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qwelly [4]
4 years ago
12

What is the sum of the geometric sequence 3,12,48... if there are 8 terms?

Mathematics
1 answer:
s344n2d4d5 [400]4 years ago
6 0

Answer:

  C)  65,535

Step-by-step explanation:

You can add up the 8 terms ...

  3, 12, 48, 192, 768, 3072, 12288, 49152

to find their sum is 65535.

_____

<em>Estimating</em>

Knowing the last term (49152) allows you to make the correct choice, since the sum will be more than that and less than double that.

_____

<em>Using the formula</em>

You know the formula for the sum of a geometric sequence is ...

  S = a1(r^n -1)/(r -1)

where a1 is the first term (3), r is the common ratio (4), and n is the number of terms (8).

Filling in the values, you find the sum is ...

  S = 3(4^8 -1)/(4-1) = 4^8 -1 = 65535

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Adela drinks 28 glasses of water per week. How many glasses does she drink per day?
USPshnik [31]

Answer:

Adela drinks 4 glasses of water per day.

Step-by-step explanation:

Since there are 7 days in a week, you want to divide, 28 / 7, which will give you 4 as a result.

6 0
3 years ago
Read 2 more answers
Write the equation of the line that passes through the two points:<br> (-4, 11) and (2,-4)
snow_tiger [21]

Answer:

<em>y</em>= -\frac{5}{2}<em>x</em>+1

Step-by-step explanation:

Utilize the formula of \frac{y2-y1}{x2-x1} to find the distance between two points, or in this case, the equation of the line that passes through two points.

<u><em>Applying the given points to identify the slope</em></u>

1. Plug the coordinates into the <em>y</em> and <em>x</em> values. \frac{-4-11}{2+4}=-\frac{15}{6}.

1.5. Simplify; divide both the numerator and the denominator by 3. -\frac{5}{2}.

<u><em>Applying slope and a point to find the y-intercept of the equation of a line</em></u>

1. Utilize the formula of <em>y=mx</em>. Though this sounds strange, morph the sign of equality into subtraction.

1.5. Result: <em>y-mx</em>

2. Do this for both points.

First point: (-4,11)

<em>y-mx</em>

11 + \frac{5}{2} (-4)

11 + -10 (11-10)

1

Plug the result and the slope into <em>y=mx+b</em> to find the slope of the line.

Result: <em>y</em>=-\frac{5}{2}<em>x</em>+1.

<u><em>Check your answer to confirm that the value of y is true for both points</em></u>

1. Do the same thing you did with the first point, but use the second point this time.

2.

<em>y-mx</em>

-4 + \frac{5}{2} (2)

-4 + 5

1

Plug the result and the slope into <em>y=mx+b</em> to find the slope of the line.

Result: <em>y</em>=-\frac{5}{2}<em>x</em>+1. <em>Identical to point one's result.</em>

<em></em>

In conclusion, both of the results are the same. Therefore, the equation of the line must be <em>y=-</em>\frac{5}{2}<em>x+1.</em>

3 0
4 years ago
Based on the output when testing to see if the population mean heart rate of UK students is not equal to 80, identify the follow
AleksAgata [21]

Answer:

Step-by-step explanation:

a)  H_o: mu =80\\H_a: mu not equals 80\\

b) Sample mean is the average of sample

c) std deviation of the sample

d) std dev/sq rt n

e) (sample mean - mu)/std error

f) p value = prob with test statistic

g) If p < alpha, reject H0.

h) If rejected, there is evidence that significant difference between population mean and sample mean.

8 0
3 years ago
I have no clue.. HELP
hram777 [196]
Imagine you covered the outer part of the wheel with paint. Then you rolled the wheel one complete revolution. The paint on the wheel would transfer to the flat ground making a straight line. The length of this straight line is exactly equal to the distance around the circle (aka circumference)

Let's find the circumference

C = 2*pi*r
C = 2*pi*14
C = 28pi

The distance around the circle is exactly 28pi inches. 
If we use pi = 3.14, which is an approximation of pi, then that approximates to 28*pi = 28*3.14 = 87.92

So one revolution corresponds to traveling 87.92 inches approximately

We want to travel 440 inches. The question is: how many revolutions do we need to go in order to achieve this goal?

Let k = number of revolutions needed to travel 440 inches

1 revolution = 87.92 inches traveled
k revolutions = k*87.92 inches traveled

Set the expressions k*87.92 and 440 equal to each other and solve 

k*87.92 = 440
k*87.92/87.92 = 440/87.92
k = 5.0045495 ... this is approximate

So it takes about 5 revolutions to travel 440 inches. We'll need a bit over 5 to make sure we get to 440. 

Final Answer: Choice B) 5 rotations

3 0
3 years ago
Reduce improper 24/5
iogann1982 [59]
The answer is 4 4/5
6 0
3 years ago
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