answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aev [14]
2 years ago
13

How many distinct 9-letter words starting with “i” can be formed from the word “committee”?

Mathematics
1 answer:
Nikitich [7]2 years ago
7 0

We have already chosen "i" to be the first letter. This means that we still have 8 letters that we can use as the second letter. Once that letter is chosen, we still have 7 letters that we can use as the third letter, and so on. This means we have

8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 8!

ways of choosing the remaining 8 letters.

<u>However,</u> some of the 8 available letters are equal: we have 2 m's, 2 t's and 2 e's. This means that we overcounted the number of words on the reasoning above. We can correct the counting by dividing three times by 2!, one time for each of the repeated letters.

The final answer is

\dfrac{8!}{2! \times 2! \times 2!} = \dfrac{40320}{8} = 5040.

You might be interested in
Rob borrows $15.00 from his father, and then he borrows $3.00 more. Drag numbers to write an equation using negative integers to
Paul [167]

Answer:

Rob owes his father=-$15-$3= -$18

Step-by-step explanation:

Rob borrows $15 first and then $3.

Since we have to use negative integers, so

-$15-$3= -$18

4 0
1 year ago
Read 2 more answers
1. Ernie Boddy had $3,620.00 on deposit at savings bank on July 1. The money earns interest at a rate of 6.5% compounded quarter
laila [671]

Answer:

235.3$ for part a

7 0
1 year ago
△ABC has vertices A(−1, 6), B(2, 10), and C(7, −2) . Find the measure of each angle of the triangle. Round decimal answers to th
kolbaska11 [484]

Answer:

<A = 90°, <B = 71.6° <C = 18.4°

Step-by-step explanation:

Given the vertices of a △ABC to be A(−1, 6), B(2, 10), and C(7, −2)

Before we can get each angle of the triangle, we need to get its sides first.

Using the formula fie finding the distance between two points

D = √(x2-x1)²+(y2-y1)²

For side AB:

Given A(−1, 6), B(2, 10)

AB = √{2-(-1)}²+(10-6)²

AB =√3²+4²

AB = √25

AB = 5

For side AC:

Given A(-1,6) and C(7, −2)

AC = √{7-(-1)}²+(-2-6)²

AC = √8²+8²

AC = √128

AC = √64×2

AC = 8√2

For side BC:

Given B(2,10) and C(7, −2)

BC = √(7-2)²+(-2-10)²

BC = √5²+12²

BC = √25+144

BC = √169

BC = 13

First we need to get theta using cosine rule

|AC|² = |AB|+|BC| - 2|AB||AC| cos theta

(8√2)² = 5²+13²-2(5)(13)cos theta

128 = 169-130costheta

128-169 = -130costheta

-41= -130costheta

Costheta = -41/-130

Cos theta = 0.315

theta = arccos 0.315

theta = 71.64°

<B = 71.6°

Using sine rule to get <A,

BC/sin A = AC/sinB

13/sinA = 8√2/sin71.6°

8√2sinA = 13sin71.6°

SinA = 12.34/8√2

SinA = 1.09°

A = arcsin1

<A = 90.0°

<C = 180°-(71.6+90)

< C = 180-161.6

<C = 18.4°

3 0
2 years ago
A rectangular piece of land is 40m long and 25m wide. A path of uniform width and 426 m^2 area sorrounds
fredd [130]

Answer:

Width of the uniform path that surrounds the piece of land = 3 m

Step-by-step explanation:

Let the width of the path that surrounds the piece of land be x.

The situation described is sketched in the attached image to this solution.

The dimension of the Length of the piece of land including the uniform path that surrounds it = (40 + 2x) m

The Breadth of the piece of land including the uniform path that surrounds it = (25 + 2x) m

The area of the piece of land including the uniform path that surrounds it

= (Area of the piece of land) + (Area of the uniform path that surrounds it)

Area of the piece of land = Length × Breadth = 40 × 25 = 1000 m²

Area of the uniform path that surrounds it = 426 m² (Given in the question)

The area of the piece of land including the uniform path that surrounds it = 1000 + 426 = 1426 m²

But the area of the piece of land including the uniform path that surrounds it is also

= (Length of the piece of land including the uniform path that surrounds it) × (Breadth of the piece of land including the uniform path that surrounds it

= (40 + 2x) + (25 + 2x)

= 1000 + 80x + 50x + 4x²

= (4x² + 130x + 1000) m²

Equation these 2 areas

4x² + 130x + 1000 = 1426

4x² + 130x - 426 = 0

Solving the quadratic equation

x = 3 or -35.5

Since the width cannot be negative,

x = 3 m

Hope this Helps!!!

7 0
2 years ago
Vannorman Corporation processes sugar beets in batches. A batch of sugar beets costs $78 to buy from farmers and $18 to crush in
NikAS [45]

Answer:

Results are below.

Step-by-step explanation:

<u>We will take into account the differential costs only. Therefore, the costs of sugar beets and to crush them are irrelevant to decision making.</u>

<u>Beet fiber:</u>

Sold as is= $25

Continue processing= 57 - 16= $41

It is more convenient to process further the beet fiber.

<u>Beet juice:</u>

Sold as is= $39

Continue processing= 84 - 22= $62

It is more convenient to process further the beet juice.

7 0
2 years ago
Other questions:
  • Timothy is re-arranging his marble collection.he has five identical blue marbles,five identical green marbles and three identica
    8·2 answers
  • A game has a rectangular board with an area of 44in2. There is a square hole near the top of the game board in which you must no
    7·1 answer
  • The sum of two numbers is 361 and the difference between the two number is 173 what are the two numbers
    15·2 answers
  • Which statements help explain this result? Check all that apply.
    14·2 answers
  • An equiangular triangle has one side of length six inches. What is the height of the triangle, drawn from that side, to the near
    10·1 answer
  • Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (◦F) at which a certain reaction
    9·1 answer
  • Mark took a loan out for $25,690 to purchase a truck. At an interest rate of 5.2% compounded annually, how much total will he ha
    15·2 answers
  • A school organised a concert for charity the graph and table showing information about 100 tickets sold
    7·2 answers
  • From Statistics and Data Analysis from Elementary to Intermediate by Tamhane and Dunlop, pg 265. A thermostat used in an electri
    8·1 answer
  • There are 25 trees on the Jackson’s property. Twenty percent of the trees are oak trees. Which equation can be used to find the
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!