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3 years ago

What is the sum of the first 7 terms of the series −4+8−16+32−... ?

1 answer:

5 0

-4 + 8 = 4;
4 - 16 = -12;
-12 + 32 = 20;
20 - 64 = -44;
-44 + 128 = 84;
84 - 256 = -172.

The sum of the first 7 terms in this series is -172.

I hope this helps!

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An ancient Chinese candle clock tells the amount of time that has passed by the amount of wax that has been melted off the candl

maxonik [38]

Answer:

$Time = 560\ mins$

Step-by-step explanation:

Given

$Candles = 2$ --- candles melted

$Divisions = 12$

$Time = 4\ hrs$ --- time to melt

Required

The time since the first was lit

If 1 candle melts in 4 hours, 2 candles will melt in 8 hours.

i.e.

$x = Candles * Time$

$x = 2 * 4hrs$

$x = 8hrs$

For the 3rd candle that has melted, 4 inches

First, calculate the fraction that melt

$Fraction = \frac{Melt}{Division}$

$Fraction = \frac{4}{12}$

$Fraction = \frac{1}{3}$

The time to melt is:

$y = Fraction * Time$

$y= 4 * \frac{1}{3}$

$y= \frac{4}{3}hrs$

So, the required time is:

$Time = x + y$

$Time = 8hrs + \frac{4}{3}hrs$

Convert to minutes

$Time = 8*60mins + \frac{4}{3}*60mins$

$Time = 480mins + 80mins$

$Time = 560\ mins$

4 0

2 years ago

Can someone help me with this question please.

Daniel [21]

For part A. 0.85

For part b. 11.9

Explain

Cost of each track in album A= total cost downloading album a/ total number of track

The problem give us a has 11 trackers and the total cost of download is 9.35 pounds

9.35/11

= 0.85

Now we are given each track cost in album b cost the same as track on A

Cost of each track in album B is 0.85

Now we are given if Jane download album B , B will be 14 tracks

Total cost of downloading is album B= number of tracks in album Bx cost of each track in album B

14x0.85 pound

= 11.9

7 0

3 years ago

Three brothers, Justin, Jared, and Jonathan decided to buy a present for their mom's birthday. Justin gave decided to spend 1/4

iVinArrow [24]

I believe that, if there are three brothers and each invested the same exact money to make a total of $33.00, each brother would have invested $11.

Jonathan's was different, as he invested 2/5. 11 divided by 2 is 5.5, in which 5.5*11 would equal 27.50.
The rest was simply their denominator times $11.
Jared had $33 dollars before the investment, and Justin has $44.

7 0

2 years ago

Describe the dimensions of two different prisms that each have a volume is 2,400 cubic centimeters

Phantasy [73]

One prism with a volume of 2400 might have a rectangular base with a length of 4 and a width of 5, as well as a height of 120.

V = l x w x h
V = 4 x 5 x 120
V = 2400

This prism would essentially look like a really tall rectangle, since the height is such a large number. I wouldn't accurately represent the units on graph paper, if I were you. Just label the sides with the numbers I gave you.

Another prism with a volume of 2400 might be a rectangular prism with a length of 8, a width of 10, and a height of 30.

V = l x w x h
V= 8 x 10 x 30
V = 2400

This would also be a tall rectangle, although it isn't as tall. Keep in mind that l x w x h is only the volume formula for a rectangular prism. I only used rectangular prisms because they would be the easiest for this example. A triangular prism has a different volume formula.

3 0

3 years ago

An eccentric philanthropist undertakes to give away $100,000. He is eccentric because he insists that each of his gifts be a num

gavmur [86]

Answer:

Step-by-step explanation:

An eccentric philanthropist undertakes to give away $100,000. He is eccentric because he insists that each of his gifts be a number of dollars that is a power of two, and he will give no more than one gift of any amount. How does he distribute the money?

To solve this problem, we will simply write 1,00,000 in base 2.

2^17 gives 131072, 2^16 gives 65536.

So, the first gift is 65536, we then need to repeat this process for 34,464 ((100,000-65536 = 34,464), to get all gifts in succession.

6 gifts in all: one each of $32, $128, $512, $1024, $32768, and $65536.

3 0

3 years ago