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2 years ago

The 700th term in a geometric sequence is 20. If the common ratio of the sequence is 0.25, what is the 699th term?

2 answers:

6 0

There are two ways to solve this problem. First, you can use the derived formula for geometric sequence which can be used to find any nth term of the sequence. Or, we can use the second easier way. Since we are given with the 700th term, and the asked is the 699th term, then that means,

(699th term)*(Common Ratio) = 700th term
699th term = 700th term/Common Ratio = 20/0.25 = 80

Jlenok [28]2 years ago

6 0

Answer:

Step-by-step explanation:

(699th term)*(Common Ratio) = 700th term

699th term = 700th term/Common Ratio = 20/0.25 = 80

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The closing price (in dollars) per share of stock of tempco electronics on the tth day it was traded is approximated by p(t) = 2

Vaselesa [24]

solution:

The closing price (in dollars) per share of stock of Tempco Electronics on the tth day it was

traded is approximated by

P(t) = 20 + 12 sin πt/30 − 6 sin πt/15 + 4 sin πt/10 − 3 sin 2πt/15 (0 ≤ t ≤ 24)

where t = 0 corresponds to the time the stock was first listed on a major stock exchange.

What was the rate of change of the stock's price at the close of the 15th day of trading?

P'(t) = 12(cos πt/30) - 6 (cos πt/15) + 4(cos πt/10) - 3(cos 2πt/15)

t = 15

P'(t) = 12(cos 15π/30) - 6 (cos 15π/15) + 4(cos 15π/10) - 3(cos 30π/15)

P'(t) = 12(cos π/2) - 6 (cos π) + 4(cos 3π/2) - 3(cos 2π)

P'(t) = 12(0) - 6(-1) + 4(0) - 3(1) = 6 - 3

P'(t) = $3 per day RATE OF CHANGE

the closing price on that day

P(t) = 20 + 12 sin πt/30 − 6 sin πt/15 + 4 sin πt/10 − 3 sin 2πt/15

t = 15

P(t) = 20 + 12 sin 15π/30 − 6 sin 15π/15 + 4 sin 15π/10 − 3 sin 30πt/15

P(t) = 20 + 12 sin π/2 − 6 sin π + 4 sin 3π/2 − 3 sin 2π

P(t) = 20 + 12(1) − 6(0) + 4(-1) − 3(0) = 20 + 12 - 0 - 4 - 0 = 20 + 12 - 4

P(t) = $28 per share close price

4 0

2 years ago

You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week

aliya0001 [1]

Answer:

$q = -6p + 104$

Step-by-step explanation:

Linear function:

A linear function has the following format:

$q = mp + b$

In which m is the slope and b is the q-intercept.

One week you charged $4 per guest and averaged 80 guests per night. The next week you charged $10 per guest and averaged 44 guests per night.

This means that we have these following points: (4,80), (10,44).

Finding the slope:

With a pair of points, the slope is given by the change in q divided by the change in p.

Change in q: 44 - 80 = -36

Change in p: 10 - 4 = 6

Slope: $m = \frac{-36}{6} = -6$

$q = -6p + b$

Finding b:

We replace one of the points. Replacing (4,80).

$q = -6p + b$

$80 = -6*4 + b$

$b = 104$

$q = -6p + 104$

7 0

2 years ago

g Steel used for water pipelines is often coated on the inside with cement mortar to prevent corrosion. In a study of the mortar

aleksandr82 [10.1K]

Answer:

$P(X$

And we can find this probability using the z table and we got:

$P(z$

Step-by-step explanation:

Let X the random variable that represent the thickness of a population, and for this case we know the distribution for X is given by:

$X \sim N(0.635,0.082)$

Where $\mu=0.635$ and $\sigma=0.032$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the z table and we got:

$P(z$

7 0

2 years ago

A motorboat covers the distance from one pier to the other pier in 4 hours and the way back in 5 hours. What is the speed of the

stiv31 [10]

Speed of current ------ y km/h

distance with the current = 4(x+y) 
distance against the current = 5(x-y) 

we know that 3.5(x+y) = 70 
x+y = 20 

but 4(x+y) = 4(20) = 80 
then 5(x-y) = 80 
x-y = 16 

x+y=20 
x-y=16 
add them 
2x = 36 
x = 18 , then y = 2

5 0

2 years ago

the trinomial x2 bx c factors to (x m)(x n). if b is negative and c is positive, what must be true about m and n?

galina1969 [7]

For c to be positive, and for b to be negative, m must be negative and n must be negative.

X^2 - bx + c = (x - m)(x - n).

c is the product of m and n. If both m and n are positive, c would be positive. However b is the sum of m and n, therefore to make b negative, both m and n must be negative to ensure that the product of m and n is positive

7 0

2 years ago

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