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3 years ago

Predict the number of times you would flip a tails and then roll a 4 if you did the expirement 96 times

Mathematics

1 answer:

GaryK [48]3 years ago

3 0

96/2 for tails and 96/6 for rolling 4 I assume

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Identify whether the series sigma notation infinity i=1 15(4)^i-1 is a convergent or divergent geometric series and find the sum

const2013 [10]

Answer: The correct option is

(d) This is a divergent geometric series. The sum cannot be found.

Step-by-step explanation: The given infinite geometric series is

$S=\sum_{i=1}^{\infty}15(4)^{i-1}.$

We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.

We have the D' Alembert's ratio test, states as follows:

Let, $\sum_{i=1}^{\infty}a_i$ is an infinite series, with complex coefficients $a_i$ and we consider the following limit:

$L=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}.$

Then, the series will be convergent if L < 1 and divergent if L > 1.

For the given series, we have

$a_i=15(4)^{i-1},\\\\a_{i+1}=15(4)^i.$

So, the limit is given by

$L\\\\\\=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i-1}}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i}4^{-1}}\\\\\\=\dfrac{1}{4^{-1}}\\\\=4>1.$

Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.

Thuds, (d) is the correct option.

7 0

3 years ago

Read 2 more answers

1+(-2-5)^2+(14-17)×4 please answer

hjlf

When you simplify the expression you get 38. Hope this helps.

Answer = 38.

6 0

3 years ago

Use the line graph to solve.

Ivahew [28]

0.10 m of difference in water levels between Week 2 and Week 4

5 0

3 years ago

Robert has 60 feet of fence to make a dog pen. He will use the house for one side of the pen, as shown above. What dimensions wi

irinina [24]

The formula for an area of a regular parallelogram is:

A = l * w

Where,

l = length

w = width

We are given that the total measurement of fence is only 60 feet and one side of the house is used as one side of the pen. Therefore,

l + 2 w = 60

or simplifying to make an explicit expression for one variable, say l:

l = 60 – 2 w

Substituting to the 1st equation:

A = (60 – 2 w) * w

A = 60 w – 2 w^2

The maxima are obtained by getting the 1st derivative then equating dA/dw = 0:

dA/dw = 60 – 4 w

60 – 4 w = 0

4 w = 60

w = 15

Since l = 60 - 2w

l = 60 – 30

l = 30

Therefore the dimension that will make the largest pen is 15 ft by 30 ft.

ANSWER: C

7 0

3 years ago

Write the equation of the line, in POINT-SLOPE FORM, through the points (-1, 5) and (6,2).

docker41 [41]

Answer:

Step-by-step explanation:

y-5/x+1 = -3/7

7(y-5)=-3(x+1)

7y-35=-3x-3

7y+3x-32=0

8 0

3 years ago