What is 6 divided by 1/2 equal

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

Savatey [412]

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

$581.25$

6 0

3 years ago

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Marie wants to know the most popular car for parents. She plans to survey the people entering the mall from 10:00 a.m. to 11:00

Andreyy89

Answer:

C. Marie should make sure she surveys both the fathers and mothers.

3 0

2 years ago

A used car is priced at $2,695. If you borrow the money for the car, your payments will be $122 a month for 30 months. How much

Studentka2010 [4]

Answer: $965

Step-by-step explanation:

The used car is priced at $2,695.

If you borrow the money for the car, your payments will be $122 a month for 30 months. This means that the total amount of money that you would have paid at the end of 30 months at a rate of $122 per month is the amount paid per month multiplied by the total number of months. It becomes

Total payment = 122×30 = $3660

This means that you ended up paying higher than you would have paid if you paid cash.

Amount that you would have saved = amount paid over 30 months - cost of the car

Amount that you would have saved

= 3660 - 2695 = $965

7 0

3 years ago

The average temperature change in degrees Fahrenheit per hour if the temperature fell 22degree Fahrenheit in 10 hours

Nonamiya [84]

Answer:

2.2 degrees per hour

Step-by-step explanation:

22/10=2.2

4 0

3 years ago

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On a January day in Michigan, the low temperature was 5 degrees colder than 2℉ and the high temperature was 5 degrees warmer tha

aliya0001 [1]

Answer:

-3 was the low and the high temp. is 7

Step-by-step explanation:

8 0

3 years ago