10-80 The Clean-Up Vacuum Company is designing a new upright vacuum cleaner.

A. What shapes can they use to model this new vacuum cleaner?

B. The Clean-Up Vacuum Company has decided to use a cylindrical model for the body of the

vacuum. They want it to be 2.5 feet tall and have a circumference of 14 inches. If only 75% of

the cylindrical body can hold the dirt from cleaning, how much dirt can the new upright

vacuum hold?

Answer:

9<✓88<10

Step-by-step explanation:

✓88 = 9.38083

Answer:

Option B.

{–9 + i√225 / 24, –9 – i√225 / 24}

Step-by-step explanation:

12a² + 9a + 7 = 0

Using formula method, the solutions to the equation can be obtained as follow:

Coefficient of a² (a) = 12

Coefficient of a (b) = 9

Constant (c) = 7

a = –b ±√(b² – 4ac) / 2a

a = –9 ±√(9² – 4 × 12 × 7) / 2 × 12

a = –9 ±√(81 – 336) / 24

a = –9 ±√(– 225) / 24

Recall

–225 = –1 × 225

Thus,

–9 ±√(– 225) / 24 = –9 ±√(–1 × 225)/24

Recall

√(–1 × 225) = √–1 × √225 = i√225

Thus,

–9 ±√(–1 × 225)/24 = –9 ± i√225/24

Therefore,

a = –9 ± i√225/24

a = –9 + i√225 / 24 or –9 – i√225 / 24

Therefore, the solutions to the equation are:

{–9 + i√225 / 24, –9 – i√225 / 24}

The calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.



To determine the number of significant figures in a calculation, we follow the rules for significant figures:

1. Addition and subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
2. Multiplication and division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

Let's break down the calculation step by step:
\(9.04-8.23+21.954+81.0\) yields \(104.764\).

Now, multiplying this result by \(3.1416\) gives \(329.5719744\).

The measurement with the fewest significant figures in the calculation is \(3.1416\), which has 5 significant figures.

According to the rule for multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures. Hence, the result, \(329.5719744\), will be rounded to 4 significant figures.

Therefore, the calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.

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Answer:

5/(1/4) = 20

Step-by-step explanation:

Each feeder holds 2 1/2 cups.

Both feeders combined hold 2 * 2 1/2 cups = 5 cups

The scoop holds 1/4 cup.

The number of scoops he needs is

5/(1/4) = 5 * 4 = 20

The maximum likelihood estimate of θ for the given data is 1/3.

The likelihood function L(θ|x) for a sample of n observations x1, x2, ..., xn from a Pareto distribution with parameter θ is given by:

L(θ|x) = f(x1|θ) × f(x2|θ) × ... × f(xn|θ)

where f(xi|θ) is the probability density function of the Pareto distribution with parameter θ evaluated at xi.

Substituting the given pdf of the Pareto distribution with parameter 0, we get:

L(θ|x) = (θ/5θ) × (θ/10θ) × (θ/8θ) = θ³ / 4000

Taking the natural logarithm of the likelihood function, we get:

ln L(θ|x) = 3 ln θ - ln 4000

To find the maximum likelihood estimate (MLE) of θ, we differentiate ln L(θ|x) with respect to θ and set the derivative equal to zero:

d/dθ ln L(θ|x) = 3/θ = 0

Solving for θ, we get:

θ = 1/3

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The maximum likelihood estimate of θ for the given data is 0.501

From the question, we have the following parameters that can be used in our computation:

\(f(x|\theta) = \frac{\theta}{x^{\theta+ 1} }\)

The likelihood function L(θ|x) for a Pareto distribution with parameter θ is calculated using

L(θ|x) = f(x₁|θ) * f(x₂|θ) * .....

Recall that

\(f(x|\theta) = \frac{\theta}{x^{\theta+ 1} }\)

And

θ = 5, 10, 8

So, we have

\(L(\theta|x) = \frac{\theta}{5^{\theta+ 1} } * \frac{\theta}{8^{\theta+ 1} } * \frac{\theta}{10^{\theta+ 1} }\)

Taking the natural logarithm both sides

\(\ln(L(\theta|x)) = \ln(\frac{\theta}{5^{\theta+ 1} } * \frac{\theta}{8^{\theta+ 1} } * \frac{\theta}{10^{\theta+ 1} })\)

Differentiate

ln L'(θ|x) = -[(ln(10) + ln(8) + ln(5))θ - 3]/θ

Set the differentiated equation to 0

So, we have

-[(ln(10) + ln(8) + ln(5))θ - 3]/θ = 0

Solve for θ, we get:

(ln(10) + ln(8) + ln(5))θ = 3

So, we have

θ = 3/(ln(10) + ln(8) + ln(5))

Evaluate

θ = 0.501

Hence, the maximum likelihood of θ is 0.501

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When a single arithemetic / logic unit (alu), which does the math in a processor, is given 2 independent register sets so that it can quickly alternate between running 2 separate threads, we call it simultaneous multithreading.

Simultaneous multithreading, or "SMT," is the term used when a single Arithmetic/Logic Unit (ALU) is given two independent register sets to swiftly switch between operating two distinct threads.

SMT is a technique used in processor design to improve overall performance by allowing multiple threads to be executed concurrently on a single physical processor core. It enables the ALU to switch between different threads, or sets of instructions, rapidly, providing the illusion of simultaneous execution and effectively utilizing the available resources.

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Here's the solution :

taking one out from each of them as square root :

square root of 3x × square root of 3x

= 2 square root of 3x

On U.S. converting to Metric System , the Advantages are Standardization , Improved Science and Technology and the Disadvantages are Cost , Resistance to change .

The Advantages of the U.S. converting to the metric system:

(i) Standardization: The metric system is used by the majority of countries in the world, making international trade and communication easier and more efficient.

(ii) Improved Science and Technology: The metric system is the standard system used in science and technology, making it easier for the U.S. to collaborate with other countries and to participate in international research.

The Disadvantages of the U.S. converting to the metric system:

(i) Cost: The conversion to the metric system would be a costly and time-consuming process, involving changes to products, labeling, and infrastructure.

(ii) Resistance to change: There may be resistance from people who are used to the imperial system and are comfortable with it.

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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Therefore, The smallest set of integers guaranteed to have a difference that is a multiple of 14 is 15. This is due to the Pigeonhole Principle and the 14 possible remainders when dividing integers by 14.

The smallest set of integers for which we are guaranteed there exist two whose difference is a multiple of 14 is 15. This can be explained by considering the possible remainders when dividing integers by 14. There are 14 possible remainders (0 to 13), but if we choose 15 integers, then by the Pigeonhole Principle, at least two of them must have the same remainder when divided by 14. The difference between these two integers will be a multiple of 14, as their remainders are the same. Therefore, the smallest set of integers required is 15.
Therefore, The smallest set of integers guaranteed to have a difference that is a multiple of 14 is 15. This is due to the Pigeonhole Principle and the 14 possible remainders when dividing integers by 14.

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9514 1404 393

Answer:

  8, 9. Correct

  10. 6.1×t

Step-by-step explanation:

8, 9. The answers shown are correct.

__

10. The only product in the given expression is 6.1t, which can be written as ...

  6.1×t

when a symbol is used to represent multiplication.

The parts of the product are the multiplicand and the multiplier. Those parts are also called factors.

There are two special right triangles:

The 45-45-90 triangle

The 30-60-90 triangle.

We have,

Special right triangles are right triangles with specific angles and side ratios that make calculations easier.

There are two special right triangles:

The 45-45-90 triangle

The 30-60-90 triangle.

45-45-90 Triangle:

In a 45-45-90 triangle, the two legs are congruent, and the length of the hypotenuse is equal to the length of a leg times the square root of 2.

The angles are 45 degrees, 45 degrees, and 90 degrees.

The ratio of the sides is 1:1:√2.

30-60-90 Triangle:

In a 30-60-90 triangle, the sides are in the ratio of 1:√3:2.

The angles are 30 degrees, 60 degrees, and 90 degrees.

The side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is the length of the hypotenuse times the square root of 3.

Thus,

There are two special right triangles:

The 45-45-90 triangle

The 30-60-90 triangle.

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Answer:

4

Step-by-step explanation:

y = 4 sin (3x)

The amplitude is the coefficient in front of sin

4 is the amplitude

Answer:

XW = 134

Step-by-step explanation:

The fact that YZ bisects VW means that the angles VX and XW are supplementary, that is, they add to 180º. So

VX + XW = 180

We have that VX = 46. So

46 + XW = 180

XW = 134

In order to find how many minutes Leann swan this week, we just need to sum the time from each day:

Monday: 24 minutes

Tuesday: 18 minutes

Wednesday: 30 minutes

Thursday: 30 minutes

Friday: 30 minutes

So in total Leann swan 132 minutes this week.

Marks obtained are 33 and 45 when two students took an exam. one of them achieved 9 marks more than the other and his marks were 56% of the sum of both of their marks.

Similar to this, we are describing an algebraic expression when we explain an expression in words that has a variable (an expression with a variable). For instance, the algebraic expression for "3 more than x" can be written. x + 3 . Variables can be written straight after a regular integer in algebraic expressions that use them, with no symbol needed in between. An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. A good example of an algebraic expression is 3x²+ 2xy + c.

Given,

Two students took an exam. one of them achieved 9 marks more than the other and his marks were 56% of the sum of both of their marks.

Let the marks be x and x+9

Algebraic equation,

x+ 9 = 56/100(x+x+9)

x + 9 = 14/25 (2x +9)

25(x+ 9) = 14(2x+9)

25x + 225 = 28x +126

28x - 25x = 225 - 126

3x = 99

x = 33

Marks obtained are 33 and 45.

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Answer:

5.49

Mental or simplified math may be used to solve such equation.

The rate of change is $7 per one square feet.

In order to determine the rate of change, the difference between each successive cost would be divided by the difference in each successive size.

Rate of change = change in cost /change in size

(980 - 840) / (140 - 120)

140 / 20

= $7

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Answer:

36.5 is the answer

Hope this helps!

Step-by-step explanation:

Let the actual pressure be x

The actual pressure is 100% of x

The pressure is showing 8% more

So the pressure showing now is the actual pressure + the extra pressure

= 100%+8% = 108%

= 108/100

So the equation is:

108/100 x = 39.42

108x = 39.42*100

108x = 3942

x= 3942/108

= 36.5

Therefore the actual pressure is 36.5

Answer:

56/100

Sorry, I looked this up so someone else might need to show you the work.

But I got the answer

The measure (in radians) of the angle formed by the hands of a clock at 1.30 PM is 3π/4 radians.

The given time is 1:30 PM.

Time is used to quantify, measure, or compare the duration of events or the intervals between them, and even, sequence events.

The angle between hour hand and minute hand is 135°.

In radians = 135° ×π/180°

= 9π/12

= 3π/4

Therefore, the measure (in radians) of the angle formed by the hands of a clock at 1.30 PM is 3π/4 radians.

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Answer:

-1   |   1   4    4

Step-by-step explanation:

Changing to the root format x- k where k is the root

(x^2+4x+4) / (x- -1)

the outside is -1  and the inside is the coefficients of the terms

-1   |   1   4    4

Answer:

z = 32

Step-by-step explanation:

Add 3 to both sides.

5 + 3 = z/4 -3 + 3

8 = z/4

Multiply 4 on both sides. 8 times 4 is 32.

32 = z

Answer:

There are 2,520 unique permutations.

Step-by-step explanation:

When we have a set of N different elements, the total number of permutations is given by:

P = N! = N*(N - 1)*(N - 2)*...*(2)*(1)

Particularly, if out of these N elements, there are a given element that is repeated K times, then the permutations of these K elements actually do not add new unique permutations, then in that case the total number of unique permutations is:

P = N!/K!

And if we have another element that is repeated L times, then with the same reasoning than above, the total number of unique permutations is:

P = N!/(K!*L!)

Now, we have the set:

{C, E, A, S, E, L, E, S, S}

So we have a set of 9 letters, then:

N = 9

And, the letter S is repeated 3 times

The letter E is repeated 3 times

Then, using the above notation, we can define:

K = 3

L = 3

The total number of permutations is then:

\(P = \frac{9!}{3!*3!} = \frac{9*8*7*6*5*4*3*2*1}{3*2*1*3*2*1} = \frac{9*8*7*6*5*4}{3*2*1} = 2,520\)

So there are 2,520 unique permutations.

Answer:

Step-by-step explanation:

hello :

This means that the scenic lookout is located N16°E using compass notation.

To describe where the scenic lookout is located in relation to the picnic area using compass notation, we need to determine the direction from the picnic area to the scenic lookout.

First, we need to find the angle between the line connecting the main entrance and the scenic lookout (i.e., the bearing of the scenic lookout from the main entrance) and the line connecting the main entrance and the picnic area (i.e., the bearing of the picnic area from the main entrance). We are given that the scenic lookout is N16°E from the main entrance, so its bearing from the main entrance is 16° east of north, or N16°E. Since the picnic area is directly to the north of the main entrance, its bearing from the main entrance is N0°.

To find the angle between the two bearings, we can subtract the second bearing from the first:

N16°E - N0° = N16°E

This means that the scenic lookout is located 16° east of due north from the picnic area. In compass notation, we would write this as:

N16°E

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Answer:

See Graph below

Step-by-step explanation:

I hope this helps anyone who needs it :)

There are 472 more buttons bought by Vance than beads.

For the stated question table is made.

So,

Total number of beads bought by Vance = Number of beads(2 packages of large beads) + Number of beads(1 package of medium beads).

= (2 × 96) + (1 × 64)

= 2 × (90 + 6) + 64

= (2 × 90) + (2 × 6) + 64

= 180 + 12 + 64

= 256 beads

Now,

Total number of buttons bought by Vance = Total number of buttons (2 packages of large buttons) + Number of buttons (2 packages of medium buttons)

= (2 × 56) + (2 × 38)

= 2 × (50 + 6) + 2 × (30 + 8)

= (2 × 50) + (2 × 6) + (2 × 30) + (2 × 8)

= 100 + 12 + 600 + 16

= 728 buttons

Thus,

Difference for the number of buttons and beads

= 728 – 256

= 472 beads

So,

Therefore, there are 472 more buttons bought by Vance than beads.

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Answer:-1/3

Step-by-step explanation: the point goes right one and down three making the slope negative

Answer: A

Step-by-step explanation: