Determine the number of terms n in each geometric series.
13) a1 = 0.75, r = 4, Sn =1023.75

Answers

Answer 1

Answer:

Number of terms: n=6

Step-by-step explanation:

We are given:

a₁ = 0.75

r = 4

Sₙ = 1023.75

We need to find number of terms i.e n

The formula used will be:[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]

Putting values and fining n

[tex]S_n=\frac{a(r^n-1)}{r-1}\\1023.75=\frac{0.75(4^n-1)}{4-1}\\ 1023.75=\frac{0.75(4^n-1)}{3}\\3\times 1023.75=0.75(4^n-1)\\3071.25=0.75(4^n-1)\\4^n-1=\frac{3071.25}{0.75}\\4^n-1=4095\\4^n=4095+1\\4^n=4096[/tex]

We know that [tex]4^6= 4096[/tex]

[tex]4^n=4^6[/tex]

Using Exponent rule: [tex]a^n=a^b => n=b[/tex]

[tex]n=6[/tex]

So, Number of terms: n=6


Related Questions

Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car shows it can drive 370 miles on 20 gallons of gas. How far could you drive on 65 gallons of gas?

Answers

Answer:

1202.5  miles

Step-by-step explanation:

It is given that.

A test of a new car shows it can drive 370 miles on 20 gallons of gas.

We need to find how far you could drive on 65 gallons of gas.

20 gallons of gas = 370 miles

1 gallon = 18.5 miles

For 65 gallons of gas, multiply 65 and 18.5.

65 gallons = 18.5 × 65 miles

= 1202.5  miles

Hence, 1202.5  miles you could drive on 65 gallons of the gas.

Which point on the graph represents they-intercept

Answers

Answer:

Where's the graph kid sir?

Step-by-step explanation:

Answer:

The y-intercept on a sloped line is where the line crosses the y-axis. Taking a look at your graph, Find a point where the line crosses the y-axis.

Jon went to a restaurant and gave a 20% gratuity of $15 on the meal. How much was the original amount of the bill?

Answers

Answer:

$75

Step-by-step explanation:

$15 divided by 0.2 = $75

0.2 = 20%

Bentley took a ride on Rudolph’s back. At 8:00 pm, he counted 68 stars. At 10:00 pm, he counted twice as many stars. At 12:00 am, he counted five times more stars than his first count.

A. How many stars did Bentley count at 10:00 pm?

B. How many stars did Bentley count at 12:00 am?

Answers

Answer:

A. 136 stars

B. 340 stars

Answer:

At 10 pm he counted 136 stars and at 12 pm he counted 340

Step-by-step explanation:

for 10 pm:

68 x 2

for 12 pm:

68 x 5

your aunt and uncle have been visiting at your home. five minutes after they drive away, you realize that they forgot their luggages you happen to know the drive slowly, so you get in your car and drive to catch up with them. Your average speed is 10 miles and hour faster that their average speed, and you catch up with them in 25 minutes. How fast did you drive.

Answers

When you catch up, the distance traveled is the same

Distance = rate x time

r = uncle's rate

30 min = 30/60 hr = uncle's time

25 min = 25/60 hr =  your time

Uncle's distance = Your distance

(r)(30/60) = (r + 10)(25/60)

(r)(1/2) = (r + 10)(5/12)

r/2 = 5r/12 + 50/12  

6r = 5r + 50

r = 50  

Uncle's rate = 50 mph

Your rate = 50 + 10 = 60 mph

On mercury, the distance d (in feet) that an object falls in time t(in seconds) can be modeled by the function f(t)=6t^2. how long would it take an object to fall 54 feet on Mercury. ( plz show the work on how u got the answer)

Answers

Answer: t=3.75

Step-by-step explanation:45=6t×2

6t=22.5

t=3.75

The object will take 3 seconds to fall 54 feet on Mercury according to the given function f(t) = 6t².

What is a function?

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

Given the function,

f(t) = 6t² where t is time in seconds while f(t) is the distance in feet.

At f(t) = 54 feet

6t² = 54

t² = 54/6 = 9

t = 3 seconds

Hence "The object will take 3 seconds to fall 54 feet on Mercury according to the given function f(t) = 6t²".

For more about the function,

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please help it is due today

Answers

Answer:

4 2/5 tons

Step-by-step explanation:

2/5 = 4/10 = .40

4.40 tons > 4.3 tons

Find all values of $x$ such that $\sqrt{4x^2} - \sqrt{x^2} = 6$.

Answers

9514 1404 393

Answer:

  x = -6 or 6

Step-by-step explanation:

The square root is always positive, so the equation simplifies to ...

  [tex]\sqrt{4x^2}-\sqrt{x^2}=6\\\\2|x|-|x|=6\\\\|x|=6\\\\x=\{-6,\ 6\}[/tex]

_____

The graph shows the solutions to f(x) = 0, where f(x) = √(4x²) -√(x²) -6.

Classify the special quadrilateral.

Answers

Answer: Rhombus

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

Explanation:

The tickmarks show that all four sides are the same length. Therefore, this figure is a rhombus. It is not a square because the angle would need to be 90 degrees. We can say it is a non-square rhombus, or a rhombus that isn't a square. It is also not a rectangle either because all rectangles have each angle at 90 degrees.

which could describe the graph of a nonproportional relationship
A- the Y - intercept is positive
B- the y-intercept is 0
C- the line intersects the origin
D- the y- intercept is negative​

Answers

D because I actually had the same exact question

Question #3: Complete the statement below to show the correct value of 100%. Part A: The expression 100 3 = 10 because 100 = 102 and = 101 = 10. Po Part B: When simplified, the answer is rational irrational​

Answers

Answer:

Step-by-step explanation:

Part A.

Expression [tex](100)^{\frac{1}{2}}[/tex] = 10

Because 100 = [tex](10)^{2}[/tex] and [tex][(10)^2]^{\frac{1}{2}}=10^1=10[/tex]

[Since, [tex](a^{2})^{\frac{1}{2}}=a^{2\times \frac{1}{2}}=a^1[/tex]]

Part B.

When simplified, the answer is RATIONAL.

[Since, 10 can be written as [tex]\frac{10}{1}[/tex]]

.........answer this for me plz ill give brainliest

Answers

Answer:

I think I donot say it is correct only peridect 4cm*4cm*3cm*8cm=384cm

Answer:

18

Step-by-step explanation:

area of the square-->12

area of the triangle--->6

area of the square + area of the triangle = area of the trapezoid

12+6=area of the trapezoid

18 = area of the trapezoid

Cho is making a rectangular garden, where the length is x feet and the width is 6x + 6 feet. He wants to add garden stones around the perimeter of the garden once he is done. If the garden is 6 feet long, how many feet will Cho need to cover with garden stones? Cho will need to cover _______ feet with garden stones.

Answers

nice profile picture

If a snowman has 3 old felt hats and 4 scarves from which to choose, how many different hat/scarf outfits can he wear?

Answers

Answer:

12 hat/scarf outfits

Step-by-step explanation:

If a snowman has 3 old felt hats and 4 scarves from which to choose, how many different hat/scarf outfits can he wear?

We solve this question using the fundamental counting principle.

This states that:

When we have two events, a and bthe number of ways both events can happen is a × b

From the above question, our two events is

a = 3 old felt hats

b = 4 scarves

Hence, the different hat/scarf outfits can he wear is given as

3 × 4 = 12 hat/scarf outfits

please help meee i dont know what i have to do

Answers

Y=2x+b is the correct answer

Find the explicit formula for the given sequence 1/4, 3/4, 5/4, 7/4​

Answers

Step-by-step explanation:

d=(3/4)-(1/4)=(5/4)-(3/4)=(7/4)-(5/4)=1/2

then it is an arithmetic sequence

by using this equation :

a(n) = a1 +(n-1)d

and we have : a1=(1/4),  d=(1/2)

So:

Explicit formula: a(n) = (1/4) +(n-1)*(1/2)

hope this helps

Answer:

Step-by-step explanation:

d=(3/4)-(1/4)=(5/4)-(3/4)=(7/4)-(5/4)=1/2

then it is an arithmetic sequence

by using this equation :

a(n) = a1 +(n-1)d

and we have: a1=(1/4),  d=(1/2)

So:

Explicit formula: a(n) = (1/4) +(n-1)*(1/2)

can someone help me plz​

Answers

Answer: The answer is 1 and 2/3

Hope this helps you bye

Here are the prices of some items and the amount of sales tax charged on each in Nevada. row 1 cost of item ($) sales tax ($) row 2 10 0.46 row 3 50 2.30 row 4 5 0.23 What is the sales tax rate in Nevada

Answers

Answer:

4.6%

Step-by-step explanation:

Cost of item __ sales tax

10 ___________0.46

50 __________ 2.30

5 ___________ 0.23

To obtain the sales tax % :

Sales tax % * cost of item = amount of sales tax

Let sales tax % = x

Using any of the rows in the table :

x * 10 = 0.46

x = 0.46 / 10

x = 0.046

x = (0.046) * 100% = 4.6%

5.5.5.5.5.5. in expanded form

Answers

Answer:

You can't even do that I'm pretty sure

Step-by-step explanation: Too many decimals points

If you can answer that would be nice, thank you.
What type of angle is shown here?

Answers

Answer:

I would say Acute. The angle is definitely less than a right angle. Reflex angles are angles more than 180 degrees, but less than 360 degrees.

A study by Great Southern Home Insurance revealed that none of the stolen goods were recovered by the homeowners in 80 percent of reported thefts: [ 6 marks] a. During a period in which 200 thefts occurred, what is the probability that no stolen goods were recovered in 170 or more of the robberies? b. During a period in which 299 thefts occurred, what is the probability that no stolen goods were recovered in 150 or more robberies?

Answers

Solution :

Given :

n = 200, p = 80% = 0.8, q = 1 - p = 0.2

[tex]$\mu = np$[/tex]

  [tex]$= 200 \times 0.8 = 160$[/tex]

[tex]$\sigma= \sqrt{npq}$[/tex]

[tex]$\sigma= \sqrt{200 \times 0.8 \times 0.2}$[/tex]

   = 5.6569

a). x = 169.5

∴ [tex]$z = \frac{x- \mu}{\sigma}$[/tex]

  [tex]$z = \frac{169.5- 160}{5.6569}$[/tex]

     = 1.6794

[tex]$P(x \geq 170) = P(z>1.6794) = 0.0465$[/tex]

Therefore, probability that the stolen goods were not recovered in 170 robberies or more is = 0.0465

b). x= 149.5

   [tex]$z = \frac{x- \mu}{\sigma}$[/tex]

   [tex]$z = \frac{149.5- 160}{5.6569} = -1.8561$[/tex]

[tex]$P(x \geq 150) = P(z>-1.8561) = 0.9683$[/tex]

Therefore the probability that the stolen goods were not recovered in the 150 or in more robberies is = 0.9683

16x2 + 4x2 – 2x – 12x2 + 4x

Answers

Answer:

8x^2  +  2x

Step-by-step explanation:

A plane is flying at an elevation of 1000 feet, directly above a straight highway. Two cars on the highway are on different sides of the plane. The angle of depression to one car is 10 degrees and to the other car is 8 degrees. How far apart are the cars, to the nearest foot

Answers

Answer:

Step-by-step explanation:

Calculate the square root of 1/2

Answers

Answer:

I looked it up and it said 0.5

Scientists released 6 rabbits into a new habitat in year 0. Each year, there were four times as many rabbits as the year before. How many rabbits were there after x years?

Answers

Answer: 6 × 4^x

Step-by-step explanation:

From the question, we are told that scientists released 6 rabbits into a new habitat in year 0 and that each year, there were four times as many rabbits as the year before.

The number of rabbits there after x years will be:

= 6 × 4^x

For example, let us say we want to calculate the number of rabbits after 2 years.

= 6 × 4^x

= 6 × 4²

= 6 × 16

= 96 rabbits

Solve the system of equations using substitution.

y = −2x + 1
4x + 2y = −2

No solution
Infinitely many solutions
(0, −4)
(−4, 0)

Answers

Answer:

no solution

Step-by-step explanation:

x cancel out each other

Answer:

no solution

Step-by-step explanation:

PLS HELP DUE AT 11:59 AND I MISSED THE LESSON ON THIS

Answers

Answer:

try -14!

Step-by-step explanation:

4x+188=6x+216

x=-14

Answer:

x = -14

Step-by-step explanation:

To start since the angles are congruent then they must be equal to each other, so we start by setting them equal to each other. The equation will be 4x + 188 = 6x + 216

Next we solve for x, subtracting 188 and 6x from each side. The new equation will be

-2x = 28

Then divide both sides by negative 2 to get x = -14.

What is an adjective that starts with t and means sweet? Okay, here's context, I'm making a u s e r n a m e, and one of the adjectives is "taro" If not, what are just some good u s e r n a m e s

Answers

Treat

The question confuses me but treat starts with t, is an adjective, and rhymes with sweet

What is the approximate circumference of the circle shown below?

A. 48.7 cm
B. 24.3 cm
C. 97.3 cm
D. 39.5 cm

Answers

Answer:

The answer is A. 48.7

Step-by-step explanation:

The approximate circumference of the circle is,

⇒ C = 48.7 cm

What is mean by Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

A circle is shown in image.

And, Diameter of circle = 15.5 cm

Since, WE know that;

Circumference of circle is,

C = πd

Where, d is diameter of circle

Hence, The approximate circumference of the circle is,

⇒ C = 3.14 × 15.5

⇒ C = 48.7 cm

Thus, the circumference of the circle is,

⇒ C = 48.7 cm

Learn more about the circle visit:

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Luis wants to buy a skateboard that usually sells for $80. All merchandise is discounted 20%.
What is the total cost of the skateboard if Luis has to pay a state sales take of 6%?

Answers

Answer: $68.80

Step-by-step explanation: the discount is 14% because it is subtracted from 20% and 0.14 x 80 is 68.80 hope this helps

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