The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
16, 80,400,...
16,80,400,...
\text{Find the 6th term.}
Find the 6th term.

Answers

Answer 1

Given:

The sequence is:

[tex]16,80,400,...[/tex]

To find:

The 6th term of the given sequence.

Solution:

We have,

[tex]16,80,400,...[/tex]

Here, the first term is:

[tex]a=16[/tex]

The ratio between consecutive terms are:

[tex]\dfrac{80}{16}=5[/tex]

[tex]\dfrac{400}{80}=5[/tex]

The given sequence has a common ratio 5. So, the given sequence is a geometric sequence.

The nth term of a geometric sequence is:

[tex]a_n=a(r)^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

Substitute [tex]a=16,r=5,n=6[/tex] to get the 6th term.

[tex]a_6=16(5)^{6-1}[/tex]

[tex]a_6=16(5)^{5}[/tex]

[tex]a_6=16(3125)[/tex]

[tex]a_6=50000[/tex]

Therefore, the 6th term of the given sequence is 50000.


Related Questions

Find the mean for the following set of data. Write the NUMBER ONLY for the answer.

25, 27, 30, 15, 18, 24, 15

Answers

Answer:

22

Step-by-step explanation:

25+27+30+15+18+24+15 all divided by 7

A 2-liter bottle of soda pop contains 2,000 milliliters.
True
False

Answers

Answer:

TRUE!

Step-by-step explanation:

1 liter (L) = 1000 milliliters (mL)

If you have 2 Liters, then you would DOUBLE the milliliters (2000)

A clothing store donated a percent of every sale to charity. The total sales were $8850, so the store donated $531 what percent of $8850 was donated to charity?

Answers

Answer:

6%

Step-by-step explanation:

[tex]\frac{531}{8850} *\frac{x}{100} \\531*100= 5310053100/8850= 6%[/tex]

Please help me find the mean and the range.

Answers

mean: 5.5 hours

range: 7.9 hours

The number of miles a car travels varies directly with the number of gallons of gas in its tank of a car with 20 gallons of gas can drive 560 miles which equation represents the number of miles an

Answers

Answer:

28 miles per gallon

560/20=28

Step-by-step explanation:

Plz give me brainliest

Number of miles a car travels are 28.

What is division?

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

Number of gallons of gas = 20

A car with 20 gallons of gas can drive 560 miles

Based on the given conditions,

= [tex]\frac{560}{20}[/tex]

= 28

Hence, number of miles are 28.

Find out more information about division here

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plz help i have been asking this question way too much

Answers

Answer:

10/3 or 3 1/3

Step-by-step explanation:

Five boys each have 8 marbles. If all
their marbles are collected and placed

into
8heaps, how many marbles will there be in each jeap ?​

Answers

5 marbles.

We first need to find how many marbles we have in total.

8 marbles * 5 boys = 40 marbles.

These 40 marbles will now be divided by 8, since we are taking the total amount of marbles we have and separating them into 8 different piles.

40/8 = 5

There will be 5 marbles in each heap.

What is the combined area of the two bases of the following cylinder
The diameter is 12cm and the height is 15cm
A. 452.16cm^2
B. 904.32cm^2
C. 113.04cm^2
D. 226.08cm^2

Answers

D. 226.08cm^2

Since we are finding the combined area of the two bases of the cylinder, we are adding the area of the first base with the second base. The formula for the base of a cylinder is pi x r^2, since it is a circle. Since the bases are the same, we can rewrite this as 2pi x r^2.

Since the diameter is 12cm and r = 1/2 diameter, r = 6cm.

Thus, A = 2(3.1415)(6)^2 = 226.08cm^2

Malcom is filling bags with rice. He starts with 5 1/4 lbs. container of rice and fills each bag with 5/8 pound of rice. How many bags can Malcom fill?

Answers

He can fill five bags with 2/8 lbs of rice left that is left over a d can not go into a bag .

Can anyone help on this i don't understand it
the chooses for the choose is
15
12
10
14
11
13
9

Answers

median means the middle number and mode means which number appears the most

What evidence shows that the uprisings at Treblinka and Sobibor were not a complete failure?

Both camps were closed after the uprising.
Prisoners attacked and killed SS men and guards.
Thousands of prisoners escaped and were never captured.
All gas chambers in camps were shut down.

Answers

Answer:

both camlps

Step-by-step explanation:

Answer:

B.) Prisoners attacked and killed SS men and guards.

Step-by-step explanation:

edge

Landon earns 10% commission on his total sales. What must be his total sales in oder to earn a commission of $ 145?

Answers

Answer: [tex]\$1450[/tex]

Step-by-step explanation:

Given

Landon earns a 10% commission on his total sales

Suppose his total sales is x to get a commission of $145 i.e.

[tex]\Rightarrow x\times 10\%=145\\\Rightarrow 0.1x=145\\\Rightarrow x=\$1450[/tex]

Therefore, the amount of total sales must be $1450

a triangle has vertices r(1,2), s(3,3) and t(-3,4)

Answers

Give The Rest of the question

Answer:

Reflection about x axis

r(1,2)-----------r'(1,-2)

, s(3,3) ..........s'(3,-3)

and t(-3,4).....t'(-3,-4)

Marulla's z score on a college entrance exam is 1.3. If the raw scores have a mean of 480 and a standard deviation of 70 points, what is her raw score?

Answers

Answer:

571

Step-by-step explanation:

We solve using z score.

z = (x-μ)/σ, where

x is the raw score = ?

μ is the population mean = 480

σ is the population standard deviation = 70

z = 1.3

Hence,

= 1.3 = x - 480/70

Cross Mulitiply

1.3 × 70 = x - 480

91 = x - 480

x = 480 + 91

x = 571

Therefore, Marulla's raw score is 571

EASY MATH PLEASE HELP!! : ) : )

NO LINKS PLEASE

EXPLANATION REQUIRED


A new school is ordering math textbooks. They are 3/4 of an inch thick. How many of these books will fit into a bookshelf that is 2 feet long?

A) 2 books

B) 12 books

C) 26 books

D) 32 books

Answers

Answer:

32 Books

Step-by-step explanation:

You know that the bookshelf is 2 feet long, and you know the book is 3/4 inches thick. To start you have to get a common measurement in this case we will use inches. You already know that 1 foot is 12 inches so 2 feet will be 24 inches. Next all you do is divide the 24 inches by 3/4 inches. This will give you 32 which is the total amount of books that can fit on the bookshelf.

Please help me I will give 30 points

Answers

Answer:

a, c, & d

Step-by-step explanation:

-6,1 , 0,5 , 1,7 hope this help

As Soon As Possible! (please)


Each day a supernatural termite can eat 35% more wood grains that it did the day before. If a 20-day old termite has eaten 97,231 grains of wood, how many wood grains (to the nearest grain) will it eat on the 22nd day?

A) 84 grains
B) 130,745 grains
C) 176,589 grains
D) 235,768 grains

Answers

I believe it is C because it I s bigger but not to big of a amount please tell me if I am wrong

Help out



Sishsbnxbxbxxnxj

Answers

Answer:

y=-6/5x -8

Step-by-step explanation:

slope is the same as gradient(m) so find the c in the equation y=mx+c using the point (-5,-2) which gives u -8 then substitute values of m and c in that very equation

Answer:

[tex]y=-\frac{6}{5}x-8[/tex]

Step-by-step explanation:

Same process as the other two lol

y= -(6/5)x+b

solve for b by plugging in the required coordinates

-2= -(6/5)(-5)+b

-2= 6+b

-8=b

put it all together

Determine the period.

Answers

Answer:

the period is the to top points of the highest points on top of the crests

The period of function is,

P = 5

Since, In order to find the period of a graph in general, first, find the period of the parent function, and divide that by the absolute value of the coefficient of the independent variable.

Here, Graph of function is shown.

Hence, The period of function is,

P = 10/2

P = 5

Because there is two wave are shown.

Therefore, The period of function is,

P = 5

Learn more about the function visit:

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a bacteria culture starts with 720 bacteria and grows at an exponential rate calculator. after 2 hours there will be 1440 bacteria. give your answer accurate to at least 4 decimal places.

Answers

Answer:

y(t) = 720e^0.3466t

y = 2036.6288

Step-by-step explanation:

The exponential relation :

y = Ae^kt

A = initial value ; y = final value ; r ; k = exponential rate, t = time

At t = 0

y = 720e^0 ; y = 720

At t = 2 ; y = 720e^2k

1440 = 720e^2k

1440/720 = e^2k

2 = e^2k

Take the In of both sides

0.6931471 = 2k

k = 0.6931471 / 2

k = 0.3466

Hence, equation becomes :

y = 720e^0.3466t

After 3 hours ;

t = 3

y = 720e^0.3466*3

y = 720e^1.0398

y = 720 * 2.8286512

y = 2036.6288

Can somebody help me with writing a real-life problem on this subject Finding angle measures of a right or isosceles triangle given angles with variables thank you?

Answers

Answer:

See Explanation

Step-by-step explanation:

See attachment for illustration

(a) Right triangle

The sum of [tex]angles[/tex] in a [tex]right[/tex] [tex]triangle[/tex]is:

[tex]x + y + 90 = 180[/tex]

Subtract 90 from bot sides

[tex]x + y = 90[/tex]

Make x the subject

[tex]x = 90 - y[/tex]

Make y the subject

[tex]y = 90 - x[/tex]

This implies that, subtract the known angle from 90 to get the unknown angle.

Assume [tex]x = 40[/tex]

We make use of: [tex]y = 90 - x[/tex]

[tex]y = 90 - 40 = 50[/tex]

(b) Isosceles triangle

The sum of angles in an isosceles triangle is:

[tex]x + y + y = 180[/tex] ---- y appear twice because the base angles are equal

[tex]x + 2y = 180[/tex]

Make x the subject

[tex]x = 180 - 2y[/tex]

Make y the subject

[tex]y = \frac{180 - x}{2}[/tex]

Assume [tex]x = 40[/tex], we make use of:

[tex]y = \frac{180 - x}{2}[/tex]

[tex]y = \frac{180 - 40}{2}[/tex]

[tex]y = \frac{140}{2}[/tex]

[tex]y = 70[/tex]

Assume [tex]y = 70[/tex], we make use of:

[tex]x = 180 - 2y[/tex]

[tex]x = 180 - 2 * 70[/tex]

[tex]x = 180 - 140[/tex]

[tex]x = 40[/tex]

Can someone please help me!

Answers

Answer:

A)

Step-by-step explanation:

it is clearly reduced so you can eliminate the middle two options as answers;

reduction is always going to be a value less than 1 because a value greater than 1 would not be a reduction

What’s the volume of one cylinder?

Answers

Answer:

For the first one its: Volume = 402.12in³

For the second one its: Volume = 201.0619 in³

Step-by-step explanation:

For the first one work:

Volume = 3.1416 x 42 x 8

= 3.1416 x 16 x 8

For the second one work:

Volume = 3.1416 x 42 x 4

= 3.1416 x 16 x 4

Answer:

the formula is : V=πr2h

the volume of the first cylinder is 402.12cm³ and the second is 201.06cm³ (these answers are rounded to two decimal places)

Step-by-step explanation:

Volume is pi times the radius squared (which is 4 in both these cylinders) times the height of the cylinder which is 8 in the first cynlinder and 4 in the second.

In the figure, OA is a diameter of the smaller circle and O is the centre of the larger circle. Find the
area of the shaded region.


Answers

Answer:

942 6/7 cm²

Step-by-step explanation:

Since O = Center of bigger circle, OA = Radius of bigger circle.

∴ Area of smaller circle - Area of bigger circle = Area of shaded part.

∴ Area of smaller circle = 22/7 × 10²

                                       = 22/7 × 100

                                       = 2200/7

                                       = 314 2/7 cm²

∴ Area of bigger circle = 22/7 × 20 ²

                                      = 22/7 × 400

                                      = 1257  1/7 cm²

∴ Area of shaded part = 1257 1/7 - 314 2/7

                                     =  942 6/7 cm²

A survey went out asking consumers about their shopping habits. The results showed that
165 people were more likely to go to a store if they had a coupon. This represents 66% of
the total number of people who took the survey
How many people took the survey?
F: 25
G: 109
H: 199
J: 250

Answers

Answer:

G

Step-by-step explanation:

In math whenever you have the word "of" it means multiply, so 66% of the total number of people who took the survey( which is 165) is 66/100 multiplied by 165.

[tex]\frac{66}{100} *165= 108.9[/tex] which rounds up to 109

G is your answer!! Hope this is right

Describe two ways to write 7/3 as a mixed number

Answers

Answer:

2 1/3 and 1 1/6

Step-by-step explanation:

Find the volume of a cone with a diameter of 12 m and a height of 5 m.
A. 60 m3
B. 60 m3
C. 240 / m3
D. 1807 m3
Please help!!! Need fast will mark Brainiest if correct!

Answers

Answer:

60[tex]\pi[/tex] m³

Step-by-step explanation:

Use the cone volume formula, V = [tex]\pi[/tex][tex]\frac{h}{3}[/tex]

If the diameter is 12 m, the radius will be 6 m.

Plug in the height and radius into the formula, and solve:

V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

V = [tex]\pi[/tex](6²)[tex]\frac{5}{y}[/tex]

V = [tex]\pi[/tex](36)[tex]\frac{5}{3}[/tex]

V = 60[tex]\pi[/tex]

So, the volume of the cone is 60[tex]\pi[/tex]

PLS HELP ILL GIVE BRAINLIEST
What are the coordinates of the center of the ellipse?

Answers

Answer:

Step-by-step explanation:

Standard equation of an ellipse,

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

(h, k) is the center of the ellipse

Value of a = Distance of the center from the vertex

b = Distance of the center from the covertex

From the picture attached,

a = Distance of the center (h, k) from the vertex (2, -2) = 3 units

b = Distance of the center (h, k) from the co-vertex (-1, 0) = 1 unit

Center of the ellipse (h, k) = (-1, -2)

Solve the following equation for a. Be sure to take into account whether a letter is capitalized or not.

d+a=h

Answers

Answer:

do you have an attatchment or guide i can use to answer this?

Step-by-step explanation:

Transposing a,

[tex]d + a = h \\ a = h - d[/tex]


[tex]\huge\mathfrak\red{solve \: please..} \\ \\ \huge\mathcal\purple{ {2}^{2} + 3 {}^{2} = {?} } \\ \\ \huge\mathfrak\green{asap \: \: ..thanks.}[/tex]

Answers

Answer:

[tex]2^2+3^2[/tex]

[tex]2^2=4[/tex]

[tex]3^2=9[/tex]

[tex]=4+9[/tex]

[tex]=13[/tex]

----------------------

hope it helps..

have a great day!!

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