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3 years ago

Find S11 for 1 + 2 + 4 + 8 +

1 answer:

4 0

Evaluating the given sequence, it is evident that the next number is twice the number prior to it. Thus, the given is a geometric sequence with first term (a1) equal to 1 and common ratio of 2. The geometric series may be calculated by the equation,

Sn = a1 x (1 - r^n) / (1 - r)

where Sn is the sum of n terms in this case, n = 11.
Substituting the known values,

 Sn = 1 x (1 - 2^11) / (1 - 2) = 2047

Thus, S11 is 2047.

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Help please if anyone knows

larisa86 [58]

Part A
To estimate this, we should first look at our fractions and see if they can be combined to form a whole number. In this case, $\frac{3}{5}$ and $\frac{2}{3}$ equal approximately 1. We can add this "1" to the other to full gallons to estimate that the painter needs about 3 gallons.

Part B
To find the exact amount, we should first change the mixed numbers to improper fractions. We do this by multiplying the denominator by the whole number, adding the numerator, and placing that value over the denominator.

$1 \frac{3}{5} \\ \\ (5*1)+3 =8 \\ \\ \frac{8}{5} \\ \\ \\ \\ 1 \frac{2}{3} \\ \\ (3*1)+2=5 \\ \\ \frac{5}{3} 
$

Now, we need to find the least common denominator. This is the lowest value that both denominators will divide evenly into. In this case, that number is 15.

Next, we should multiply both fractions so that the denominator is that number. Remember that we must also multiply the numerator for the fraction to remain equivalent to its original value.

$\frac{8}{5} *3 = \frac{24}{15} \\ \\ \frac{5}{3} *5 = \frac{25}{15}$

Now, we can simply add our numerators.

$25+24=49$

We know that he needs $\frac{49}{15}$ gallons of paint, but this is not in the most simplified format. To simplify, we need to turn our improper fraction back to a mixed number. To do this, we need to divide our numerator by the denominator to create our whole number, and the remainder becomes our new numerator.

$\frac{49}{15} \\ \\ 49 / 15 = 3(Remainder: 4) \\ \\ 3\frac{4}{15}$

Using that logic, we can see that the painter needs exactly $3 \frac{4}{15}$ gallons of paint.

4 0

2 years ago

Convert y=9 from rectangular to polar form

Crazy boy [7]

Answer:

r = 9/sin Ф or r = 9 csc Ф

Step-by-step explanation:

The polar form is represented as:

x = r cos Ф and

y = r sin Ф

We are given:

y = 9

Putting value in y = r sin Ф

9 = r sin Ф

=> r = 9/sin Ф

1/sin Ф = csc Ф

or, r = 9 csc Ф

5 0

2 years ago

Read 2 more answers

Again with this please

ElenaW [278]

Answer:

a) A dozen= 24

3 dozen= 24 x 3

= 72

b) 1 dozen= 12 bananas

A dozen cost= 24

So, 1 banana cost= 24/12

= 2

So, 6 bananas would be 2 x 6 = 12

c) 1 dozen= 12 bananas

A dozen cost= 24

1 banana cost= 24/12

= 2

d) I need to know how many people are there in your class so please mention that first :)

Mark me brainliest pleaseee

5 0

1 year ago

on july 20th 2018, 1 U.S. dollar (1$) war worth 0.87 euros (0.87) how much $150 was worth in euros on that day

Alchen [17]

Answer:

130.5 euros

Step-by-step explanation:

$150 x .87

130.5

3 0

2 years ago

Read 2 more answers

How to solve 76×327 step by step

hram777 [196]

Here's a method that takes advantage of the values of these particular numbers.

... 76 = 80 - 4

... 76 × 327 = (80 -4)×327

... = 80×327 - 4×327

Repeated doubling will give us values that are 2, 4, and 8 times 327.

... 2×327 = 327+327 = 654

... 2×654 = 4×327 = 654+654 = 1308 . . . . we'll use this later

... 2×1308 = 8×327 = 2616

We want 80×327, so we can add a zero to the end of this last:

... 80×327 = 26160

Now, we can subtract 4×327 to get 76×327

... 80×327 - 4×327 = 26160 -1308 = 24852 = 76×327

_____

More conventionally, you would multiply every digit of one number by every digit of the other and add the products according to their respective place values.

327 × 076 = (3×0)×10000 + (3×7 +2×0)×1000 +(3×6 +7×0 +2×7)×100 +(2×6 +7×7)×10 +(7×6)×1

... = 0 +21,000 +3,200 + 610 +42

... = 24,852

Note the pattern of partial products here. This is a method taught to/by practitioners of Vedic mathematics, and can be done in your head. At most, you would write down the partial product sums 21, 32, 61, and 42 to keep from having to carry more than one number in your head at a time.

5 0

2 years ago