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3 years ago

Find the sum of this infinite geometric series where a1=0.3 and r=0.1

Mathematics

1 answer:

ratelena [41]3 years ago

8 0

Answer:

1/3

Step-by-step explanation:

The formula for computing the sum of an infinite geometric series is

$S=\frac{a_1}{1-r}$ where r is between -1 and 1 and $r$ is the common ratio, and $a_1$ is the first term of the series.

So let's plug in:

$S=\frac{0.3}{1-0.1}$

$S=\frac{0.3}{0.9}$

$S=\frac{3}{9}$ I multiplied bottom and top by 10.

$S=\frac{1}{3}$ I divided top and bottom by 3.

The sum is 1/3.

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A number cube with faces labeled from 1 to 6 will be rolled once.

tresset_1 [31]

Question:

A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.

Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of rolling a number greater than 2.

If there is more than one element in the set, separate them with commas.

Answer:

$S = \{1,2,3,4,5,6\}$

$Greater2 = \{3,4,5,6\}$

Step-by-step explanation:

Given

A roll of a 6 sided number cube

Solving (a): The sample space

This implies that we list out all number on the number cube.

So:

$S = \{1,2,3,4,5,6\}$

Solving (b): Outcomes greater than 2

This implies that we list out all number on the number cube greater than 2 i.e. 3 to 6.

So:

$Greater2 = \{3,4,5,6\}$

3 0

3 years ago

A study of consumer smoking habits includes A people in the 18-22 age bracket (B of whom smoke), C people in the 23-30 age brack

madreJ [45]

The correct question is:

A study of consumer smoking habits includes 167 people in the 18-22 age bracket (59 of whom smoke), 148 people in the 23-30 age bracket (31 of whom smoke), and 85 people in the 31-40 age bracket (23 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes

Answer:

The probability of getting someone who is age 23-30 or smokes = 0.575

Step-by-step explanation:

We are given;

Number consumers of age 18 - 22 = 167

Number of consumers of ages 22 - 30 = 148

Number of consumers of ages 31 - 40 = 85

Thus,total number of consumers in the survey = 167 + 148 + 85 = 400

We are also given;

Number consumers of age 18 - 22 who smoke = 59

Number of consumers of ages 22 - 30 who smoke = 31

Number of consumers of ages 31 - 40 who smoke = 23

Total number of people who smoke = 59 + 31 + 23 = 113

Let event A = someone of age 23-30 and event B = someone who smokes. Thus;

P(A) = 148/400

P(B) = 113/400

P(A & B) = 31/400

Now, from addition rule in sets which is given by;

P(A or B) = P (A) + P (B) – P (A and B)

We can now solve the question.

Thus;

P(A or B) = (148/400) + (113/400) - (31/400)

P(A or B) = 230/400 = 0.575

4 0

3 years ago

What are some ways to describe the relationship between sets of numbers?

Tamiku [17]

Even numbers odd numbers prime numbers composite numbers (I tried)

5 0

3 years ago

In right △ABC , the right angle is at C, m∠A=30∘ , and AC=5√ 5 units.

Makovka662 [10]

Answer:

5 $\sqrt{15}$ +5 $\sqrt{5}$

Step-by-step explanation:

The core uses the value of the Pythagorean theorem and special angles.

6 0

3 years ago

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castortr0y [4]

Answer:

1. 300

2. x-axis

3. 150

Step-by-step explanation:

3 0

3 years ago