1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Pie
3 years ago
12

Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below. 18.75 93.75 581.25 145.3125

Mathematics
2 answers:
Rainbow [258]3 years ago
7 0
It's a geometric sequence.

300, 150, 75,... \\ \\ a_1=300 \\ r=\frac{a_2}{a_1}=\frac{150}{300}=\frac{1}{2} \\ \\ S_n=\frac{a_1 (1-r^n)}{1-r} \\ \Downarrow \\ S_5=\frac{300(1-(\frac{1}{2})^5)}{1-\frac{1}{2}}=\frac{300(1-\frac{1}{32})}{\frac{1}{2}}=\frac{300 \times \frac{31}{32}}{\frac{1}{2}}=\frac{75 \times \frac{31}{8}}{\frac{1}{2}}=\frac{\frac{2325}{8}}{\frac{1}{2}}=\frac{2325}{8} \times 2= \\
=\frac{2325}{4}=581 \frac{1}{4}=581.25

The answer is 581.25.
Savatey [412]3 years ago
6 0

we have that

300 + 150 + 75 +...

Let

a1=300\\ a2=150\\ a3=75

we know that

\frac{a2}{a1} =\frac{150}{300} \\\\ \frac{a2}{a1}=0.5 \\ \\ a2=a1*0.50

\frac{a3}{a2} =\frac{75}{150} \\\\ \frac{a3}{a2}=0.5 \\ \\ a3=a2*0.50

so

a(n+1)=an*0.50

Is a geometric sequence

Find the value of a4

a(4)=a3*0.50

a(4)=75*0.50

a(4)=37.5

Find the value of a5

a(5)=a4*0.50

a(5)=37.5*0.50

a(5)=18.75

Find S5

S5=a1+a2+a3+a4+a5\\ S5=300+150+75+37.5+18.75\\ S5=581.25

therefore

the answer is

581.25

Alternative Method

Applying the formula

S_n=\frac{a_1 (1-r^n)}{1-r} \\\\a_1=300 \\ r=\frac{1}{2}\\\\ S_5=\frac{300(1-(\frac{1}{2})^5)}{1-\frac{1}{2}}\\\\=\frac{300(1-\frac{1}{32})}{\frac{1}{2}}\\\\=\frac{300 \times \frac{31}{32}}{\frac{1}{2}}\\\\=\frac{75 \times \frac{31}{8}}{\frac{1}{2}}\\\\=\frac{\frac{2325}{8}}{\frac{1}{2}}\\\\=\frac{2325}{8} \times 2\\\\=\frac{2325}{4}\\\\=581 \frac{1}{4}\\\\=581.25

therefore

the answer is

581.25

You might be interested in
To better understand how husbands and wives feel about their finances, Money Magazine conducted a national poll of 1010 married
Xelga [282]

Answer:

  • a. See the table below
  • b. See the table below
  • c. 0.548
  • d. 0.576
  • e. 0.534
  • f) i) 0.201, ii) 0.208

Explanation:

First, order the information provided:

Table: "Who is better at getting deals?"

                                       Who Is Better?

Respondent      I Am        My Spouse     We Are Equal

Husband           278             127                     102

Wife                   290            111                       102

<u>a. Develop a joint probability table and use it to answer the following questions. </u>

The<em> joint probability table</em> shows the same information but as proportions. Hence, you must divide each number of the table by the total number of people in the set of responses.

1. Number of responses: 278 + 127 + 102 + 290 + 111 + 102 = 1,010.

2. Calculate each proportion:

  • 278/1,010 = 0.275
  • 127/1,010 = 0.126
  • 102/1,010 = 0.101
  • 290/1,010 = 0.287
  • 111/1,010 = 0.110
  • 102/1,010 = 0.101

3. Construct the table with those numbers:

<em>Joint probability table</em>:

Respondent      I Am        My Spouse     We Are Equal

Husband           0.275           0.126                 0.101

Wife                   0.287           0.110                  0.101

Look what that table means: it tells that the joint probability of being a husband and responding "I am" is 0.275. And so for every cell: every cell shows the joint probability of a particular gender with a particular response.

Hence, that is why that is the joint probability table.

<u>b. Construct the marginal probabilities for Who Is Better (I Am, My Spouse, We Are Equal). Comment.</u>

The marginal probabilities are calculated for each for each row and each column of the table. They are shown at the margins, that is why they are called marginal probabilities.

For the colum "I am" it is: 0.275 + 0.287 = 0.562

Do the same for the other two colums.

For the row "Husband" it is 0.275 + 0.126 + 0.101 = 0.502. Do the same for the row "Wife".

Table<em> Marginal probabilities</em>:

Respondent      I Am        My Spouse     We Are Equal     Total

Husband           0.275           0.126                 0.101             0.502

Wife                   0.287           0.110                  0.101             0.498

Total                 0.562           0.236                0.202             1.000

Note that when you add the marginal probabilities of the each total, either for the colums or for the rows, you get 1. Which is always true for the marginal probabilities.

<u>c. Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife? </u>

For this you use conditional probability.

You want to determine the probability of the response be " I am" given that the respondent is a "Husband".

Using conditional probability:

  • P ( "I am" / "Husband") = P ("I am" ∩ "Husband) / P("Husband")

  • P ("I am" ∩ "Husband) = 0.275 (from the intersection of the column "I am" and the row "Husband)

  • P("Husband") = 0.502 (from the total of the row "Husband")

  • P ("I am" ∩ "Husband) / P("Husband") = 0.275 / 0.502 = 0.548

<u>d. Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband?</u>

You want to determine the probability of the response being "I am" given that the respondent is a "Wife", for which you use again the formula for conditional probability:

  • P ("I am" / "Wife") = P ("I am" ∩ "Wife") / P ("Wife")

  • P ("I am" / "Wife") = 0.287 / 0.498

  • P ("I am" / "Wife") = 0.576

<u>e. Given a response "My spouse," is better at getting deals, what is the probability that the response came from a husband?</u>

You want to determine: P ("Husband" / "My spouse")

Using the formula of conditional probability:

  • P("Husband" / "My spouse") = P("Husband" ∩ "My spouse")/P("My spouse")

  • P("Husband" / "My spouse") = 0.126/0.236

  • P("Husband" / "My spouse") = 0.534

<u>f. Given a response "We are equal" what is the probability that the response came from a husband? What is the probability that the response came from a wife?</u>

<u>What is the probability that the response came from a husband?</u>

  • P("Husband" / "We are equal") = P("Husband" ∩ "We are equal" / P ("We are equal")

  • P("Husband" / "We are equal") = 0.101 / 0.502 = 0.201

<u>What is the probability that the response came from a wife:</u>

  • P("Wife") / "We are equal") = P("Wife" ∩ "We are equal") / P("We are equal")

  • P("Wife") / "We are equal") = 0.101 / 0.498 = 0.208
6 0
3 years ago
Part D<br> What is the measurement of angle C?
NeX [460]

Step-by-step explanation:

I think we are missing some information (angle F or B or a side length would be great).

but just the right angles are not enough to calculate specific numbers. they would depend on the angle F or e.g. the side length of AB.

without any further information F and AB can be freely changed without changing the known facts, but it changes also C, B, G

so, all I can say is C = 180 - B.

and that G = B.

5 0
3 years ago
Find the length of arc XY and <br> find the measure of arc XY
max2010maxim [7]

Answer:

the answer is 65

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please help !!! I’ll mark you as brainliest if correct
kozerog [31]

Answer:

10 seconds

Step-by-step explanation:

we are given the height (s) which is 1600ft. and the formula—where t is time in seconds— t= 1/4\sqrt{s}, so we can plug 1600ft in for s and solve:

t= 1/4\sqrt{1600}

t= 1/4(40)

t= 10 seconds

5 0
3 years ago
What is the schumer box?
ollegr [7]

Description
The Schumer box is a summary of the costs of a credit card in the United States. It is named after Chuck Schumer, then New York congressman who was responsible for the legislation requiring that terms of credit cards be clearly outlined in any promotional material. Hope it helps
5 0
2 years ago
Other questions:
  • The capacity of a beaker is 150 mL. How many beakers can be filled from a 4L container?
    13·1 answer
  • There are 20 parrots at the animal sanctuary. Their population is increasing at a rate of 15% per year. There are also 24 snakes
    8·1 answer
  • Please help me and answer
    14·2 answers
  • Classify a triangle with angle measurements of 40∘, 30∘,110∘
    9·1 answer
  • The calculated average of a data set best describes which of the following? (4 points) Group of answer choices Mean Median Mode
    14·1 answer
  • Help meeeeeeeeee
    14·1 answer
  • Can someone answer the last two questions
    14·2 answers
  • What is the simple interest on $40,000 for 10 years at 12%?
    10·2 answers
  • Find the range of the data set 7,510,9,15,12,6,9,7,10
    15·2 answers
  • Suppose that \Join is an operation defined by x Join y = (x+2)(y-3). What is (t) \Join (t+2) - (t+1) \Join (t+1)?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!