Find the sum of the arithmetic series given a1
12, d = 4, and n = 30.
A. 8434
B. 4200
C.4216
D. 2100

Answers

Answer 1

Answer:

D

Step-by-step explanation:

The sum to n terms of an arithmetic series is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 12, d = 4 and n = 30 , then

[tex]S_{30}[/tex] = [tex]\frac{30}{2}[/tex] [ (2 × 12) + (29 × 4) ]

     = 15(24 + 116)

     = 15 × 140

     = 2100 → D

Answer 2

The sum of the arithmetic series given a₁ =12, d = 4, and n = 30 is 2100, therefore the correct answer is D.

What is the Sum of arithmetic series?

The sum of n terms of an arithmetic series can be easily found using a simple formula which says that, if we have an arithmetic series whose first term is a and the common difference is d, then the formula of the sum of n terms of the arithmetic series is as follows

Sn = n/2 [2a₁ + (n-1)d].

as given in the problem

a₁ =12, d = 4, and n = 30

Sn = 30/2 [2×12 + (30-1)×4]

    = 2100

The sum of the arithmetic series given a₁ =12, d = 4, and n = 30 is 2100.

Learn more about the arithmetic series from here

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Related Questions

The ABC Book Club charges a $40 monthly fee, plus $2 per book read in that month. The Easy Book Club charges a 35$ monthly fee, plus 3$ per book read in that month. For each club, how many books must be read in 1 month for the total charges from each club to be equal.

Answers

The expression for the cost of the ABC Book Club is 2x + 40. The expression for the cost of the Easy Book Club is 3x + 35. To find when the total charge for both book clubs is equal, the two expressions must equal each other. (x = the number of books read)

2x + 40 = 3x + 35

Subtract 35 from both sides.

2x + 5 = 3x

Subtract 2x from both sides.

5 = x

So, the total charge for each club is equal when 5 books are read.

10.
X/2 + X-3/5 = 3

If anyone could help with #10 I would be very grateful

Answers

answer: x= 36/7 or 5.143

the radius of a circle is 17 yards. What is the circles area ?

Answers

Answer:

907.46

Step-by-step explanation:

Area = pi x radius^2

17^2 = 289

289 x 3.14 = 907.46

Hope this helps. Pls give brainliest.

Answer:

Area = 907.92 square yards

Step-by-step explanation:

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

[tex]A=\pi 17^2[/tex]

[tex]A=907.92[/tex]

Brainly plz :))


What is the measure of angle 6, to the nearest degree?
81°
90
99°
105°

Answers

Answer: 99

Step-by-step explanation:

10x-9=9x

-9=-x

x=9

angle 7 = 9*(9)=81

angle 6 = 180-81= 99

NOTE: DO NOT hit 90 because I did that and got it wrong. Just a heads up. Get luck!

Can someone me out plz

Answers

Answer:

I think it's B

Step-by-step explanation:

hopes this helps

Find the radius of the button.

A circular button with a diameter of 28 millimeters.

Answers

14 ^^^^^^^^^^^^hes right

The radius of the button will be 14 millimetres.

What is the radius of the circle?

The radius of the circler is defined as the distance from the centre of the circle to the outermost surface of the circle. The diameter of the circle is the distance between the two points on the surface of a circle passing through the centre of the circle.

Given that the diameter of the circle is 28 millimetres. the radius of the circle is calculated as,

Radius = Diameter / 2

Radius = 24 / 2

Radius = 12 millimetres

Therefore, the radius of the button will be 14 millimetres.

To know more about the radius of the circle follow

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I am to lazy, you will get 73 points if you answer.

Answers

Answer:9

Step-by-step explanation:

3/4 times 12=3(12/4)=3x3=9

Another way:

3/4=0.75

0.75x12=9

Step-by-step explanation:

9 that's your answer your welcome

Is anyone good at this:{

Answers

Answer:

no not really

Step-by-step explanation:

i lowkey suck at graphs and charts, sorry :(

A colony of 50 bacteria double in size every 30 minutes. What will the population be 120 mintues from now?

Answers

Answer:

800 bacteria

Step-by-step explanation:

Over here, we have exponential growth.

So we have 50 bacteria

Every 30 minutes, it doubles in size

In 120 minutes, there are four 30 minutes.

So you do 50 * 2 * 2 * 2 * 2

Do that out and you get 800

Let me know if you have any questions

The sales tax on a $25,000 car is $1375. What is the sales tax rate?

PLEASE SHOW HOW YOU SLOVED IT!!! THX <3

Answers

Answer:

$11 sales tax per $200

Step-by-step explanation:

1375/25,000 = 11/200

Answer:

5.5%

Step-by-step explanation:

1375/25000= 5.5%

25000 * 5.5% = $1375.00

What is the slope of a line that passes through the origin and the point (6, 3)

Answers

Answer:

Slope = 1/2

Step-by-step explanation:

Formula for getting slope using 2 points...

(y2 - y1) / (x2 - x1)

= (3 - 0) / (6 - 0)

= 3 / 6

= 1/2

So...

Slope is 1/2

Hope this helps :)

Let me know if there are any mistakes!!

Answer:  The slope is   1/2

Step-by-step explanation:

When a line passes through the origin the equation of the line will be represented in the form    y= kx   where k is the slope.

To to find k you will need to divide both sides by x.

y = kx

y/x = kx/x

  k = y/x  

This means that to find k, you will need to divide the y coordinate of the point by the x coordinate.  

  k = 3/6

K = 1/2

what does t equal? t/-2 - 8 = 10

Answers

-36 due to math and I have to get more words

Answer:

-36=t

Step-by-step explanation:

if u add eight to both sides u get t/-2 = 18, then all you have to do is multiply both sides by -2, then u get t=-36

Which pair of points have a slope of -3/5?

A (4, 0), (-2, 10)

B (10, -2), (0, 4)

C (4, 2), (10, 4)

D (-4, -10), (0, -2)

Answers

Answer:

No of these answers has a slope of  [tex]\frac{-3}{5}[/tex] . My guess is B becasue its close to [tex]\frac{-3}{5}[/tex] unless the 5 is supposed to be negative

Step-by-step explanation:

You have to use the slope formula [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

([tex]x_{1}[/tex],[tex]y_{1}[/tex]), ([tex]x_{2}[/tex],[tex]y_{2}[/tex])

(4, 0), (-2, 10)   [tex]\frac{10 - 0 }{-2 - 4 }= \frac{10}{6}[/tex] you have to simplfy, the answer will be [tex]\frac{5}{3}[/tex]

(10, -2), (0, 4)  [tex]\frac{4 - -2 }{0- 10 }= \frac{6}{-10}[/tex] you have to simplfy, the answer will be [tex]\frac{3}{-5}[/tex]

 (4, 2), (10, 4)  [tex]\frac{4 - 2 }{10 - 4 }= \frac{2}{6}[/tex] you have to simplfy, the answer will be [tex]\frac{1}{3}[/tex]

 (-4, -10),(0, -2) [tex]\frac{{-2- -10} }{0 - -4 }= \frac{8}{4}[/tex] you have to simplfy, the answer will be [tex]\frac{2}{1} =2[/tex]

Look at the picture....

Answers

Answer:

now what

Step-by-step explanation:

Answer:

The graph of g is a vertical stretch of the graph of f.

Step-by-step explanation:

rory campbell plz help me, or at least anyone that can give me the right answer plzzz

Answers

the answer is (1.5, 1)

what is
Which expression is equivalent to 9y – 3y?
3
3

3y
3y

6
6

6y please help

Answers

Answer:

9y-3y=6y is equivalent to 9y – 3y.

What’s the correct answer 9x+3-5x >2

Answers

Answer:

x>-1/4

Step-by-step explanation:

9x+3-5x>2

9x-5x+3>2

4x+3>2

4x>-1

x>-1/4

Therefore, x>-1/4

What is the height of a rectangular prism that has a volume of 231 cubic
feet, a length of 11 feet and a width of 3 feet.

Answers

Answer:

7 ft

Step-by-step explanation:

V = length • width * height

231 = (11)(3)(h)

231 = (33)(h)

h = 7 ft

Find the slope of the line passing through the 2 points (-7,8), (-4,3

Answers

Answer:

5/-3

Step-by-step explanation:

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

m = (8 - 3)/(-7 + 4)

m = 5/-3

Find the area of the shape below giving your answer to 1 decimal place.

Answers

Answer:

198.5 cm²

Step-by-step explanation:

From the figure above we can treat the two semi circles as 1 circle.

Now, the diameter is 10 cm

Thus;

Radius; r = 10/2

r = 5cm

Now, formula for area of a circle is;

A = πr²

Thus;

Area of 2 semi circles = Area of 1 circle = π × 5²

A_circle = 78.54 ≈ 78.5 cm²

When we take out the 2 semi circles, what we have left is a rectangle.

Now, the length of the rectangle will be;

Length; L = 22 - 5 - 5 = 12 cm

*This is because the radius of the semi circle is 5 and distance from the edge of the 22 cm length to the centre of the semi circle is 5 cm

Thus, area of rectangle is given by;

A_rect = LW

W in the image is 10 cm

Thus;

A_rect = 12 × 10

Total area of shape is;

A_total = 120 + 78.5

A_total = 198.5 cm²

solve for X

Please help

Answers

Answer:

x = 5

Step-by-step explanation:

set JN and NL equal to each other...

14x – 17 = 3x + 38

11x = 55

x = 5

Which set of values makes the inequality 1/4x + 2≥0
A. {-8,-4, 0, 4, 8}
O
B. {-12, -8, 0, 4, 8}
o
C. {-20, -16, -12, 0,4}
D. {-20, -16, 0, 16, 20}

Answers

Answer:

the answe is A.{-8,-4,0,4,8}

a - 2 + 3 = -2
Please answer with solving steps!

Answers

Answer: a=−3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

a−2+3=−2

a+−2+3=−2

(a)+(−2+3)=−2(Combine Like Terms)

a+1=−2

a+1=−2

Step 2: Subtract 1 from both sides.

a+1−1=−2−1

a=−3

Answer:

a=-1

Step-by-step explanation:

move -2 and 3 to the right side to have the variable by itself and then just add them together.

a = -2+3-2

a= -4+3

a= -1

Solve 3X-5 = 9.
Ox= -3
Ox= 2
Ox= 7
OX= 8
NEED HELP ASAP

Answers

Answer:

The value of x = 14/3

Step-by-step explanation:

Given the equation

[tex]3x-5 = 9[/tex]

Add 5 to both sides

[tex]3x-5+5=9+5[/tex]

Simplify

[tex]3x=14[/tex]

Divide both sides by 3

[tex]\frac{3x}{3}=\frac{14}{3}[/tex]

Simplify

[tex]x=\frac{14}{3}[/tex]

Therefore, the value of x = 14/3

Note: It seems you may have missed entering the correct answer choice as the value of x = 14/3 is not mentioned in your answer choices.

please help asap i’m failing
The lines shown below are parallel. If the green line has a slope of -3/7, what is
the slope of the red line?

Answers

They look parallel so it should be the same as the green line.

Can someone help me?

Answers

Answer: m=−3

Step-by-step explanation: −40−2(3m+1/2)=7m−2

−40+(−2)(3m)+(−2)(1/2)=7m+−2

−40+−6m+−1=7m+−2

(−6m)+(−40+−1)=7m−2

−6m+−41=7m−2

−6m−41−7m=7m−2−7m

−13m−41+41=−2+41

−13m/−13=39/−13

m=−3

What mistake I guess Keith did make is he subtracted 2 from -39 which equaled to -37 which caused him divide -37 by 13 when it should have been 39 divided by 13 because he should have left 39 alone and not have subtracted 2 from it also it should not have been negative basically what I'm trying to say is that he did his division and subtraction wrong.

 

m = -3, hope it was helpful! :)

Alexander was offered a job that paid a salary of $24,000 in its first year. The salary was set to increase by 4% per year every year. If Alexander worked at the job for 5 years, what was the total amount of money earned over the 5 years, to the nearest whole number?

Answers

9514 1404 393

Answer:

  $129,992

Step-by-step explanation:

The sum of a geometric series is given by ...

  Sn = a1·(r^n -1)/(r -1)

Here, the first term is 24000, and the growth factor r is 1+4% = 1.04. The sum is then ...

  S5 = 24000·(1.04^5 -1)/(1.04 -1) ≈ 129992

The total earned over 5 years was $129,992.

___

A spreadsheet can list the annual salaries and add them up. The salary each year is 1.04 times that of the previous year. That is shown in the attachment.

4g find the monomial

Answers

The monomial of 4g is 1

PLEASE HELP!!!!!!!!!!

Answers

Answer:

y+1 1/4=3 3/4 or y.1 1/4=3 3/4

Step-by-step explanation:

WILL MARK BRAINLIEST what is the standard deviation for the normal distribution shown at the right?

Answers

Answer: 916. Because if you do 856+60=916.

Step-by-step explanation: The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. Formula: and natural statistics x and x2. The dual expectation parameters for normal distribution are η1 = μ and η2 = μ2 + σ2.

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