing / size of corresponding object in real life

scale factor = 28 cm / 7 cm

scale factor = 4

So, the scale factor in this scale drawing is 4.

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Step-by-step explanation:

to vary inversely means that

y = k/x

the opposite would be to vary directly :

y = kx

so, in our case

5 = k/1

k = 5

y = 5/x

therefore, for x = -3

y = 5/-3 = -5/3 = -1.666666666...

The heights that people had a foot size smaller than 24 centimetres would be = 162cm, 152cm, 162cm, 161cm,162cm.

The total number of people whose foot sizes and heights where obtained for the study = 15

The heights that had foot sizes less than 24cm= 162cm, 152cm,162cm,161cm,162cm.

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Answer:

562496

Step-by-step explanation:

i think

Answer:189504

Step-by-step explanation:

To get the 1.4% of population you need to multiply it like this: 752000 × 1.4% = 10528.

10528 is the population decrease every year, to find the population decrease after 18 years you need to multiply it again like this: 10528 × 18 = 189504.

189504 is the population decrease after 18 years.

There are two real solutions if the radicand is positive.

There is one real solution if the radicand is zero.

There are no real solutions if the radicand is negative.

In mathematics, the radicand refers to the value inside a square root (√) symbol. In the given equations and solutions, we can see that there are square root symbols involved, and we can determine the nature of the solutions based on the sign of the radicand.

For the first equation, y = -16x² + 32x - 10, the solutions for x are given as x = (-32 ± √384) / -32. The radicand in this case is 384. Since 384 is positive, greater than 0, there will be two real solutions for x.

For the second equation, y = 4x² + 12x + 9, the solutions for x are given as x = (-12 ± √0) / 8. The radicand in this case is 0. Since the square root of 0 is 0, there is only one real solution for x in this case.

Therefore, For the third equation, y = 3x² - 5x + 4, the solutions for x are given as x = (5 ± √(-23)) / 6. The radicand in this case is -23. Since the square root of a negative number is not a real number, there are no real solutions for x in this case.

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See full text below

Study the solutions of the three equations on the right. Then, complete the statements below. There are two real solutions if the radicand is There is one real solution if the radicand is There are no real solutions if the radicand is 1. y = negative 16 x squared + 32 x minus 10. x = StartFraction negative 32 plus-or-minus StartRoot 384 EndRoot Over negative 32 EndFraction. 2. y = 4 x squared + 12 x + 9. x = StartFraction negative 12 plus-or-minus StartRoot 0 EndRoot Over 8 EndFraction. 3. y = 3x squared minus 5 x + 4. x = StartFraction 5 plus-or-minus StartRoot negative 23 EndRoot Over 6 EndFraction.

By simplifying the given square root , we get Simplified Root : 6 xz • [tex]\sqrt{(2xz) }[/tex]

Factor 72 into its prime factors

          72 = 23 • 32

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          36 = 22 • 32

Factors which will remain inside the root are :

          2 = 2

To complete this part of the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          6 = 2 • 3

At the end of this step the partly simplified square root looks like this:

        6 • [tex]\sqrt{ (2x3z3) }[/tex]

Simplify the Variable part of the square root

Rules for simplifing variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

   [tex]\sqrt{(x8)}[/tex]=x4

 [tex]\sqrt{ (x^6)}[/tex]=x-3

   (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

   [tex]\sqrt{ (x5)}[/tex]=x2•[tex]\sqrt{x}[/tex]

  [tex]\sqrt{ (x^7)}[/tex]=x-3•[tex]\sqrt{x}[/tex]

Applying these rules to our case we find out that

[tex]\sqrt{ (x3z3)}[/tex] = xz • [tex]\sqrt{(xz) }[/tex]

Combine both simplifications

      [tex]\sqrt{ (72x3z3)}[/tex] = 6 xz •[tex]\sqrt{(2xz) }[/tex]

Simplified Root :

6 xz • [tex]\sqrt{(2xz) }[/tex]

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Answer: 0.956 * 100% = 95.6%

Step-by-step explanation: To convert a decimal to a percent, you can multiply the decimal by 100 and add a percent sign.

So, to convert 0.956 to a percent:

0.956 * 100% = 95.6%

Therefore, 0.956 is equivalent to 95.6%.

Answer:

95.6%

Step-by-step explanation:

In order to solve this, you can just move the decimal point two places to the right to get the answer!