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mylen [45]
3 years ago
11

Suppose that 10 sophomores, 3 juniors, and 10 seniors are candidates for a prestigious mathematics award of which three will be

given out. In how many different ways can the recipients of these three awards be chosen?
Mathematics
1 answer:
faltersainse [42]3 years ago
7 0

Answer:

1771 possible ways

Step-by-step explanation:

In this case, we need to know first how many candidates are in total:

10 + 3 + 10 = 23 candidates in total.

Now, we need to choose 3 of them to receive an award. In this case, we have several scenarios, but as it's an award we can also assume that the order in which the candidates are chosen do not matter, so, the formula to use is the following:

C = m! / n! (m - n)!

Where m is the total candidates and n, is the number of candidates to be chosen. Replacing this data we have:

C = 23! / 3! (23 - 3)!

C = 2.59x10^22 / 6(2.43x10^18)

C = 1771

So we have 1771 ways of choose the candidates.

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James earns $9.45 per hour. IfJames worked 37.75 hours last week, what was his gross pay?
tresset_1 [31]

Answer:

$9.45 * 37.75 hours = $356.7375

Step-by-step explanation:

6 0
3 years ago
What is the distance between the points (-5, -9) and (-5,14 )?
netineya [11]

Answer:

-4, 19

Step-by-step explanation:

4 0
3 years ago
This is a problem that I have to solve with matrixes, Please show me all of the work. I will award brainliest.
Elina [12.6K]

Answer:

The total points by Washington High School =  162 points

The total points by  Johnson High School   =  159 points

The total points by  Roosevelt High School =  108 points

The total points by  Lewis High School =  196 points

Washington High School  has WON the meet.

Johnson High School came second.

The difference in the points= 2 points

Step-by-step explanation:

Points awarded for first place = 10 points

Points awarded for second place = 8 points

Points awarded for third place = 7 points

About Washington High School

10 first places  = 10 x ( 10) = 100 points

6 second places  = 6 x ( 8) = 48 points

2 first places  = 2 x ( 7) = 14 points

So, the total points by  Washington High School  = Sum of all points  

=  100 + 48 + 14   =  162 points     .............. (1)

About Johnson High School

8 first places  = 8 x ( 10) = 80 points

9 second places  = 9 x ( 8) = 72 points

1 first places  = 1 x ( 7) = 7 points

So, the total points by  Johnson High School  = Sum of all points  

=  80 + 72 + 7   =  159 points    .............. (2)

About Roosevelt High School

4 first places  = 4 x ( 10) = 40 points

5 second places  = 5 x ( 8) = 40 points

4 first places  = 4 x ( 7) = 28 points

So, the total points by  Roosevelt High School  = Sum of all points  

=  40 + 40 + 28   =  108 points  .............. (3)

About Lewis High School

3 first places  = 3 x ( 10) = 30 points

3 second places  = 3 x ( 8) = 24 points

6 first places  = 6 x ( 7) = 42 points

So, the total points by  Lewis High School  = Sum of all points  

=  30 + 42 + 24   =  96 points      .............. (4)

Now, comparing all four equation, we get that:

Washington High School  has WON the meet.

Johnson High School came second.

The difference in the points  = 162 - 159 = 2 points

6 0
3 years ago
The sum of three odd consecutive numbers is fifty-one. What are the numbers?
Fantom [35]

Answer:

15,17,19

Step-by-step explanation:

Make an equation : x+(x+2)+(x+4)=51

Solve the equation:3x+6=51

3x=51-6

3x=45

x=15

Since x=15 then the second number is 17 and then 19

Hope this helps!

Stay Safe

7 0
3 years ago
Leona purchased a $1,000 bond having a quoted price of 99.875. She had to pay a 5.5% brokerage fee (of the selling price). What
Ede4ka [16]

Answer:

None of these choices are correct.

Step-by-step explanation:

The quoted value of 99.875, means that this bond is sold at 99.875%  of the face value and not at a price of  $99.875.

Therefore, calculate price;

Price = 0.99875 * 1000

Price = $998.75

Since brokerage fees is 5.5% of the selling price, Leona will pay additional cost to the quoted price making the total cost to be more than $998.75;

Brokerage fees = (0.055*998.75) = $54.93

Total cost = $998.75 +$54.93

= $1053.68

Therefore, none of the choices is correct.

3 0
3 years ago
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