8/3 = 3 (c + 5/3) how to solve step by step

Step-by-step explanation:

As I do not have the work shown to calculate the number of ways to choose the passengers, I cannot identify the specific error made. However, I can provide some insight on how to approach this type of problem correctly.

When choosing 2 people from a group of 10, we can use combinations, which are denoted as "n choose k" and represented by the formula:

n choose k = n! / (k! * (n-k)!)

where n is the total number of items in the group and k is the number of items to be chosen.

In this case, we want to choose one passenger for first class and one passenger for coach. Therefore, we can separate the group of 10 into two subgroups: one subgroup with 1 person (for first class) and another subgroup with 9 people (for coach).

Using combinations, we can calculate the number of ways to choose 1 person from the subgroup of 1 and 1 person from the subgroup of 9:

(1 choose 1) * (9 choose 1) = 1 * 9 = 9

Therefore, there are 9 ways to choose the passengers to fill the seats.

The simplified form of the given fraction \(\frac{4^{11} }{4^{-8} }\) is given by 4¹⁹.

As given in the question,

Given fraction :\(\frac{4^{11} }{4^{-8} }\)

Simplify the given fraction using the formula of exponents

\(\frac{x^{a} }{x^{b} } =x^{a-b}\)

The simplified form of the given fraction is given by :

\(\frac{4^{11} }{4^{-8} }\)

Substitute the value in the formula of exponent we get:

Here the value of x= 4 ,value of a=11 and value of b= -8

=(4¹¹ ⁻ ⁽⁻⁸⁾)

=(4¹¹ ⁺ ⁸)

=4¹⁹

Therefore, the simplified form of the given fraction \(\frac{4^{11} }{4^{-8} }\) is given by 4¹⁹.

The complete question is:

Simplify the given fraction in simplified form: \(\frac{4^{11} }{4^{-8} }\).

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Answer:

a. 64

b. 24

c. 16

d. 6/16

e. 1/8

Explanation:

a. How many different codones are there?

Answer: there are 64 different codons

b. How many different codons are there in which all three bases are different?

Answer:there are 24 different codons in which all three bases are different

c. The base A and G are called purines, while C and T are called pyrimidines. How many different codons are there in which first base is purines and second base is pyrimidines

Answer: there are 16 different codons where the which first base is purines and second base is pyrimidines

d. What is the probability that all three bases are different?

Answer: probability of all three bases being different is

Number of codons with three different bases / total number of codons

= 24/64 = 6/16

e. What is the probability that first base is purines and second and third base is pyrimidines?

Answer: prob is number of codons with first base being purine and second and third base being pyrimidines / total number of codons

= 8/64 = 1/8

Answer:

18

Step-by-step explanation:

18

Hence, the cost for each couples ticket is $8 and each individual ticket is $4.

Let the cost of a couples ticket be x, and the cost of an individual ticket be y.

Therefore, 5 couples tickets and 2 individual tickets sold on the first day can be represented as 5x + 2y, and we know that the total amount made on the first day is $48.

Hence,

      5x + 2y = 48 -----------(1)

Similarly, the sales on the second day can be represented as 3x + 2y, and we know that the total amount made on the second day is $32.

Hence,

        3x + 2y = 32 ------------- (2)

Solving (1) and (2), we get:

       5x + 2y = 48

Multiply (2) by 5 on both sides, we get:

    15x + 10y = 160

     3x + 2y = 32

Subtract (2) from (1), we get:

     2x = 16

Therefore,

    x = $8 (the cost of a couples ticket)

Substituting this value in equation (1), we get:

    5($8) + 2y = 48

or  40 + 2y = 48

Therefore,

2y = 8,

and

y = $4 (the cost of an individual ticket)

Hence, the cost for each couples ticket is $8 and each individual ticket is $4.

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Answer:

\(\pmb{12 }\)

Step-by-step explanation:

12 is the coefficient of the third term in the expression shown

Answer:

360

Step-by-step explanation:

8% of 4500 is 360

Given the selling prices for homes in a certain community are approximately normally distributed

Mean = μ = $321,000

Standard deviation = σ = $38,000

For the following cases, we will find the z-score as follows:

And we will use the following chart:

Estimate the percentage of homes in this community with selling prices:

A) between $245,000 and $397,000

So, the z-score for the given prices will be:

So, the percentage when -2 < z < 2 will be as shown from the chart = 95%

B) above $435,000

The area under the curve = 100%

So, the percentage when z > 3 will be = 0.5%

C) below $283,000

so, the percentage when z < -1 will be = 50 - 34 = 16%

D) between $283,000 and $435,000

We will find the percentage in case if: -1 < z < 3

So, the percentage will be = 34 + 34 + 13.5 + 2 = 83.5%

Answer: the first term in the sequence is 9.

Step-by-step explanation:

Let the primary term be x.

At that point the moment term is 2x + 4.

And the third term is 2(2x + 4) + 4 = 4x + 12.

Since the third term is given as 48, we will set up an condition and unravel for x:

4x + 12 = 48

4x = 36

x = 9

Answer:

B. >

Step-by-step explanation:

Yes, you got it correct! Anything with a "-" is always less than a "+". Look at it this way:

I have 11 dollars (+11) and you owe me one dollar (-1). Now which is better?

Hope this helps

~R3VO

Laplace transforms of given functions are given below:

a)  f(t) = cosh ωtLaplace Transform of f(t) is L[f(t)] = 1 / (s - ω) + 1 / (s + ω)

Explanation:  Using the definition of Laplace transform, we have L[f(t)] = ∫[0,∞] e^(-st) cosh ωt dt =  1/2 ∫[0,∞] e^(-st) (e^(ωt) + e^(-ωt)) dt

Taking Laplace Transform L[f(t)] = 1/2 ∫[0,∞] e^(-st) e^(ωt) dt + 1/2 ∫[0,∞] e^(-st) e^(-ωt) dt

Now we can see that both integrals are of the same form as shown below,

∫[0,∞] e^(-(s-ω)t) dt = 1 / (s - ω)∫[0,∞] e^(-(s+ω)t) dt = 1 / (s + ω)

Therefore, we have L[f(t)] = 1 / (s - ω) + 1 / (s + ω)

b) f(t) = 2 sin3t + cos3t Laplace Transform of f(t) is L[f(t)] = (2s) / (s² + 9) + (s) / (s² + 9)

Explanation: Using the definition of Laplace transform, we have L[f(t)] = ∫[0,∞] e^(-st) (2 sin3t + cos3t) dt

Taking Laplace Transform L[f(t)] = 2∫[0,∞] e^(-st) sin3t dt + ∫[0,∞] e^(-st) cos3t dt

Using Laplace Transform of sin3t and cos3t, we get L[f(t)] = 2(3 / (s² + 9)) + (s / (s² + 9))

Therefore, L[f(t)] = (2s) / (s² + 9) + (s) / (s² + 9)

c) f(t) = (t² – 3)² Laplace Transform of f(t) is L[f(t)] = (s⁶ - 6s⁴ + 9s²) / s⁹

Explanation: Using the definition of Laplace transform, we have L[f(t)] = ∫[0,∞] e^(-st) (t² – 3)² dt

Taking Laplace Transform L[f(t)] = ∫[0,∞] e^(-st) (t⁴ - 6t² + 9) dt

Using Laplace Transform of t⁴, t² and 1, we get L[f(t)] = (4! / s⁵) - (6! / s⁷) + (9 / s³)

Therefore, L[f(t)] = (s⁶ - 6s⁴ + 9s²) / s⁹

d)  2e³ᵗ (4sin3t - 5cos3t) Laplace Transform of f(t) is L[f(t)] = 2(5s - 12) / ((s - 3)² + 9)

Explanation: Using the definition of Laplace transform, we have L[f(t)] = ∫[0,∞] e^(-st) 2e³ᵗ (4sin3t - 5cos3t) dt Taking Laplace Transform L[f(t)] = 2∫[0,∞] e^(-(s-3)t) (4sin3t - 5cos3t) dt Using Laplace Transform of sin3t and cos3t, we get L[f(t)] = 2(4(3) / ((s-3)² + 9) - 5((s-3) / ((s-3)² + 9)))

Therefore, L[f(t)] = 2(5s - 12) / ((s - 3)² + 9)

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Answer:

-6

Step-by-step explanation:

Answer:600

Step-by-step explanation:

300,000/ 500 =600

Answer:

18.64 ft/s

Step-by-step explanation:

Use the formula for speed, speed = distance/time or s = d/t

Here, Distance = 63,360 Feet and Time = 3400 Seconds

Therefore, using the formula with these specifications we get speed = 63360/3400 = 18.64 ft/s

Nina Travels at 18.64 ft/s

-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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Answer:

Slope m = 1/6

General Formulas and Concepts:

Pre-Algebra

Algebra I

Standard Form: Ax + By = C

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

x - 6y = -12

Step 2: Rearrange

Find slope-intercept form.

Step 3: Break Function

Identify Parts.

Slope m = 1/6

y-intercept b = 2

Answer:

D\

;,lm,ml;m'l

The diagram attached below shows that ΔABC and ΔADC share a common side AC, AB ≅ AD, and BC ≅ DC.

Both triangles have three pairs of congruent sides and can be proven to be congruent by the SSS Congruence Theorem (Option D is correct).

The SSS Congruence Theorem states that if two triangles have three pairs of congruent sides, both triangles are congruent.

The image attached below shows ΔABC and ΔADC that share a common side AC.

It also shows AB ≅ AD and BC ≅ DC.

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The given exponential function satisfies the property of increasing by a factor of 3 between any two points separated by x2−x1=1.

An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive constant and x is any real number. The base a is typically a number greater than 1, and the function grows or decays rapidly depending on whether a is greater than or less than 1.

Exponential functions are commonly used to model processes that exhibit exponential growth or decay, such as population growth, radioactive decay, and compound interest. They also arise in various areas of mathematics and science, including calculus, probability theory, and physics.

We are given the exponential function \(y=3^x.\)

Let x1 be any value of x, then the corresponding y-value is \(y1=3^{(x_1)\)

Let x2=x1+1 be the next value of x, then the corresponding y-value is \(y2=3^x2=3^(x1+1)=3*3^x1.\)

So, we can see that y2 is 3 times y1, which means the y-values increase by a factor of 3 between any two points separated by x2−x1=1.

Therefore, the given exponential function satisfies the property of increasing by a factor of 3 between any two points separated by x2−x1=1.

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Answer:

\(\frac{4}{5}\)

Step-by-step explanation:

\(\frac{-\frac{5}{9}}{-\frac{25}{36}}=\\\\-\frac{5}{9}*(-\frac{36}{25})=\\\\\frac{4}{5}\)

Answer:

471.24 yd²

Step-by-step explanation:

The formula for the surface area of the cylinder

= 2πr(r + h)

Height = 10 yd

Radius = 5 yd

Surface area =

2 × π × 5(5 + 10)

= 471.24 yd²

The surface area of the cylinder = 471.24 yd²

Answer:

answer is yes,yes, no

Step-by-step explanation:

The area of the rectangular carpet is equivalent to 397.7 ft².

        Area = Length x Breadth

        [A] = [L] x [B]

Given is that the length of the carpet is 24.25 feet and the width is 16.4 feet.

The area of the rectangle is equivalent to -

A = L x B

A = 24.25 x 16.4

A = 397.7 ft²

Therefore, the area of the rectangular carpet is equivalent to 397.7 ft².

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Answer:

7y=7-5x

Divide through by 7

y= (7-5x)÷7

y = 1 - 5x/7

25% is the larger circle area is gray.

Area of a Circle: The area of a circle is pi times the radius squared.

To calculate the area of the circle we have the formula:

A = π r²-----(1)

where

A=area

r=radius.

First, we have to analyze the given data, the large circle center o passes through d, so

Gray circle area=π*(radius)^2----(2)

The radius of the smaller circle = OD/2 substitute in (2)

Gray circle area=π*(OD/2)^2

Gray circle area=π*OD^2/4

Larger circle area=π*(radius)2    

radius of the larger circle = OD

larger circle area=π*OD^2  

To know the percentage of a large circle we have a small formula:

gray circle area/large circle area--------(3)

=π*OD^2/4/π*OD^2  

=π*OD^2/4*1/π*OD^2=1/4

=25/100

=25%

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The quotient of 6/8 divided by 1/4 is 3.

It should be noted that the information is to find the quotient of 6/8 divided by 1/4.

This will be:

= 6/8 ÷ 1/4

= 6/8 × 4/1

= 3

Therefore, the quotient is 3.

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You are a district sales manager at the sales target for your team 135,000 per month. Your team's annual sales target is $1,620,000.

To calculate the annual sales target for your team, you need to multiply the monthly target by 12 (the number of months in a year):

Annual sales target = Monthly sales target x 12

Given that the monthly sales target for your team is $135,000, the annual sales target would be:

Annual sales target = $135,000 x 12

= $1,620,000

A Sales Manager is a professional responsible for managing a team of sales representatives within a specific geographic area or district. The role typically involves setting and achieving sales targets, developing and implementing sales strategies, and managing relationships with key customers.

Sales Managers are responsible for recruiting, training, and supervising sales staff, as well as monitoring their performance and providing coaching and guidance as needed. They also work closely with other departments within the organization, such as marketing and finance, to ensure that sales goals are aligned with overall business objectives. They must possess strong leadership and communication skills, as well as a deep understanding of their company's products or services and the competitive landscape in which they operate.

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Complete Question:-

You are a district sales manager at the sales target for your team 135,000 per month ? What is your annual sales?

Answer:

Step-by-step explanation: