Does anyone know the answer???

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

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Use the method illustrated in the solutions to Exercise 9.2.39 to answer the following questions. (a) How many ways can the letters of the word DANCER be arranged in a row? Since the letters in the given word are distinct, there are as many arrangements of these letters in a row as there are permutations of a set with elements. So the answer is . (b) How many ways can the letters of the word DANCER be arranged in a row if D and A must remain together (in order) as a unit? (c) How many ways can the letters of the word DANCER be arranged in a row if the letters NCE must remain together (in order) as a unit?

Answers

Answer:

(a) 720 ways

(b) 120 ways

Step-by-step explanation:

Given

$Word = DANCER$

$n =6$ --- number of letters

Solving (a): Number of arrangements.

We have:

$n =6$

So, the number of arrangements is calculated as:

$Total =n!$

This gives:

$Total =6!$

This gives:

$Total =6*5*4*3*2*1$

$Total =720$

Solving (b): DA as a unit

DA as a unit implies that, we have:

[DA] N C E R

So, we have:

$n = 5$

So, the number of arrangements is calculated as:

$Total =n!$

This gives:

$Total =5!$

This gives:

$Total =5*4*3*2*1$

$Total =120$

Solving (c): NCE as a unit

NCE as a unit implies that, we have:

D A [NCE] R

So, we have:

$n = 4$

So, the number of arrangements is calculated as:

$Total =n!$

This gives:

$Total =4!$

This gives:

$Total =4*3*2*1$

$Total =24$

At swim practice, several swimmers take turns, swimming 100 meters each. The total distance they swim is less than 1,200 meters. Which inequality can be solved to determine, s, the possible number of swimmers?1,200 greater-than 100 s
1,200 less-than 100 s
1,200 s greater-than 100
1,200 s less-than 100

Answers

Answer:

1,200 greater-than 100 s

Step-by-step explanation:

Each swimmer swims 100m.

So the total distance they swim is given by:

T = 100s.

The total distance they swim is less than 1,200 meters.

This means that:

T < 1200

100s < 1200

1200 greater than 100s.

So the correct answer is:

1,200 greater-than 100 s

Answer:

Step-by-step explanation:

A set of cards contains cards numbered 1 – 8. Mrs. Jacob’s class is conducting an experiment in which a card is drawn from the pile, the number is recorded, and then the card is returned to the set. The class will conduct 1,000 trials. Based on the theoretical probability, which is the best prediction for the number of times a 4 will be drawn from the pile?

Answers

Answer: 125

The best prediction for the number of times a 4 will be drawn from the pile is:

A set of cards contains cards numbered 1 – 8.

So, the theoretical probability that 4 comes up is:

Ratio of Number of favorable outcome( outcome of 4) to the total umber outcome(i.e. 8 )

Hence, Theoretical Probability that 4 is drawn=1/8

Now, out of 1000 trials the best prediction of number of times 4 is drawn is:

(The probability of drawing 4)×(Number of experiments or trials)

=(1/8)×1000

=125

Bob has a concession at Yankee Stadium. He can sell 500 umbrellas at $10 each if it rains. (The umbrellas cost him $5 each.) If it shines, he can sell only 100 umbrellas at $10 each and 1000 sunglasses at $5 each. (The sunglasses cost him $2 each.) He has $2500 to invest in one day, but everything that isn’t sold is trampled by the fans and is a total loss. This is a game against nature. Nature has two strategies: rain and shine. Bob also has two strategies: buy for rain or buy for shine. Find the optimal strategy for Bob assuming that the probability for rain is 50%.

Answers

Answer:

The optimal strategy for Bob is buying for shine (unless he can watch a forecast to know the next day weather).

Step-by-step explanation:

This is a typical problem of hopes to win vs hopes to lose. Let's analyze each of the strategies Bob can adopt in both kinds of weather.

Bob buy for rain:

Bob will buy 500 umbrellas for a cost of $5 each. This is a total cost of $2500.

If it rain, Bob can sell all umbrellas for $10 each. This gives a maximum revenue of $5000. Therefore the maximum profit is $2500. Remember that:

Profit= Revenue - Cost

If it's a sunny day, Bob can only sell 100 umbrellas for $10 each. This gives a maximum revenue of $1000. Therefore the maximum profit is -$1500. That means that in this case, the minimum loss is $1500.

Bob buy for Shine:

Bob will buy 100 umbrellas for a cost of $5 each and 1000 sunglasses for a cost of $2 each. This is a total cost of $2500.

If it's a sunny day, Bob can only sell all umbrellas for $10 each and all sunglasses for $5. This gives a maximum revenue of $6000. Therefore the maximum profit is $3500.

If it rains, Bob can sell only sell all the 100 umbrellas for $10 each but none of the sunglasses. Therefore the maximum profit is $1000. Therefore the maximum profit is -$1500. That means that in this case, the minimum loss is $1500.

In both cases, the worst-case scenario is the same: a loss of $1500.

Nevertheless in the best case scenario buying to shine gives a bigger profit. Therefore if the risk is the same, is better to go for the strategy with better profits.

Match the postions on the number line with the numbers they represent