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Serjik [45]
3 years ago
14

The crew of apollo 17 consisted of 2 pilots and a geologist. Suppose that nasa had actually trained 9 pilots and 4 geologists as

candidates for the flight. How many different crews could they have assembled?
Mathematics
1 answer:
Troyanec [42]3 years ago
8 0

They could have assembled total 336 different possible crews.

<em><u>Explanation</u></em>

Total number of trained pilots is 9 and geologists is 4.

The crew should be consisted of 2 pilots and 1 geologist. That means, <u>2 pilots are chosen from total 9 and 1 geologist is chosen from total 4</u>.

Number of ways for choosing 2 pilots from 9 = ^9C_{3} =84 and

Number of ways for choosing 1 geologist from 4 =^4C_{1}= 4

So, the total possible number of different crews they could have assembled =84*4= 336

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A music store sold a total of 27 used trumpets and clarinets in one month. Trumpets cost $149 and clarinets cost $99. If total s
vodomira [7]
Answer: 16

Solution:

1) Use letters to identify the variables:

Number of trumpets: t
Number of clarinets: c

2) Translate each statement into algebraic (mathematical) language.

2.1) Sold a total of 27 used trumpets and clarinets

=> t + c = 27

2.2) Trumpets cost $149 and clarinets cost $99

Total cost of the trumpets: 149t
Total cost of clarinets: 99c

Total cost = 149t + 99c

2.3) Total sales were $3223

=> 149t + 99c = 3223.

3) State the system of equations:

Equation (1) t + c = 27
Equation (2) 149t + 99c = 3223

4) Solve the system of equations:

4.1) Multiply equation 1 by 149:

=> 149t + 149c = 4023

4.2) Subtract the equation (2) from the equation obtained in 4.1

=> 149c - 99c = 4023 - 3223

=> 50c = 800

=> c = 800 / 50 = 16

5) Verify the solution:

From equation (1) t = 27 - 16 = 11

Total cost = 149*11 + 99*16 = 3223

Now you have a verified answer: they sold 16 clarinets
7 0
3 years ago
Write as an expression:<br> the total of n and 16
Mekhanik [1.2K]
Total is just add
n+16 is total of 16 and n
4 0
3 years ago
Avoiding an accident while driving can depend on reaction time. Suppose that reaction time, measured from the time the driver fi
Nadya [2.5K]

Answer:

2.5% of drivers have a reaction time more than 2.14 seconds

16% of drivers have a reaction time less than 1.78 seconds

84% of drivers have a reaction time less than 2.02 seconds

Step-by-step explanation:

The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

In this problem, we have that:

Mean = 1.9s

Standard deviation = 0.12

What percentage of drivers have a reaction time more than 2.14 seconds?

2.14 = 1.9 + 2*0.12

So 2.14 is two standard deviations above the mean.

Of the 50% of the measures above the mean, 95% are within 2 standard deviations of the mean, so, below 2.14. The other 5% is above.

0.05*0.5 = 0.025

2.5% of drivers have a reaction time more than 2.14 seconds

What percentage of drivers have a reaction time less than 1.78 seconds?

1.78 = 1.9 - 0.12

So 1.78 is one standard deviation below the mean.

Of the 50% of the measures that are below the mean, 68% are within one standard deviation of the mean, that is, greater than 1.78.

100 - 68 = 32

0.32*50 = 0.16

16% of drivers have a reaction time less than 1.78 seconds

What percentage of drivers have a reaction time less than 2.02 seconds?

2.02 = 1.9 + 0.12

So 2.02 is one standard deviation above the mean.

Of the measures that are below the mean, all are below 2.02.

Of those that are above, 68% are below 2.02.

0.5 + 0.68*0.5 = 0.84

84% of drivers have a reaction time less than 2.02 seconds

5 0
3 years ago
Which theorem shows how the triangles are similar:
yan [13]

Answer:

AA similarly is correct....

6 0
3 years ago
Write a function rule for the relationship. the amount c of energy you burn and the time t you spend exercising, if you burn Cal
gregori [183]

Answer:

c= 12t

c is the amount of energy you burn, so it'll be the "solution" to the equation. Multiply 12 times the amount of time you spend exercising to find how much energy you'll burn.

6 0
3 years ago
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