Consider the sequence 3, 6, 12, 24, 48, .... (a) Write a recursive rule to represent the sequence. (b) Write an explicit rule to represent the sequence. (c) Find the 15th term in the sequence.

Answers

Answer 1

Answer:

  a. a[1] = 3; a[n] = 2a[n-1]

  b. a[n] = 3·2^(n-1)

  c. a[15] = 49,152

Step-by-step explanation:

Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.

The first term is 3, and the common ratio is 2.

(a)

The recursive rule is ...

  a[1] = 3

  a[n] = 2×a[n-1]

__

(b)

The explicit rule is ...

  a[n] = a[1]×r^(n-1)

  a[n] = 3×2^(n-1)

__

(c)

The 15th term is ...

  a[15] = 3×2^(15-1) = 3×2^14

  a[15] = 49,152


Related Questions

apter 13
4. The base rate for workers' compensation insurance for roolers
in one state is $16.95 per $100 paid to employees. The total
monthly payroll for Certified Roofing is $15,738.00. What is the
monthly premium for workers' compensation insurance?

Answers

Answer:

  $2,667.59

Step-by-step explanation:

The insurance premium is found by multiplying the payroll amount by the premium rate.

  ($15,738) × $16.95/$100 = $15,738 × 0.1695 ≈ $2,667.59

The monthly workers' compensation insurance premium is $2,667.59.

_____

Additional comment

The roofers in that state must have an exceptionally high rate of accident, injury, or illness. Many places, the average rate of workers' comp insurance is less than $2 per $100.

Answer:

The roofers in that state must have an exceptionally high rate of accident, injury, or illness. Many places, the average rate of workers' comp insurance is less than $2 per $100.

Step-by-step explanation:

Please help I'll mark brainliest.

Answers

Answer:

Step-by-step explanation:

10

12

8

13

13

7

6

12

9

10

11

9        

120

Total = 120

Number of entrees = 12

Mean = 120 / 12

Mean = 10

Solve the equation:

[tex]6-(3w+1) = 8w-2[/tex]

Answers

Step-by-step explanation:

please mark me as brainlest

Hello!

[tex]===================================[/tex]

Step 1:

Use the Distributive Property:

[tex]\hookrightarrow\sf{-(3w+1)=-3w-1}[/tex]

Hence, the equation is

[tex]\hookrightarrow\sf{6-3w-1=8w-2}[/tex]

Move 8w to the left side

[tex]\hookrightarrow\sf{6-3w-1-8w=-2}[/tex]

Combine Like Terms

[tex]\hookrightarrow\sf{6-3w-8w-1=-2}[/tex]

Simplify

[tex]\hookrightarrow\sf{6-11w-1=-2}[/tex]

Move 6 and 1 to the right

[tex]\hookrightarrow\sf{-11w=-2+1-6}[/tex]

[tex]\hookrightarrow\sf{-11w=-7[/tex]

Divide both sides by -11

[tex]\hookrightarrow\sf{w=7/11}\\=============================[/tex]

Notes:Hope everything is clear.Let me know if you have any questions!Enjoy your day!Always remember: Knowledge Is Power!

Look at the chart and complete the function rule.
y = 5x + ?

Answers

Answer:

Step-by-step explanation:

The slope-intercept form is

y

=

m

x

+

b

, where

m

is the slope and

b

is the y-intercept.

y

=

m

x

+

b

Find the values of

m

and

b

using the form

y

=

m

x

+

b

.

m

=

5

b

=

0

The slope of the line is the value of

m

, and the y-intercept is the value of

b

.

Slope:

5

y-intercept:

0

The area of the triangle below is 3/40


square meters. What is the length of the base? Express your answer as a fraction in simplest form.

Answers

Answer:

b = 3/4

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

3/ 40 = 1/2 b ( 1/5)

Multiply

3/40 = 1/10 b

Multiply each side by 10

10 *3/40 = 10* 1/10 b

3/4 = b

Mr. Garcia has 15 boys and 10 girls in his math class. He selects wo students at random to demonstrate how they solved the day's challenge assignment What is the probability that both students are girls?​

Answers

Answer: 3/20

Step-by-step explanation:

A 50kg ball rolls off a building it is going 5 m/s when it hits the ground. How tall is the building

Answers

Answer:

1.25m

Step-by-step explanation:

s=ut+1/2gt^2

Newton's second law of motion

F=ma

50x10

500N

500/50

g/a=10m/s^2

u=0m/s

s= 1/2gt^2

v=u+gt

5=0+(10t)

5=10t

t=0.5s

s=0.5×10×(0.5)^2

=1.25m

A soup can has a radius of 4.3 cm and a height of 11.6 cm. What is the approximate volume of the soup can?

Answers

Answer:

673.82 cm³

Explanation:

soup can are usually in the form of a cylinder.

cylinder volume : [tex]\sf \pi r^2h[/tex]

[tex]\rightarrow \sf \pi (4.3)^2(11.6)[/tex]

[tex]\rightarrow \sf 673.82 \ cm^3[/tex]

What is the area Of the desk

Answers

Answer:

28 ft²

Step-by-step explanation:

area of the desk = (5×4) + (4×2) = 20 + 8 = 28 ft²

Answer:

28

Step-by-step explanation:

5 times 4 = 20

4 times 2= 8

20 plus 8=28

image below ill give branliest 20 points question

Answers

Answer:

I can't see image

Step-by-step explanation:

why I not see image

how to tell if something is cubed or squared being ft^3 or ft^2

Answers

Answer:

Check the power

Step-by-step explanation:

You can tell if a quantity has been cubed or squared by looking at its power.

For example, ft^3 has a power of 3 (meaning feet is raised to 3) which means whichever number ft^3 is used with, has been cubed, generally volume of any shape

Similarly, ft^2 has a power of 2 (meaning feet is raised to 2) which means whichever number ft^2 is used with, has been squared, generally area of any shape

hello!

===========================================================

If something is squared, it's multiplied times itself 2 times.

Example:-

[tex]\bigstar\boxed{\pmb{4*4=4^2}}\longleftarrow\sf{4~squared~}[/tex]

You should also notice that the exponent of 4 is 2.

So if something is squared, its exponent is 2.

If something is cubed, it's multiplied times itself 3 times.

Example:-

[tex]\bigstar{\boxed{\pmb{4*4*4=4^3}}\longleftarrow\sf{4~cubed}[/tex]

You should also notice that the exponent of 4 is 3.

So if something is cubed, its exponent is 3.

=======================================================

note:-

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Complete the state symbol in the equation. CuCO3+H2SO4(aq)+H2O+CO2

Answers

Answer:

H2O = liquid (l)

CO2 = gas (g)

CuCO3 = solid (s)

Step-by-step explanation:

H2O is water

CO2 is carbon dioxide

CuCO3 is copper carbonate

A school needs 138 5 meters of fencing for a new playground Fencing is
sold in 12-foot sections. How many sections of fencing should be
purchased to fence the playground? PLEASE ANSWER AS QUICKLY AS YOU CAN!!!!

Answers

Answer:

12 Sections

Step-by-step explanation:

With 138.5 meters needed and fencing being purchased in 12-foot sections, you would need 12 sections purchased. 138.5/12=11.54, this is rounded up to 12 because of the purchase size.

The table shows the number of apples needed to make apple pies and applesauce sold at a farm
store. During a recent picking at the farm, 169 Granny Smith apples and 95 Red Delicious apples
were picked. Write and solve a system to determine how many apple pies and how many batches
of applesauce can be made if every apple is used. (Hint: read across each row to create your equations!)
# Needed # Needed Total
Type of Apple for 1 (Pie) for Sauce
Granny Smith 5
4
169
Red Delicious
3
2
95

Answers

Answer:

pie - 38

sauce - 37.5

Step-by-step explanation:

For the Red Delicious apples you keep subtracting 5 from the total (95) and adding 1 to both of the total numbers of pies and apple-sauce. For the Granny Smith apples you keep subtracting 9 from the total and adding 1 to both of the total numbers of pies and apple-sauce until you get to 7 then you subtract 5 and 1 to the total of pies then you only have 2 left and that is half of the appl-sauce.

The value of x from the equation is 21 pies and the value of y from the equation is 16 batches of apple sauces

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total number of apple pies be x

Let the number of batches of apple sauce be y

Now , the system of equations are

5x + 4y = 169   be equation (1)

3x + 2y = 95   be equation (2)

Multiply equation (2) by 2 , we get

6x + 4y = 190   be equation (3)

Subtracting equation (1) from equation (3) , we get

x = 190 - 169

x = 21

Substitute the value of x in equation (2) , we get

3x + 2y = 95

3 ( 21 ) + 2y = 95

63 + 2y = 95

Subtracting 63 on both sides of the equation , we get

2y = 32

Divide by 2 on both sides of the equation , we get

y = 16

Therefore , the value of x and y are 21 and 16 respectively

Hence , the number of apple pies and apple sauces are 21 and 16 respectively

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

I NEED THAT ANSWER ASAP

Answers

Answer:

2064.19 km^3

Step-by-step explanation:

Formula for volume of a sphere

V = 4/3 pi r^3

  = 4/3  *  3.14  * 7.9^3  =

Answer:

[tex]2064\ km^3[/tex]

Step-by-step explanation:

Volume of a Sphere: [tex]\frac{4}{3}\pi r^3[/tex]

r (radius) = 7.9 km

[tex]V=\frac{4}{3}\pi r^3[/tex]

[tex]V=\frac{4}{3}*3.14*(7.9)^3 \\\\V=\frac{4}{3}*3.14*493.039\\\\V=\frac{4}{3}*1548.142\\\\V=\frac{4}{3}*\frac{1548.142}{1}\\\\V=\frac{6192.568}{3}\\\\V=2064.18933 < == round\ to\ the\ nearest\ whole\ number\\\\V=2064\ km^3[/tex]

Therefore, the volume of the sphere is [tex]2064\ km^3[/tex]

Hope this helps!

Which angles are complementary to each other?

Answers

Answer:

<1 and <2

Step-by-step explanation:

Complementary angles are two angles which their measure add up to 90 degrees.

There are only one angle pair that meet this requirement:

angle 2 and angle 1

What is the frequency?

Answers

Answer:

Its A

Step-by-step explanation:

12
Devonte and 19 other students are in
an afterschool robotics program. In order to
attend the state's competition they need to
raise $835.72 for transportation and other
expenses. So far, they have raised $311.12. If
each of the team members were to split the
remaining amount evenly, how much would each
team member be responsible for contributing?
A. $26.23
C. $41.79
B. $15.56
D. $57.34

Answers

A
1) Subtract what they already have from what they need
835.72-311.12=524.6
2)Then divide what’s remaining by the number of people.
524.6/20
3) Then round to the hundredths place because it’s money and your answer is 26.23.

Can anyone solve this correctly?

Answers

Answer:

ANSWER

160 in³

Step-by-step explanation:

First, Find the area of the base (rectangle)

A = LxW

= (10 in) x (8 in)

= 80 in²

Then, Find the volume of the pyramid using the formula (V = x B x H)

V = x B x H

= x (80 in²) x (6 in)

= (2 in) x (80 in²)

= 160 in³

Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 6?
A. 31/36

B. 1/18

C. 1/6

D. 5/36

Answers

Answer:

D. 5/36

Step-by-step explanation:

Write the expression. Then, complete the statements.


twice the difference of a number and seven


The word "twice" means
.

The words "the difference of" indicate


.

The expression is written as

Answers

Answer:

The equation is 2(x-7)

Hope it is correct

Answer: Write the expression. Then, Complete the statements.

.

.

twice the difference of a number and seven

Step-by-step explanation:

1. multiplication by 2

2. subtraction in parentheses

3. 2(n-7)

Calculate the compound interest on $6 000 if invested for 3 years at 7.5% per annum.



multiple choice answers:
$6000 $7453.78 $1453.78 $7534.87​

Answers

Your answer is B, $7453.80

Attached is the compound growth formula I used.

Given AB and AC are lines that are tangent to the circle with
the measure of angle BAC = 40°, what is the measure of angle BDC?

Answers

Answer:

C

Step-by-step explanation:

Givens

You are given 2 tangent lines.

You are also given a 4 sided figure.

All 4 sided figures have 360 degrees

A radius meets a tangent at 90 degrees

Formula

<BDA + <DCA + <BCA + <BDC = 360

Solution

90 + 90 +40 + <BDC = 360               Combine

220 + <BDC = 360                             Subtract 220 from both sides

220- 220 +BDC =360 - 220

<BDC = 140

Answer: C

   

A survey stopped men and women at random to ask them where they purchased
groceries, at a local grocery store or online.


How many men surveyed shop at a local grocery store.

Answers

35 men because it says 35 men shop at a grocery store

Write the ratio 2 : 5 in the form of 1 : n ?

Answers

Answer:

1:2.5

Step-by-step explanation:

just divide each side by 2

answer is it 1 2 3 or 4

Answers

Answer: C. 125.66 in²

Step-by-step explanation:

      This is asking us to find the surface area of this cone. We can use the formula and solve.

A = πrl + πr²

A = π(4)(6) + π(4)²

A = π(4)(6) + π(4)²

A ≈ 125.66 in²

      It would take C. 125.66 in² of toilet paper to cover the surface of this cone.

Urgent!!! Need help Please!!
Find the area of the triangle.
a. 620 sq. m b. 270 sq. m c. 540 sq. m d. 980 sq. m

Answers

Answer:

270 sq. m [b]

Step-by-step explanation:

So the area of a triangle is 1/2 bh (1/2 of base x height).

The base of the triangle shown is 20m. The height is 27m.

(1/2) (20)(27) = 270.

The area of this triangle is 270 sq. m (b)

What is the velocity of the plane that travels 3000km in 5 hours?

Answers

Answer:

600km/h

546.807 fps

0.1666667 km/s

Step-by-step explanation:

Use which ever unit youd want to in this scenereo, I'd use 600km/h

3000 / 5 = 600

In a small town, there are 4 times as many left-handed males as there are left-handed females, and there are 3 times as many right-handed females as there are right-handed males. There are a total of 204 males and 348 females in the town.

Let x represent the number of left-handed females, and let y represent the number of right-handed males. Write a system of equations to represent the situation. What is the value of x, the number of left-handed females?
6
24
96
108

Answers

Answer:

  (b)  24

Step-by-step explanation:

The given variable definitions and the given relationships let us write these statements:

  LH males = 4 × LH females = 4x

  RH females = 3 × RH males = 3y

  LH males + RH males = 204 = 4x +y

  RH females + LH females = 348 = 3y +x

Your favorite method of solving equations of this sort can tell you ...

  (x, y) = (24, 108)

There are 24 left-handed females.

__

Additional comment

Other numbers involved here are ...

  y = 108 . . . . right-handed males

  204-108 = 96 . . . . left-handed males (=4×24)

  348-24 = 324 . . . . right-handed females (=3×108)

__

If you want to solve the equations by hand, you can use substitution for y to get an equation in x:

  3(204 -4x) +x = 348   ⇒   -11x = -264   ⇒   x = 24

The equation to model Exponential Decay is:
y = a[1 – r)
y= total amount
a= starting amount
r= the growth rate as a decimal
t= number of growth periods
Question 1 (1 point)
Sarah takes 550 mg of an antibiotic. Every hour,
her body breaks down 25% of the remaining drug.
How much will be left after 12 hours?
Guys help me please I really don’t understand this

Answers

Exponential functions are used to represent growth or decay of a substance. The amount that will be left after 12 hours is 17.42mg

How to model exponential equations

The standard form of an exponential equation is given as:

[tex]y=a(1-r)^t[/tex]

where;

y= total amounta= starting amountr= the growth rate as a decimalt= number of growth periods

Given the following parameters

a = 550mg

r = 0.25

t = 12

Substitute into the formula

[tex]y=550(1-0.25)^{12}\\y = 550(0.75)^{12}\\y=17.42mg[/tex]

Hence the amount that will be left after 12 hours is 17.42mg

Learn more on exponential equation here: https://brainly.com/question/12940982

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