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3 years ago

Which formula can be used to sum the first n terms of a geometric sequence?

Mathematics

2 answers:

Dafna1 [17]3 years ago

8 0

Answer:

wat

Step-by-step explanation:

Anika [276]3 years ago

6 0

Answer: Choice B (the second one) is correct

Step-by-step explanation:

i memorized the formula.

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Suppose that a computer chip company has just shipped computer chips to a computer company. Unfortunately, of the chips are def

Varvara68 [4.7K]

Answer:

(a) 0.0000245

(b) 0.000025

Step-by-step explanation:

The complete question is:

Suppose that a computer chip company has just shipped 10,000 computer chips to a computer company. Unfortunately, 50 of the chips are defective. (a) Compute the probability that two randomly selected chips are defective using conditional probability. (b) There are 50 defective chips out of 10,000 shipped. The probability that the first chip randomly selected is defective is 50 /10,000 = 0.005. Compute the probability that two randomly selected chips are defective under the assumption of independent events.

Solution:

(a)

In this case we need to compute the conditional probability of selecting two defective chips, i.e. the selection of the second defective chip is dependent on the first defective chip.

The probability of selecting the first defective chip is:

$P(1D)=\frac{50}{10000}=0.005$

Now there are 9999 chips left and 49 defective chips among them.

The probability of selecting the second defective chip is:

$P(2D)=\frac{49}{9999}=0.0049$

Compute the probability that two randomly selected chips are defective using conditional probability as follows:

P (Two defective chips) $=P(1D)\times P(2D)=0.005\times 0.0049=0.0000245$

Thus, the answer is 0.0000245.

(b)

Compute the probability that two randomly selected chips are defective under the assumption of independent events as follows:

The above statement implies that the selection was done with replacement.

The probability is:

P (Two defective chips) $=P(1D)\times P(2D)$

$=\frac{50}{10000}\times \frac{50}{10000}\\\\=0.005\times 0.005\\\\=0.000025$

Thus, the probability that two randomly selected chips are defective under the assumption of independent events is 0.000025.

6 0

3 years ago

Determine whether the given sequence could be geometric, arithmetic, or neither. if possible, identify either the common ratio o

REY [17]

ARITHMETIC CHECK: A sequence is said to be arithmetic if any two consecutive terms differ by the same constant.

So, the test to check if a series is arithmetic is to compute consecutive differences, and see if they all return the same number.

If we subtract the first two terms, we have $2-4 = -2$ . If we subtract the third and second terms, we have $1-2 = -1$ .

These two differences returned two different values, so the series is not arithmetic.

GEOMETRIC CHECK: A sequence is said to be geometric if any two consecutive terms are in the same ratio.

So, the test to check if a series is geometric is to compute consecutive ratios, and see if they all return the same number.

If we divide the first two terms, we have

$\dfrac{2}{4} = \dfrac{1}{2}$

If we divide the third and second terms, we have

$\dfrac{1}{2} = \dfrac{1}{2}$

Finally, if we divide the last two terms we have

$\dfrac{\frac{1}{2}}{1} = \dfrac{1}{2}$

So, all ratios return the same number. This means that the series is geometric, and the common ratio is 1/2

7 0

4 years ago

Joe’s family has completed 60% of a trip. They have traveled 30 miles.<br> How far is the trip?

galben [10]

The full road trip is 50 miles.
Step-by-step explanation:
Given,
Distance traveled by Joe's family = 30 miles
This represents 60% of the total distance to be traveled.

5 0

3 years ago

Read 2 more answers

A bouncy ball is dropped such that the height of its first bounce is 2.75 feet and each successive bounce is 80% of the previous

Allushta [10]

Answer:

0.3 feet

Step-by-step explanation:

2.75(0.8)^x

in which x is the number of bounces after the firts bouce

bouce 12 would mean x=11

2.75(0.8)^11 = 0.2

7 0

3 years ago

Zapisz w jak najprostszej postaci:<br> a) -x-4(1-x)<br> b) 3(5x-2)-5(3-4x)<br> c) √2(3-x)-2(1-x√2)

Sonja [21]

Answer:

Step-by-step explanation:

a) -x-4(1-x) =

− 2 x −4 ( 1 − x ) .

2 x − 4

b) 3(5x-2)-5(3-4x) =

3 ⋅ (5 x − 2 ) − 5 ⋅ ( 5 − 4 x )

35 x − 31

c) √2(3-x)-2(1-x√2) =

√ 2 x ⋅ ( 3 −x ) − 2 ⋅( 1 − x √ 2 ) .

2 x √ 2 + 3 √ 2 x -√ 2 x x − 2

4 0

3 years ago