plz help 35 pointsss im desperateee

Plz Help 35 Pointsss Im Desperateee

Answers

Answer 1

Answer:

Yes. Proportion works out. Ratio equals 1:48

Step-by-step explanation:

Yes. Proportion works out


Related Questions

A water tank has 200 gallons but is leaking 2.5 gallons per hour.in how many hours will there be zero gallons left

Answers

80 hours because 200÷2.5 is 80

Ericka observed the total variation in the water level over 6.2 years to be −13.64 mm. She compared this to the average annual trend, which shows the water level rising 1.8 mm/year. Remember, she used 6.2 years as her time period. What is the difference between how much average water levels rose and how much the water level fell in the part of the river she observed?

__________millimeters

Answers

Answer:

In the area that she observed, the water level fell 13.64mm over 6.4 years, for an average annual rate of change of: -13.64 ÷ 6.2 = -2.2 mm/ year.

work out the differences in minutes between 2 hours 25 minutes and 1 1/2 hours

Answers

Half of an hour is 30 minutes
Therefore 1 1/2 hours is 1 hour 30 minutes
2 25 - 1 30 = 95 minutes
an hour has 60 minutes. So 60x2+25 is 145. 145-90=55 minutes.

Help me on this please

Help me on this please

Answers

Answer:

1,620π in³

Step-by-step explanation:

The volume of a cylinder can be found with the following formula;

V = πr²h

    [] Basically, the area of the circle-shape times the height.

We can plug-in our values, plug-in x, and then solve for V.

V = πr²h

V = π(4x - 6)²(11x + 12)

V = π(4(3) - 6)²(11(3) + 12)

V = π(12 - 6)²(33 + 12)

V = π(12 - 6)²(33 + 12)

V = π(6)²(45)

V ≈ 5089.38 in³

Since it is asking for in terms of pi, the answer will be 1,620π in³

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

Fill in the blanks.The domain of f is the _____of f −1, and the _____ of f −1 is the range of f.

Answers

The domain of f is the range of f −1, and the domain of f −1 is the range of f.

The domain of a function f is the set of all possible input values for which the function is defined and produces a unique output. The inverse function of f, denoted by f^(-1), is a function that reverses the input and output of f. That is, if f(x) = y, then f^(-1)(y) = x.

The domain of f^(-1) is the range of f because the output values of f become the input values of f^(-1), and the input values of f become the output values of f^(-1). Therefore, the range of f becomes the set of possible input values for f^(-1), which is the domain of f^(-1). Similarly, the range of f^(-1) is the domain of f because the output values of f^(-1) become the input values of f, and the input values of f^(-1) become the output values of f.

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Which of the following is not a differential equation?
I'm having trouble because they all have derivatives?
A) d^2y/dt^2= t^2+(y/4)
B) 4 +y= 2x+dx/dy
C) t^2= s+(ds/dt)^2
D) (x-x^3)dx= 4-y^2
E) y'=0

Answers

Among the given options, y′ = 0 is not a differential equation.

Definition of Differential Equation

A differential equation is defined as a mathematical equation that relates a function to its derivatives or differentials. In other words, a differential equation involves derivatives and differentials of a function.

Differential equations have various applications in several scientific fields. These include mathematics, physics, engineering, biology, economics, and more.

What is y′ = 0?

The derivative of a function with respect to the variable x is given by y′.

The derivative of a function that is constant will always be zero (0). Hence, the differential equation y′ = 0 means that the derivative of the function y with respect to the variable x is zero, which implies that the function is a constant that does not depend on x.

Therefore, y′ = 0 is not a differential equation. It is a first-order ordinary differential equation with constant coefficients.

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Final answer:

The equation 4 + y = 2x + dx/dy (option B) is not a differential equation. It does not follow the general format of differential equations, where a derivative or derivatives are equated to a function.

Explanation:

A differential equation is an equation that relates a function with its derivatives. In the options given in the question, we are asked to identify which are not differential equations.

The equation 4 + y = 2x + dx/dy (option B) is not a differential equation. In general, a differential equation should have the derivative or derivatives as part of the equation. However, in the case of option B, the derivative dx/dy is not being equated to a function of x and y, rather it is part of the algebraic equation. Hence B is not a differential equation in the traditional sense.

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a postal worker counts the number of complaint letters received by the united states postal service in a given day. identify the type of data collected.

Answers

When a postal worker counts the number of complaint letters received by the united states postal service in a given day, the type of data collected is quantitative.

How to explain the data

Quantitative data is data that can be measured and expressed in numbers. In this case, the number of complaint letters received by the United States Postal Service in a given day can be measured and expressed as a number.

Qualitative data, on the other hand, is data that cannot be measured or expressed in numbers. For example, the contents of the complaint letters would be qualitative data.

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What is the solution to the system of equations

What is the solution to the system of equations

Answers

Step-by-step explanation:

\(5x + 3y = 13 \\ 7x + 8y = - 16 \\ 5x = 13 - 3y \\ x = \frac{13 - 3y}{5} \\ 7( \frac{13 - 3y}{5} ) + 8y = - 16 \\ 18.2 - 4.2y + 8y = - 16 \\ 3.8y = - 34.2 \\ y = - 9 \\\)

\( x = \frac{13 - 3( - 9)}{5} = \frac{13 + 27}{5} = \frac{40}{5} = 8 \\ x = 8 \\ y = - 9\)

why do we divide our data into training and test sets? what is the point of a test set, and why do we only want to use the test set once?

Answers

We divide our data into training and test sets to evaluate the performance of a machine learning model. The training set is used to train the model, while the test set is used to evaluate its performance.

The point of a test set is to estimate how well the model will perform on new, unseen data. This is important because the ultimate goal of a machine learning model is to generalize well to new data, not just to fit the training data well. If a model performs well on the test set, it is likely to perform well on new data.

We only want to use the test set once because if we use it multiple times, we may inadvertently overfit the model to the test set. That is, we may make changes to the model based on the performance on the test set, which will lead to a model that performs well on the test set but poorly on new data. This defeats the purpose of having a test set in the first place. Therefore, we typically use the test set only once, at the end of the model development process, to evaluate the final model.

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the numbers of tomatoes growing on 7 different tomato plants are 2, 3, 3, 4, 7, 8, and 8. what is the range of this data set?

Answers

Answer:

range = 6

Step-by-step explanation:

the range is the difference between the maximum and minimum values in the data set.

maximum = 8 and minimum = 2 , then

range = 8 - 2 = 6

A line passes through (−1, 5) and (1, 3).

Which answer is the equation of the line? PLEASE HELP

Answers

The answer is y=1x+6

HELP WITH THIS OLEASE I WILL MAKE BRWINLIST

HELP WITH THIS OLEASE I WILL MAKE BRWINLIST

Answers

Answer:

y=6x-2

Step-by-step explanation:

I THINK I DID THIS LAST YEAR SO IM NOT COMPLETELY SURE HOPE THIS HELPS:)

Answer:

y=1.2x-2

Step-by-step explanation:

add 6x to both sides (5y = 6x-10)

divide both sides by 5 (y = 1.2x - 2)

one point you will find on (0,-2) and another point will be (5,4)

you need at least 2 points to graph the line

plz help me i don’t understand

plz help me i dont understand

Answers

Answer:

A it wold be pushing 40 newton to the left

B opposite

C subtract

D i don know that one

E unbalanced

Step-by-step explanation:

PLEASE HELP!! what is the equation of a line that is perpendicular to y = 2x + 4 and passes through the point (4, 6)?

PLEASE HELP!! what is the equation of a line that is perpendicular to y = 2x + 4 and passes through the

Answers

Answer:

The answer is B)

\(y = - \frac{1}{2}x + 8\)

PLEASE HELP!! what is the equation of a line that is perpendicular to y = 2x + 4 and passes through the

Answer:

B.  y = -\(\frac{1}{2}\)x + 8

Step-by-step explanation:

The line is perpendicular to line whose equation is:

y = 2x + 4 and;

passes through point (4,6) .

The product slopes of two perpendicular lines is -1.

The slope of the line whose equation is y = 2x + 4 is; 2

Let the slope of the perpendicular line (l2) be \(m_{l2}\)

\(m_{l2} * 2 = -1\)

\(m_{l2}\) = \(-\frac{1}{2}\)

Taking another point xy on line l2;

\(\frac{y - 6}{x - 4} = -\frac{1}{2}\)

Cross multiplying this gives;

y = -\(\frac{1}{2}\)x + 8 which is the equation of the perpendicular line!

Johnnie runs 4.5 km everyday to stay in shape. It takes him 30 minutes to run his route. What is his average speed per hour?

Answers

Answer:

6.6

Step-by-step explanation:

What two tens does 192 fall between?

Answers

The number 192 falls between the tens 190 and 200.

What is Number system?

A system for representing and expressing numbers is referred to as a number system. It is a system of guidelines, icons, and conventions for presenting and communicating numerical data. There are various number systems that differ according to the symbols used and the positional values given to each symbol.

The decimal system, usually referred to as the base-10 system, is the most widely used numbering scheme. Ten digits are used to express numbers in the decimal system: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Based on powers of 10, the position of each digit in a number affects that number's value. For instance, in the number 123, the digits 3 and 2 correspond to ones, tens, and hundreds, respectively.

Let us first contrast 192 with 190:

192 - 190 = 2

2 separates the numbers 192 and 190. We can infer that 192 is greater than the lower bound 190 because it is greater than 190.

Compare 192 to 200 next: 200 - 192 = 8

There are 8 decimal places between 200 and 192. We can infer that 192 is less than the upper bound of 200 because it is less than 200.

Combining the findings, we were able to demonstrate that 192 is higher than 190 and lower than 200. As a result, we can say that 192 is between tens 190 and 200.

Therefore the number 192 falls between the tens 190 and 200.

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While playing a board game, players start their turn by
rolling a six-sided die numbered 1 through 6 twice.
Part A
Find the probability of rolling two numbers that have a
sum of 7. Express your answer as a fraction in simplest
form.
10
Part B
If the players take 150 turns during the game, how
many times would you expect a sum of 7 to be rolled?

Answers

A. The probability of rolling two numbers with a sum of 7 is given as follows: p = 1/6.

B. The expected number of rolls with a sum of 7 is given as follows: 25 rolls.

How to calculate a probability?

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of outcomes when two dice are rolled is given as follows:

6² = 36.

There are six outcomes with a sum of 7, as follows:

(1,6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1).

Hence the probability is given as follows:

p = 6/36 = 1/6.

Hence, out of 150 rolls, the expected number of sums of seven is given as follows:

E(X) = 1/6 x 150

E(X) = 25 rolls.

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It is estimated that the world's population is growing at a rate of 1.14% per year. On January 1st 2014 the population was 7.23 billion. (a) Find the expected population on January 1st 2020. (b) Find the year when the population is expected to reach 10 billion.​

Answers

Answer:

\(f(t) = 7.23( {1.0114}^{t} )\)

t = 0 represents January 1, 2014

(a)

\(f(6) = 7.23( {1.0114}^{6} ) = 7.739\)

The population of the world is expected to be about 7.739 billion people on January 1, 2020.

(b)

\(7.23( {1.0114}^{t} ) = 10\)

\(t = about \: 28.61 \: years\)

The population of the world is expected to be 10 billion people in about 28.61 years after January 1, 2014 (sometime in August 2042).

related questions please help with 6 and 7​

related questions please help with 6 and 7

Answers

The perimeter of this rectangle with the given vertices is equal to 18 units.

The area of this rectangle with the given vertices is equal to 20 square units.

How to calculate the perimeter of a rectangle?

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W)

Where:

P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.

For the width, we would determine the distance between the vertices (-2, 2) and (3, 2)

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(3 - (-2))² + (2 - 2)²]

Distance = √[(5² + 0²]

Distance = √25

Distance = 5 units.

For the length, we have:

Length = 4 units.

Perimeter of this rectangle, P = 2(5 + 4)

Perimeter of this rectangle, P = 18 units.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

A = 4 × 5

A = 20 square units.

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ind the circulation of F = 3xi + 4zj + 2yk around the closed path consisting of the following three curves traversed in the direction of increasing t. (0, 1,3 Cy: ry(t) = (cos t)i + (sin t)j + tk, Ostsa/2 Cz: r2(t) = j+ (1/2)(1 – t)k, Osts1 Cz: 13(t)= ti + (1 – t)j, Osts 1 (1, 0, 0) (0, 1, 0) ca X

Answers

The circulation of the vector field F = 3xi + 4zj + 2yk around the closed path formed by three curves is equal to 10π.

To find the circulation of F around the closed path, we need to calculate the line integral of F along each curve and sum them up.

The first curve, C1, is given by ry(t) = cos(t)i + sin(t)j + tk, where t ranges from 0 to π/2. To calculate the line integral along C1, we substitute the parametric equations into the vector field F:

∫F · dr = ∫(3x, 4z, 2y) · (dx, dy, dz)

= ∫(3cos(t), 4t, 2sin(t)) · (-sin(t)dt, cos(t)dt, dt)

= ∫(-3cos(t)sin(t)dt + 4tdt + 2sin(t)dt)

= ∫(-3/2sin(2t)dt + 4tdt + 2sin(t)dt)

Evaluating this integral from t = 0 to π/2, we get the contribution from C1.

The second and third curves, C2 and C3, can be similarly evaluated using their respective parameterizations and integrating along the paths.

After calculating the line integrals along each curve, we sum them up to obtain the circulation of F around the closed path.

The final result is 10π, which represents the circulation of F around the given closed path.

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A train from Philadelphia to Boston left Philadelphia at 1 pm and arrived to Boston at 4 pm. What was its average speed if the distance it covered was 270 miles?

Answers

Answer:

90 miles per hour is the average speed.

Step-by-step explanation:

The formula for Average Speed can be given as follows:

\(\text{Average Speed}= \dfrac{\text{Total Distance Traveled}} {\text{Total Time Taken}}\)

Here time taken is from 1 PM to 4 PM i.e.

Total Time taken = (4-1) hours = 3 hours

Also, it is given that the Total distance covered = 270 miles

As per the formula above:

\(\text{Average Speed} = \dfrac{270}{3}\\\Rightarrow \text{Average Speed} = 90\ miles/hour\)

So, answer is: 270 miles/ hour is the average speed of the train from Philadelphia to Boston.

Sally is 54 years old and her mother is 80, how many years ago was Sally’s mother times her age?

Answers

 

41 years ago, when Sally was 13 and her mother was 39.

Step-by-step explanation: I've heard this question b4

This year, there are eight freshmen, ten sophomores, nine juniors, and eight seniors are eligible to be on a committee.
In how many ways can a dance committee of 8 students be chosen?
_____ways
In how many ways can a dance committee be chosen if it is to consist of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors.
_____ways
In how many ways can a dance committee be chosen if it is to consist of 4 juniors and 4 senions.
_____ways
Determine the probability of selecting a committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors. Write your answer in decimal form, rounded to the nearest thousandth.
Answer: _____
Determine the probability of selecting a committee consisting of 4 juniors and 4 senions. Write your answer in decimal form, rounded to the nearest thousandth.
Answer: _____

Answers

The number of ways to choose a dance committee of 8 students is 6,096,454 ways.

The number of ways to choose a dance committee with 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors is 1,134,000 ways.

The number of ways to choose a dance committee with 4 juniors and 4 seniors is 12,870 ways.

The probability of selecting a committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors is 0.186.

The probability of selecting a committee consisting of 4 juniors and 4 seniors is 0.002.

To solve these problems, we can use the concept of combinations. The number of ways to choose k items from a set of n items is given by the binomial coefficient, also known as "n choose k," denoted as C(n, k) or nCk.

In general, the formula for the binomial coefficient is:
C(n, k) = n! / (k! * (n - k)!)

Now, let's solve each problem:

In how many ways can a dance committee of 8 students be chosen?
We have a total of 35 eligible students (8 freshmen + 10 sophomores + 9 juniors + 8 seniors). To choose a committee of 8 students, we need to calculate C(35, 8):
C(35, 8) = 35! / (8! * (35 - 8)!)
= 35! / (8! * 27!)
Therefore, the number of ways to choose a dance committee of 8 students is:
35! / (8! * 27!) = 6,096,454 ways

In how many ways can a dance committee be chosen if it is to consist of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors?
We need to choose 2 students from each category. The number of ways can be calculated by multiplying the number of ways to choose 2 students from each category:
C(8, 2) * C(10, 2) * C(9, 2) * C(8, 2)
Therefore, the number of ways to choose a dance committee with 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors is:
C(8, 2) * C(10, 2) * C(9, 2) * C(8, 2) = 1,134,000 ways

In how many ways can a dance committee be chosen if it is to consist of 4 juniors and 4 seniors?
We need to choose 4 juniors from the 9 available and 4 seniors from the 8 available. The number of ways can be calculated as:
C(9, 4) * C(8, 4)
Therefore, the number of ways to choose a dance committee with 4 juniors and 4 seniors is:
C(9, 4) * C(8, 4) = 12,870 ways

Probability of selecting a committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors.
To find the probability, we need to divide the number of ways to choose the desired committee (as calculated in question 2) by the total number of ways to choose a committee of 8 students (as calculated in question 1):
Probability = (Number of ways to choose the desired committee) / (Total number of ways to choose a committee of 8 students)
Therefore, the probability of selecting a committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors is:
1,134,000 / 6,096,454 ≈ 0.186

Rounded to the nearest thousandth, the probability is approximately 0.186.

Probability of selecting a committee consisting of 4 juniors and 4 seniors.
Similarly, to find the probability, we divide the number of ways to choose the desired committee (as calculated in question 3) by the total number of ways to choose a committee of 8 students (as calculated in question 1):
Probability = (Number of ways to choose the desired committee) / (Total number of ways to choose a committee of 8 students)
Therefore, the probability of selecting a committee consisting of 4 juniors and 4 seniors is:
12,870 / 6,096,454 ≈ 0.002

Rounded to the nearest thousandth, the probability is approximately 0.002.

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The quality and credibility of the risk analysis requires a PM to define risk probability and _____, which can then be made into a Probability and (X) Matrix.

Answers

The quality and credibility of the risk analysis requires a PM to define risk probability and impact, which can then be made into a Probability and Impact Matrix.

The quality and credibility of risk analysis in project management require a comprehensive approach that includes defining risk probability and impact. The probability of a risk event is the likelihood of it occurring, and impact is the magnitude of its consequences on project objectives. Once these factors are defined, they can be used to create a Probability and Impact Matrix, also known as a Risk Matrix, which is a useful tool for assessing and prioritizing risks.

The Probability and Impact Matrix is a grid that lists the probability of an event occurring on one axis and the impact of that event on project objectives on the other axis. The intersection of these two factors represents the level of risk associated with that event. By assigning a probability and impact score to each risk, the PM can prioritize them and allocate resources to mitigate or manage them accordingly.

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During his shift, Damion filled 8 orders in 30 minutes. If he keeps up that rate, how many orders will he fill in 7 hours?

Answers

The answer is 28
30 minutes is half of an hour so you have to divide 7 by 2 which is 3.5 and then multiply 3.5 by 8 to get 28

4 thumb drives and 1 compact disk have a
total capacity of 18 gigabytes. 3 compact
disks and 4 thumb drives have a total
capacity of 22 gigabytes. Find the capacity
of 1 thumb drive (x) and the capacity of 1
compact disk (y).

Answers

The capacity of thumb drive disc is 4 gigabytes and the capacity of compact disc is 2 gigabytes.

How to calculate the equation?

Let thumb drive = (x)

Let the capacity of 1 compact disk = (y).

Therefore, the appropriate equation will be:

4x + y = 18

4x + 3y = 22

Subtract the equations

2y = 4

y = 4/2

y = 2

The capacity of compact disc is 2 gigabytes.

Since 4x + y = 18

4x + 2 = 18

4x = 18 - 2

4x = 16

x = 16/4

x = 4

The capacity of thumb drive disc is 4 gigabytes.

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a normal distribution has a mean of 50, and a standard deviation of 3. what is the probability of a score above 56?

Answers

The probability of a score above 56 is 0.025.

Define probability.

The probability of an event occurring is defined by probability. Probability is the unit of measurement for an event's likelihood. It is the proportion of successful outcomes to all possible outcomes. For instance: (1) Throwing a die and getting the numbers 3 and 5 (2) Throwing a die and getting both an even and an odd number

Given,

A normal distribution has a mean of 50, and a standard deviation of 3.

P( x > 56)

= P(X - mean/standard deviation > 56-50/3)

= P(Z > 6/3)

= P( Z > 2)

= 1 - P(Z<2)

= 1 - 0.9772

= 0.0228

0.025 (Approximately)

The probability of a score above 56 is 0.025.

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Select correct answer pls^^

Select correct answer pls^^

Answers

It takes 48 hours if 12 people built the same wall.

Please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Select correct answer pls^^

Answer:

3 x 12 x 129

Step-by-step explanation:

You can get your answer

Janet buys 4 bags of potatoes.

The first bag has 8 potatoes in it.
The second bag has 6 potatoes in it.
The third bag has 10 potatoes in it.
She has not yet counted the number of potatoes in the fourth bag.
To represent the total number of potatoes she has, Janet writes (8+6+10)
+x, where x is the number of potatoes in the fourth bag. Which expression
also represents the total number of potatoes Janet has?
2(4+3+5+x)
O 25+1+B)4x
O (8+6)(10+x)
O (8+6)+(10+x)

Answers

Answer:

(8+6)+(10+x)

Step-by-step explanation:

2(4+3+5+x)  Not valid since x represents the total number of potatoes in the fourth bag.  The expression expands to (8+6+10 + 2x), not just x.25+1+B)4x   Not valid as written, the expression has a new, undefined variable, B.  Plus the 25+1 are not related to the actual inforamation.  (8+6)(10+x)  Not valid since there is no logic in multiplying the two expressions.(8+6)+(10+x)  Valid:  The expression can also be writte as 8+6+10+x, which matches the potatoe count in the four bags.

Let f(x)=\sqrt(x) and g(x)=5\sqrt(x). Find (f-g)(x).

Answers

your messageConvert to number of atoms 294 grams AuTo convert 294 grams of Au to the number of atoms, we need to use the Avogadro's number, which is 6.022 x 10^23 atoms/mole. First, we need to find the number of moles of Au in 294 grams: 294 grams Au / 196.97 g/mole = 1.49 moles Au Next, we can calculate the number of atoms: 1.49 moles Au x 6.022 x 10^23 atoms/mole = 8.97 x 10^23 atoms Au Therefore, there are approximately 8.97 x 10^23 atoms of gold in 294 grams.PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!This figure is a rectangle with a semicircle on the shorter side.What is the perimeter of this figure?Use 3.14 for pi.A. 20.28 ftB. 30.28 ftC. 46.28 ftD. 74.24 ftTo find the perimeter of the figure, we need to add up the lengths of all the sides. Let's call the length of the rectangle "L" and the width "W". The rectangle has two sides of length L and two sides of length W, so the perimeter of the rectangle is: 2L + 2W The semicircle has a diameter equal to the width of the rectangle (W), so the circumference of the semicircle is: 1/2 (pi) W To get the total perimeter, we need to add the circumference of the semicircle to the perimeter of the rectangle. Since the semicircle only covers half of the width of the rectangle, we only need to add one width (W) to the perimeter of the rectangle. So the total perimeter is: 2L + 3W + 1/2 (pi) Wevaluate C(4,2)C(4,2) represents the number of ways to choose 2 items from a set of 4 distinct items. The formula for C(n,r) is n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen. Plugging in the values for C(4,2), we get: C(4,2) = 4! / (2! * (4-2)!) = 24 / (2 * 2) = 6 Therefore, there are 6 ways to choose 2 items from a set of 4 distinct items.Let f(x)=\sqrt(x) and g(x)=5\sqrt(x). Find (f-g)(x).(f-g)(x) represents the difference between f(x) and g(x). So we can write: (f-g)(x) = f(x) - g(x) Substituting the given expressions for f(x) and g(x), we get: (f-g)(x) = sqrt(x) - 5sqrt(x) To simplify this expression, we can factor out sqrt(x) as a common factor: (f-g)(x) = sqrt(x) * (1 - 5) Simplifying the expression in the parentheses, we get: (f-g)(x) = -4sqrt(x) Therefore, (f-g)(x) = -4sqrt(x)

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