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3 years ago

Express the series using sigma notation. 4 + 16 + 64 + 256 + 1,024

Mathematics

2 answers:

ch4aika [34]3 years ago

7 0

Answer:

E 4(4)^n-1

n-1

Step-by-step explanation:

The series is being multiplied by 4 each time making it a geometric series. Which means that the common ratio is 4, r=4.

Secondly, you can determine the value of K by counting the number of numbers in the series. In this case there are 5, k=5.

Finally, the last value we need to find is a1 which is found by looking at the first value in the set, a1=4.

Once we have all of these values, we put them into the finite Sigma Notation equation.

E a1(r)^n-1

n-1

The values go where their equivalents are, and then we have our answer:

E 4(4)^n-1

n-1

Hatshy [7]3 years ago

3 0

Answer:

EASSYYY

Step-by-step explanation:

1364

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ohn is interested in purchasing a multi-office building containing five offices. The current owner provides the following probab

Galina-37 [17]

Answer:

$28,875

Step-by-step explanation:

The given table is:

$\left|\begin{array}{c|cccccc}$Number of Lease Offices&0&1&2&3&4&5\\$Probability&5/32&3/16&3/32&1/4&9/32&1/32\end{array}\right|$

The expected probability is derived using the formula: $\sum_{i=0}^{5}x_iP(x_i)$

Therefore, for the given distribution,

Expected Probability

$=(0*\frac{5}{32})+ (1*\frac{3}{16})+ (2*\frac{3}{32})+ (3*\frac{1}{4})+ (4*\frac{9}{32})+ (5*\frac{1}{32})\\=2.40625$

If each yearly lease is $12,000

The Expected Yearly Lease for the Whole Building=2.40625 X 12000

=$28,875

4 0

3 years ago

Mr. Ramsey has 14 girls and 10 boys in her class she will randomly create one group of three students to work on a project what

Mrrafil [7]

The probability that the group will be all girls is 91/506

<h3 /><h3>Number of ways of selecting 3 students out of the total</h3>

Since there are 14 girls and 10 boys, the total number of students is 10 + 14 = 24.

So, the total number of ways of selecting 3 students from 24 is ²⁴C₃.

<h3 /><h3>Number of ways of selecting 3 girls out of 14</h3>

Also, the total number of ways of selecting a group of 3 of all girls out of the 14 girls is ¹⁴C₃ = 14

<h3 /><h3>Probability of all girls</h3>

So, the probability of selecting a group of 3 of all girls = number of ways of selecting 3 girls/total number of selections = ¹⁴C₃ ÷ ²⁴C₃

= 14 × 13 × 12/3! ÷ 24 × 23 × 22/3!

= 7 × 13/23 × 22

= 91/506

So, the probability that the group will be all girls is 91/506

Learn more about probability here:

brainly.com/question/24756209

4 0

3 years ago

Which points are solutions to the system of inequalities shown below check all that apply y>x+1

Arte-miy333 [17]

The points which satisfy the inequalities in discuss are; Choices D (7,10) and F(8,17).

<h3>Which points omg the answer choices satisfy the system of inequalities?</h3>

It follows from the inequality; x > 5.

Also, substituting 5 for x in; y < 2(x); we have;

y < 10.

Hence, the points which satisfy the inequalities are; (8,17) and (7,10).