After four years of higher education, Marshall just graduated with a Bachelor's degree in Physics from NYU where the annual cost of tuition was $20,000. He paid for college by earning $11,000 annually through the work study program and receiving an annual scholarship. He covered the remainder of the costs by taking out $20,000 in student loans. If he didn't fund his education with savings or grant money, what was the amount of Marshall's annual academic scholarship?

The solution of given system of equations is 6 and 7.

To solve the system of equations using elimination, we will equate any one variable. In this case, we will be equating variable y.

Rewriting the equations -

-6x - 6y = −42 : equation 1

-x + 2y = 8 : equation 2

Multiplying equation 2 with 3

-3x + 6y = 24 : equation 3

Adding equation 1 and equation 3 to solve the given system of equations

-6x - 6y = −42

3x + 6y = 24

We get the answer :

-3x = -18

Negative sign will be cancelled and performing division

x = 6

Keep the value of x in equation 2

-6 + 2y = 8

2y = 8 + 6

2y = 14

y = 14 ÷ 2

y = 7

Therefore, the value of x and y is 6 and 7 in given system of equations.

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The maximum and minimum number of people will be 19700 and 17300 respectively.

It should be noted that it was stated that the arena can hold 18500 people.

Therefore, the equation to represent the number of people that can attend the event will be:

= 18500 +/- 1200

The maximum number of people will be:

= 18500 + 1200

= 19700

The minimum number of people will be:

= 18500 - 1200

= 17300

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There is No Extraneous solution to the equation

The equation is

[tex]\sqrt{3x - 2}[/tex] - [tex]\sqrt{2x - 7}[/tex] = 0

We need to find the value of x,

[tex]\sqrt{3x + 2}[/tex] = [tex]\sqrt{2x + 7}[/tex]

Squaring both sides of the equation

[tex](\sqrt{3x + 2} )^{2}[/tex] = [tex](\sqrt{2x + 7} )^{2}[/tex]

3x + 2 = 2x + 7

x = 5

Now we need to put the value of x in the equation to know whether it is an extraneous solution or not.

[tex]\sqrt{(3 * 5 ) + 2}[/tex] - [tex]\sqrt{(2 * 5 ) + 7}[/tex] = 0

[tex]\sqrt{17}[/tex] - [tex]\sqrt{17}[/tex] = 0

0 = 0

Therefore we get to know that the equation has no extraneous solution.

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The marginal distribution of males is 13 %

A two-way frequency table shows the frequencies (or "counts") of two categorical variables.

For example, the following two-way table displays the results of a study in which 100 participants were asked which sport they preferred: baseball, basketball, or football.

The rows represent the respondent's gender, while the columns show which sport they chose:

There are two variables in this example: Sports and Gender.

A marginal distribution is simply the sum of the distributions of these separate variables. The marginal distributions in a two-way table are shown in the table margins: Marginal distributions are valuable because, while we frequently collect data for two variables (such as Sports and Gender), we may have particular questions regarding only one variable.

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2y+x/3=-6  is a linear equation.

An equation is written to equate two or more unknown variables and formulating a relation between them.

Equations are of various types such as:

The given equation is 2y+x/3=-6.

Here the power of both the variables is 1. Hence it can be classified as a linear equation in two variables.

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Answer:

Step-by-step explanation:

(2x^(4)y^(-3))

= 2x^4/ y^3.

Answer:

subtract 6

Step-by-step explanation:

note there is a common difference between consecutive terms, that is

45 - 51 = - 6

39 - 45 = - 6

33 - 39 = - 6

27 - 33 = - 6

21 - 27 = - 6

the rule being used to make the pattern is subtract 6

this is an arithmetic sequence for which an nth term rule can be found

Answer:

subtract 6

Step-by-step explanation:

the pattern is made by subtracting 6 from the previous number

If x and y are directly proportional and we take a third of x we also have to take a third of y, which means we have to multiply y by 1/3.

Two quantities when they are in direct proportion increase or decrease by the same constant and when they are inversely proportional if one quantity increases the other quantity decreases.

We know when two quantities are directly proportional we can relate them by proportionality as x ∝ y or x = ky.

∴ if we take 1/3 of x to maintain the equality we have to multiply y also by 1/3.

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The expression that represents the maximum number of attendees at Jets, Dolphins, and Patriots home games during the season is 82,500 j + 65,326 d + 66829 p.

We are given that:

Team                        Number of seats

Jets                                 82,500

Dolphins                         65,326

Patriots                           66,829

The number of attendees at the jets home games = j

The number of attendees at the Dolphins home games = d

The number of attendees at the Patriots home games = p

So, the maximum number of attendees can be written by the expression:

82,500 j + 65,326 d + 66829 p.

Therefore, we get that, the expression that represents the maximum number of attendees at Jets, Dolphins, and Patriots home games during the season is 82,500 j + 65,326 d + 66829 p.

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Your question was incomplete. Please refer the content below:

We are given the data as:

Team                        Number of seats

Jets                                 82,500

Dolphins                         65,326

Patriots                           66,829

Write an expression that represents the maximum number of attendees at Jets, Dolphins, and Patriots home games during the season. Let j be the number of Jets home games, d be the number of Dolphins home games, and p be the number of Patriots home games.

the expression that models the situation of the total cost of a diner, less a $10 coupon divided by 4 is (x - $10)÷4

Here we have the total cost of a dinner, less a $10 coupon, divided by 4 people.

If the total cost is x, then the total cost less a $10 coupon is:

x - $10.

Now, taking the quotient (dividing the above amount by 4) we will get:

(x - $10)÷4

This is the expression that models the situation of the total cost of a dinner, less a $10 coupon divided by 4.

So the correct option is the first one.

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Answer:

a) 10n -6

b) -5n +105

c) 7f + 1

d) -11n +48

Step-by-step explanation:

for an example let's take a) 4, 14, 24, 34

term value:

14 - 4 = 10 (coefficient)

term number:

4 = 34

4×10=40

34 - 40 = -6

coefficient and constant

therefore v = 10n -6

lol are you a Bhutanese?

[tex]4\frac{6}{12}[/tex] hours play speed, what is the total running time of the video.

What does "speed" mean in mathematics?

Running time of cassettes

at standard speed = 1 hr

at standard speed = 4 hr

at standard speed = 4 hr

given the 1/4 part of tape is recorded at standard speed, 1/3 at long-play speed , 5/12 at super long-play speed,

so the running time of standard speed = 1/4 * 1 = 1/4

at long play speed

1/3 * 4 = 4/3 hours

and at super long-play speed,

5/12 * 7 = 35/12 hours

so, the total running time of the video

1/4 + 4/3 + 35/12 = 54/12 = [tex]4\frac{6}{12}[/tex] hours

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Answer: A. A one time discount of 38%.

How much will the shirt cost when given scenario (a) that gives a one time discount of 38%? : $46.50

How much will the Shirt cost when giving scenario (b) that gives a discount of 14% followed by a 24% discount? $49.02

Answer: D

Step-by-step explanation:

:)

The equation of the line for the  point (-1, 2) is [tex]y=x+3[/tex]

It is given that line is parallel to the line y = x + 4 .    ....(2)

On comparing equation (2) with the slope intercept form which is  y = mx +c , we get  m = 1 . For parallel lines slope is same .

It is given that line passes through the point (-1, 2).

Putting [tex]y_1=2,\ x_1=-1[/tex] and m = 1 in equation (1) , we get

     [tex]y-2=1(x-(-1))\\y-2=x+1\\y=x+3[/tex]

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We have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.

Mathematical Induction : For each and every natural number n, mathematical induction is a method of demonstrating a statement, theorem, or formula that is presumed to be true.

It is given that the statement is true for n = k

Explanation:

According to the principle of Mathematical Induction,

Let d(n) be a statement involving Natural Number n such that

d(1) is true

d(m) is true

d(m+1) is true

So ,  the statement d(n) is true for all the n natural numbers.

According to the second principle of Mathematical Induction

Let d(n) be a statement involving Natural number n such that

d(1) is true

d(m) is true when d(n) is true for all n where 1 ≤ n ≤m .

Then the statement d(n) is true for all the values of n ( natural number)

Therefore , we have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.

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The formula 3x-y=5 is a linear function.

We must first examine the slope of the original function in order to determine the equation of parallel lines. We are also given the other function's intercept in this issue.

The function's slope-intercept form is y=3x-5.

In order to locate the parallel line that corresponds to the point (0,-7)

Parallel lines are those that share the same slope but have different y-intercepts, as you may have seen.

As a result, we must put in the point to solve for the y-intercept.

Thus,

y = 3x + b

-7 = 3(0) + b

-7 = b

b = -7

Thus the equation of a parallel line is y = 3x - 7

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Answer: Be careful. There is a slight difference in the order of the questions

The values of "x" and "y" in the given matrix equation is 5 and 3 respectively.

A matrix equation is an equation in which a matrix acts as a variable.

The given system of equation;

x + 2y = 11

x + 4y = 17

[1    2 ] =  [11]

[1   4  ]  =  [17]

determinate of the equation, Δ

Δ = [1    2 ]

      [1   4  ]  

Δ = (4 x 1) - (2 x 1) = 2

Δx =  [11    2 ]

        [17   4  ]  

Δx  = (4 x 11) - (17 x 2) = 10

Δy =  [1    11 ]

        [1   17  ]  

Δy = (17 x 1) - (11 x 1) = 6

x = Δx/Δ

x = 10/2 = 5

y = Δy/Δ

y = 6/2 = 3

Thus, the values of "x" and "y" in the given matrix equation is 5 and 3 respectively.

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The unit rate is $26.98

Unit rate can be described as the price of a single item. From the question, we are required to find the unit rate of 1 penguin

The unit rate can be calculated as follows

7 penguins = 188.88

1 Penguin= x

Cross multiply both sides

7x= 188.88

x= 188.88/7

x= 26.98

Hence the unit rate is $26.98

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Answer:

Either -8b - 24 or b = 3

Step-by-step explanation:

Answer: - 8b - 24

Distributive property

a) The line segment PQ has a length of √85 (approx. 9.219).

b) The coordinates of the midpoint of the line segment PQ is (4, 0.5).

Herein we find a line segment whose endpoints are known: P(x, y) = (3, 5), Q(x, y) = (5, - 4), and we are asked to determine the length of the line segment and the coordinates of the midpoint as well. a) First, we determine the vector between the points P and Q by sum of vectors:

PQ = Q(x, y) - P(x, y)

PQ = (5, - 4) - (3, 5)

PQ = (2, - 9)

And its magnitude is determined by using the Pythagorean theorem:

PQ = √[2² + (- 9)²]

PQ = √85

b) The coordinates of the midpoint is found by using the following formula:

M(x, y) = 0.5 · P(x, y) + 0.5 · Q(x, y)

M(x, y) = 0.5 · (3, 5) + 0.5 · (5, - 4)

M(x, y) = (1.5, 2.5) + (2.5, - 2)

M(x, y) = (4, 0.5)

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Answer: Aiza have left from her lifeguarding job = $ 700

Step-by-step explanation:

Given that,

Aiza made $55 a day lifeguarding in the summer.

She worked six days a week for five weeks.

For two weeks of the summer she went on vacation.

She spent approximately $68 a day each for two weeks.

Aiza earning per day = $55

Aiza worked for six days in a week.

Aiza worked for five weeks.

Total earning for weeks

                          = $ 55(6)

                          = $ 330 / week

Total earning for 5 weeks

                           = $ 330(5)

                           = $ 1650

Aiza spent per day for vacation = $ 68

Aiza was an vacation for two weeks.

Total expenditure for two weeks,

Number of days in each week = 7 days

                                                   = 2(7)($ 68)

                                                   = $ 952

Aiza have left with = Total earning - Total expenditure

                               = $ 1650 - $ 952

                               = $ 700

Therefore, Aiza have left from her lifeguarding job = $ 700

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The percentage of increase in the price of  the car is 32%

Percentage increase means adding the given percentage of  value to the original value.

To calculate this percentage increase:

            =  100{( final value - initial value )/initial value}

Given that last month online price of powered ride-on car was $250

and this month this cost is $330

Initial value = $250

Final value  = $330

Percentage increase =  100{ ( 330 -250 )/250} =100*0.32 = 32%

This the percentage increase in the price of the powered ride-on car is 32%

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His final payment will be $271.66464 at the end of the third year.

The term "compound interest" refers to interest that is added back to the principal amount during each compounding period.

Compound interest is calculated using the formula

A = P(1+r )ⁿ,  where

P = principal balance,

r = interest rate,

n =  number of periods.

Given that a man borrows $760 at 4% and of the first year he pays back $270.

Amount owned by him at the end of the first year after repaying $270 =  (1+4%)760 - 270

= 1.04×760 - 270

= $520.4

Amount owned by him at the end of the second year after repaying $280 =  (1+4%)520.4 - 280

= 1.04×520.4 - 280

= 541.216 - 280

= $261.216

Let his final payment be x.

So, the amount owned by him at the end of the third year will be 0.

⇒ (1+4%)261.216 - x = 0

⇒ 1.04×261.216 - x = 0

⇒ 271.66464 = x

Therefore, his final payment will be $271.66464.

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The simplest form of the expression is a⁴ b¹/₂ which is option (B)   .

We have given an expression  (a²/¹ b¹/⁴)² .

On simplifying , we get

(a²/¹ b¹/⁴)² = [tex]a^{2\times2} \ \ b^{2/4}[/tex]

                 = a⁴ b¹/₂

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The complete question is given below :

What is the simplified form of (a²/¹ b¹/⁴)²?

(A) a⁴/₅ b⁹/₁₆ (B) a⁴ b¹/₂ (C) a b (D) (a b)¹⁷/₆

Answer:

Rise/Run

or

[tex]\frac{rise}{run}[/tex]

Step-by-step explanation:

The formula for slope is referred to rise over run,

Because the fraction consists of the rise (the change in y, going up or down) divided by the run (the change in x, going from left to the right).

A rise over run equation would be formatted like this:

Rise/Run

or

[tex]\frac{rise}{run}[/tex]

(i used to struggle with slopes, and i understand how much of a pain they are)