Frank and Linda just finished a meal and received their bill for $47.60. They would like to leave their server a 20 percent tip. Which expression could be used to find the total bill including gratuity?
0.2 (47.60)
47.60 minus left-bracket (0.2) (47.60) right-bracket
47.60 + left-bracket (0.2) (47.60) right-bracket
0.8 (47.60)

Tom can paint the room alone in 12 hours.

Let's assume that the work required to paint the room is equivalent to 1 unit of work. If John can paint the room alone in 6 hours, his work rate per hour is 1/6.

Similarly, if John and Tom together can paint the room in 4 hours, their combined work rate per hour is 1/4. Let x be Tom's work rate per hour.

Then, we can set up the following equation:1/6 + x = 1/4

To solve for x, we can simplify the equation as follows:

Multiplying both sides by 12 (the LCM of 6 and 4) yields:2 + 12x = 3Solving for x gives:12x = 1x = 1/12Therefore, Tom's work rate per hour is 1/12, which means he can paint the room alone in 12 hours.

Summary:Tom can paint the room alone in 12 hours

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Answer: The volume of the cylinder is 125, 600 cm^3

Step-by-step explanation:

Volume = 3.14 x Radius^2 x Height

Volume = 3.14 x 20^2 x 100

Volume = 3.14 x 400 x 100

Volume = 125,600 cm^3

Shapes that are identical to each other are considered congruent. There are no differences in the matching sides or angles.

What is a congruent shape?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them.

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

Here is the format you requested:

△ABC = △DEC due to AAS

Angle A = Angle D Given

Angle B = Angle E Alternate Interior

Angle C1 = Angle C2 Vertically Opposite

AB = DE Congruent Sides

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Answer:

18 people

Step-by-step explanation:

to find 90% of 20, multiply 90x20 and then divide by 100.

90x20/100=18

Daniela can expect 18 people to attend her party.

A percentage is a number or ratio that represents a fraction of 100.

Given Daniela can expects 90% of the people she invites will attend.

so 90% of the 20 is 18.

Therefore, Daniela can expect 18 people to attend her party.

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Answer:

$43.30

Step-by-step explanation:

What we know,

3 hamburgers = $12.99

Coleman wants to know how much would he have to pay for 10 hamburgers,

In order to find out how much 10 hamburgers cost, you need to find out how much 1 hamburger costs,

To find how much 1 hamburger costs divide 12.99 by 3,

12.99/3

= 4.33

Now we know that 1 hamburger cost $4.33,

Now time to find out how much 10 hamburgers cost,

Multiply 4.33 by 10,

4.33 × 10

= 43.30

Therefore it cost $43.30 for 10 hamburgers.

Answer:

Step-by-step explanation:

Yes

the answer is 32.........

Answer:

EQUATION: X - 12 = 7X. SOLUTION: X = - 2.

Step-by-step explanation:

First, we do not know the number. When the number is unknown, it is a variable. I chose the variable, "X."

12 less than signals that we subtract 12. So that would be X - 12.

A product of 7 AND that number means we multiply 7 by X. That can be notated as 7X.

12 less than X is EQUAL to the product of 7 and X. So X - 12 = 7X.

To find the solution, we want to know the value of X. Move X to one side of the equation.

X - 12 = 7X

-X           -X

_________

-12     =   6X

Divide both sides by 6 to get X by itself.

X = - 2.

3) The extra number of feet of coiled tubing Tom needs to run into the well is: 5445 ft

4) The total length of coiled tubing Brendan ran in the wellbore is: 994 ft

5) The distance that the coiled tubing has reached after the first four hours is:  a depth of 16,776 feet in the well.

3) Initial amount of coiled tubing he had after 81 minutes = 9,153 feet

Amount of tubing after another 10 minutes = 10,283 feet

The total tubing required = 15,728 feet.

The extra number of feet of coiled tubing Tom needs to run into the well is: Needed tubing length - Current tubing length

15,728 feet - 10,283 feet = 5,445 feet

4) Speed at which Brendan is running coiled tubing = 99.4 feet per minute.

Coiled tubing inside the wellbore after 8 minutes is: 795.2 feet

Coiled tubing inside the wellbore after 2 more minutes is: 198.8 feet

The total length of coiled tubing Brendan ran in the wellbore is:

Total length = Initial length + Additional length

Total length =  795.2 feet + 198.8 feet

Total Length = 994 feet

5) Rate at which coiled tubing is being run into a 22,000-foot wellbore = 69.9 feet per minute. After the first four hours, we need to determine how deep the coiled tubing has reached.

A time of 4 hours is same as 240 minutes

Thus, the distance covered in the first four hours is:

Distance = Rate * Time

Distance = 69.9 feet/minute * 240 minutes

Distance = 16,776 feet

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The  probability that the sample mean would differ from the true mean by greater than 158 dollars if a sample of 226 persons is randomly selected is 0.99

mean per capita income is 19,695 dollars per annum , μ = 19695

a variance of 802,816, σ² = 802816

Standard deviation σ = √802816= 896

Sample size = 226

To find the probability that the sample mean would differ from the true mean by greater than 158 dollars i.e. less than 19537 dollars and more than 19853 dollars.

The formula for z-score :-

\(z = \frac{x - mean}{\frac{\alpha }{\sqrt{n} } } \\\)

For x = 19537 dollars

\(z = \frac{19537 - 19695}{\frac{\ 896 }{\sqrt{226} } } \\\)

z = -2.65

For x = 19853 dollars

\(z = \frac{19853 - 19695}{\frac{\ 896 }{\sqrt{226} } } \\\)

z = 2.65

The P-value=

P(z < -2.65) + P(z > 2.65 = 2P(z > 2.65) = 2x. 0.495975

= 0.99

Therefore, the  probability that the sample mean would differ from the true mean by greater than 158 dollars if a sample of 226 persons is randomly selected is 0.99

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The  frequency table formed using tally marks can be analyzed by using the numbers indicated by the tally  marks as follows;

The true statements are as follows;

Tally marks makes use of vertical lines to represent data, in which the fifth count is represented by a diagonal line across four vertical lines;

The data in the table are as follows

The number of students that prefer red = 5 + 1 = 6

The number of students that prefer yellow = 2

The number of students that prefer Blue = 5

The number of students that prefer purple = 3

The number of students that prefer Green = 6

Therefore;

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Let A = playing football, B = playing basketball,  P(A) = 32%,  P(A ∩ B) = 18% .

We are supposed to calculate the probability of playing basketball given the student plays football that is P(B|A).The probability of playing both football and basketball can be given as, P(A ∩ B) = P(B|A) * P(A).

Now, substituting the values given in the problem, we get, 18% = P(B|A) * 32%Thus, P(B|A) = 18%/32% = 9/16 = 0.5625 = 56%.Therefore, the required probability is 56% (option a).

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Answer:

Step-by-step explanation:

Let's divide by 2's.

Since 11 is a prime number, we cannot simplify it anymore. Hence, 11 x 2 x 2 is the product of prime factors.

\(BrainiacUser1357\)

Answer:

A^2+B^2= C^2 or A+B=C

Step-by-step explanation:

Hope this helps

To find the indefinite integral of \(\( \int\left[\cos x-\csc ^{2} x\right] d x \)\), we can integrate each term separately.

Let's start with the first term:

\(\[ \int \cos x \, dx \]\)

The integral of cosine is sine, so we have:

\(\[ \int \cos x \, dx = \sin x + C \]\)

Now let's move on to the second term:

\(\[ \int \csc^2 x \, dx \]\)

We can rewrite \(\(\csc^2 x\) as \(\frac{1}{\sin^2 x}\)\). To integrate this term, we can use a substitution.

\(Let \( u = \sin x \), then \( du = \cos x \, dx \).\)

Rearranging, we have \(\( dx = \frac{du}{\cos x} \).\)

Substituting into the integral:

\(\[ \int \csc^2 x \, dx = \int \frac{1}{\sin^2 x} \, dx = \int \frac{1}{u^2} \, \frac{du}{\cos x} = \int \frac{1}{u^2} \, \sec x \, du \]\)

Using the trigonometric identity \(\(\sec x = \frac{1}{\cos x}\), we have:\[ \int \frac{1}{u^2} \, \sec x \, du = \int \frac{1}{u^2} \, \frac{1}{\cos x} \, du = \int \frac{1}{u^2 \cos x} \, du \]\)

Now we can integrate this term:

\(\[ \int \frac{1}{u^2 \cos x} \, du = \int u^{-2} \sec x \, du = \int \cos^{-1} x \, du \]\)

The integral of \(\( u^{-2} \) is \( -u^{-1} \)\), so we have:

\(\[ \int \cos^{-1} x \, du = -u^{-1} + C \]\)

Substituting back \(\( u = \sin x \):\)

\(\[ \int \cos^{-1} x \, du = -(\sin^{-1} x)^{-1} + C \]\)

Now we can combine the two integrals:

\(\[ \int\left[\cos x-\csc ^{2} x\right] d x = \sin x - (\sin^{-1} x)^{-1} + C \]\)

Therefore, the indefinite integral of \(\( \int\left[\cos x-\csc ^{2} x\right] d x \)\)  is \(\( \sin x - (\sin^{-1} x)^{-1} + C \), where \( C \)\) is the constant of integration.

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The hοrizοntal distance frοm yοu tο the οbject is apprοximately 2.33 feet.

The angle οf depressiοn is the angle between a hοrizοntal line frοm the οbserver and the line οf sight tο an οbject that is belοw the hοrizοntal line.

Let's call the hοrizοntal distance frοm yοu tο the οbject "d" (in feet).

Where A is yοur pοsitiοn abοve the water, B is the pοsitiοn οf the οbject οn the bοttοm οf the pοοl, h is the depth οf the pοοl (which is 5 feet), θ is the angle οf depressiοn (which is 65 degrees), and d is the hοrizοntal distance we want tο find.

We can use trigοnοmetry tο find the value οf "d". In particular, we can use the tangent functiοn:

tan(θ) = οppοsite / adjacent

In this case, the οppοsite side is the depth οf the pοοl, which is 5 feet, and the adjacent side is the hοrizοntal distance we want tο find, which is "d". Sο we can write:

tan(65 degrees) = 5 / d

Tο sοlve fοr "d", we can rearrange the equatiοn as fοllοws:

d x tan(65 degrees) = 5

d = 5 / tan(65 degrees)

Using a calculatοr, we can evaluate the tangent οf 65 degrees:

tan(65 degrees) = 2.1445

Sο we have:

d = 5 / 2.1445

d ≈ 2.33

Therefοre, the hοrizοntal distance frοm yοu tο the οbject is apprοximately 2.33 feet.

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It all depends on how you want your hamburger. If you're serving it as a main dish, 300 hamburger patties (each around 4 ounces) should be plenty to feed 300 people. If you utilize hamburger meat as a topping or filler in a meal, you'll need a different amount.

Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on. The four basic arithmetic operations are addition, subtraction, multiplication, and division. Arithmetic mean is a number calculated by dividing the sum of a set's elements by the number of values in the set.

Here,

It all depends on how you want to eat the hamburger. If you're serving it as a main course, 300 hamburger patties, each weighing around 4 ounces, should plenty to satisfy 300 people. It will need a different quantity of hamburger meat if you use it as a topping or filler in a dish.

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Complete question:

How much hamburger will it take to make 300 three oz patties with a 20% shrinkage?

Solution:

Question 1.

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Question 15.

There are 25 students in the class and 3 students are undecided about the type of party they want.

We know that 20% (percent)of the students want an ice cream party. Let's call the total number of students in the class "x." Then we can set up an equation:

0.2x = 5

Solving for x, we get:

x = 5 / 0.2

x = 25

So there are 25 students in the class. We also know that 5 want an ice cream party, 7 want a movie party, and 10 want a costume party. That adds up to 22 students. So the rest of the students must be undecided:

25 - 22 = 3

Therefore, 3 students are undecided about the type of party they want.

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Complete Question

Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class, 5 want an ice cream party, 7 want a movie party, 10 want a costume party, and the rest are undecided. If 20%, percent want an ice cream party, how many students are in the class?

The distance from Allen's house as a fraction is 18/25.

A decimal is used to denote integers and non-integers.  The integers are separated from the non-integers by a point known as the decimal point. An example of a decimal is 0.71.  

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 1/2.

In order to change a decimal to a fraction, divide the value of the fraction by the value of the digit in the decimal.

Division is the process that is used to calculate the quotient of a number. Division is the process of grouping a number into equal parts using another number.

72 / 100

Divide both the numerator and denominator by 4

18 / 25

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When the diameter is 9 cm, the rate at which the diameter decreases is  -0.071 cm/min.

The surface area of a sphere is given by the formula:

A = 4πr²,

where

r is the radius of the sphere.

Since the diameter is twice the radius, we have:

D = 2r,

where D is the diameter.

We can differentiate both sides of the equation with respect to time (t) to get the rate of change of the diameter:

dD/dt = 2(dr/dt)

Now, we are given that the surface area decreases at a rate of 4 cm^2/min, which means dA/dt = -4 cm²/min.

We need to find the rate at which the diameter decreases, so we need to solve for dr/dt.

First, express the surface area in terms of the diameter:

A = 4πr²

A = 4π(D/2)²

A = πD²

Now, differentiate both sides of the equation with respect to time:

dA/dt = d(πD²)/dt

-4 = 2πD(dD/dt)

Substituting the given value for dA/dt and the value for D when the diameter is 9 cm:

-4 = 2π(9)(dD/dt)

Now solve for dD/dt:

dD/dt = -4 / (2π(9))

dD/dt = -2 / (9π)

To find the numerical value, substitute π with its approximation, 3.14159:

dD/dt = -2 / (9 * 3.14159)

dD/dt = -0.071 cm/min

Therefore, when the diameter is 9 cm, the rate at which the diameter decreases is approximately -0.071 cm/min.

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The estimation of the equation 1/6 + 5/6  is 1 (option C).

For rounding a fraction to the nearest whole number, use the "rounding half up" rule if necessary.

To estimate the solution for the equation 1/6 + 5/6, we can round each fraction to the nearest whole number.

The fraction 1/6 is closer to 0 than it is to 1, so we will round it to 0.

The fraction 5/6 is closer to 1 than it is to 0, so we will round it to 1.

Now we can estimate the solution for the equation as follows:

0 + 1 = 1

Therefore, the estimated solution for the equation 1/6 + 5/6 is 1.

The correct answer is C. 1.

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To estimate variable consideration, businesses can use alternative approaches such as the expected value method, the most likely amount method, the portfolio method, and the residual approach.

Variable consideration is an estimation of the amount a company expects to receive from a customer for its products or services, which may vary due to factors such as discounts, rebates, refunds, or incentives. The expected value method is used when there are multiple possible outcomes, and each outcome has a probability assigned to it. The most likely amount method is used when there are only two possible outcomes, and the outcome that is most likely to occur is estimated.

The portfolio method is used when there are multiple contracts with similar characteristics, and the revenue is estimated based on the expected outcome of the portfolio. The residual approach is used when the company cannot estimate the variable consideration reliably, and the remaining amount is recognized as revenue after all other variables have been estimated.

Therefore, businesses have various alternative approaches to estimate variable consideration, depending on the circumstances and available information.

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Answer:

.36

Step-by-step explanation:

Answer:

-3/8

Step-by-step explanation:

8y = 4 - 3x

~Divide 8 to everything

y = 1/2 - 3/8x

~Reorder

y = -3/8x + 1/2

In slope intercept form [ y = mx + b ] m resembles the slope so -3/8 is the slope.

Best of Luck!

For the time-invariant system x′=Ax for which ∅(t)=\(e^{At}\) where ∅(t)=∅(−t) (option d).

For a time-invariant system x' = Ax, the matrix exponential ∅(t) = \(e^{At}\) satisfies the property ∅(t) = ∅(-t), which means that the matrix exponential evaluated at positive time is equal to the matrix exponential evaluated at negative time.

This property arises from the fact that the matrix exponential represents the time evolution of the system, and since the system is time-invariant, the evolution is symmetric with respect to positive and negative time.

Therefore, the correct statement is ∅(t) = ∅(-t).

The complete question is:

For the time-invariant system x′=Ax for which ∅(t)=\(e^{At}\) where:

a) ∅(−t)=[∅(t)]⁻¹

b) −∅(t)=[∅(−t)]⁻¹

c) ∅(t)=[∅(t)]⁻¹

d) ∅(t)=∅(−t)

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