Consider a geometric sequence whose first term is 64 and fourth term is 125.
Part A: Determine the value of the common ratio.

Part B: Write the recursive formula for this sequence.

Part C: Write the explicit formula for this sequence.

Please help!

Answers

Answer 1

Answer:

Given a GP where:

a₁ = 64a₄ = 125Part A

Formula for nth term:

aₙ = a₁rⁿ⁻¹a₄ = a₁r³125 = 64r³r³ = 125/64r = 5/4Part B

Recursive formula

a₁ = 64aₙ = (5/4)aₙ₋₁Part C

Explicit formula:

aₙ = 64(5/4)ⁿ⁻¹

Related Questions

I’m stuck, help would be nice :D

Answers

Answer:

-14

Explanation:

3 x -3 - 5 = -14

Answer:

-14, -5, 4, and 13

Step-by-step explanation:

For each x value, substitute it for x in the equation.

For the first one where x = -3,

y = 3(-3) - 5

y = -9 - 5

y = -14

So the first one is -14. The next x value is 0

y = 3(0) - 5

y = 0 - 5

y = -5

Second one is -5. The next x value is 3

y = 3(3) - 5

y = 9 - 5

y = 4

Third is 4. The next x value is 6

y = 3(6) - 5

y = 18 - 5

y = 13

So the last one is 13.

Blank probability is the prediction ratio of favorable outcomes to the total number of outcomes.

Answers

Isn’t it the theoretical probability?

determine the area of the parallelogram below

Answers

Answer:

A= BH

A=8cm ×2.2 cm

A= 17.6cm²

Find Area, can't figure out how to get answer.
Which numbers do I use for each figure??

Answers

Answer:

Use L x W x H

Step-by-step explanation:

So...

5 x 12 x 8 = 480

A ball is launched from a 25.48-meter tall platform. The equation
for the ball's height h at time t seconds after launch is h (t) =
-4.9t² + 2.94t + 25.48, where his in meters. When does the object
strike the ground?

Answers

Therefore the solution of the given question of equation comes out to be the object will hit the ground after 6 seconds.

Define equation.

Two variables that are equal—one on each side of a "equals" sign—are represented mathematically by an equation. Equations can be used to solve problems in daily life. To tackle challenges in real life, we frequently seek pre algebra assistance. The very foundation of mathematics is pre-algebra.

Here,

Given : -4.9t² + 2.94t + 25.48

Then,

To find the When does the object strike the ground :

We get :

=> -4.9t² + 2.94t + 25.48 = 0

Using discriminant formula

We find the value of t:

=> t = -19.6 ±[tex]\sqrt{19.6^{2} - 4 (-4.9)(25.48)}[/tex] /  2(-4.9)

=> t =-2 or 6

So we neglect -2

So solution for t = 6 seconds

Therefore the solution of the given question of equation comes out to be the object will hit the ground after 6 seconds.

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Multiply and combine like terms to determine the product of these polynomials. (2x – 3)(5x + 6)

Answers

Answer:

Step-by-step explanation:

(2x – 3)(5x + 6)

10x2 + 12x - 15x - 18

10x2 - 3x - 18

The product of the given polynomials is 10x² - 3x - 18

What is a polynomial?

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

The given polynomials are:

(2x – 3)(5x + 6)

By multiplying the two polynomials, we get

10x² + 12x - 15x - 18

10x²- 3x - 18

Hence, 10x²- 3x - 18 is the product of the given polynomials.

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Write an equation of a line

Answers

Answer:

Step-by-step explanation:

Steps to find the equation of a line from two points:

   1) Find the slope using the slope formula. ...

   2) Use the slope and one of the points to solve for the y-intercept (b). ...

   3) Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = MX + b) to get the equation for the line.

Solve it please
Please please please ​

Answers

Answer:   x = 30

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

Explanation:

When adding three angles of any triangle, they always add up to 180

3x+2x+x = 180

6x = 180

x = 180/6

x = 30

This then means,

3x = 3*30 = 902x = 2*30 = 60

This triangle is a 30-60-90 triangle.

Solve.
5370
Please help please

Answers

The answer is 1
Any number to the power of zero is always 1

Answer:

[tex]5370^{0}=1 [/tex] is a required answer.

2. Two sidewalks in a park are represented by lines on a coordinate grid.
Sidewalk 1: 3x + 3y = 6
Sidewalk 2: y = x + 6
(a) Find the solution to the system of equations by using the substitution method.
(b) Show ALL of your steps.

Answers

Answer: x is -2 and y is 4 if needed (-2,4) is the origin form

Step-by-step explanation: first we take side walk one we subtract -3x on both sides then you get 3y=-3x+6 divide both by 3 you get y=-x+2 finally we can substitute. substitute y for x+6 you get x+6 = -x+2 do the inverse of -x on both sides you get 2x+6=2 do the inverse of 6 on both sides you get 2x=-4 divide 2 on both sides you get x=-2. substitute x of  y=-x+2 to y=-(-2)+2 mult  -1 x -2 is 2, 2+2 is four so y= 4 put that together x is -2 and y is 4

simplify expression: 3f+8(2m-7)

Answers

After simplification we got the above expression in the form 3f + 16m -56

What is simplify in mathematics?

The word "simplify" implies to turn something in a simpler form.

In mathematics, simplify an expression means write an expression in such a way that is comparatively less complicated than before. The main purpose of simplify an expression is to make it easy to solve as well as calculation.

How to simplify the above expression?

3f + 8(2m-7)

we rearrange the expression by removing the parenthesis.

we remove the parenthesis by multiplying the factors.

3f + 8 × 2m - 8 × 7

3f + 16m -56

the above expression has no like terms to add or subtract so it is kept in this form.

Hence, 3f + 16m -56 is the simpler form.

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cos(x)<.025
cos^2(x)<.25
sin(x)<.25
sin^2(x)<.25

PLZ HELP

Answers

Step-by-step explanation:

First

since its follow the pattern Intercept Max... Intercept Min...

Its a positive sine graph

Asin(B(x-0))<0.25

A=1

B=2π/period

period From the graph = 2π

B=2π/2π

B=1

Sin(x)<0.25

I'd go with C.

On Saturday morning, Wendy watched one and a half hours of her favorite shows on television. During the shows there were 27 commercials. What is the unit rate of commercials per hour? 9 hours per commercial 12 commercials per hour
14 commercials per hour 18 commercials per hour

Answers

The unit rate is 18 commercials per hour.

What is Division?

A division is a process of splitting a specific amount into equal parts.

On Saturday morning, Wendy watched one and a half hours of her favorite shows on television.

During the shows there were 27 commercials.

We need to find the unit rate of commercials per hour.

To find this we have to divide 27 by number of hours

27/[tex]1\frac{1}{2}[/tex]

Convert [tex]1\frac{1}{2}[/tex] to improper fraction

27/(3/2)

When whole number is divided by fraction, the denominator is multiplied with whole number

27×2/3

54/3

18

Hence, the unit rate is 18 commercials per hour.

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Answer:18 commercials per hour

Step-by-step explanation:

Find the circumference of a circle with an area of 254.47 sq. in.

Answers

Answer:

56.55 in is the answer

Hope this helps

Have a good day :)

Step-by-step explanation:

-√8 - √54 + 2√6 how to simplify

Answers

Answer:

6√2

Step-by-step explanation:

-√2×2×2 -√2×3×3×3 + 2√3×3

-2√2 - 3✓6 + 2×3

-2√2 - 3√2×2 +2 + 6

6√2

X
Let f(x) = 3x2 - 6x + 2. Find f(2)
A
B
10
16
C 12
E
D 2
8

Answers

On solving the provided question, we can say that -  f(x) = 3x2 - 6x + 2, and the value of the equation f(x) = +2

What is equation?

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

f(x) = 3x2 - 6x + 2

x = 1

f(x) = +2

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Three neighbors each decide to plant a garden of petunias and daffodils. The table below shows the number of flowers in each garden.

which one has the greatest ratio of petunias to daffodils in their garden.


Neighbor
Ms. Herrera
Mr. Marks
Mrs. Perry
Number of Petunias
Ms. Herrera 48,
Mr. Marks 84,
Mrs. Perry 30
Number of Daffodils
Ms. Herrera 16,
Mr. Marks 24,
Mrs. Perry 8

Answers

Answer:

Mrs. Perry

Step-by-step explanation:

find the ratio by dividing the petunias by the daffodils

Ms. H =3

Mr. M = 3.5

mrs. P= 3.75

Write the equation of the line ( will mark brainlist)

Answers

The answer is y=-(5/3)x+5

Answer:

[tex]y=-\frac{5}{3} x+5[/tex]

Step-by-step explanation:

Points on the graph: (0, 5) and (3, 0)

Slope:

m=(y2-y1)/(x2-x1)

m=(0-5)/(3-0)

m= (-5)/3

m= -5/3

Slope-intercept:

y - y1 = m(x - x1)

y - 5 = -5/3(x - 0)

y - 5 = -5/3x

y = -5/3x + 5

Plz help me well mark brainliest if correct!!....

Answers

Answer:

The first one is correct.

WHAT IS A PRICE OF A 7 - MINUTE DIAL DIRECT CALL TO NEW YORK, NY, WHEN YOU
CALL IN THE EVENING?

Answers

The price of a seven minute call direct to New York, in the evening, is given as follows:

$5.82.

How to obtain the cost of the call?

The cost of the call is obtained considering the information given in the table, for which the proportions are applied.

We have a direct call, meaning that it is a person-to-person call, thus the flat rate is of $3.00 per minute.

Then the minute proportions, considering that the call happens in the evening, are given as follows:

First minute: 0.38 of $3.Each additional minute: 0.26 of $3.

A seven minute call is composed by six additional minutes after the first, hence the total cost is obtained as follows:

0.38 x 3 + 6 x 0.26 x 3 = $5.82.

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120 students appeared in an examination. how many have failed if 2/3 of them have passed​

Answers

Answer:

40 failed

Step-by-step explanation:

2/3 of 120 is 80, so you subtract the 80 who passed from the 120 total to get 40 students who failed

Answer:

Step-by-step explanation:

If [tex]\frac{2}{3}[/tex] passed the exam then:

[tex]\frac{3}{3} -\frac{2}{3} = \frac{1}{3}[/tex] failed the exam

now to find the number which failed we multiply:

[tex]\frac{1}{3} \cdot 120 = 40[/tex] and 40 is our answer

There are 12 girls and 18 boys in a class. What is the largest number of group they can be split into and have the same of boys and girls on each team?

Answers

Answer: The largest number of groups they can be split into and have the same number of boys and girls on each team is 6 groups with 2 boys and 2 girls in each group.

A sailor cut a 40 foot length of rope in two pieces. If the longer piece is five feet less than twice the shorter piece of rope, then how long is the longer piece.

Answers

Answer:

23ft longer

Step-by-step explanation:

The shorter piece is 15 feet, while the longer piece is 25 feet

Let the longer piece be y, and the shorter piece be x.

So, we have:

[tex]x + y = 40[/tex] --- the length of the rope

[tex]y =2x - 5[/tex] --- the relationship between the short and the long piece

Substitute 2x - 5 for y in [tex]x + y = 40[/tex]

[tex]x + 2x - 5 =40[/tex]

[tex]3x - 5 =40[/tex]

Add 5 to both sides

[tex]3x =45[/tex]

Divide both sides by 3

[tex]x =15[/tex]

Substitute 15 for x in [tex]y =2x - 5[/tex]

[tex]y =2 \times 15 -5[/tex]

[tex]y =30 -5[/tex]

[tex]y =25[/tex]

Hence, the shorter piece is 15 feet, while the longer piece is 25 feet

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PLS HELP! YOU DONT NEED TO DO ANYTHING JUST LET ME KNOW IF ITS RIGHT OR NOT AND GIVE ME A REASON WHY

Question: what angle below is adjacent to angle CBD?
Me:EBD

Answers

Answer:

your answer is right

Step-by-step explanation:

adjacent angles = angles with a common side and corner point

Answer:

u are correct bc adjacent means: next to or adjoining something else.

hope u get a good mark gl

Step-by-step explanation:

What does 69 divided by 310.5 equal in decimal form?

Answers

The answer would be 0.22222222
You need to take 69 and divide it by 310.5 and you will get your answer.

Which equation should be used to find the volume of the figure?
12 cm
13.cm
6 cm
10 cm

Answers

Answer:

O V=3(10XB)(12)

Step-by-step explanation:

The makers of a popular brand of laundry detergent have discovered a new secret ingredient that they believe will boost the cleaning power of their detergent. The new ingredient is expensive, and if they use it, they would have to increase the retail price of the detergent (and they worry that the price increase will cause them to lose customers). However, they believe that if the improved detergent gets clothes drastically cleaner, customers will recognize that it is worth the extra cost. They conduct an experiment to compare the performance of the new and old formulas at removing grass stains, red wine, and chocolate from white t-shirts. Each cleaned shirt was rated on a scale from 1 (stain did not get removed) to 10 (no evidence of the stain) by trained experts. They compared the average rating for the new and old formulas. Suppose, at the 5% significance level, they find that the new formula cleaned the shirts significantly better than the old formula, with a p-value of 0.046. Interpret the p-value, in terms of the probability of the results happening by random chance, in this context.

Answers

Answer:

The p-value is of 0.046 < 0.05, which means that there is a low probability of the results happening by random chance, and thus there is significant evidence to conclude that the new formula cleaned the shirts significantly better than the old formula.

Step-by-step explanation:

If the p-value is less than the significance level, it means that there is a low probability of the results happening by random chance.

In this question:

The p-value is of 0.046 < 0.05, which means that there is a low probability of the results happening by random chance, and thus there is significant evidence to conclude that the new formula cleaned the shirts significantly better than the old formula.

(2.1)to the power of2 +5.2-7.2)x7.1

Answers

The numeric value of the expression ((2.1)² + 5.2 - 7.2) x 7.1 is given as follows:

17.1.

How to obtain the numeric value of the expression?

The expression for this problem is defined as follows:

((2.1)² + 5.2 - 7.2) x 7.1

The precedence of operators follows the PEMDAS acronym, as follows:

P: power operations.E: exponent operations, with the same precedence as power operations, depending which appears first on the expression.M: multiplication operations.D: division operations, with the same precedence as division operations, depending which appears first on the expression.A: addition operations.S: subtraction operations, with the same precedence as subtraction operations, depending which appears first on the expression.

Hence the parenthesis takes precedence, thus:

(2.1)² + 5.2 - 7.2.

Then the power takes precedence, thus:

(2.1)² + 5.2 - 7.2 = 4.41 + 5.2 - 7.2

Addition and subtraction can be done in any order, hence:

4.41 + 5.2 - 7.2 = 2.41.

Then the multiplication is given as follows:

2.41 x 7.1 = 17.1.

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I NEED HELP. PLEASE ANSWER QUICK. BRAINLIEST WILL BE GIVEN. THERE IS A BOT AUTO ANSWERING. PLEASE ANSWER ANYWAY

Answers

Answer:

The answer is A

Step-by-step explanation:

The shape is a rhombus when plotted on a quardanent plane. The shape is similar to a diamond.

please answersssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss

Answers

Answer: 89,596

Step-by-step explanation:Hope I helped

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