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deff fn [24]
3 years ago
8

A certain mathematics contest has a peculiar way of giving prizes. Five people are named as Grand Prize winners, but their finis

hing order is not listed. Then from among the other entrants, a 6thplace, 7thplace, 8thplace, 9thplace, and 10thplace winner are each named.If 22 people enter this year, how many complete award announcements are possible?
Mathematics
1 answer:
bixtya [17]3 years ago
6 0

Answer:

The number of complete award announcements possible are 19,554,575,040.

Step-by-step explanation:

Combination is the number of ways to select <em>k</em> items from <em>n</em> distinct items when the order of selection does not matters.

Whereas permutation is the number of ways to select <em>k</em> item from <em>n</em> items when order of selection matters.

The number of people entering this year is 22.

The number of ways to select 5 people for Grand Prize is, {22\choose 5}=\frac{22!}{5!(22-5)!} =26334.

The remaining number of people is, 22 - 5 = 17.

It is provided that the other 5 are selected according to an order.

The number of ways to select other 5 winners is,

^{17}P_{5}=\frac{17!}{(17-5)!} =742560

The total number of ways to select 10 winners of 22 is:

Total number of ways = 26334 × 742560 = 19,554,575,040.

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A 2000 gallon fish aquarium can be filled by water flowing at a constant rate in 10 hours. When a decorativve rock is placed in
Elza [17]

Answer:

The volume of the rock is 13.368 cubic feet.

Step-by-step explanation:

The volume of the rock (V_{r}), measured in gallons, is equal to the volume of the fish aquarium without the decorative rock (V') minus the volume of the fish aquarium with the decorative rock (V''), both measured in gallons.

Since the water flow is at constant rate, the volume of the rock is expressed by the following equation:

V_{r} = V' - V''

V_{r} = \dot V \cdot (\Delta t_{1}-\Delta t_{2}) (1)

Where:

\dot V - Flow rate, measured in gallons per hour.

\Delta t_{1} - Filling time of the fish aquarium without the decorative rock, measured in hours.

\Delta t_{2} - Filling time of the fish aquarium with the decorative rock, measured in hours.

And the flow rate is:

\dot V = \frac{2000\,gal}{10\,h}

\dot V = 200\,\frac{gal}{h}

The flow rate is 200 gallons per hour.

If we know that \dot V = 200\,\frac{gal}{h}, \Delta t_{1} = 10\,h and \Delta t_{2} = 9.5\,h, then the volume of the rock is:

V_{r} = \left(200\,\frac{gal}{h}\right)\cdot (10\,h-9.5\,h)

V_{r} = 100\,gal

V_{r} = 13.368\,ft^{3}

The volume of the rock is 13.368 cubic feet.

8 0
2 years ago
Shaunnie and Marlon missed the lesson on exponents. Shaunnie incorrectly wrote 10⁵ = 50 on her paper, and Marlon incorrectly wro
Jobisdone [24]

a. Shaunnie's mistake was that she multiplied 10 times 5. When you multiply 10x5, it is the same as 10+10+10+10+10. However, the question asked about 10⁵. 10⁵ means 10 to the fifth power which is the same as 10x10x10x10x10. She needs to multiply 10 to itself, ten times. This equals 1,000,000.

b. Marlon made the mistake of not moving the decimal point. Marlon added the two zeros to the end when he multiplied 2.5 to 10² because 10² is the same as 100. However, when multiplying with a decimal, the decimal needs to move as well. He needs to move the decimal place to the right two places. His answer should be 250. The last zero is dropped because it is to the right of the decimal and not followed by another number.

<h3>Further Explanation</h3>

Numbers to the nth power.

When a number has a power as in 10², this means that you multiply that number by itself however many times the power indicates. A number to the 29th power would be multiplied by itself 29 times.

Multiplying Decimals

When multiplying decimals, it is important to remember to shift the decimal to the correct place. A number multiplied by ten moves the decimal one place to the right. A number multiplied by 100 moves the decimal two places to the right. A number multiplied by 1000 moves the decimal three places to the right. A trick for remembering is the number of zeros in 10, 100, or 1000. For each zero, move the decimal

<h3>Answer Details</h3>

Subject: Math

Level: Middle School

Topic: Powers

<h3>Keywords</h3>

powers, multiplication, multiplying with decimals

<h3>Learn More</h3>

Checking decimal multiplication: brainly.com/question/923608

Math Powers: brainly.com/question/100928

3 0
3 years ago
Read 2 more answers
What does h(3.2) represent?
nalin [4]

Answer:

B

Step-by-step explanation:


7 0
2 years ago
Least to Greatest Show your work
HACTEHA [7]
4/8 = 0.5
5/12 = 0.42
1/6 = 0.17

<span>Least to Greatest 
</span>
1/6, 5/12, 4/8

without using decimal

4/8 = 12/24
5/12 = 10/24
1/6 = 4/24

Least to Greatest 

1/6, 5/12, 4/8
6 0
3 years ago
Read 2 more answers
Shkfdbhjgfdgxbvcb b c bxc
sergij07 [2.7K]

Answer:

X = 1553/19  Hope this helped :)

4 0
2 years ago
Read 2 more answers
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