MATHEMATICS COLLEGE

Susan decides to take a job as a transcriptionist so that she can work part time from home. To get started, she has to buy a computer, headphones, and some special software. The equipment and software together cost her $1000. The company pays her $0.004 per word, and Susan can type 90 words per minute. How many hours must Susan work to break even, that is, to make enough to cover her $1000 start-up cost? If Susan works 4 hours a day, 3days a week, how much will she earn in a month.

Answers

Answer 1

Answer:

Answer:

46.3 hours of work to break even.

$1036.8 per month (4 weeks)

Step-by-step explanation:

First let's find how much Susan earns per hour.

She earns $0.004 per word, and she does 90 words per minute, so she will earn per minute:

0.004 * 90 = $0.36

Then, per hour, she will earn:

0.36 * 60 = $21.6

Now, to find how many hours she needs to work to earn $1000, we just need to divide this value by the amount she earns per hour:

1000 / 21.6 = 46.3 hours.

She works 4 hours a day and 3 days a week, so she works 4*3 = 12 hours a week.

If a month has 4 weeks, she will work 12*4 = 48 hours a month, so she will earn:

48 * 21.6 = $1036.8

Answer 2

Answer:

Answer:

46.3 hours of work to break even.

$1036.8 per month (4 weeks)

Step-by-step explanation:

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The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:

Answers

The answer is 5.87x10^14 this is because when you multiply 5870000000000 times 100 you get 5.87x10^14

What is the median of 6, 7, 10, 12, 15? 12 10 9.6

Answers

Answer:

Step-by-step explanation:

it is the middle value after you have put the numbers in numerical order

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Answers

Answer:

Step-by-step explanation:

A firm has 18 senior and 22 junior partners. A committee of three partners is selected at random to represent the firm at a conference. In how many ways can at least one of the junior partners be chosen to be on the committee?

Answers

Answer:

Answer is 24288.

Step-by-step explanation:

Given that there are 18 senior and 22 junior partners.

To find:

Number of ways of selecting at least one junior partner to form a committee of 3 partners.

Solution:

At least junior 1 member means 3 case:

1. Exactly 1 junior member

2. Exactly 2 junior member

3. Exactly 3 junior member

Let us find number of ways for each case and then add them.

Case 1:

Exactly 1 junior member:

Number of ways to select 1 junior member out of 22: 22

Number of ways to select 2 senior members out of 18: 18 $*$ 17

Total number of ways to select exactly 1 junior member in 3 member committee: 22 $*$ 18 $*$ 17 = 6732

Case 2:

Exactly 2 junior member:

Number of ways to select 2 junior members out of 22: 22 $*$ 21

Number of ways to select 1 senior member out of 18: 18

Total number of ways to select exactly 2 junior members in 3 member committee: 22 $*$ 21 $*$ 18 = 8316

Case 3:

Exactly 3 junior member:

Number of ways to select 3 junior members out of 22: 22 $*$ 21 $*$ 20 = 9240

So, Total number of ways = 24288

Final answer:

The problem can be solved by finding the total number of ways to form a committee of three from all partners and the ways to form a committee solely from senior partners. Subtracting the number of all-senior committees from the total committees yields the number of committees that include at least one junior partner.

Explanation:

This problem is a combination problem dealing with probability and involves the use of the formula for combinations: C(n, k) = n! / [k!(n-k)!], where n is the total number of options, k is the number of options chosen, and '!' denotes a factorial.

The total number of ways to select 3 partners from the 40 (18 senior + 22 junior) is C(40, 3).

The only scenario where a junior partner is not present in the committee is when all three are senior partners. The number of ways to select 3 senior partners from the 18 available is C(18, 3).

So, to find the number of ways to form a committee with at least one junior partner, subtract the number of all-senior committees from the total number of committees. Therefore, the solution is C(40, 3) - C(18, 3).

Learn more about combinations here:

brainly.com/question/39347572

#SPJ12

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.y = (ln x2)2

Answers

Answer:

$(dy)/(dx)=(8lnx)/(x)$

Step-by-step explanation:

We are given that a function

$y=(lnx^2)^2$

We have to find the derivative of the function

Differentiate w.r.t x

$(dy)/(dx)=2(lnx^2)* (1)/(x^2)* 2x$

By using formula

$(d(lnx))/(dx)=(1)/(x)$

$(dx^n)/(dx)=nx^(n-1)$

$(dy)/(dx)=(4lnx^2)/(x)=(4(2)lnx)/(x)$

by using $lnx^y=ylnx$

Hence, the derivative of function

$(dy)/(dx)==(8lnx)/(x)$

Answer: The required derivative is $(dy)/(dx)=\nfrac{4}{x\ln x^2}$

Step-by-step explanation:

Since we have given that

$y=(\ln x^2)^2$

We need to derivative it w.r.t 'x'., using "Chain rule"

As we know that

$(d)/(dx) \ln x=(1)/(x)\n\nand\n\n(d)/(dx)x^n=nx^(n-1)$

So, it becomes,

$(dy)/(dx)=(1)/(\ln (x^2)^2)* 2\ln(x^2)* (1)/(x^2)* 2x\n\n(dy)/(dx)=(4)/(x\ln x^2)$

Hence, the required derivative is $(dy)/(dx)=\nfrac{4}{x\ln x^2}$

Given: 44 - 2(3x + 4) = -18Prove: x = 9

Answers

Substitute 9 as x in the given function:
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Now check and see if the statement it true and simplify.
44-2(27+4)=-18
44-2(31)=-18
44-62=-18
-18=-18
You can see this is true !!
Show my work to answer this question .

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