4/5=/20 math...........

4/5=/20 Math...........

Answers

Answer 1

Answer:

1.) 16/20

2.) 15/35

3.) 12/9

4.) 52/60

5.) 9 inches

6.) 24 centimeters

7.) 16 logs

8.) $15.40

9.) 10 miles

10.) 1.5 inches

I hope this is good enough:


Related Questions

What is 4/8 into decimal form?

Answers

4/8 into decimal form is 0.5

4/8into decimal form is 0.5

Help please!!!Eric runs everyday.He delivers 189 papers in 3 hours.What is the unit rate his deliveries per hour?please put the answer in the comments

Answers

Answer:

63 papers per hour

please help me answer this

Answers

Sequence 1: 13, 16, 19, 22, 25, Sequence 2: 15, 13, 11, 9, 7 and Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7).

what is sequence?

An ordered list of numbers is a sequence. The three dots indicate that the established pattern should move forward.

A. Sequence 1: 13, 16, 19, 22, 25

Sequence 2: 15, 13, 11, 9, 7

Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7)

B. Sequence 1: 1, 5, 17, 53, 161

Sequence 2: 6, 15, 33, 69, 141

Ordered Pair: (1, 6), (5, 15), (17, 33), (53, 69), (161, 141)

C. Input (x) | Output

1 | 17,  2 | 19, 3 | 21, 4 | 23

D. Input (x) | Output

1 | 30, 2 | 15, 3 | 7.5

To find the outputs, we use the formula: output = 60 ÷ 2x.

For x = 1, output = 60 ÷ 2(1) = 30

For x = 2, output = 60 ÷ 2(2) = 15

For x = 3, output = 60 ÷ 2(3) = 7.5

E. Input (x) | Output

1 | 23, 2 | 30, 3 | 37, 14 | 102, 15 | 109, 16 | 116, 27 | 205, 70 | 498

To find the outputs, we use the formula: output = 16 + 7x.

For x = 1, output = 16 + 7(1) = 23

For x = 2, output = 16 + 7(2) = 30

For x = 3, output = 16 + 7(3) = 37

For x = 14, output = 16 + 7(14) = 102

For x = 15, output = 16 + 7(15) = 109

For x = 16, output = 16 + 7(16) = 116

For x = 27, output = 16 + 7(27) = 205

For x = 70, output = 16 + 7(70) = 498

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Simplify 5 - 2 x 3 + 4. Choices are A.) 13 B.) 3 C.) -5 D.) 21

Answers

Answer:

Answer. c

Step-by-step explanation:

Answer: its c

Step-by-step explanation:

If f(x) = 2x2 – 3x – 1, then f(-1)=

Answers

ANSWER:
Given:f(x)=2x^2-3x-1
Then,f(-1)=2(-1)^2-3(-1)-1
f(-1)=2(1)+3-1
f(-1)=5-1
f(-1)=4


HOPE IT HELPS!!!!!!
PLEASE MARK BRAINLIEST!!!!!

The value of function at x= -1 is f(-1) = 4.

We have the function as

f(x) = 2x² - 3x -1

To find the value of f(-1) when f(x) = 2x² - 3x -1, we substitute x = -1 into the expression:

f(-1) = 2(-1)² - 3(-1) - 1

      = 2(1) + 3 - 1

      = 2 + 3 - 1

      = 4.

Therefore, the value of function at x= -1 is f(-1) = 4.

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Which of the following functions is graphed below? HELP

Which of the following functions is graphed below? HELP

Answers

The solution is: Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1, the following functions is graphed below.

Option C is correct.

Explanation:

We are given a graph of piece-wise function which break at x=1

We need to choose correct option for graph.

Function is break at x=1.

We will get two function

For x≤1 and x>1

As we can see x≤1, graph is linear and x>1 graph is parabolic.

Equation of linear graph, x≤1

Take two point of graph (0,6) and (-6,0)

Equation of line:

y-y1/y2-y1 = x-x1/x2-x1

y = x+1

f(x)=x+6 , x≤1

Equation of parabolic graph, x>1

f(x) = x^2 + 3

Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1

Please see the attached figure.

Hence, The option C is correct.

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Which of the following functions is graphed below? HELP

Quadrilateral ABCD is a square and the length of BD¯¯¯¯¯ is 10 cm.

What is the length of AE¯¯¯¯¯ ?



Enter your answer in the box.

the length of AE¯¯¯¯¯ =
cm

Answers

The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

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Divide.
(-15z^7 u^5 - 12zu +22z²u³)
÷ (-3z²u³)

Answers

Answer:

(-15z^7 u^5 - 12zu +22z²u³)÷ (-3z²u³)

The answer is 7y6z−5z / y4

:)

River c is 500 miles longer than River D. If the sum of their lengths is 5,520 what is the length of each River. (C and d)

Answers

Let's call the length of River C "c" and the length of River D "d". We know that:

c = d + 500

And the sum of their lengths is 5,520:

c + d = 5,520

We can substitute the first equation into the second equation:

c + d = c + d + 500

So:

500 = 5,520 - c - d

Rearranging, we can find the value of d:

d = 5,520 - c - 500

d = 5,020 - c

We can now use either equation to find the value of c:

c = 5,520 - d
c = 5,520 - (5,020 - c)

Solving for c, we get:

c = 2,500

And using either equation, we can find the value of d:

d = 5,520 - c = 5,520 - 2,500 = 3,020

So River C is 2,500 miles long, and River D is 3,020 miles long.

Divide( use long division):
6×^3+2x-17x^2+15 by 2x-3​

Answers

Answer:

3x² - 4x - 5

Step-by-step explanation:

Definitions:

Dividend: The polynomial which has to be divided.Divisor: The expression by which the dividend is divided.Quotient: The result of the division.Remainder: The part left over.

Long Division Method of dividing polynomials:

Divide the first term of the dividend by the first term of the divisor and put that in the answer.Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.Repeat until no more division is possible.Write the solution as the quotient plus the remainder divided by the divisor.

Given:

Dividend:  6x³ + 2x - 17x² + 15Divisor:  2x - 3

Rearrange the dividend in descending order of the exponents:

6x³ - 17x² + 2x  + 15

Now use the method of long division to divide (6x³ - 17x² + 2x  + 15) by (2x - 3):

\(\large \begin{array}{r}3x^2-4x-5\phantom{)}\\2x-3{\overline{\smash{\big)}\,6x^3-17x^2+2x+15\phantom{)}}}\\{-~\phantom{(}\underline{(6x^3-9x^2)\phantom{-b)))))))).)}}\\-8x^2+2x+15\phantom{)}\\-~\phantom{()}\underline{(-8x^2+12x)\phantom{)))..}}\\-10x+15\phantom{)}\\-~\phantom{()}\underline{(-10x+15)\phantom{}}\\0\phantom{)}\\\end{array}\)

Therefore, the quotient is:

\(\boxed{\boxed{3x^2-4x-5}}\)

Enter the degree of the polynomial below.
6x + 9x + 3x – 4410 - 9x5 – 5x6
A. 9
B. 10
c. 6.
OD. 4

Answers

Answer:

the answer is d

Step-by-step explanation:

At the movies, Josh
purchase tickets at a rate of
5 for $25. He also wants to
buy one $10 snack pack.
If he needs to buy 8 tickets,
and only has $50, would he
have enough money to also
buy the snack pack?

Answers

Yes he would have enough money

Answer:

40 + 10 = 50

Step-by-step explanation:

Yes he does, if the tickets cost 5 for 25 that means that they cost $5 each. Josh needs 8 so he needs to multiply 8x5. The price for the tickets is $40. Since he wants to buy a snack pack for $10 he needs to add that to the $40. This makes exactly $50.

Hope this helps!

During an experiment, the current in a circuit was measured 8 times and recorded as shown below. Calculate the standard deviation of the current to two decimal places.

During an experiment, the current in a circuit was measured 8 times and recorded as shown below. Calculate

Answers

Standard Deviation for given set of data is 0.25634797778466.

What is standard deviation?

Standard deviation is a measurement of how evenly distributed a set of numbers is. Since the variance is the squared average of the squared deviations from the mean, it represents the square root of the variance.For instance: To determine the standard deviation, sum all of the numbers inside this data set, divide by the total number of numbers, and the result is the standard deviation.

Given that,

Sample size :12.3,11.9,12.5,12.1,12.6,11.9,12.2,12.1

Count, N: 8

Sum, submission x: 97.6

Mean, x: 12.2

Variance, s2:  0.065714285714286

s^2 = Σ(xi - x)^2/N - 1

= (12.3 - 12.2)2 + ... + (12.1 - 12.2)^2/8 - 1

= 0.46/7

=  0.065714285714286

s =  √0.065714285714286

=  0.25634797778466

Standard Deviation for given set of data is 0.25634797778466.

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Convert 6 months to​ years

Answers

Answer: 0.500001

Step-by-step explanation: Hope that helps!

all sales are on credit. if sales in april and may are budgeted to be $900,000 and $1,000,000, respectively, the cash expected to be collected in may is

Answers

If budgeted credit sales in April and May are to be $900,000 and $1,000,000, respectively, the cash collection in May is expected to be $920,000.

How is the cash collection determined?

The cash collected in May is based on the given percentages of collection.

In May, the cash collection includes the cash receipts for April credit sales of 80% and 20% for May credit sales.

                                     April           May

Credit Sales            $900,000   $1,000,000

Cash collection:

20% month of sale $180,000      $200,000 ($1,000,000 x 20%)

80% following month                      720,000 ($900,000 x 80%)

Total cash collection for May      $920,000

Thus, the expected cash collection in May should be $920,000.

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Question Completion:

Accounts receivable collection pattern:

20% month of sale

80% following month of sale.

help me pls

Angle Relationships

help me pls Angle Relationships

Answers

As a result, the answer to the given angle problem can be found by comparing the position, measurement, and congruence of two or more angles.

Define angle.

When two lines come together at a common point, an angle is created. They are expressed as a number of degrees, denoted by the symbol °. Acute, right, obtuse, and reflex angles are the other three significant types of angles. 360 degrees make up a circle. A 720° angle indicates that the object has completed two full rotations.

Here,

You can compare angles and take into account their relationships to other angles in addition to calculating degrees or radians.

Since we are comparing the position, measurement, and congruence of two or more angles, we refer to them as having "angle relationships."

For instance, two lines or line segments that cross each other create two pairs of vertical angles.

When a transversal intersects two parallel lines, complex angle relationships, such as alternating interior angles, matching angles, and so forth, result.

As a result, the answer to the given angle problem can be found by comparing the position, measurement, and congruence of two or more angles.

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A clothing company produced 600 items of clothing. Of those, 15% were jackets, 25% were dresses, and 15% were shoes. How many of the items of clothing were NOT jackets, dresses, or shoes?

Answers

Answer:

270 items

Step-by-step explanation:

Answer:

270 of them were not jackets dresses or shoes

Step-by-step explanation:

At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.07 and the probability that the flight will be delayed is 0.18. The probability that it will not rain and the flight will leave on time is 0.8. What is the probability that it is raining if the flight has been delayed? Round your answer to the nearest thousandth.

Answers

The probability that it is raining if the flight has been delayed is 0.07, or 7%.

How to calculate the probability

We can use the following formula to calculate the probability that it is raining if the flight has been delayed:

P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)

We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):

= 0.07 * 0.18

= 0.0126.

Substituting these values into the formula, we get:

P(Rain|Delayed) = 0.0126 / 0.18 = 0.07

Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.

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5.
a.
A study conducted at a school showed that the batteries used by calculators lasted an average of 101 days with a margin of error of ‡9 %.
What is the minimum average number of days a teacher can expect to have the batteries last in her classroom?
b.
There are roughly 279 days from the first day of school until the last day of school, the teacher has 24
TI-84 calculators and each one requires 4 triple A batteries. If the teacher can buy triple A batteries wholesale at 52 cents a battery, how much do you think she will need to spend at most on batteries for calculators over the year?

Answers

a. The teacher can expect the batteries to last at least 92.09 days  on minimum average.

b. The teacher will need to spend at most $49.92 on batteries for calculators over the year.

What is minimum average day?

a. The margin of error of ‡9% means that we can be 95% confident that the true average number of days the batteries will last is within 9% of the sample average. To find the minimum average number of days a teacher can expect to have the batteries last in her classroom, we subtract the margin of error from the sample average:

Minimum average = 101 - (0.09)(101) = 92.09 days (rounded to two decimal places)

Therefore, the teacher can expect the batteries to last at least 92.09 days on average.

What is spend ?

b. The total number of batteries required for the 24 TI-84 calculators is:

24 calculators x 4 batteries per calculator = 96 batteries

The total cost of the batteries will be:

96 batteries x $0.52 per battery = $49.92 (rounded to two decimal places)

Therefore, the teacher will need to spend at most $49.92 on batteries for calculators over the year, assuming all batteries need to be replaced.

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what value of x is in the solution set of 2(3x–1)>4x–6?

Answers

Answer:

x > -2

Step-by-step explanation:

2(3x–1)>4x–6

Divide each side by 2

2/2(3x–1)>4x/2–6/2

3x-1 > 2x-3

Subtract 2x from each side

3x-2x-1 > 2x-3-2x

x-1 > -3

Add 1 to each side

x-1+1 > -3+1

x > -2

If base 8 has numbers from 0 t0 7 then decimal base will have numbers from​

Answers

The decimal base, also known as base 10, has numbers from 0 to 9.

What is a decimal numbering system?

In a decimal numbering system, we use ten symbols, 0 through 9, to represent any number. Each digit in a decimal number has a place value that is determined by its position in the number.

The rightmost digit represents the one's place, the digit to the left of it represents the tens place, the digit to the left of that represents the hundreds place, and so on.

In the decimal numbering system, each digit can have one of ten possible values, from 0 to 9. The value of a number in decimal depends on the position of each digit, with each position representing a power of 10.

Thus, the decimal base, also known as base 10, has numbers from 0 to 9.

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The complete question would be as:

If base 8 has numbers from 0 to 7 then decimal base 10 will have numbers from​ ____.

mations to Determine Similarity
What steps would you take to determine if these
figures are similar? Check all that apply.
Use a scale factor of 2.
Multiply the vertices of polygon ABCD by
O Translate the intermediate image 4 units down.
Perform two different dilations.
Reflect the intermediate image.

Answers

The steps which you would take to determine if these figures are similar include the following:

2. Multiply the vertices of polygon ABCD by 1/2.

5. Reflect the intermediate image.

What is a dilation?

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

By critically observing the graph representing polygon ABCD, we can logically deduce that a sequence of transformations that would polygon ABCD (pre-image) onto polygon A"B"C"D" (image) is a dilation by a scale factor of 1/2 and a reflection of intermediate image.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

mations to Determine SimilarityWhat steps would you take to determine if thesefigures are similar? Check

6. A shoe store stocks x pair of sneakers and y pairs of sandals. During a promotion, a pair of sneakers is priced at $50 and a pair of sandals at $36. The shop manages to sell half the sneakers and 80% of the sandals. Write an expression for the total amount of sales the store makes.​

Answers

The expression for the total amount of sales the store makes will be:25s + 28.8p

How to illustrate the expression?

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information, the shoe store stocks x pair of sneakers and y pairs of sandals. During a promotion, a pair of sneakers is priced at $50 and a pair of sandals at $36. The shop manages to sell half the sneakers and 80% of the sandal.

Let sneakers = s

Let sandals = p

An expression for the total amount of sales the store makes will be: 1/2(50s) + 0.8(36p).

= 25s + 28.8p

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Find the area of the green region in the circle to the nearest tenth

Find the area of the green region in the circle to the nearest tenth

Answers

The area of the green region of the circle is 96.4 ft².

What is area?

Area is the region bounded by a plane shape.

To calculate the area of the green region of the circle, we use the formula below

Formula:

A = πr²∅/360

Where:

A = Area of the green regionr = Radius of the circle∅ = Angle of the sector at the center of the circle

From the diagram,

Given:

r = 17/2 = 8.5 feet∅ = (180-27°) = 153°π = 3.14

Substitute these values into equation 1

A = 3.14×8.5²×153/360A = 96.4 ft²

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The area of the green region in the circle given is expressed as approximately: a. 96.5 square feet.

How to Find the Area of a Sector in a Circle?

The sector of a circle is calculated as:

A = ∅/360 * πr², where r is the radius and ∅ is the reference or central angle of the sector.

Given the following:

Central or reference angle (∅) = 180 - 27 = 153 degrees

Radius (r) = 17/2 = 8.5 feet

Plug in the values:

Area of the green region = 153/360 * π * 8.5²

Area of the green region ≈ 96.5 square feet.

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Felix has a gross income of $16,500. He is filing as Single. What is his total tax due?

Answers

Therefore , the solution of the given problem of unitary method comes out to be Felix's overall tax due is $395.

Unitary method: What is it?

The task can be finished by applying what was learnt, making use of this access to the world, and fusing all essential components from earlier researchers who used a certain methodology. If the required claim outcome materialises, the entity stated expression in the statement can then either be additionally discovered or both important processes will absolutely miss the expression.

Here,

The tax brackets and rates for single taxpayers are as follows, per the IRS tax tables for 2021:

=> 10% of taxable earnings between $0 and $9,950

=> 12 percent of taxable income between $9,950 and $40,525

=> 22% of tax-exempt income between $40,525 and $86,375

=> 24% of taxable income between $164,925 and $86,375

=> over $164,925 to $209,425 in taxable income, 32%

=> over $209,425 to $523,600 in taxable income, 35%

=> above $523,600 in taxable income, 37%

Felix's yearly gross income is $16,500, and in 2021, the single filer standard deduction is $12,550. His taxable income is thus:

=> $16,500 - $12,550 = $3,950

Felix is subject to 10% tax because his taxable income is less than $9,950. Thus, the amount of his tax is:

=> 10% of $3,950 = $395

Hence, Felix's overall tax due is $395.

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Find the difference: 1 - 5

Answers

Answer:

-4

Step-by-step explanation

1 - 5 = -4

indicated operations g(t)=-2t-4 h(t)=t2+2-t
find (g+h)(t)

Answers

To find (g+h)(t), we need to add the two functions g(t) and h(t) together, which means adding their respective outputs for any given input   \(t. (g+h)(t) = t^2 - 3t - 2.\)

What simply add the two functions?

First, let's write out the functions:

\(g(t) = -2t - 4\)

\(h(t) = t^2 + 2 - t\)

Now, we can add them together:

\((g+h)(t) = g(t) + h(t)\)

\(= (-2t - 4) + (t^2 + 2 - t)\)

\(= t^2 - 3t - 2\)

Therefore, the function (g+h)(t) is given by the equation:

\((g+h)(t) = t^2 - 3t - 2\)

This function is a quadratic polynomial in t, with the coefficient of the t^2 term being 1, the coefficient of the t term being -3, and the constant term being -2.

To find (g+h)(t), we simply add the two functions g(t) and h(t) together and simplify:

\((g+h)(t) = g(t) + h(t)\)

\(= (-2t-4) + (t^2 + 2 - t)\)

\(= t^2 - 3t - 2\)

Therefore,  \((g+h)(t) = t^2 - 3t - 2.\)

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Two vacationing families leave New York at the same time. They take 20 and 6 days, respectively, to reach their destination and return to New York. The vacationing families each take continuous trips to and from New York. How many days will pass before the two vacationing families leave New York on the same day again?​

Answers

Answer:

Step-by-step explanation: evagline has 3/5 of box of nuts.she uses it to fill 6 bowls

can someone solve this for me????? (10−523)⋅(−2)+x=823

Answers

Answer:

the answer is -203 i got 100%

Step-by-step explanation:

Marissa Palmer's charge account statement showed a previous balance of $142.55, a finance charge of $2.82, new purchases of $56.22 and $30.28, and a payment of $80.00. What is her new balance?

Answers

Answer:

Marissa Palmer owes $26.77

Step-by-step explanation:

       142.55

-          2.82

        56.22

        30.28

        80.00

____________

        -26.77

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A ship moves due north at 100kmh on a river flowing due east at 25km Calculate the magnitude of the resultant velocity of the ship. whenever i have anxiety i cant eat, why is that? What is the example of linear inequality in two variables? how do you turn 72 percent into a fraction 7. 4a + 21 > 10a - 9 solve the inequality How does an investor make money?. The formula mass of HC2H302 is1.592.603.724.80 U.S. trade policies with regard to sugar import restrictions reflect the fact that OA. U.S. sugar cane farmers have significant political power. OB. the U.S. imports most of the sugar consumed in the country. OC. there are gains from trade that the U.S. captures by engaging in free trade in sugar. OD. the U.S. has a comparative advantage in sugar production and therefore exports most of its sugar crop. O E. there would be no gains from trade available to the U.S. if it engaged in free trade in sugar. If you multiply all of the numbers in a calculator, what will it be? Dario purchased a party size sub, and he decides to share it with 3 of his friends. So, he cuts the sub into 4 equal pieces. However, another one of his friends also showed up, and there are now 5 people in total.Part A -- Now that the sub will be shared equally among 5 people, will each person get more or less sub? Briefly state why you think so.Part B -- Dario decides to take each one of the 4 pieces and share it equally among the 5 of them.First, he divides one piece into 5 equal parts and shares it, then the next one, and so on. What fraction of the party size sub did each person get after all the parts were shared out? Briefly explain your reasoning. Determine whether a quadratic model exists for the set of values below. If so, write the model. f(0) = -4, f(3) = -19, f(-1) = -11Select the correct choice below:A) A quadratic model does exist. It is f(x)= ?B) A quadratic model does not exist. The point P(3,5) is rotated 180 degrees CW about the point A(3,2) and then rotated 90 degrees CCW about point B(1,1). What is the coordinate of P after the rotations? Which scenario is an example of plagiarism? Answer this fast please If I add 26 mL of water to 172 mL of a 4 M NaOH solution, what will the molarity of the diluted solution be? solve for n. 15n / 15 = 534 / 15 and 4n / 4 = 307 / 4 **PLEASE ONLY ANSWER IF U KNOW BOTH OF THEM** Which of the following should you doDURING your interview?A. During the interview, make preparations to takeaccurate notes.B. During the interview, take a moment to make sure yournotes are accurate and complete.C. During the interview, ask questions frequently so yourinterviewee won't end up talking too much. PLEASE HELP ME this is my last question Which best explains President Wilsons use of the word "autocratic"?a.He is saying the United States needs to operate alone.b.He is discussing the free will of the United States.c.He is speaking of acting independently.d.He is emphasizing the enemys tyranny. In the normal course of business an entity's purchasesresult in recognition ofa.a liability.b.an expensec.a receivabled.income.