Find the sum of the first 9 terms of the following series, to the nearest integer 3, 3.75, 4.6875

Answers

Answer 1

Answer:

77.4

Step-by-step explanation:

The first term, a, of the series is 3.

It is a geometric progression, so we can calculate the common ratio, r:

3.75 / 3 = 1.25

The sum of n terms of a geometric progression is given as:

[tex]S = \frac{a(1 - r^n)}{(1 - r)}[/tex]

where n =  number of terms considered

The sum of the first 9 terms will therefore be:

[tex]S_9 = \frac{3(1 - 1.25^9)}{(1 - 1.25)} \\\\S_9 = \frac{3(1 - 7.45)}{-0.25}\\ \\S_9 = \frac{3 * -6.45}{-0.25}\\ S_9 = \frac{-19.35}{-0.25}\\ \\S_9 = 77.4[/tex]


Related Questions

What two whole, positive numbers that have a one-digit answer when multiplied and a two-digit answer when added?

Answers

Answer:

1 & 9

Step-by-step explanation:

I believe that the numbers 1 and 9 fit the statement- as they would be 1 x 9= 9 and 1 + 9=10.

Hope this helped!! Please mark as Brainliest and/or give a rating !! Thank You :)

The price of a gallon milk was $2.65 the price rose why dollars after the last hurricane then the price dropped $.15 and later Rosie came by five cents which expression represents the current price of milk

Answers

Answer:

p =  y + 2.55

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

The price of a gallon of milk was $2.65. The price rose y dollars after the last hurricane. Then the price dropped $0.15 and later rose again by $0.05. Which expression represents the current price of milk

My answer:

Let p is the price of milk

Given the information:

Stage 1: The price of a gallon milk was $2.65

<=> p = 2.65  

Stage 2: rose y dollar

<=> p = 2.65   + y

Stage 3:  price dropped $.15

<=> p =  2.65   + y  - 0.15

Stage 4: rose again by $0.05

<=> p = 2.65  + y  - 0.15  + 0.05

<=> p =  y + 2.55

Hope it will find you well.

Find the y-intercept of the following equation. Simplify your answer.


y
=
–6
7
x
+
5
9


y-intercept =

Answers

Answer:

Y-intercept: 59

Step-by-step explanation:

Y=mx+b, in which b stands for y intercept

Answer:

59

Step-by-step explanation:

Question - Find the y-intercept of the following equation. Simplify your answer.

We write graphical equation as:

y = mx + b

where:

y: point on y axis

m: gradient/ slope (RISE/RUN)

x: point on x axis

b: y intercept (point where the line touches the y axis)

Now in:

y  =  –6 7  x  +  5 9

y-intercept = 59

The point (2,9) lies on a circle and the center of the circle is at the point (2,1). What is the equation of this circle? A. (x - 2)2 - (y - 1)2 = 64 B. (x - 2)2 + (y - 1)2 = 64 C. (x + 2)2 + (y + 1)2 = 64 D. (x - 1)2 - (y - 2)2 = 8

Answers

Answer:

B:(x-2)^2+(y-1)^2=64

Step-by-step explanation:

center is (2,1), point is (2,9)

so the radius=9-1=8

(x-2)^2+(y-1)^2=64

please help with this

Answers

Answer:

37

Step-by-step explanation:

Using the Pythagorean theorem:

[tex]x=\sqrt{12^2+35^2}=\sqrt{144+1225}=\sqrt{1369}=37[/tex]

Hope this helps!

How many points does a plane have that is on the same line



Answers

In a three-dimensional space, a plane can be defined by three points it contains, as long as those points are not on the same line.


Factor the trinomial by grouping.
- 13x + 6 + 6x^2

Answers

Answer:

(2x-3)(3x-2)

Step-by-step explanation:

[tex]-13x+6+6x^2= \\\\6x^2-13x+6= \\\\6x^2-4x-9x+6= \\\\2x(3x-2)-3(3x-2)= \\\\(2x-3)(3x-2)[/tex]

Hope this helps!

Select all of the equations for which x = -4 *
1 point
x + 4 = 0
-3x = 12
x - 4 = -8
x + 4 = 4

Answers

Answer:

x + 4 = 0. / -3x = 12. / x - 4 = -8

Step-by-step explanation:

x + 4 = 0

-4. -4

x = -4

-3x = 12

÷-3. ÷-3

x = -4

x - 4 = -8

+ 4. +4

x = -4

x + 4 = 4

-4. -4

x = 0

What are the factors of 36xyz?

A. 36,x,y
B. 36x,y,z
C. x,y,z
D. 36,x,y and z

Answers

Answer:

ç

Step-by-step explanation:

the two-way table below shows the intended careers among the incoming class of first-year college students, divided by gender. If a student is chosen and random, what is the probability of the student is female who intends to be a research scientist?​

Answers

Answer:

c. 2.2%

Step-by-step explanation:

The total number of all students in all fields, male and female is 4663.

There are 103 female research scientists.

p(female scientist) = 103/4663 = 0.022 = 2.2%

PLEASE HELP!! In Moose, Wyoming, the snow level is modeled by the function y = 2x + 14. Here, y is the amount of snow in inches, and x is the number of hours after midnight (x = 0). 8. What is the meaning of the y-intercept in terms of the problem? 9. What is the meaning of the slope in terms of the problem? 10. What was the snow level at 8 a.m., when x = 8?

Answers

Answer:

8. The y-intercept represents the 14 inches of snow 0 hours after midnight.

9. The slope indicates that the snow level increases 2 inches for every hour that passes after midnight.

10. 30 inches

Step-by-step explanation:

8. given in the text

9. given in the text

10.

[tex]y=2x+14[/tex]

[tex]y=2(8)+14[/tex]

[tex]y=30[/tex]

Point AAA is at {(-3, 4)}(−3,4)left parenthesis, minus, 3, comma, 4, right parenthesis and point CCC is at {(2,-6)}(2,−6)left parenthesis, 2, comma, minus, 6, right parenthesis. Find the coordinates of point BBB on \overline{AC} AC started overline, A, C, end overline such that the ratio of ABABA, B to ACACA, C is 4:54:54, colon, 5.

Answers

Answer:

The coordinates of point B = (1, -4)

Step-by-step explanation:

Complete Question

Point A is at (−3,4) and point C is at (2,−6). Find the coordinates of point B on line AC such that the ratio of AB to AC is 4:5.

Solution

Point B divides line AC into two parts

A = (-3, 4)

C = (2, -6)

AB:AC = 4:5

If (AB/AC) = (4/5)

5AB = 4AC

But AC = AB + BC

5AB = 4(AB + BC)

5AB = 4AB + 4BC

5AB - 4AB = 4BC

AB = 4BC

(AB/BC) = (4/1)

AB:BC = 4:1

Hence, point B divides line AC internally into two parts with ratio 4:1

Mathematically, if a point P(x, y) divides the coordinates (x₁, y₁) and (x₂, y₂) internally in the ratio m:n then point P(x, y) is given as

x = [(mx₂ + mx₁)/(m + n)]

y = [(my₂ + my₁)/(m + n)]

For this question,

x₂ = 2

x₁ = -3

y₂ = -6

y₁ = 4

m = 4

n = 1

Point B is then described with coordinates

x = [(4×2 + 1×-3)/(4+1)] = (5/5) = 1

y = [(4×-6 + 1×4)/(4+1)] = (-20/5) = -4

Hence, the coordinates of point B is given as

(x, y) = (1, -4)

Hope this Helps!!!

Answer:

(-3,-3)

Step-by-step explanation:

above.

What is the diameter of the smallest circle that would enclose 2,000 pennies?

Answers

Answer:

Almost about 4500 mm

Step-by-step explanation:

Measure the pennies width and estimate. Multilpy by 2000 and there you go!

Find the area and perimeter of a square that has a side length of 4. Remember area is a length times width and perimeter is when you add all the sides together.

Answers

Answer:

Area= 16

Perimeter= 16

Answer:

A = l*w

P = 2l + 2w

A = 4*4 = 16

A = area

l = length

l = 4

w = width

w = 4

The area is equal to 16.

P = 2*4 + 2*4 = 16

P = perimeter

2l = 2*length

2l = 2*4

2w = 2*width

2w = 2*4

The perimeter is equal to 16.

It can be concluded both are equal to each other.

Hope this helps

Mr. Johnson has a garden in the shape of a kite with a length of 5 feet and a width of 4 feet. A bag of topsoil covers 10 square feet.

Answers

The area of each triangle is 5 ft²

The area of the garden is 10 ft²

The number of bags of topsoil needed is 1 bag

Hope this helps

-Carrie

Please mark brainliest

Stay safe

Answer:

The area of each triangle is ft

The area of the garden is 10  ft2.

The number of bags of topsoil needed is 1 .

Topic: Probability


Only complete question 9.

Answers

Answer:

see below

Step-by-step explanation:

a. H 1, H2 ,H3  T1 ,T2, H3

b  6 possible outcomes

c 2 outcomes for the coin ( h,T) 3 outcomes for the spinner

2*3 = 6

I need help ASAP I shall give brainlyist (idk how to spell) figure out how much A cand hold and how much B can hold

Answers

Answer:

A) 84.78

B) 42.39

Step-by-step explanation:

A)

[tex]\pi r^2 h= \\\\3.14 \cdot 3^2 \cdot 3= \\\\84.78[/tex]

B)

[tex]\pi r^2 h= \\\\3.14 \cdot 1.5^2 \cdot 6=\\\\42.39[/tex]

Hope this helps!

What is the length of HG? What is the length of HI?

Answers

? + 8 = 11
Subtract 8 from both sides.
? = 3
HG = 8

? + 6 = 9
Subtract 6 from both sides.
? = 3
HI = 3

Answer:

HI = 3 and HG = 3

Step-by-step explanation:

As you see from the bottom line, the length of the HIJ line = 9. 9 - 6 (6 is the length of the IJ line) = 3, so 3 is the length of the HI line. On the second picture, 11-8=3, so HJ = 3.

Edit: Whoops, i didn't see the second picture.

Solve for n.
2/3 (1 + n ) = -1/2n

Answers

Answer: -4/7

Step-by-step explanation:

2/3 (1 + n ) = -1/2n

2/3 + 2/3n = -1/2n

Multiply both sides by 6

4 + 4n = -3n

4n + 3n = -4

7n = -4

Divide both sides by 7

n = -4/7

Answer:

Answer above its explained fully


Which shows the fractions in order from greatest to least?

A.5/10,1/4,3/4,5/7
B. 3/4,5/7,5/10, 1/4
C. 5/10,5/7,3/4,1/4
D.1/4, 3/4, 5/7,5/10

Answers

Answer:

Step-by-step explanation:

D

find the circumference

Answers

Answer:

[tex]31.42 \: cm[/tex]

Step-by-step explanation:

[tex]C=\pi d[/tex]

[tex]C=2\pi r[/tex]

[tex]C=2\pi \times 5[/tex]

[tex]C=10\pi[/tex]

[tex]C=31.41592...[/tex]

[tex]answer \\ 31.4 \: cm \\ solution \\ r = 5 \: cm \\ d = 5 \times 2 = 10 \: cm \\ circumference = \pi \: d \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times 10 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 31.4 \: cm \\ hope \: it \: helps[/tex]

A woman hikes 503 m, turns and jogs 415 m, turns again and runs 365 m returning to her starting point.

What is the area of the triangle
formed by her path?

Round to the nearest tenth. ​

Answers

Answer:

74594.2 m

Step-by-step explanation:

Heron's formula

area=sqrt(p(p-a)(p-b)(p-c)) where p=(a+b+c)/2

[tex]\sqrt{641.5(641.5 - 503)(641.5 -415)(641.5 - 365)}[/tex]The total amount of area of the triangle which she has covered is 74594.17.

What is a triangle?

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

Area of triangle = 1/2 ×base ×height.

Given that A woman hikes 503 m, turns and jogs 415 m, turns again, and runs 365 m returning to her starting point

so the triangle which is made by the woman(no matter what kind of triangle is) has a side as

A = 503m , B = 415m , C = 365m

Now S = (A + B + C)/2

S = (503 + 415 + 365)/2

S = 641.5

Now the area of a triangle is given by

Area = [tex]\sqrt{S(S - A)(S -B)(S - C)}[/tex]

Area = [tex]\sqrt{641.5 (641.5 - 503)(641.5 -415)(641.5 - 365)}[/tex]

Area = 74594.17 hence, the area of the triangle will be this.

For more information about triangle

https://brainly.com/question/2773823

#SPJ6

Hey everyone! Please help me figure this out...

Answers

Answer:

See below

Step-by-step explanation:

0.82=82/100=82%

22%=22/100=0.22

3/4=0.75=75/100=75%

0.8=0.80=80/100=80%

Hope this helps!

Answer:

column 2: 41/50, 0.82, 82%

column 3: 11/50, 0.22, 22%

column 4: 3/4, 0.75, 75%

column 5: 4/5, 0.80, 80%

Are theses exaponents correct!??? 20 points

Answers

Answer:

YES

Step-by-step explanation:

YESSSSSSSSSSSSSSSSS IS THE ANSWER i think :))

Answer:yes they are all correct

Step-by-step explanation:

Put in a calculator 2^0=1

And 2^1=2

Remember the exponents tell you how many times you multiply the base number to itself

Hope that helps

Juliet baked 30 brownies for a party.she gave 6 brownies to a friend. What percent of the brownies did juliet give het friend

Answers

Answer:

20%

Step-by-step explanation:

6/30 = blank/100

cross multiply

6 x 100

600/30 =20

HELLPPP LOTS OF POINTSS

Answers

Answer:

B.

Step-by-step explanation:

Lines EI and HG would be parallel if the two triangles are congruent. The first option is not correct since we can not determine if that statement is true. The third option is not correct since points E, F, and G are not collinear or not in the same line. The last option is not correct because we can not determone that statement. The second option would be correct since the two lines never intersect.

Answer:

I'm not sure if we're supposed to find all the statements that apply but if so then the answer would be B, C, and D. If we're not to find all the statements then the best answer would be D.

Step-by-step explanation:

When triangles are similar it would mean that when you put their lines in a fraction like choice D you can find what the other value for a side of a triangle that's missing. I don't exactly know how to explain but I'm pretty sure that's the answer if you're not supposed to pick all true statements. Hopefully this helps!

, 8 technicians can test 560 samples in 36 hours. How long
(in days) can 15 technicians'test 525 samples?

Answers

Answer:

0.75 days (im a bit unsure but i tried my best, hope this helps :) )

Step-by-step explanation:

If it takes 8 technicians 36 hours to test 560 samples, find how many technicians can test 525 samples.

8: 560

x: 525

x= 7.5 (which is considered 7)

Then, find how long it takes to sample 525 samples, when 560 are done in 36  hours;

560: 36

525: x

x= 33.75 (which is considered 34 hours)

The last step is to check how long 15 technicians take to sample 525 samples when 8 can do the same number in 34 hours. this is inverse proportion so dont forget to flip one numerator and denominator

8; 34

15; x

it will become

15:34

8: x

x= 18 hours

Divide by 24 for days hence 0.75 days

How many cookies would you expect to be rejected in a sample of 10,000 cookies?

Answers

Answer: 456

Step-by-step explanation:

idk if this is right i dont have anouf to be 100% sure but thats about right sorry if its not, i would try and put more info in next time to get a closer answer

Answer: Depending on who is tasting them, and their love for cookies iam going for something along the lines of 4750

There is a bag filled with 3 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 red?

Answers

Answer:

4/6 chance

One is taken at random, we do not know the colour so we just take away 1 from both colours, this leaves us with 4/6 chance.

Can someone help me this question?

Answers

Answer:

The answer is B.

Step-by-step explanation:

Answer:

Answer is B because it makes the most sense and AL ot of other people said it's B

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