What is the length of PS?

Step-by-step explanation:

To work out the height of the cuboid, we need to use the formula:

Volume = Length x Width x Height

We have been given the volume and the length, so we can substitute those values into the formula:

540 = 6 x Width x Height

Now we need to convert the width from millimeters to centimeters, so we divide it by 10:

150mm ÷ 10 = 15cm

Substituting this value into the formula:

540 = 6 x 15 x Height

Simplifying:

540 = 90 x Height

Dividing both sides by 90:

6 = Height

Therefore, the height of the cuboid is 6cm.

Autumn's bank registry will be :

Transaction Amount Balance

Paycheck $1275.00 $1275.00

Rent $400.00 $875.00

Utilities $75.00 $800.00

Cell Phone $80.00 $720.00

Subway Pass $120.00 $600.00

Groceries $200.00 $400.00

Work Clothes $100.00 $300.00

Entertainment $100.00 $200.00

Savings $200.00 $0.00

As you can see, Autumn has $0.00 left over at the end of the month. This means that she is spending more money than she is earning. In order to create a budget that works for her, Autumn will need to find ways to cut back on her expenses. Some possible areas where she could cut back include:

Autumn could look for a cheaper apartment or move in with more roommates. Autumn could turn off lights and appliances when she's not using them and seal up any cracks or holes in her apartment to keep the heat in during the winter and the cool air in during the summer.

By cutting back on her expenses, Autumn can create a budget that works for her and save money for the future.

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Answer: There are 19 classes

Step-by-step explanation:

divide the total amount amount of students by the amount of students in each class

Answer:

19

Step-by-step explanation:

If I´m correct you should divide 456 by 19 then you should get your answer (dont quote me on that )

Answer: 392m^2

Step-by-step explanation:

Area of parallelogram is base x height

56 x 7 = 392m^2

The correct ways to describe the set of nonnegative integers less than or equal to 100 that are perfect cubes are {0, 1, 8, 27, 64}, {1, 8, 27, 64} So correct option are a. and d.

Integers are a set of numbers that includes all positive and negative whole numbers (including zero), as well as their opposites. Integers can be represented on the number line, with positive integers to the right of zero and negative integers to the left of zero.

The correct ways to describe the set of nonnegative integers less than or equal to 100 that are perfect cubes are:

a. {0, 1, 8, 27, 64}

d. {1, 8, 27, 64}

Option a contains all the perfect cubes less than or equal to 100, including 0.

Option d contains the perfect cubes greater than 0 and less than or equal to 100.

Option b is not correct because it describes the set of integers x that satisfy x^3 = y, where y is a nonnegative integer not exceeding C. This set includes all the integers whose cubes are nonnegative integers not exceeding C, not just the perfect cubes less than or equal to 100.

Option c is not correct because it describes the set of integers x that are perfect cubes and also satisfy 0 < x < 100. This set includes all the perfect cubes, not just the ones less than or equal to 100.

Option e is not correct because it includes integers that are not perfect cubes.

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Work Shown:

Two points on this line are (0,0) and (1,-6)

The slope of the line through these points can be found through the slope formula

m = (y2-y1)/(x2-x1)

m = (-6-0)/(1-0)

m = -6/1

m = -6 is the slope

The y intercept is b = 0 as this is the location on the vertical y axis where the graph crosses.

Using m = -6 and b = 0, we go from y = mx+b to y = -6x+0

This simplifies to y = -6x

Answer:

y = -6x

Step-by-step explanation:

Take 2 points:

(-1,6)

(1,-6)

Find the slope:

-6 - 6/1 - - 1

-12/2 = -6

So we have the equation:

y = -6x + b

now to find b, insert one of the points from before for x and y

-6 = -6(1) + b

-6 = -6 + b

b = 0

So then we get y = -6x + 0 which we can write as y = -6x

Answer:

\(\frac{27}{8}\)

Step-by-step explanation:

\(\left(\frac{16}{81}\right)^{\frac{-3}{4}}=\frac{16^{\frac{-3}{4}}}{81^{\frac{-3}{4}}}\)

\(=\frac{2^{-3} }{3^{-3} }\)

\(=\frac{\frac{1}{8}}{\frac{1}{27}}\)

\(=\frac{1*27}{8*1}\)

\(=\frac{27}{8}\)

Answer:

Dwane has 25 rare edition stamps, or 5/6.

Step-by-step explanation:

The question is basically answered in the problem.

It says, "25 of the stamps are a rare edition."

And the question is, "How many rare edition stamps does Dwane have?"

So, 25 is the answer.

Hope this helps!

Answer:

The answer is J.

Step-by-step explanation:

Answer:

2.5th percentile and the 97.5th percentile.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.95}{2} = 0.025\)

So we obtain the 0.025*100 = 2.5th percentile and the (1-0.025)*100 = 97.5th percentile.

So the answer is:

2.5th percentile and the 97.5th percentile.

Answer:

x=10

Step-by-step explanation:

1/2x+4=9

subtract 4 from both sides

1/2x=5

multiply both sides by 2 to get x by itself

x=10

Answer:

1/2x+4=9 is x=1/10

Step-by-step explanation:

theres no explanation

Answer:

slope = 9/2

Step-by-step explanation:

y2 - y1 / x2 - x1

-4 - 5/0- 2 = 9/2

Step-by-step explanation:

The three rectangles that have perimeter of 36 inches are

A. C. and D

Just check by using the formula of perimeter of rectangle ; 2 (L + b)

Hope it will help :)

Answer:

ok

Step-by-step explanation:

donnnnnnnnnnnnnnnnnnnne

To verify if the relation is a function, it must be verified if from each value of x only one arrow departs.

A relation represents a function when each input value is mapped to a single output value.

In mapping notation, with the arrows, it must be verified if there is no input from which more than one arrow departs.

The problem is incomplete, hence the general procedure to verify if the relation is a function was presented.

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The probability of roll outcome:

1st 2 = 1/6

2nd prime = 1/2, and

3rd more than 4 = 1/3.

Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.

In a fair die, considering the outcomes from the question:

probability of the 1st roll to be 2 = 1/6

probability of 2nd roll to be prime = 3/6

probability of 2nd roll to be prime = 1/2

probability of 3rd roll to be more than 4 = 2/6

probability of 3rd roll to be more than 4 = 1/3

Therefore, the fracions 1/6, 1/2, and 1/3 are the probabilities of the 1st, 2nd, and 3rd rolls outcome respectively.

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Answer:

\(3x^{3} +10x^{2} +17x+12\)

Step-by-step explanation:

Answer:

3x³ + 10x² + 17x + 12

Step-by-step explanation:

Step 1: Write expression

(3x + 4)(x² + 2x + 3)

Step 2: Distribute 3x

3x³ + 6x² + 9x

Step 3: Distribute 4

4x² + 8x + 12

Step 4: Combine

3x³ + 6x² + 9x + 4x² + 8x + 12

Step 5: Combine like terms

3x³ + 10x² + 17x + 12

The equivalent cost will be $5.4 per gallon.

The equivalent is the expression that is in different forms but is equal to the same value. Conversion means to convert the same thing into different units.

In September 2016, the cost of gasoline in Berlin was around 1.25 euros per liter.

We know that 1 U.S. dollar = 0.876 euros and 1 gallon = 3.785 liters.

The equivalent cost would be dollars per gallon will be

⇒ 1.25 euros per liter

⇒ 1.25 x [(1/0.876) / (1/3.785)] dollars per gallon

⇒ 1.25 x 1.1415 / 0.2642

⇒ $5.4 per gallon

The equivalent cost will be $5.4 per gallon.

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Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.

This common convenience, already-existing variables, or all important elements from the original Diocesan customizable survey that followed a particular event methodology can all be used to achieve the goal. If it does, there will be another chance to get in touch with the entity. If it doesn't, each of the crucial elements of a term proof outcome will surely be lost.

Here,

The quantity of punch produced by the recipe is:

If the punch bowl has an 8-quart capacity and the recipe fills it 3/4 full.

=> 6 pints =  8 * 3/4.

The formula yields 6 quarts of punch as a result.

Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.

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The correct statements regarding the transformations are given as follows:

Examples of transformations are given as follows:

Parallel lines are lines that have the same slope, that is, lines that do not intercept, and the transformations do not change whether the lines are parallel or not.

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√(a² + b²)²  - 4a²b²cos²θ is the product of the lengths of the two diagonals is given by the expression.

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division.

                                An expression's structure is as follows: Number/variable, Math Operator, Number/Variable is an expression.

we have AB as a, AD as b and the angle between them is theta.

So using the cosine rule, we have

  BD = √a² + b² - 2abcosθ

So now consider the triangle ABC

Here AB is a, BC is b and the angle is 180-theta

So using cosine rule, we get AC as

   AC = √a² + b² - 2abcosθ( 180 - θ )

    AC = √a² + b² - 2ab(-cosθ )

    AC = √a² + b² - 2abcosθ

Now we have the two diagonals AC and BD. So multiplying, we get

 AC × BD = √a² + b² + 2abcosθ × √a² + b² - 2abcosθ

Simplifying, we get

AC × BD = √(a² + b² + 2abcosθ) × (√a² + b² - 2abcosθ)

AC × BD = √(a² + b²)² - (2abcosθ)²

AC × BD = √(a² + b²)²  - 4a²b²cos²θ

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Answer:

B

Step-by-step explanation:

a prime polynomial is one which does not factor into 2 binomials.

its only factors are 1 and itself

attempt to factorise the given polynomials

3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )

= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(3x² - 2) ← in factored form

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

3x³ - 2x² + 3x - 4 ( factor the first/second terms

= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored

thus this polynomial is prime

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

4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )

= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term

= (2x + 1)(2x² + 3) ← in factored form

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

4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )

= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(4x² - 3) ← in factored form

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

the only polynomial which does not factorise is

3x³ - 2x² + 3x - 4

Answer:

Step-by-step explanation:

I'm a little confused by the wording of the question. If 3 pieces of the pie are shaded the fraction would be 3/8. I hope that's what you meant have a great day!

The volume of a cylinder whose diameter measures 2.5 cm and has a height of 15.5 cm is equal to 76.10 cubic centimeters.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Note: Radius = diameter/2 = 2.5/2 = 1.25 cm.

By substituting the parameters, we have:

Volume of cylinder, V = 3.142 × 1.25² × 15.5

Volume of cylinder, V = 76.10 cubic centimeters.

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Complete Question:

Calculate the volume of a cylinder whose diameter measures 2.5 cm and has a height of 15.5 cm.

Winston's economic profit based on the forgone salary of $60,000, and the revenue of $150,000 is $78,000. The correct option is therefore;

$78,000

An economic profit is a profit that accounts for both the explicit and implicit costs of a business. The economic profit is obtained from the difference between the total revenue and the costs including the opportunity costs.

The annual salary of Winston as an accountant = $60,000

The amount Winston's financial asset generates = $4,000 per year

The cost of running the business = $8,000

The amount Winston earns as revenue = $150,000

Therefore;

Winston's opportunity cost which is the forgone alternative, is the amount he earns as an accountant = $60,000

The interest of $4,000, earned from the financial asset = The cost of using the financial asset for the business

The cost of running the business = $8,000

The total cost = Opportunity cost + Cost of making use of the financial asset + The business running cost

The total cost = $60,000 + $4,000 + $8,000 = $72,000

The economic profit = The total revenue - The total cost

Therefore;

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Answer:

Jess is 26, Cece is 29

Step-by-step explanation:

Hey there!

Let's solve these equations.

The first one is

3x=15

Divide both sides by 3:

x=5 (Answer)

\(\rule{250}{1}\)

x+4=7

x=7-4

x=3 (Answer)

\(\rule{250}{2}\)

4y+3=11

4y=11-3

4y=8

y=2 (Answer)

\(\rule{200}{2}\)

2x+1=13

2x=13-1

2x=12

x=6 (Answer)

\(\rule{200}{2}\)

x/2-4=1

x/2=5

x=10 (Answer)

\(\rule{200}{2}\)

x+3=8

x=8-3

x=5 (Answer)

\(\rule{200}{2}\)

2y-5=1

2y=1+5

2y=6

y=3 (Answer)

_______________________

5x=40

x=8 (Answer)

_________________________

y/3+1=7

y/3=7-1

y/3=6

y=18 (Answer)

Hope everything is clear.

Let me know if you have any questions; if so, please comment.

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Answer:

Step-by-step explanation:

ok so  u convert the x by 9 and then u mulitply that by 291 and u get 45,789x :)