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love history [14]
3 years ago
11

The bus fare in a city is People who use the bus have the option of purchasing a monthly coupon book for With the coupon​ book,

the fare is reduced to​ $0.50. How many times must someone use the bus so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon​ book? Express the total monthly cost to use the bus with a coupon​ book, f, as a function of the number of times in the month the bus is​ used, x. Then express the total monthly cost to use the bus without a coupon​ book, g, as a function of the number of times in the month the bus is​ used, x.
Mathematics
1 answer:
SashulF [63]3 years ago
7 0

Answer:

26 times

Step-by-step explanation:

The question has missing details. However, the given parameters are

Given

Without Coupon

Bus Fare = $2.00

With Coupon

Coupon = $39.00

Bus Fare = $0.50

Represent the number of fares with x

Without Coupon, cost of fares is

Cost = 2x

i.e.

f(x) = 2x

With Coupon, cost of fares is

Cost = 39 + 0.5x

i.e.

g(x) = 39 + 0.5x

To calculate when both fares will be equal, we must have:

f(x) = g(x)

2x = 39 + 0.5x

Collect like terms

2x - 0.5x = 39

1.5x = 39

Solve for x

x = 39/1.5

x = 26

This implies that, for both cost to be equal, the person must go 26 times

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2 years ago
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murzikaleks [220]

Answer:

6/10 i think

Step-by-step explanation:

625 divided by 15 is 41.6 so i'd be 40+1+6/10

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3 years ago
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Mr. Montes is writing a short, three-question, true or false quiz for his Algebra 2 classes. He had planned on using a random an
belka [17]

Answer:

There are 4 questions to answer here and the answers are given below:

1. COMBINATION

2. SET 2  

3. {S2, S3, S4, S5}

4. { }  OR  ∅

Step-by-step explanation:

The key topics here are PERMUTATION & COMBINATION and SETS & VENN DIAGRAMS.

The assignment has 5 questions in all. The options for each question are listed below and separated by commas:

1. True, False

2. True, False

3. A, B, C, D

4. A, B, C, D

5. A, B, C, D

Mr. Montes derives his answers from a random answer generator; same way Amisha generated her answers by random selection.

<u>QUESTION 1</u>

If you want to find the odds that Amisha got at least 3/5 of the answers correctly, would you use a permutation or a combination?

<u>ANSWER TO QUESTION 1</u>

You would use a combination. Note that as much as 'permutation' is distinctly defined from 'combination', in many complex cases both are used to derive the solution. In this case though, a combination is used. For each of the 5 questions, there are a number of possible answers. Questions 1 and 2 have only <em>two possible answers</em> (also known as options) while questions 3, 4 and 5 have <em>four possible answers</em>/<em>options</em> to choose from. Amisha can only have one set of five answers; each to each question. So this is a combination! If you want to find the odds that Amisha got at least 3 of her 5 answers correct, you would use a combination of the various possible answers to check.

<u>QUESTION 2</u>

Find "Set 1 ∩ Set 2" and explain the notation in the sentence.

<u>ANSWER TO QUESTION 2</u>

First list out relevant information:

- The correct answers to questions 3, 4 and 5 are respectively C, B, A

- The universal set consists of five students: S1, S2, S3, S4, S5 hence

Ц = {S1, S2, S3, S4, S5}

Next, enlist the elements of each defined set

Set 1: {S1, S2, S3, S4, S5}     Set 2: {S2, S3, S4}     Set 3: {S4, S5}

Note: Set 1 is equal to the universal set.

Now this notation "∩" means "intersect". It requires an action - checking out which elements in one set also appear in a second set and then bringing those elements to form a new set.

In the case of this question, we're to find Set 1 intersect Set 2. The elements present in Set 1 and also present in Set 2 are {S2, S3, S4}.

If you look closely, you'll observe that these are the same elements in Set 2! This brings to remembrance, one of the laws of sets:

The intersect of any subset and the universal set (recall that Set 1 happens to be equal to or have the same elements as the universal set) is equal to that subset.

So the answer to question 2 is

Set 1 ∩ Set 2 = Set 2

<u>QUESTION 3</u>

Find "Set 2 ∪ Set 3" and explain the notation in the sentence.

<u>ANSWER TO QUESTION 3</u>

The notation ∪ represents "union". This is the act of putting together the elements in two sets, to form a new set. In this activity, if an element appears in both sets, it is only written once in the new set, not twice.

So, Set 2 union Set 3 = {S2, S3, S4, S5}

As earlier stated, Student 4 isn't appearing twice in the new set.

<u>QUESTION 4</u>

Find the ' of Set 1 and explain the notation in this sentence.

<u>ANSWER TO QUESTION 4</u>

The symbol ' means "complement of a set". Finding the complement of a set is like subtracting the elements of that set from the universal set.

Since Set 1 contains the same elements as the universal set, subtracting Set 1 from the universal set will give you nothing. In this case, the complement of Set 1 is a null set!

Set 1 ' Ц = { }  or  ∅

where the empty bracket symbol and the slashed zero symbol represent null set.

Kudos!

3 0
3 years ago
Angelo bought a chain that is 4 yards long he wants to cut the chain into 5 equal length pieces how long will each piece of chai
Semmy [17]

Each piece = (4/5) yards

(4/5) yards * 3 feet = 2.4 feet each piece

which equals 2 feet 4.8 inches each


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3 years ago
What value of n makes the equation true? (2x^9y^n)(4x^2y^10)=8x^11y^20
Komok [63]
Hi there! The answer is n = 10.

(2 {x}^{9}  {y}^{n} )(4 {x}^{2}  {y}^{10} ) = 8 {x}^{11}  {y}^{20}

As you see at the powers of x, we need to add the exponents of the power we when multiply them.
{x}^{9}  \times  {x}^{2}  =  {x}^{9 + 2}  = x {}^{11}

The powers of y work the same way.
{y}^{n}  \times  {y}^{10}  =  {y}^{n + 10}  =  {y}^{20}

Hence, n = 10, since
{y}^{10 + 10}  =  {y}^{20}
8 0
3 years ago
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