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3 years ago

In how many ways can the letters in the word MATHEMATICS be reshuffled so that all consonants appear together?

Mathematics

1 answer:

steposvetlana [31]3 years ago

4 0

Answer:

75600

Step-by-step explanation:

We are given that a word MATHEMATICS

Total letters =11

M repeated 2 times

T repeated 2 times

A repeated 2 times

Total vowels=4

Let MTHMTCS=P

Total number of ways in which MTHMTCS can be arranged= $\frac{7!}{2!2!}$

PAEAI

Total number of ways in which PAEAI can arranged= $\frac{5!}{2!}$

Total number of arrangements when all consonant appear together= $\frac{7!}{2!2!}\times \frac{5!}{2!}$

Total number of arrangements when all consonant appear together= $\frac{7!5!}{2\times 2\times 2}=\frac{7\times 6\times 5\times 4\times 3\times 2\times 1\times 5\times 4\times 3\times 2\times 1}{8}=75600$

By using formula ; $n!=n(n-1)(n-2)...2\times 1$

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singh works at a restaurant where he is paid by the hour plus time and a half for his hours over 40. last week he worked four ho

padilas [110]

Answer:

$8.5 per hour

Step-by-step explanation:

Number of overtime hours = 4 hours

Since overtime starts after 40 hours, then the number of hours worked = 40 + 4 = 44 hours

Total amount earned = $391

Let Hourly pay = x

Overtime pay = 1 1/2x = 3/2x

Therefore ;

40x + (4*3/2x) = 391

40x + 6x = 391

46x = 391

x = 391 / 46

x = 8.5

Hourly pay = $8.5 per hour

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3 years ago

Which of the following phrases can be used to represent -11?

Reptile [31]

Answer:

eleven below zero

Step-by-step explanation:

opposite of -11 =11 so that doesn't work

positive eleven=11 so that doesn't work

eleven greater than zero=11 so that doesn't work

eleven below zer0= -11 so it works

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3 years ago

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Frank is a two digit number on his baseball uniform the number is a multiple of 10 and has 3 for one of its factors what three n

Yanka [14]

Th three numbers he could of had on his uniform are 60 30 or 90

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3 years ago

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Question text You have just won the lottery. The Lottery Corporation offers you two options: 1. a lump-sum payment of $400,000,

igomit [66]

Use present value equation.
If present value of annuity equals 400,000, then you are indifferent.

$PV = A(v + v^2 + ...v^{20}) \\ \\ PV = A\frac{v(1-v^{20})}{1-v}$

where v = 1/(1+r) and A = annual payment = 800,000/20 = 40,000

PV = 400,000
After subbing in the numbers, the equation is:
$10 = \frac{v(1-v^{20})}{1-v} \\ \\ 10 - 10v = v - v^{21} \\ \\ v^{21} - 11v+10 = 0 \\ \\ v = 0.928034 \\ \\ \frac{1}{1+r} = 0.928034 \\ \\ r = 0.0775$

Therefore at interest rate of about 7.75% you are indifferent.

6 0

3 years ago

A zipline is constructed over a ravine as shown in the diagram at the right. What is the horizontal distance from the bottom of

Katyanochek1 [597]

Answer: X= 284.04

To solve for x, you must first find the missing angle in the left corner. I will name it "< Y" (Angle Y)

Sin50/250 = SinY/60

Set up your problem, then cross multiply.

60(Sin50)= 250(Sin Y)

60(Sin50)/250= Sin Y

After cross multiplying, you should be left with this. You then cancel out 250 by dividing it on both sides to get Sin Y by itself.

Sin Y = 0.183

Y= Sin-1 x 0.183

This is what it solves out to.

Now you cancel out Sin on both sides, and it should look like the bottom problem.

Y= 10.5

This is now your answer to plug into the problem needed to solve for X.

Now because you have 2 out of 3 angles, you can solve for the missing angle that lays opposite to x. ( in SOHCAHTOA you need the OPPOSITE and the HYPOTENUSE. The Hypotenuse is originally give, but we had to do extra solving to find the Opposite's degree.)

Because degree's in a triangle add to 180, we will add 50 degrees + 10.5 degrees to get 60.5 degrees. Now subtract 60.5 from the full 180 degrees and we get 119.5 degrees as the missing number that lays opposite from X. Now we can solve for X.

(Sin 119.5)/x = (Sin 50)/250

Set up your final problem as so and cross multiply.

X(Sin 50) = 250(Sin 119.5)

X = 250(Sin119.5)/(Sin50)

After cross multiplying, the problem should look like the one at the top. Cancel out Sin 50 to get X by itself by dividing both sides by Sin 50, then solve for X.

Step-by-step explanation:

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3 years ago