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Julli [10]
3 years ago
8

the first term of an arithmetic sequence is -27. the common difference of the sequence is 6. What is the sum of the first 30 ter

ms
Mathematics
1 answer:
Nina [5.8K]3 years ago
4 0

Answer:

1800

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

S_{n} = \frac{n}{2} [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = - 27 and d = 6, thus

S_{30} = \frac{30}{2} [ (2 × - 27) + (29 × 6) ]

     = 15( - 54 + 174)

     = 15(120)

     = 1800

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7x 1 1/5 enter answer as a mixed number
Leno4ka [110]

The answer is

8 \frac{2}{5}

6 0
2 years ago
PLEASE HELP!! A classmate wrote the set notation for the values of the domain of a function {−5, −4, −3, −2, −1, 0} as {x | −5 ≤
vfiekz [6]
<h3>Answer: Choice B</h3>

The set notation includes all values from -5 to 0, but the domain only includes the integer values

eg: something like -1.2 is in the second set, but it is not in the set {-5,-4,-3,-2,-1}

==========================================================

Further explanation:

Let's go through the answer choices one by one

  • A. This is false because 0 does not come before -5, but instead -5 is listed first. The order -5,-4,-3,-2,-1,0 is correct meaning that -5 \le x \le 0 is the correct order as well.
  • B. This is true. A value like x = -1.2 is in the set \left\{x| -5 \le x \le 0\right\} since -1.2 is between -5 and 0; but -1.2 is not in the set {-5, -4, -3, -2, -1, 0}. So the distinction is that we're either considering integers only or all real numbers in this interval. To ensure that we only look at integers, the student would have to write \left\{x| x\in\mathbb{Z}, \ -5 \le x \le 0\right\}. The portion x \in \mathbb{Z} means "x is in the set of integers". The Z refers to the German word Zahlen, which translates to "numbers".
  • C. This is false. The student used the correct inequality signs to indicate x is -5 or larger and also 0 or smaller; basically x is between -5 and 0 inclusive of both endpoints. The "or equal to" portions indicate we are keeping the endpoints and not excluding them.
  • D. This is false. Writing -5 \ge x \ge 0 would not make any sense. This is because that compound inequality breaks down into -5 \ge x \ \text{ and } \ x \ge 0. Try to think of a number that is both smaller than -5 AND also larger than 0. It can't be done. No such number exists.
8 0
2 years ago
John runs a computer software store. Yesterday he counted 123 people who walked by the store, 56 of whom came into the store. Of
vaieri [72.5K]

Answer:

a) There is a 45.53% probability that a person who walks by the store will enter the store.

b) There is a 41.07% probability that a person who walks into the store will buy something.

c) There is a 18.70% probability that a person who walks by the store will come in and buy something.

d) There is a 58.93% probability that a person who comes into the store will buy nothing.

Step-by-step explanation:

This a probability problem.

The probability formula is given by:

P = \frac{D}{T}

In which P is the probability, D is the number of desired outcomes and T is the number of total outcomes.

The problem states that:

123 people walked by the store.

56 people came into the store.

23 bought something in the store.

(a) Estimate the probability that a person who walks by the store will enter the store.

123 people walked by the store and 56 entered the store, so T = 123, D = 56.

So

P = \frac{D}{T} = \frac{56}{123} = 0.4553

There is a 45.53% probability that a person who walks by the store will enter the store.

(b) Estimate the probability that a person who walks into the store will buy something.

56 people came into the store and 23 bought something, so T = 56, D = 23.

So

P = \frac{D}{T} = \frac{23}{56} = 0.4107

There is a 41.07% probability that a person who walks into the store will buy something.

(c) Estimate the probability that a person who walks by the store will come in and buy something.

123 people walked by the store and 23 came in and bought something, so T = 123, D = 23.

So

P = \frac{D}{T} = \frac{23}{123} = 0.1870

There is a 18.70% probability that a person who walks by the store will come in and buy something.

(d) Estimate the probability that a person who comes into the store will buy nothing.

Of the 56 people whom came into the store, 23 bought something. This means that 56-23 = 33 of them did not buy anything. So:

D = 33, T = 56

P = \frac{D}{T} = \frac{33}{56} = 0.5893

There is a 58.93% probability that a person who comes into the store will buy nothing.

8 0
3 years ago
If f(x) = x^4-x^3+x^2 and g(x)= -x^2, where x does not = 0, what is (f/g)(x)?
Korvikt [17]

For this case we have the following functions:

f (x) = x ^ 4-x ^ 3 x ^ 2\\g (x) = - x ^ 2

By definition of composition of functions we have to:(f \ g) (x) = \frac {f (x)} {g (x)}

So:

\frac {f (x)} {g (x)} = \frac {x ^ 4-x ^ 3 x ^ 2} {- x ^ 2} = \frac {x ^ 4} {- x ^ 2} +\frac {-x ^ 3} {- x ^ 2}+ \frac {x ^ 2} {- x ^ 2} =

By definition of division of powers of the same base we have to place the same base and subtract the exponents:

\frac {f (x)} {g (x)} = - x ^ 2+x-1

ANswer:

(\frac {f} {g}) (x) = - x ^ 2 +x-1

3 0
3 years ago
A gym membership is $100 sign-up fee and charges $20 a month thereafter. How much is the membership fee in a month?
trapecia [35]

Answer:

$120

Step-by-step explanation:

y = mx + b

The $100 sign up fee is a set amount, or the b value.

The $20 would be the m value since it the constant change, or the slope.

Thus, the equation would be y=20x + 100

The membership fee for 1 month would be --->

y= 20(1) +100

y= 20 + 100

y= $120

                                     

4 0
2 years ago
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