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3 years ago

What is the explicit formula for this sequence? 5, 10, 20, 40 , 80, 160

Mathematics

1 answer:

8_murik_8 [283]3 years ago

4 0

Answer:

Multiply by two. Formula could be x * 2

Step-by-step explanation:

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Louann is shopping at a Columbus day sale. She spent $276.66 on a new Michael Kors handbag. If it was on sale for 25% off the re

cupoosta [38]

I'm taking a guess that regular price would be $1,106.64 plus the 6% tax

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3 years ago

On a trip, Duke encounters some road construction that slows him down. While he is able to go 60 mph on the highway and 40 mph t

natulia [17]

Answer:

Time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

Step-by-step explanation:

Speed by which Duke travels a distance on highway $d_1$ = 60 mph

Let the time taken to travel on highway = $t_1$ hours

Distance traveled = $60t_1$ miles

Speed in the city = 40 mph

Let the time taken = $t_2$ hours

Distance traveled in the city = $40t_2$ miles

Speed on the construction = 20 mph

Let the time spend on the construction = $t_3$ hours

Distance traveled on the construction = $20t_3$ miles

Since, total distance covered = 380 miles

$d_1+d_2+d_3=60t_1+40t_2+20t_3$

He spends one half the time on the highway as he does on the construction,

$t_3=2t_1$

Total time spent in the trip = 11 hours

Therefore, $t_1+t_2+t_3=11$

$t_1+t_2+2t_1=11$

$t_2=11-3t_1$

From equation (1),

$60t_1+40(11-3t_1)+20(2t_1)=380$

$60t_1-120t_1+40t_1+440=380$

$440-20t_1=380$

$20t_1=440-380$

$t_1=\frac{60}{20}$

$t_1=3$ hours

$t_2=11-3t_1=2$ hours

$t_3=2t_1=6$ hours

Therefore, time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

3 0

3 years ago

What is the second term in the binomial expansion of (2r-3s)12?

Reptile [31]

$(a+b)^n=\displaystyle\sum_{k=0}^n\binom nka^{n-k}b^k$

where $\dbinom nk=\dfrac{n!}{k!(n-k)!}$ . The second term of the expansion occurs when $k=1$ .

So the second term of the expansion of $(2r-3s)^{12}$ is

$\dbinom{12}1(2r)^{12-1}(-3s)^1=12(2r)^{11}(-3s)=-73728r^{11}s$

5 0

3 years ago

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The cost of renting a fishing boat is $25 per hour for the first 7 hours, $10 per hour for the next 10 hours, and $5 per hour fo

yKpoI14uk [10]

Answer: $340

Step-by-step explanation:

To identify the cost of renting the boat for 30 hours, breakdown the 30hours into specific renting hours

i.e 30 hours = (7 hours + 10 hours + 13 hours)

Then calculate each of the renting cost based on the hour breakdown given above

- Since the Cost of renting a fishing boat is $25 per hour for the first 7 hours, then (25 x 7 hours = $175)

- For the $10 per hour for the next 10 hours, then (10 x 10 hours = $100)

- and for $5 per hour for any additional hours. (5 x 13 additional hours = $65)

Now, sum up all of the cost of the hourly breakdown

i.e 30 hours = (7 hours + 10 hours + 13 hours)

= $175 + $100 + $65

= $340

Thus, the cost of renting the boat for 30 hours is $340

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3 years ago

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Elizabeth lives in San Francisco and works in Mountain View. In the morning she has 3 transportation options (take a bus, a cab,

topjm [15]

There are nine possible combinations as follows: bb, bc, bt, cb, cc, ct, tb, tc, tt, each having a probability of 1/9. The four combinations with a cab exactly one time are: bc, cb, ct, tc. Therefore the probability that she'll use a cab exactly one time is: 4/9.

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3 years ago

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