Find an explicit rule for each geometric sequence using subscript notation. Use a calculator and round your answers to the nearest tenth if necessary.

The fifth term of a geometric sequence is 7. The sixth term is 3.5.

Answers

Answer 1

Answer:

aₙ = 224(1/2)ⁿ  

Step-by-step explanation:

Given GP with:

a₅ = 7a₆ = 3.5

We can find the common ratio:

r = 3.5/7 = 1/2

Using the nth term formula we can work out the first term:

aₙ = a₁rⁿ⁻¹a₅ = a₁(1/2)⁴7 = a₁ (1/16)a₁ = 7*16a₁ = 112

So the explicit rule is:

aₙ = 112(1/2)ⁿ⁻¹ = 224(1/2)ⁿ

Related Questions

Am I right? They want us to round to the nearest degree. I got 72 degrees. Answer ASAP

Answers

This looks good to me!

Misty is making a necklace with
beads that are 0.75 inch long.
The necklace will be 15.75 inches
long. How many beads will
Misty use?

Answers

Answer:

21 beads

Step-by-step explanation:

15.75 divided by 0.75 = 21

sorry im late hope this helps out :) <3

helppppppppp!!! need work

Answers

Answer:

d. y = 3x + 5

Step-by-step explanation:

plug x = 2 in the equation y = 3x +5

y = 3*2 + 5

y = 11

so x = 2, y = 11

we know d is the correct statement

Answer:

your question and is d option

Mr. Wellborn arrives at work at 8:40 AM. he leaves for work 50 minutes before he arrives. At what time does Mr Wellborn Leave for work?

Answers

Answer:

7:50

Step-by-step explanation:

Mr. Wellborn arrives 50 minutes before 8:40 so that means you subtracts 50 minutes from 8:40. 8:40-50=7:50

Therefore, the answer is 7:50

Hope this helps

Answer:

The answer is 7:50 A.M

Step-by-step explanation:

First we know that 50 is less than 40 so we subtract one hour. that get 50 so the answer is 7:50!

By the way, the person who answered this is a 3rd grader!  If the answer is worng am sorry i tried my best.

WHAT IS THE AREA OF THE SHADED REGION?

Answers

Answer:

240cm

Step-by-step explanation:

Find the value of h(x) = -3x – 12 when x = -2? Show work

Answers

Answer:

-6

Step-by-step explanation:

h(x) = -3x – 12 becomes h(-2) =  -3(-2) – 12 = -6

Casey has a litter of five puppies and four of them are gray at this rate how many puppies would be gray in a litter of 25 puppies?

Answers

Answer:

20

Step-by-step explanation:

ou intend to draw a random sample in order to test a hypothesis about an unknown population mean. You will use a hypothesis test. A description of each of the steps of a hypothesis test follows, but they may be specified in the incorrect order. Specify the correct order of the steps. Determine the null and alternative hypotheses. Draw a conclusion about the unknown population using what is known about the sample. Determine the probability at which you will conclude that the sample outcome is very unlikely. Draw a random sample, and calculate the sample statistic.

Answers

Answer:

Determine the null and alternative hypotheses :  STEP 1

Draw a conclusion about the unknown  population using what is known about the sample :  STEP 4

Determine the probability at which you will conclude that the sample outcome is very unlikely :  STEP 2

Draw a random sample and calculate the sample statistic : STEP 3

Step-by-step explanation:

The correct order of the steps are :

Determine the null and alternative hypotheses :  STEP 1

Draw a conclusion about the unknown  population using what is known about the sample :  STEP 4

Determine the probability at which you will conclude that the sample outcome is very unlikely :  STEP 2

Draw a random sample and calculate the sample statistic : STEP 3

On the maturity date of a $6,600, 9-month, 12% note, the borrower sends a check that includes the principal and all of the interest due on the note. What is the amount of the borrower’s check?

Answers

Answer:

$7194

Step-by-step explanation:

Given the following

Principal = $6600

Time = 9months = 9/12 year

Rate R = 12%

Interest = PRT/100

Interest = 6600*9/12 * 12/100

Interest = 66*9

Interest = $594

Amount on the borrowers check  = principal + interest

Amount on the borrowers check = 6600 + 594

Amount on the borrowers check = $7194

Select all the correct answers.
In which pairs of matrices does AB = BA?

Answers

Answer:

its the second and third option

Step-by-step explanation:

I took the test

In order to multiply a matrix by another matrix, we multiply the rows in the first matrix by the columns in the other matrix (How this is done is shown below)

To determine the pairs of matrices that AB=BA, we will determine AB and BA for each of the options below.

For the first option

[tex]A= \left[\begin{array}{cc}1&0&-2&1&\end{array}\right]; B= \left[\begin{array}{cc}5&0&3&2&\end{array}\right] \\[/tex]

[tex]AB= \left[\begin{array}{cc}(1\times5)+(0\times3)&(1\times0)+(0\times 2)&(-2\times5)+(1\times3)&(-2\times0)+(1\times2)&\end{array}\right]\\AB= \left[\begin{array}{cc}5+0&0+0&-10+3&0+2&\end{array}\right]\\AB = \left[\begin{array}{cc}5&0&-7&2&\end{array}\right] \\[/tex]

and

[tex]BA= \left[\begin{array}{cc}(5\times1)+(0\times-2)&(5\times0)+(0\times 1)&(3\times1)+(2\times-2)&(3\times0)+(1\times2)&\end{array}\right]\\BA= \left[\begin{array}{cc}5+0&0+0&3+-4&0+2&\end{array}\right]\\BA = \left[\begin{array}{cc}5&0&-1&2&\end{array}\right] \\[/tex]

∴ AB≠BA

For the second option

[tex]A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right]; B= \left[\begin{array}{cc}3&0&6&-3&\end{array}\right] \\[/tex]

[tex]AB= \left[\begin{array}{cc}(1\times3)+(0\times6)&(1\times0)+(0\times -3)&(-1\times3)+(2\times6)&(-1\times0)+(2\times-3)&\end{array}\right]\\AB= \left[\begin{array}{cc}3+0&0+0&-3+12&0+-6&\end{array}\right]\\AB = \left[\begin{array}{cc}3&0&9&-6&\end{array}\right] \\[/tex]

and

[tex]BA= \left[\begin{array}{cc}(3\times1)+(0\times-1)&(3\times0)+(0\times 2)&(6\times1)+(-3\times-1)&(6\times0)+(-3\times2)&\end{array}\right]\\BA= \left[\begin{array}{cc}3+0&0+0&6+3&0+-6&\end{array}\right]\\BA = \left[\begin{array}{cc}3&0&9&-6&\end{array}\right] \\[/tex]

Here AB = BA

For the third option

[tex]A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right]; B= \left[\begin{array}{cc}5&0&3&2&\end{array}\right] \\[/tex]

[tex]AB= \left[\begin{array}{cc}(1\times5)+(0\times3)&(1\times0)+(0\times 2)&(-1\times5)+(2\times3)&(-1\times0)+(2\times2)&\end{array}\right]\\AB= \left[\begin{array}{cc}5+0&0+0&-5+6&0+4&\end{array}\right]\\AB = \left[\begin{array}{cc}5&0&1&4&\end{array}\right] \\[/tex]

and

[tex]BA= \left[\begin{array}{cc}(5\times1)+(0\times-1)&(5\times0)+(0\times 2)&(3\times1)+(2\times-1)&(3\times0)+(2\times2)&\end{array}\right]\\BA= \left[\begin{array}{cc}5+0&0+0&3+-2&0+4&\end{array}\right]\\BA = \left[\begin{array}{cc}5&0&1&4&\end{array}\right] \\[/tex]

Here also, AB=BA

For the fourth option

[tex]A= \left[\begin{array}{cc}1&0&-2&1&\end{array}\right]; B= \left[\begin{array}{cc}3&0&6&-3&\end{array}\right] \\[/tex]

[tex]AB= \left[\begin{array}{cc}(1\times3)+(0\times6)&(1\times0)+(0\times -3)&(-2\times3)+(1\times6)&(-2\times0)+(1\times-3)&\end{array}\right]\\AB= \left[\begin{array}{cc}3+0&0+0&-6+6&0+-3&\end{array}\right]\\AB = \left[\begin{array}{cc}3&0&0&-3&\end{array}\right] \\[/tex]

and

[tex]BA= \left[\begin{array}{cc}(3\times1)+(0\times-2)&(3\times0)+(0\times 1)&(6\times1)+(-3\times-2)&(6\times0)+(-3\times1)&\end{array}\right]\\BA= \left[\begin{array}{cc}3+0&0+0&6+6&0+-3&\end{array}\right]\\BA = \left[\begin{array}{cc}3&0&12&-3&\end{array}\right] \\[/tex]

Here, AB≠BA

Hence, it is only in the second and third options that AB = BA

[tex]A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right] B= \left[\begin{array}{cc}3&0&6&-3&\end{array}\right] \\[/tex] and [tex]A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right]B= \left[\begin{array}{cc}5&0&3&2&\end{array}\right] \\[/tex]

Learn more on matrices multiplication here: https://brainly.com/question/12755004

WILL GIVE BRAINLIEST

Answers

0,0 1,4 2,8 is the answer

Doughnuts are sold in bag and cartons. A bag holds 4 doughnuts and a carton holds 10 doughnuts. Tome buys b bags of doughnuts and c cartons of doughnuts. He buys a total of t doughnuts. Write down the formula for t in terms of b and c

Answers

Answer:

[tex]t = 4b + 10c[/tex]

Step-by-step explanation:

Given

1 bag = 4 doughnuts

1 carton = 10 doughnuts

Required

Determine the amount of doughnuts in b bags and c cartons

If 1 bag contains 4 doughnuts, then b bags contain 4b doughnuts

If 1 carton contains 10 doughnuts, then c cartons contain 10b doughnuts

So, the total (t) is calculated by adding up the amount of doughnuts in the cartons and the bags:

i.e.

[tex]t = 4b + 10c[/tex]

139 / 263 Marks
The pictogram shows the amounts Judy saves in four months.
August
Key:
September
represents £20
October
November
a)
Work out the total amount of money that Judy saves in the four months.
b)
Judy spends £172 on Christmas presents.
How much money does she have left?

Answers

The total Judy saved was £200. Moreover, if she spends £172 on Christmas presents, she will have £28 left.

What is the total of money Judy saved?

If you observe the pictogram, two squares are equivalent to £20. This means one square is equivalent to £10. Based on this, let's determine the total she saved every month.

August:  3 squares = £30September: 4 squares = £40October: 5 squares = £50November: 8 squares = £80Total: £30 + £40 + £50 + £80 = £200

How much money does she have left if she spends £172 on Christmas presents?

To find out the total money she will have in this situation is equivalent to the total of money she saved - £172 she spent.

£200 - £172 = £28

Note: This question is incomplete because the pictogram is missing, here I attach the missing section.

Learn more about money in: https://brainly.com/question/2696748

Write the equation 3x+2y- 5 = 0 in normal form. Then, find the length of the normal and the angle it makes with the


positive x axis.

Answers

Answer: x= -2/3y+5/3

Step-by-step explanation:

Let's solve for x.

3x+2y−5=0

Step 1: Add -2y to both sides.

3x+2y−5+−2y=0+−2y

3x−5=−2y

Step 2: Add 5 to both sides.

3x−5+5=−2y+5

3x=−2y+5

Step 3: Divide both sides by 3.

3x/3=-2y+5/3

x= -2/3y+5/3

In JKL, J = 7.9 inches, K = 2 inches and L =9.8 inches. Find the measure of K to the nearest degree

Answers

Answer:

4

Step-by-step explanation:

Delta math

The measure of K to the nearest degree is 4°.

What is the laws of cosines?

The law of cosines, commonly referred to as the cosine rule or the cosine formula, in trigonometry essentially connects the length of the triangle to the cosines of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.

Given ΔJKL,

j = 7.9 inches, k = 2 inches, l = 9.8 inches

to find the measure of angle K,

we can calculate the angle by cosine law,

cosK = (j² + l² - k²)/(2.j.l)

cosK = (7.9² + 9.8²  - 2²)/(2*7.9*9.8)

cosK = 154.45/154.81

K = cos⁻¹(0.99748)

K = 4.067⁰ ≈ 4°

Hence angle K is 4°.

Learn more about the laws of cosines;

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please help if you are good at math :( thank you

Answers

Answer:

your answer will be

A)(6,10)

B)(2,12)

C)(4,4)

Step-by-step explanation:

hope this helps

have a nice day/night ^_^

find the slope of the line passing through the points (-3,2) and (-3,-7)​

Answers

Slope = change in Y / change in x

Slope = (-7 - 2) / (-3 - -3)

Slope = -9/0

Because the change in x = 0, the slope is undefined.

The answer is the slope is  undefined.

What does a geometric sequence contain

Answers

The geometric sequence is a sequence with a common ratio. The common ratio is the ratio between the succeeding term and the preceding term of a sequence and must be equal to a constant k.

Given a sequence 2, 4, 8, 16... This sequence is geometric in nature because of a constant common ratio of 2.'

Common ratio = 4/2 = 8/4 = 2

Hence a geometric sequence is characterized by its common ratio

3.Not Answered 4.Not Answered 5.Not Answered 6.Not Answered 7.Not Answered 8.Not Answered 9.Not Answered 10.Not Answered 11.Not Answered 12.Not Answered 13.Not Answered 14.Not Answered 15.Not Answered 16.Not Answered 17.Not Answered 18.Not Answered 19.Not Answered 20.Not Answered Question Workspace Check My Work In a linear regression model, the variable that is being predicted or explained is known as _____________. It is denoted by y and is often referred to as the response variable

Answers

Answer:

The answer to your question is Dependent Variable.

In a linear regression model, the variable that is being predicted or explained is known as Dependent Variable . It is denoted by y and is often referred to as the response variable

Step-by-step explanation:

I don't really know how to explain sorry.

Brainliest pls! :)

Answer:Dependent Variable

In how many ways can you
select 3 books to bring on
vacation from a group of 11
books?

Answers

Answer:

165

Step-by-step explanation:

In 165 ways i can select 3 books to bring on vacation from a group of 11 books.

What is Combination?

A combination is when you choose data from a group without any order or sequence. If the group of data is relatively lesser, you can calculate the number of possible combinations.

According to the question

Select 3 books to bring on vacation from a group of 11 books.

By using combinations formula

[tex]^{n} C _{r}=\frac{n!}{r!(n-r)!}[/tex]

[tex]^{11} C_{3}[/tex] = [tex]\frac{11!}{3!(11-3)!}[/tex]

= [tex]\frac{11.(10)(9)(8!)}{3!.8!}[/tex]

Cancelling out 8! from denominator and numerator

= [tex]\frac{11(10)(9)}{3(2)(1)}[/tex]

= 165

Thus, In 165 ways i can select 3 books to bring on vacation from a group of 11 books.

Find out more information about combinations here

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The area of a cross section through the center of a sphere is 46 square inches. Find the surface area of the sphere.

Answers

Answer:

184 in.^2

Step-by-step explanation:

The cross section through the center of a sphere is a circle whose radius is equal to the radius of the sphere.

area of circle

[tex]A_{circle} = \pi r^2[/tex]

[tex] \pi r^2 = 46 [/tex]

[tex] r^2 = \dfrac{46}{\pi} [/tex]

[tex] r = \sqrt{\dfrac{46}{\pi}} [/tex]

[tex] r = 3.83 ~in.[/tex]

surface area of sphere

[tex] SA = 4 \pi r^2 [/tex]

[tex] SA = 4 \times \pi \times (3.83)^2 [/tex]

[tex] SA = 184~in.^2 [/tex]

Math Problem 30 points please help

Answers

Answer: One solution

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

they intersect at 1 point

Sean had 3 building sets and 18 toy cars in his toy box. At his birthday party, he received 20 gifts. He got 3 train sets, 4 building sets and 9 toy cars. The rest of the gifts are comic books. 3/4 of the gifts are wrapped. 1/3 of the wrapped gifts are wrapped in blue wrapping paper and 1/ 5 of them are wrapped with ribbons. What fraction of the gifts are train sets? What fraction of the gifts are comic books? What fraction of his toy cars are new?

Answers

Answer:

1.3/20   2.4/20 or 1/5   3.9/27 or 1/3

Step-by-step explanation:

I hope this helped!

PLEASE HELP ASAP!!!!!

which triangle makes this sentence true?


answers:

Answers

What sentence? Please make sureEee you know what your submitting before submitting

The measures of angles X and Y are the same, x degrees. The measure of angle Z is twice the measure of angle Y.

Answers

Answer:

angles X = 45°

angles Y = 45°

angles Z = 90°

Step-by-step explanation:

Given:

angles X = angles Y = x°

angles Z = 2 angles Y = 2x°

Find:

Each angle

Computation:

Using angle sum property

angles X + angles Y + angles Z = 180

x + x + 2x = 180

4x = 180

x = 45°

So,

angles X = 45°

angles Y = 45°

angles Z = 90°

This figure is made up of a rectangle and parallelogram. What is the area of this figure.

Answers

Answer:

area of the parallelogram=6

area of the rectangle=20

total area=26 square units

Official unemployment rates for the U.S. population are reported on a monthly basis by the Bureau of Labor Statistics. For the period October, 2011, through January, 2012, the official unemployment rates were 8.9% (Oct.), 8.7% (Nov.), 8.5% (Dec.), and 8.3% (Jan.). (Source: U.S. Bureau of Labor Statistics, www.bls.gov.) If the unemployment rates were to continue to decrease following a linear model, (a) predict the unemployment rate on January, 2013. (b) predict when the United States would reach a zero unemployment rate.

Answers

Step-by-step explanation:

Clearly, there is a common difference between the monthly employment rates:

8.7% - 8.9% = -0.2%

8.5% - 8.7% = -0.2%

8.3% - 8.5% = -0.2%

a) So, for every month x, the percentage will go down 0.2%, starting at 8.9%. So, we can make this equation:

y = -0.2x + 9.1, where x = 1 would be October 2011.

January 2013 is 16 months after October 2011, so:

y = -0.2(16) + 9.1

y = 5.9%

b) To find when the unemployment rate will be zero, we set the equation equal to zero:

0 = -0.2x + 9.1

-0.2x = -9.1

x = 45.5 months

So, rounding up, the U.S. would reach a zero unemployment rate in 46 months or around September 2014? Not completely sure.

Pls help ASAP I’ll brainlest pls

Answers

Answer:

i think d

Step-by-step explanation:

Answer:

its d

Step-by-step explanation:

.....................

Find x and Find m<MNO please help fast​

Answers

MNO is a right triangle so you would so 6x-3+3x+13=90
9x+10=90
X=8.8

5x+7=8.8
X=2.7 or MNO=2.7

Who Am I?

t = 2 x h
t=6
The sum of my digits is equal to fourteen.

Answers

Answer:

[tex]6[/tex]

12....................may be

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