Shiloh is splitting a quart of mac n cheese with seven friends. If all 8 of them share the quart equally, how many cups will each person get?
Can someone please help me

Using the permutation formula, it is found that Professor Bartlett can assign the students in 90,720 ways.

------------------------------

The permutation formula states that the number of ways x elements from a set of n can be assigned is:

\(P_{(n,x)} = \frac{n!}{(n-x)!}\)

\(T = 6 \times P_{9,5} = 6 \times \frac{9!}{4!} = 90720\)

The students can be assigned in 90,720 ways.

A similar problem is given at https://brainly.com/question/14632626

To earn an average score of 90, the score on the fourth test needs to be 98.

The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a particular set of numerical data.

Given the score of the first three tests as:

91, 84, 87.

The average is given by the following formula:

Average = Sum of scores ÷ total number of tests

Let us suppose the score of fourth test as x.

Given that A = 90:

90 = (91 + 84 + 87 + x) ÷ 4

x = 98

Hence, the score on the fourth test must be equal to 98, to get an average score of 90.

Learn more about average here:

https://brainly.com/question/24057012

#SPJ1

The inclination of the line represented by the equation y = x + 3 is 1, and the inclination of the line represented by the equation 3x - 2y = 6 is 3/2.

To determine the inclination (or slope) of a straight line, we can examine the coefficients of the variables x and y in the equation of the line.

The inclination represents the ratio of how much y changes with respect to x.

Equation: y = x + 3

In this equation, the coefficient of x is 1, which means that for every increase of 1 in x, y also increases by 1.

This indicates that the inclination of the line is positive, meaning it slopes upwards as x increases.

Since the coefficient of x is 1, the inclination can be expressed as 1/1 or simply 1.

Equation: 3x - 2y = 6

To determine the inclination, we need to rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope.

First, isolate y:

-2y = -3x + 6

Divide the entire equation by -2 to solve for y:

y = (3/2)x - 3

Now we can observe that the coefficient of x is 3/2.

This indicates that for every increase of 1 in x, y increases by 3/2. Therefore, the inclination of this line is positive, indicating an upward slope.

The inclination can be expressed as 3/2.

For similar question on inclination.

https://brainly.com/question/29723347

#SPJ11

Answer:

4. Infinitely many

Step-by-step explanation:

5x + 3(x − 1) = 10x − 2x − 3

5x+3x-3=8x-3

5x+3x-8x=3-3

0=0

x∈R

Answer:

c is the anser

Step-by-step explanation:

Answer:

Around 10 days ( 9.28 days: 9 days 6 hours 43 minutes 12 seconds).

Step-by-step explanation:

Given that 25 gizmos are produced each day, and 75 ¢ are made off of each one, a 174$ repair job will take away money that will need to be paid off.

We can create the following equation by using the amount of gizmos earned per day(x or time) multiplied the money made off of each one(in cents ¢), is equal to the repair job since it will be paid off once it is canceled out.

25x(75¢) = 174$.

Since the money made by each gizmo is in cents and not dollars, it is best to convert this into dollars since the repair job is in this form. Because 100¢ are in each dollar, 75¢ = 75/100 dollars = 3/4 dollars.

3/4 * 25 x = (3/4) * (25x) = (25*3) / 4 = 75/4x

(75/4)x = 174$

(75/4x) * (4/75) = (174$) * (4/75)

x = (174 * 4) / 75

x = 696 / 75

x = 9.28

We are multiplying by the reciprocal (numerator and denominator are switched) since it will make your coefficient 1 which is the variable itself. anything times it's reciprocal is equal to one.

75/4x = 174$

×4 ×4

(cancel out the denominator)

____________

75x = 696$

÷ 75 ÷ 75

(cancel out 75 to get the variable by itself)

___________

x = 696/75

x = 232/25

x = 928/100

x = 9.28

___________

Using a system of equation, the number of days it will take to recuvwr the repair cost is 58 days.

The increase in amount of gizmo produced after repair :

Prize per gizmo = 75 cent = $0.75

Repair cost = $174

The number of days it will take to recover the repair fee can be calculated thus :

(Increase on gizmo per day × cost per gizmo)× number of days = repair fee

(4 × 0.75)d= 174

3d = 174

d = 174 / 3

d = 58

Therefore, it will take 58 days to recover the repair fee.

Learn more : https://brainly.com/question/18796573

Answer:

10

Step-by-step explanation:

not 10

A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.

To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.

Let's calculate the sum of the digits in 1234:

1 + 2 + 3 + 4 = 10

The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.

To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.

The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.

1234 + 2 = 1236

we obtain the number 1236, which is divisible by 3.

For more such questions on divisible

https://brainly.com/question/29373718

#SPJ8

Answer:

The answer is $221

Step-by-step explanation:

$276×.20=55.2

$276-55.2 = $220.8 roundup by $221

Answer:

- 4,134,560 is the answer

Answer:

x = -5/3

Step-by-step explanation:

-4 = \( \dfrac{20}{3}x\)

-4×3 = 20 x

-12 = 20 x

\(x = \dfrac{-5}{3}\)

Angle Pair                                                                      Examples

Corresponding Angles                                            ∠1 and ∠5, ∠2 and ∠6,      

                                                                               ∠3 and ∠7, and ∠4 and∠8

Alternate Interior Angles                                       ∠4 and ∠6, ∠3 and ∠5

Alternate Exterior Angles                                        ∠1 and ∠7, ∠2 and∠8

Consecutive(Same-Side) Interior Angles              ∠4 and ∠5, ∠3 and ∠6

Consecutive(Same-Side)Exterior Angles              ∠1 and ∠8, ∠2 and ∠7

To learn more about Angle Pair visit:

https://brainly.com/question/11838535

#SPJ9

The best way to solve these sorts of problems that involve two factors of unknown quantities but with certain properties is to use equations:

Let's set some variables

Now based on the information given by the question, let's set up some equations:

              ⇒ \(s + h = 166\)

             ⇒ h = s - 54

Now lets put the equation together

  s + h = 166 -- equation 1

  h = s - 54   -- equation 2

Solve:

  Plug the value of h from equation 2 into equation 1

      s + (s - 54) = 166

        2s - 54 = 166

           2s = 220

             s = 110 -- equation 3

   Plug the value of s from equation 3 into equation 2

      h = 110 - 54 = 56

            h = 56

Therefore:

Hope that helps!

Answer:8%

Step-by-step explanation:

8% of her income because I did

280

-----

3500

=

X

------

100 ( Sorry if I'm wrong <3 )

Let's start with one-step equations. These equations are technically called linear equations. That's because the degree, or exponent, of the variable, x, is 1.

In order to obtain the variable by itself when solving one-step equations, we do the inverse (opposite) of the operation that is being applied to the variable.The most crucial thing to keep in mind is that anything you do for one side of the equation, you must also do for the other side.

Let x be the number for Debra.

Write equation as you read the problem

   Debra + Brian + Austin = 87

    x   + (x+7) + 2x     = 87

Simplify and solve

           4x            = 87 - 7 = 80

            x                     = 80/4 = 20.

 Debra 20;  Brian 20+7 = 27;  Austin 2*20 = 40.

To learn more about  integers refer

https://brainly.com/question/929808

#SPJ1

The average rate of change over is 1.

Given that;

the function is,

⇒ g (t) = - (t - 1)² + 5

Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.

The value of G(-4):

The value of G(-4) can be determined by substituting t = -4 in the function

⇒ g (t) = - (t - 1)² + 5

Thus, we have,

⇒ g (t) = - (-4 - 1)² + 5

⇒ g (t) = - 20

Thus, the value of G(-4) = -20

The value of G(5):

The value of G(5) can be determined by substituting t = 5 in the function , we get,

⇒ g (t) = - (t - 1)² + 5

⇒ g (t) = - (5 - 1)² + 5

⇒ g (t) = - 11

Thus, the value of G(5) is, -11

Now, Average rate of change:

The average rate of change can be determined using the formula,

⇒ G(b) - G (a) / (b - a)

where, a = - 4 and b = 5

Substituting the values, we get,

⇒ G(5) - G (-4) / (5 - (-4))

⇒ ( - 11 - (- 20)) / 9

⇒ 9/9

⇒ 1

Thus, the average rate of change over the interval is. 1.

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

Assuming no employees are subject to ceilings for their earnings IS $7,450

The computation of Salaries Payable is shown below:-

Gross Payroll $10,000

Less:

Federal income tax withheld $1,800

Social security rate at 6% -$600

Medicare rate at 1.5% -$150

Total deduction -$2,550

Salary Payable $7,450

We simply deduct three above taxes from the gross payroll so that we get to know for the salary payable amount

To learn more about employees visit:

https://brainly.com/question/13405418

#SPJ4

Answer:

Last answer.

Step-by-step explanation:

The equation that represents the cost of the van rental is $598.74 = 136.20 + $0.39m .

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

The general form of linear equations is:

y = a + bx

Where:

a = intercept

b = slope

The form of the equation that models the cost is:

Total cost = cost of renting the van + [cost per mile x (m - 120 miles)

$598.74 = $183 + [$0.39 x (m - 120)

$598.74 = $183 + $0.39m - 46.80

$598.74 = 136.20 + $0.39m

Thus, they travelled 1186 miles.

learn more about Equation here:

brainly.com/question/26434260

#SPJ9

Answer:

7)  Domain:  (-∞, ∞)

    Range:  [-1, ∞)

8)  Domain:  (-∞, ∞)

    Range:  (-∞, ∞)

Step-by-step explanation:

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

Domain & Range

The domain is the set of all possible input values (x-values).

The range is the set of all possible output values (y-values).

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

From inspection of the graph, the minimum y-value is y = -1.  

The end behavior of the relation is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow + \infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the range of the relation is restricted:  [-1, ∞)

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

The end behavior of the function is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow -\infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

Answer:

a. Negation of ∃x ∀y(P(x,y) → Q(x,y)) = ∀x  ∃y P(x,y)  ∧ ¬Q(x,y) ]

b. Negation of ∃x ∀y(P(x,y) → P(y,x)) = ∀x ∃y  [ ¬P(x,y) ∨ ¬P(y,x) ] ∧ [P(x,y) ∨ P(y,x)]

c. Negation of ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y) = ∀x ∀y ¬ [P(x,y)]  ∨ ∃x ∃y ¬ [Q(x,y)]

Step-by-step explanation:

a.∃x ∀y(P(x,y) → Q(x,y))

Negation = ¬ [ ∃x ∀y(P(x,y) → Q(x,y)) ]

                = ∀x  ¬ [ ∀y(P(x,y) → Q(x,y)) ]

                = ∀x  ∃y ¬ [ (P(x,y) → Q(x,y)) ]

                = ∀x  ∃y ¬ [  ¬P(x,y)  ∨ Q(x,y) ]

                = ∀x  ∃y P(x,y)  ∧ ¬Q(x,y) ]

Negation of ∃x ∀y(P(x,y) → Q(x,y)) = ∀x  ∃y P(x,y)  ∧ ¬Q(x,y) ]

b. ∃x ∀y(P(x,y) → P(y,x))

Negation = ¬ [ ∃x ∀y(P(x,y) → P(y,x)) ]

               = ∀x ¬ [ ∀y(P(x,y) → P(y,x)) ]

               = ∀x ∃y ¬ [ (P(x,y) → P(y,x)) ]

               = ∀x ∃y ¬ [ ( P(x,y) ∧ P(y,x) ) ∨ ( ¬P(x,y) ∧ ¬P(y,x) )]

               = ∀x ∃y ¬ [ P(x,y) ∧ P(y,x) ] ∧ ¬[ ¬P(x,y) ∧ ¬P(y,x) ]

               = ∀x ∃y  [ ¬P(x,y) ∨ ¬P(y,x) ] ∧ [ P(x,y) ∨ P(y,x) ]

∴ we get

Negation of ∃x ∀y(P(x,y) → P(y,x)) = ∀x ∃y  [ ¬P(x,y) ∨ ¬P(y,x) ] ∧ [P(x,y) ∨ P(y,x)]

c. ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y)

Negation = ¬ [ ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y) ]

                = ¬ [ ∃x ∃y P(x,y) ]  ∨ ¬ [ ∀x ∀y Q(x,y) ]

                = ∀x¬ [  ∃y P(x,y) ]  ∨ ∃x ¬ [ ∀y Q(x,y) ]

                = ∀x ∀y ¬ [ P(x,y) ]  ∨ ∃x ∃y ¬ [ Q(x,y) ]

∴ we get

Negation of ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y) = ∀x ∀y ¬ [ P(x,y) ]  ∨ ∃x ∃y ¬ [ Q(x,y) ]

Answer:

Step-by-step explanation:

Answer:

⟶ We can express the sum 1^2 + 2^2 + 3^2 + ... + 750^2 using summation notation as:

∑i^2, where i goes from 1 to 750.

⟶ Here, the symbol ∑ represents the summation, and i is the index variable, which takes on the values 1, 2, 3, ..., 750. The expression i^2 is the term being summed.

⟶ So the sum can be written as:

∑i^2 = 1^2 + 2^2 + 3^2 + ... + 750^2

⟶ Note that the upper limit of the index variable is 750, which corresponds to the last term in the sum.

Learn more about Summation Notations here:

https://brainly.com/question/29334900

#SPJ1

Answer:

\(\sum \limits^{750}_{n=1} {n^2}\)

Step-by-step explanation:

General explanation of summation notation

Any sum of terms whose format is the same can be represented more concisely using a Summation symbol.

The Summation symbol is a capital greek letter Sigma:  \(\sum\)

The summation will take a general format of each term, and increase a "dummy variable" by 1, summing together terms until the summation is complete.  To write the summation expression, find the common format of each term, and write it using a "dummy variable" to represent the number that is changing.

If the change of the number within each term increases by 1 each time, that makes the transition easier because the dummy variable increases by 1.  If the change of the number within each term does not change by 1 each time, using summation notation can be more challenging, as one needs to develop a formula to represent the amount that it is changing each time.

The common format of each term & the changing number

In our case, each term is some number squared, and the number that is squared changes from 1, to 2, to 3, ... and so on .. up to 750 (changing by 1 each time).  Since the number that is square changes by 1 each time, that will be our "dummy variable".

Using "n" for the "dummy variable", our terms look like \(n^2\)

The start and end of the list

Lastly, to specify where the list starts and ends, we write where the list starts (lowest number) at the bottom with the "dummy variable", and where the list ends (largest number) at the top.

So, in the end, the summation would look like this:  \(\sum \limits^{750}_{n=1} {n^2}\)

This represents adding a bunch of terms that look like \(n^2\), starting at n=1, each time, increasing the value of n by 1, and stopping with the last term when n=750.

Extension of knowledge (NOT about THIS problem)

For a similar example where the changing number doesn't increase by 1 each time, look at a similar sequence of, where it's just the odd numbers squared up to 99:

1^2 + 3^2 + 5^2 + … + 99^2

While the terms do have the format of a number squared, since the number that is squared isn't just increasing by 1 each time, there would need to be a formula to describe how they are increasing.  One way to represent that would be:

\(\sum \limits^{50}_{n=1} {(2n-1)^2}\)

Note that this does cause the final endpoint of the dummy variable to not necessarily be intuitive, but the "99 squared" is the 50th term (observe 2*50-1 is 99).

Answer:

1. The value of 5 is fifty thousand

2. The value of 6 is six thousand

Step-by-step explanation:

1. 8.156 million - 8,156,000

2. 6,521

^ 6000

Answer:

4 is greater than 3 or 2 is less than 4 or 11 is equal to 11

Answer:

1<2   2>1  1=1

Step-by-step explanation:

this is because 1 is less than 2, 2 is more than 1 , and one is equal to one.

Answer:

x = 13, z = 184

Step-by-step explanation:

(14x-94) = 88

14x = 182

x = 13

z = 360 - 88*2 = 360 - 176 = 184

Answer:

x = 13; z = 92

Step-by-step explanation:

88 = 14x - 94

14x = 182

x = 13

180 = z + 88

z = 92

Answer:

2.3 hours

Step-by-step explanation:

From 3:12 pm to 4:12 pm, one hour passes.

From 4:12 pm to 5:12 pm, another hour passes.

From 5:12 pm to 5:30 pm, there are 18 minutes that pass.

Therefore, the total time elapsed is 2 hours and 18 minutes out of 60 minutes in an hour.

To convert this to a fraction, we can write:

2 hours + 18 minutes = 2 + 18/60 hours = 2.3 hours

So, 2.3/1 hour passes from 3:12 pm to 5:30 pm.

Answer:

$15.08

Step-by-step explanation:

When subtract 84.92 from 100 you get 12.08 which is how much he clerk should give back

Answer:

15.08

Step-by-step explanation: