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3 years ago

Write the first five terms of a geometric sequence in which the sixth term is 64.

Mathematics

1 answer:

azamat3 years ago

8 0

Answer:

1st term : 2

2nd term : 4

3rd term: 8

4th term : 16

5th term : 32

Step-by-step explanation:

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What is the surface area of a cylinder that has the following measurements? area of each base: 50.24 ft2 area of lateral surface

irinina [24]

Answer:

TSA = 175.84 ft²

Step-by-step explanation:

We are given;

Lateral surface area; A_L = 75.36 ft²

Area of base; A_b = 50.24 ft²

Height of cylinder; h = 3ft

Formula for total surface area of Cylinder is;

TSA = 2πr² + 2πrh

Now, lateral surface area is given by the formula; A_L = 2πrh

Area of base is given by the formula;

A_b = πr²

Thus, let's apply these 2 formulas to the formula for total surface area;

TSA = 2(Area of base) + Lateral surface area

TSA = (2 * 50.24) + 75.36

TSA = 175.84 ft²

3 0

3 years ago

Scientists have discovered a vaccine for a debilitating disease. This year there were 570,000 reported new cases of the disease

Ket [755]

Answer: There are approximately 853827 new cases in 6 years.

Step-by-step explanation:

Since we have given that

Initial population = 570000

Rate at which population decreases is given by

$\frac{2}{3}$

Now,

First year =570000

Second year is given by

$570000\times (\frac{1}{3})$

Third year is given by

$570000(\frac{1}{3})^2$

so, there is common ratio ,

it becomes geometric progression, as there is exponential decline.

so,

$570000,570000\times \frac{1}{3},570000\times( \frac{1}{3})^2,......,570000\times (\frac{1}{3})^6$

a=570000

common ratio is given by

$r=\frac{a_2}{a_1}=\frac{1}{3}$

number of terms = 6

Sum of terms will be given by

$S_n=\frac{a(1-r^n)}{(1-r)}$

We'll put this value in this formula,

$S_6=\frac{570000(1-(\frac{1}{3})^6}{(1-\frac{1}{3})}\\\\=853827.16$

So, there are approximately 853827 new cases in 6 years.

6 0

2 years ago

Amy's yearly salary is given by the equation y = 25,000 + 700x, where x is the number of years since 2007 and y is her salary in

yanalaym [24]

2007 would be 0 years since 2007

y=25000+700(0)
y=25000

Answer: Her yearly salary in 2007 was $25,000

Hope this helps:)

3 0

3 years ago

AfilCa [17]

Answer:

(A) Your friend will save $282.

(B) Your friend will get 23.5% off the original price of the mattress.

Step-by-step explanation:

We first need to find out the price of the mattress after the 15% discount. Our first step is to find what 15% of 1,200 is. We can do this by multiplying the two numbers.

1,200 x 15% -----> 1,200 x 0.15= 180.

15% of $1,200 is $180.

Next subtract $180 from $1,200, which equals $1,020. We can now apply the 10% off internet coupon.

1,020 x 10% ------> 1,020 x 0.10= 102.

10% of $1,020 is $102.

Next we subtract $102 from $1,020 and we get $918, the final price of the discounted mattress.

We subtract to see how much money the friend saved.

$1,200 - $918= $282.

We can get the percentage by dividing $282 by $1,200.

282 / 1200= 0.235 decimal form ----> 23.5%

6 0

2 years ago

Jamie's older brother and his three friends want to split the cost of lunch they also want to leave a 15% tip how much should ea

goldfiish [28.3K]

Answer:
$22.43

Explanation:
We can start by finding the amount that they should tip. The total bill is $78, so we should take 15% of 78 and add it to the total.
0.15 * 78 = 11.7
78 + 11.7 = 89.7
This means that the total cost of the bill, with a tip, is $89.70.
Since there are 4 people, we have to split this total into 4 if they all want to pay equally.
89.70 / 4 = 22.425 = $22.43 !

Hope this helps

4 0

2 years ago