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2 years ago

Let $c(t)$ be the number of customers in a restaurant $t$ hours after 8 A.M. Match each statement with its meaning.

Mathematics

1 answer:

Leto [7]2 years ago

8 0

Answer:

The meaning of each statement is shown below.

Step-by-step explanation:

Assume that the given statements are

(a) c(0)=0

(b) c(3)=c(8)

(d) c(13)<c(12)

Let c(t) be the number of customers in a restaurant t hours after 8 A.M.

We need to find the meaning of each given statement.

(a) c(0)=0 means the number of customers 0 hours after 8 A.M (i.e., 8 A.M.) is 0.

(b) c(3)=c(8) means the number of customers 3 hours after 8 A.M (i.e., 11 A.M.) is equal to the number of customers 8 hours after 8 A.M (i.e., 4 P.M.).

(d) c(13)<c(12) means the number of customers 13 hours after 8 A.M (i.e., 9 P.M.) is less than the number of customers 12 hours after 8 A.M (i.e., 8 P.M.).

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On a certain route, an airline carries 7000 passengers per month, each paying $30. A market survey indicates that for each $

KengaRu [80]

Answer:

The ticket price that maximizes revenue is $50.

The maximum monthly revenue is $250,000.

Step-by-step explanation:

We have to write a function that describes the revenue of the airline.

We know one point of this function: when the price is $30, the amount of passengers is 7000.

We also know that for an increase of $1 in the ticket price, the amount of passengers will decrease by 100.

Then, we can write the revenue as the multiplication of price and passengers:

$R=p\cdot N=(30+x)(7000-x)$

where x is the variation in the price of the ticket.

Then, if we derive R in function of x, and equal to 0, we will have the value of x that maximizes the revenue.

$R(x)=(30+x)(7000-100x)=30\cdot7000-30\cdot100x+7000x-100x^2\\\\R(x)=-100x^2+(7000-3000)x+210000\\\\R(x)=-100x^2+4000x+210000\\\\\\\dfrac{dR}{dx}=100(-2x)+4000=0\\\\\\200x=4000\\\\x=4000/200=20$

We know that the increment in price (from the $30 level) that maximizes the revenue is $20, so the price should be:

$p=30+x=30+20=50$

The maximum monthly revenue is:

$R(x)=(30+x)(7000-100x)\\\\R(20)=(30+20)(7000-100\cdot20)\\\\R(20)=50\cdot5000\\\\R(20)=250000$

3 0

2 years ago

Damien , Jake , and Makayla shared a bowl of grapes . Damien ate x grapes . Jake ate 1 more than twice the number of grapes that

vivado [14]

Answer:

There were (4x + 2) grapes in the bowl

Step-by-step explanation:

Here, we are interested in calculating the total number of grapes in the bowl.

We have 3 people sharing the total

Damien are x grapes

Jake ate 1 more than twice what Damien and that is (1 + 2x) grapes

Makayla ate 5 fewer grapes than Damien: So what Makayla ate is (x-5) grapes

And now, we have 6 grapes left.

To find the total number of grapes in the bowl, we need to add up all what they ate plus what is left.

Mathematically, that would be;

x + 1 + 2x + x -5 + 6

= 4x + 2

8 0

2 years ago

Read 2 more answers

isco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence

maks197457 [2]

Answer:

0.8894 is the probability that the test result comes back negative if the disease is present .

Step-by-step explanation:

We are given the following in the question:

P(Disco Fever) = P( Disease) =

$P(D) = \dfrac{1}{2}\times 1\% = 0.5 \times 0.01 = 0.005$

Thus, we can write:

P(No Disease) =

$P(ND) =1 - P(D)= 0.995$

P(Test Positive given the presence of the disease) = 0.99

$P(TP | D ) = 0.99$

P( false-positive) = 4%

$P( TP | ND) = 0.04$

We have to evaluate the probability that the test result comes back negative if the disease is present, that is

P(test result comes back negative if the disease is present)

By Bayes's theorem, we can write:

$P(ND|TP) = \dfrac{P(ND)P(TP|ND)}{P(ND)P(TP|ND) + P(D)P(TP|D)}\\\\P(ND|TP) = \dfrac{0.995(0.04)}{0.995(0.04) + 0.005(0.99)} = 0.8894$

0.8894 is the probability that the test result comes back negative if the disease is present .

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1 year ago

Shannon rolls 2 fair dice and adds the results from each. Work out the probability of getting a total of 13.

Bingel [31]

Answer:

Step-by-step explanation:

Fair dice are dice that have 6 sides, and the probability of rolling a side is the same as rolling another.

Since each die has 6 sides, the most you can get from the two dice are 6 + 6 = 12. Therefore, getting a 13 is impossible. So, there is a probability of 0.

Hope this helps!

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1 year ago

26. A positive whole number is called stable if at least one of its digits has the same value

Kisachek [45]

Answer:

Step-by-step explanation:

Given the value 78247 a s a stable number because at least one of its digits has the same value as its position in the number. The 4th number in the value is 4, this makes the number a stable number.

The following are the 3-digits stable numbers that appears in 78247

The first number is 824. This digits are stable numbers because 2 as a number is situated in the same place as the number (2nd position).

Hence, there are only 1 stable 3-digit numbers in the value 78247 since only a value exists as 2 in the value and there is no 1 and 3 in the value.

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2 years ago