Yall I need help asap pls

question 7

You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.

The company's first task is to cast the lead female roles of Fantine, adult Cosette, and Éponine, and the lead male roles of Jean Valjean, Inspector Javert, and Marius. You have received headshots and resumes from 28 women and 22 men who are interested in auditioning for these parts.



A: If no one has been cast yet, how many different ways are there to cast Jean Valjean from the 22 men?


B: If Jean Valjean has already been cast, how many different ways are there to cast Inspector Javert from the remaining men?


C: If Jean Valjean and Inspector Javert have already been cast, how many different ways are there to cast Marius from the remaining men?


Select one answer choice for part A, one answer choice for part B, and one answer choice for part C.


A: 22P3

A: 22!

B: 21!

C: 20P1

B: 21

B: 21P2

C: 20!

A: 22

C: 20



Question 2:


A: Which of the following expressions will calculate the number of ways the three lead male roles could be cast?


B: Evaluate the permutation from part A.


Select one answer choice for part A, and one answer choice for part B.


A: 22P19

B: ≈1.12×1021

B: 9240

A: 3P22

A: 22P3

B: ≈1.87×1020

Answer: Look for the closes thing to 10

Step-by-step explanation:

Step-by-step explanation:

[tex] = - \frac{5}{9} - ( - \frac{14}{15} )[/tex]

[tex] = - \frac{5}{9} + \frac{14}{15} [/tex]

[tex] = - \frac{5 \times 5}{9 \times 5} + \frac{14 \times 3}{15 \times 3} [/tex]

[tex] = - \frac{25}{45} + \frac{42}{45} [/tex]

[tex] = \frac{ - 25 + 42}{45} [/tex]

[tex] = \frac{42 - 25}{45} [/tex]

[tex] = \frac{17}{45} [/tex]

Answer:

  15.4 years

Step-by-step explanation:

An investment is doubled when it is twice its initial value. The equation can be solved for the value of t that makes this true.

In the exponential equation for investment value, the factor y₀ is the initial value of the investment. We want to find t when y = 2y₀.

  2y₀ = y₀·e^(0.045t)

Dividing by y₀ gives ...

  2 = e^(0.045t)

Taking natural logarithms, we have ...

  ln(2) = 0.045t

Dividing by the coefficient of t gives its value:

  t = ln(2)/0.045 ≈ 15.4

The investment will be doubled after 15.4 years.

__

Additional comment

The continuously compounded interest rate for this investment is 4.5%. The doubling time is 0.693 divided by this: 0.693/0.045 ≈ 15.4. This relationship holds for any sort of continuous compounding.

Answer:

16 days

Step-by-step explanation:

OK, The pet snail only moves a foot per day because at night it falls again, SO ima going with 16 days.

[<Answer>] (2):
Hello! I'm Avery. And I'm here to help! :)

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[<The Explanation>}:

Sally has  pet snail that fell into a well.

(Depth of the well = 16 feet)

Snail climbs up 5 feet but each night it slides back down 4 feet.

So the snail climbs up per day = 5 feet - 4 feet = 1 feet.

Number of days snail took to reach at 11 feet = 11 × 1 = 11 feet

Remaining distance to cover by the snail = 16 - 11 = 5 feet

Number of days to cover remaining 5 feet to reach the top of the well = 1 day

Therefore, snail will take 12 days to reach the top of the well.

----------------------------------------------------------------------------------------------------------
[<Ending>] <3

Hope this helps and if it's wrong, you can't sue me! :D

Bye! Hope this works for you :)

Have a nice day! - Avery <3

Answer:

A square is a rectangle but a rectangle is not a square. A square consists of  four sides of equal lengths. A rectangle has two sides shorter than the two other sides.

Two more examples of relationship patterns found in mathematics are Geometric sequences and Fibonacci numbers.

Mathematical patterns are a sequence of repeated arrangements of numbers, shapes, colors, letters, etc.

Mathematical patterns are usually abstract.

A geometric sequence is a sequence of non-zero numbers.  The first number is the product of multiplying a previous number by a fixed, non-zero number, called the common ratio.

A Geometric sequence may look like: 2, 4, 8, 16, 32, 64, 128, ..., where the common ratio is 2.

A Fibonacci number starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers.

The rule of the Fibonacci sequence is that each number is equal to the sum of the preceding two numbers, for example, 0, 1, 1, 2, 3, 5, 8, 13.

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Answer:

10√2

Step-by-step explanation:

The square root of 200 in its simplest radical form is 10√2.

If we know the prime factorization of a number, we can write the radical form of the square root of that number. As a result, the prime factorization of 200 is 2 × 2 × 2 × 5 × 5.

As a result, the square root of 200 in the simplest radical form should be 10√2.

Answer:

?

Step-by-step explanation:

Please explain-WHAT TRACKS?

Answer:

5.275

Step-by-step explanation:

Got the answer from Emma on Gauth Math

Answer:

370,000 centimeters

Step-by-step explanation:

1. There are 1000 meters in a kilometer.

2. 3.7 kilometers x 1000 = 3,700 meters

3. There are 100 centimeters in a meter

4. 3,700 x 100 = 370,000 centimeters

There are 7,315 different combinations, thus, the correct option is c

If we have a set of N elements, the number of different combinations of K elements (such that K ≤ N) of these N elements that we can make is:

[tex]C(N, K) = \frac{N!}{(N - K)!K!}[/tex]

In this case we have K = 4 and N = 22, replacing that, we get:

[tex]C(22, 4) = \frac{22!}{(22 - 4)!*4!} = \frac{22*21*20*19}{4*3*2*1} = 7,315[/tex]

So there are 7,315 different combinations, thus, the correct option is c.

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Answer: -211/76

Step-by-step explanation:

to solve this word problem equation, we need to first convert the words to numbers and variables we can solve for:

we can replace "a number" for a variable such as x

this gives:

-76·x-61=x+89

now all you have to do is solve the equation and you're done!

Answer:

19

Step-by-step explanation:

fx=16+4

fx=20

gx= 20-1

gx=19

19

Answer:

a = -17/30

Step-by-step explanation:

So the first step is to distribute the negative sign, if that's a bit confusing think of the negative sign as a -1 instead of just a negative sign, and then think of distributing that negative 1 to the 23a and -13.

Original Equation:

-(23a - 13) + 53a

Distribute negative sign

-23a + 13 + 53a

Group like terms:

(-23a + 53a) + 13

Simplify

30a + 13 = -4

Subtract 13 from both sides

30a = -17

Divide both sides by 30

a = -17/30

The Inventory Turnover for 2021 is 5.9 times and for 2022 is 10 times.

2021

Inventory Turnover = Cost of Goods sold / Average Inventory

Cost of Goods sold = $1,165,250/[($170,000+$225,000)/2]

Cost of Goods sold = $1,165,250/($395,000/2)

Cost of Goods sold = $1,165,250/197,500

Cost of Goods sold = 5.9 times

2022

Inventory Turnover = Cost of Goods sold / Average Inventory

Cost of Goods sold = $1,525,000/[($225,000+$80,000)/2]

Cost of Goods sold =  $1,525,000/($305,000/2)

Cost of Goods sold =  $1,525,000/152,500

Cost of Goods sold = 10 times

Therefore the Inventory Turnover for 2021 is 5.9 times and for 2022 is 10 times.

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The complete question is:

Pina Colada Corp. switched to a just-in-time inventory system. Its sales and Inventory amounts for 2021 and 2022 are shown below.

                                 2021            2022

Sales revenue $3,360,000  $3,900,000

Cost of goods sold  1,165,250 1,525,000

Beginning inventory  170,000 225,000

Ending inventory        225,000  80,000

Determine the inventory turnover for 2021 and 2022.

[tex]f(x) = x {}^{3} - 2 \\ f(3) = 3 {}^{3} - 2 = 27 - 2 = 25[/tex]

[tex]f(3) = 25[/tex]

[tex]5x - 7 \leqslant 13 \\ add \: 7 \: on \: both \: sides \\ 5x - 7 + 7 \leqslant 13 + 7 \\ 5x \leqslant 20 \\ divide \: both \: sides \: by \: 5 \\ \frac{5x}{5} \leqslant \frac{20}{5} \\ x \leqslant 4[/tex]

5.7099 is the margin of error.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.

Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

According to the question,

The standard sampling error of the sample mean is σₓ ,

The sampling distribution is: N (u,σₓ/n)

Therefore,

By using the standard deviation formula:

σₓ = √∑(xi -μ)/N

Where,

∑= population standard deviation

N= the size of the population

xi= each value from the population

μ =the population mean

So ,

σₓ = [tex]\frac{20.6}{\sqrt{50} }[/tex] = 2.913

Since, a = 1- 95% = 0.05

therefore [tex]Z\frac{a}{2}[/tex] = (1-0.005 x 2) = 1.959964

Here, the margin of error for a 95% confidence interval for this sample is given by:

[tex]Z\frac{a}{2}[/tex] * σₓ = 1.959964 x 2.913    

           = 5.7099

5.7099 is the margin of error for a 95% confidence interval for this sample.

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a+a=a
→a+a-a=0
→a=0
(proved)

Step-by-step explanation:

[tex]a + a = a[/tex]

[tex]2a = a[/tex]

[tex]2a - a = 0[/tex]

[tex]a = 0[/tex]

Proved.

Answer:

-42

Step-by-step explanation:

You have to To subtract the fractions, then find the Least common denominator (LCD) and then combine.

pls brainliest Hope this helps have a nice day :>

[tex]\boldsymbol{(-1-3^{2})-\dfrac{4^{3} }{2} }[/tex]

Calculates 3 to the power of 2 and gets 9.

[tex]\boldsymbol{-1-9-\dfrac{4^{3} }{2} }[/tex]

Subtract 9 from −1 to get −10.

[tex]\boldsymbol{-10-\dfrac{4^{3} }{2} }[/tex]

Calculates 4 to the power of 3 and gets 64.

[tex]\boldsymbol{-10-\dfrac{64}{2} }[/tex]

Divide 64 by 2 to get 32.

[tex]\bf{-10-32 }[/tex]

Subtract 32 from −10 to get −42.

[tex]\bf{-42 \ \ \to \ \ \ Answer}[/tex]

The spring .2m far when it is compressed on being supported by a mass of 10kg.

Given: Mass of 30 kg which compresses spring by 0.6m

To find: The compression of the spring when it is supported by a mass of 10 kg

Concept: Compression springs are coiled springs that hold mechanical energy in a compressed state. When these springs are subjected to compressive loads, they compress and shorten, capturing and storing significant potential force.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

By using unitary method,

10 is 3 times less than 30.

so, 30/3=10

Also applying the same proportion over the lengths compressed,

we get, 0.6/3=.2

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Answer:

12(x+y)=42

60(y-x)=42

Step-by-step explanation:

12(x+y)=42 (12 seconds, x+y speed each second, 42 metres)

60(y-x)=42 (1 minute = 60 seconds, x-y speed each second, 42 metres)

The required Comparison of the inequalities are

The range of values encompassing the region's junction is (-13, 15).

When comparing two numbers, an inequality indicates whether one is less than, larger than, or not equal to the other.

We take into account the various variables of the inequality

|x – 1| + 1 > 15

Therefore

|-x-1|+1-1<15-1

|-x-1|-1 <14

13<x<15

The required region lies between the inequality -13 <x< 15.

Simplify the inequality Ix-11+1 > 15 we get,

|x-1|+1 > 15

|x+1| +1-1 >15-1

|x-1| > 14

x> 15  

x<-13

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Answer:

x = 35.537677791974°

y = 63.434948822922°

Step-by-step explanation:

let x be the measure of the angle of elevation of the sun.

tan(x) = 10/14

Then

x = tan⁻¹ (10÷14) = 35.537677791974°

………………………………………………

let y be the measure of the angle of elevation of the sun

where the shadow decreases to 5m.

tan(y) = 10/5 = 2

Then

y = tan⁻¹ (2) = 63.434948822922°

Answer:

a) 35.54°

b) 63.43°

Given following:

Determining, the shadow is adjacent side and length of the pole is the opposite side. Hence, use the tan rule. Let the angle be x.

(a)

[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]

[tex]\sf tan(x) = \dfrac{10}{14}[/tex]

[tex]\sf x = tan^{-1}(\dfrac{10}{14} )[/tex]

[tex]\sf x = 35.54^{\circ \:} \quad (rounded \ to \ nearest \ hundredth )[/tex]

(b) If the shadow decreases to 5 meter.

[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]

[tex]\sf tan(x) = \dfrac{10}{5}[/tex]

[tex]\sf x = tan^{-1} (\dfrac{10}{5})[/tex]

[tex]\sf x = 63.43 ^\circ \quad (rounded \ to \ nearest \ hundredth)[/tex]

Using the Empirical Rule, the percentages are given as follows:

a) 99.7%.

b) 32%.

c) 16%.

It states that, for a normally distributed random variable:

Item a:

61 and 139 is within 3 standard deviations of the mean, hence the percentage is of 99.7%.

Item b:

87 and 113 is within one standard deviation of the mean, hence 68% of the data is within this interval and 100 - 68 = 32% of the data is outside this interval.

Item c:

Considering that the normal distribution is symmetric, and item b, this percentage is of 32%/2 = 16%.

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The equation which is a function of x is x²=y.

Given an equation that is a function of x.

A function may be a relation between a collection of inputs and a collection of permissible outputs with the property that every input is said to precisely one output.

If we input a value of x then we get the output f(x) = y, which is the function of x.

We are given four options out of which we are to pick the one which may be a function of 'x'.

The first option is x=5 in which no term of y is included and its a constant. So, option 1 is not correct.

The second option is x=y²+9 in which y contains a power 2. So, option 2 is not correct.

The third option is x²=y in which y contains power 1. So, option 3 is correct.

The fourth option is x²=y²+16 in which y contains a power 2. So, option 3 is not correct.

Hence, the equation which is a function of x is x²=y.

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Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial whose factors are (a²-6) and (a²+4) is a⁴ - 2a² - 24.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Example: x²+3x+5 is a polynomial.

The polynomial whose factors are (a²-6) and (a²+4) is,

P(x) =  (a²-6)(a²+4)

      = a⁴ + 4a² - 6a² - 24

      = a⁴ - 2a² - 24

Hence, The polynomial whose factors are (a²-6) and (a²+4) is a⁴ - 2a² - 24.

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Using it's concept, the average rate of change of the function over the interval 10 < x < 22 is given by:

[tex]r = \frac{f(22) - f(10)}{12}[/tex]

It is given by the change in the output divided by the change in input.

Over the interval 10 < x < 22, the outputs are f(10) and f(22), hence the rate of change is given by:

[tex]r = \frac{f(22) - f(10)}{12}[/tex]

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Answer:

The first answer

4x-2y=0

Answer:

a)

[tex](x^{2} + 2)(x^{2} + 2)\\x^{4} + 2x^{2} + 2x^{2} + 4\\= x^{4} + 4x^{2} + 4\\[/tex]

b)

[tex](x +1)(x + 1)(x^{2} -2x +3) = (x + 1)^{2} (x^{2} -2x +3)[/tex]