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Viktor [21]
3 years ago
15

Consider the first four terms of an arithmetic sequence below.

Mathematics
1 answer:
VMariaS [17]3 years ago
6 0
7, 13, 19 and 25 have a common difference:  6.  
6 added to 7 gives us 13; 6 added to 13 gives us 19, and so on.

Explicit formula:  a(n) = 7 + 6(n-1), where 7 is the first term and n is the counter (1, 2, 3, ...).

The first term is 7 (given).  This corresponds to n=1.

The second term is a(2) = 7 + 6(2-1), or 7 + 6, or 13.  This corresponds to n = 2.

and so on.


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1. The county fair charges $1.50 per ticket for the rides. Jermaine bought 20 tickets for the rides and spent a
makvit [3.9K]

Cost per ticket for the rides = $1.50.

a) Let us assume the number of ride tickets = x.

Total cost of x number of rides = y.

Total amount spent = $48.75.

Amount spent on 20 tickets = 20 × 1.50 = $30

<em>Fair admission charge = Total amount spent - Amount spent on 20 tickets</em>

<em> =  $48.75 - $30 = $18.75.</em>

Let us apply slope-intercept form y=mx+b to get the equation.

Total cost of x number of tickets at the rate $1.50 each ticket = 1.50x.

To<em>tal cost of fair = Total cost of x number of tickets + Fair admission charge.</em>

<h3>b) y = 1.50x + 18.75.</h3>

4 0
3 years ago
Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. Th
dexar [7]

Answer:

The labor fee is $14.25, each quart of oil costs $2.25.

Step-by-step explanation:

Let $x be thee price of each quart of oil and $y be a flat fee for labor.

1. If the oil change for one car required 5 quarts of oil, then these 5 quarts cost $5x and together with a flat fee for labor it cost $25.50. Thus,

5x+y=25.50.

2. If the oil change for another car required 7 quarts of oil, then these 7 quarts cost $7x and together with a flat fee for labor it cost $30.00. Thus,

7x+y=30.00.

3. Subtract from the second equation the first one, then

7x+y-(5x+y)=30.00-25.50,\\ \\7x+y-5x-y=4.50,\\ \\2x=4.50,\\ \\x=\$2.25.

Substitute it into the first equation:

5\cdot 2.25+y=25.50,\\ \\y=25.50-11.25,\\ \\y=\$14.25.

The labor fee is $14.25, each quart of oil costs $2.25.

6 0
2 years ago
How many times longer is 1 cm than 0.00004 cm
podryga [215]

Answer:

To convert centimeters to meters, multiply the centimeter value by 0.01 or divide by 100. For example, to find out how many meters there are in 10 centimeters, multiply 10 by 0.01, that makes 0.1 meter in 10 cm. What is a Centimeter? Centimeter (centimetre) is a metric system length unit. 1 cm = 0.01 m.

Step-by-step explanation:

5 0
2 years ago
Aubrey says that the product of 104 and 10–2 is 10–8. Is she correct? If not, explain why.
konstantin123 [22]

Answer:

C

Step-by-step explanation:

No, she multiplied the exponents instead of adding them.

6 0
3 years ago
Read 2 more answers
A certain university has 18 vehicles available for use by faculty and staff. Five of these are vans and 13 are cars. On a partic
Reil [10]

Answer:

a

 P(E) = 0.278

b

  P(F |E) = 0.2353

c

P(E and  F) = 0.0654

Step-by-step explanation:

The number of vehicles available is N  =  18

The number of vans is k = 5

The number of cars is n = 13

Generally P(E) is mathematically represented as

P(E) =  \frac{k}{N}

=>    P(E) =  \frac{5}{18}

=>    P(E) = 0.278

Generally P(F| E)  means the probability that the second vehicle assigned is  a van given that the first one selected is a van this mathematically calculated as

      P(F |E) =  \frac{5 -1}{18-1}

        P(F |E) =  \frac{4}{17}

        P(F |E) = 0.2353

Generally  P(F | E) is also mathematically represented as

      P(F | E) = \frac{P(E and F)}{P(E)}

=>   P(E and  F) =P(E) * P(F | E)

=>   P(E and  F) = 0.278  * 0.2353

=>P(E and  F) = 0.0654

5 0
3 years ago
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