Mathematics College

Find the sum of the first 41 terms of the following series, to the nearest integer.
12, 19, 26, ...

Answers

Answer 1

Answer:

The sum of the first 41 terms is 6232

Step-by-step explanation:

The sequence is an arithmetic progression with:

[tex]a = 12[/tex] -- first term

[tex]d = 7[/tex] --- common difference (this is calculated by 19 - 12 or 26 -19)

Required

The sum of the first 41 terms

This is calculated as:

[tex]S_n = \frac{n}{2}(2a + (n-1)*d)[/tex]

In this case: [tex]n = 41[/tex]

So:

[tex]S_{41} = \frac{41}{2}(2*12 + (41-1)*7)[/tex]

[tex]S_{41}= \frac{41}{2}*304[/tex]

[tex]S_{41} = 6232[/tex]

Related Questions

A store is having a sale on trail mix and jelly beans. For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $18. For 2 pounds of trail mix and 12 pounds of jelly beans, the total cost is $45. Find the cost for each pound of trail mix and each pound of jelly beans.

Answers

The store is at least 4

The cost for each pound of trail mix is $1.5 and each pound of jelly beans is $3.5 .

What is elimination method?

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

According to the question

A store is having a sale on trail mix and jelly beans .

Let trail mix = T

and  jelly beans = J

For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $18.

i.e

5T + 3J = 18 -------------------------- (1)

For 2 pounds of trail mix and 12 pounds of jelly beans, the total cost is $45.  

i.e

2T + 12J = 45 -------------------------------(2)

Now,

multiplying eq (1) from 4

20T + 12J = 72 -----------------(3)

Solving equation (3) and (2) the equation by elimination method

20T + 12J = 72 -----------------(3)

2T + 12J = 45  -------------------------(2)

subtracting equation (2) from (3)

18T = 27

T = 1.5

substituting the value of T in equation 1

5T + 3J = 18

5*1.5 + 3J = 18

7.5 + 3J = 18

3J = 18 - 7.5

3J = 10.5

J = 3.5

Hence, the cost for each pound of trail mix is $1.5 and each pound of jelly beans is $3.5 .

To know more about elimination method here:

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Could you help with some geometry questions today!
Please only answer if you know the answer and can support it by showing you work. If you have a comment or do not know the answer, tell me that in the comment section, do not answer the question. Don't take my points and I want take yours!

Anyways, please show all of you work and explain your thinking! There are 3 parts to this, please do all 3! Good luck!

Answers

Answer:

A) 29, B) 18, C) 12

Step-by-step explanation:

A) r = 29

Answered here: https://brainly.com/question/22226669

B) The tangents to a circle have same length:

LK = LM4x - 2 = 3x + 34x - 3x = 2 + 3x = 5

LM = 3*5 + 3 = 18

C) Use the intersecting secants theorem:

PQ*PQ = SQ*RQy² = (10 + 8)*8y² = 144y = 12

WILL MARK BRAINLIEST just need answers no explanation :)

Answers

Answer:

x=50

H=115

Step-by-step explanation:

Just answering so you can give that person brainliest, they are correct

Customers are charged a late fee of 20% of their bill. This person is a week late on a bill of $200.00. What should we charge for the late fee?"

Answers

Answer:

$40

Step-by-step explanation:

The charge for the late fee would be $40.00. This is because 20% of 200 = 40.

Given the equation Square root of 2x plus 1 = 3, solve for x and identify if it is an extraneous solution

Answers

To answer the question above, raise both sides of the equation to the power of two.
(sqrt (2x + 1))² = 3²
This will simplify into,
2x + 1 = 9
Solving for the value of x gives an answer of x = 4. This value is not an extraneous root as it satisfy the original equation even if it is inside the radical sign. (I hope this is right)
Use socratic. Hold up lemme find the answer

Evaluating function rules
f(x)= -3x^2
f(x)=(1+x)^2​

Answers

Answer:

4x^+2x+1=0

Step-by-step explanation:

Help with Geometry, find X.

Answers

the answer would be 270.7

Answer:

541.9

Step-by-step explanation:

Should be, don’t trust me 100%

A right triangle is shown with an angle that measures 60 degrees. The leg adjacent to the 60 degree angle is labeled 5. The leg opposite of the 60 degree angle is labeled x. The hypotenuse is labeled 10. Find the value of x. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.

Answers

Answer:

[tex]x = 5 \sqrt{3} [/tex]

Step-by-step explanation:

Please see the attached pictures for the full solution.

Michela is training for a race. She runs 5 miles in 52 minutes. Her goal is to run 6 miles in 1 hour. By how many minutes per mile must Michela decrease the rate to meet her goal? explain your reasoning.

Answers

Answer:

.4

Step-by-step explanation:

52/ /4= 10.4

60/6=10

10.4-10=.4

Michela needs to increase her speed by 0.23 miles/hour to attain her goal.

What is the rate of change?

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

For example the speed 3meter/second.

As per the given,

She runs 5 miles in 52 minutes.

5 miles in (52/60) hour

In 1 hour → 5(60/52) = 300/52 = 5.769

Her goal was 6 miles in 1 hour.

5.769 + x = 6

x = 0.23 miles/hour

Hence "Michela needs to increase her speed by 0.23 miles/hour to attain her goal".

To learn more about the rate of change here,

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What is the volume of this composite solid

​

Answers

there is no picture attached.
explanation:


A rectangular prism has a length of 18 feet, a height of 14 feet, and a width of 2 feet.
What is its volume, in cubic feet?
feet3

Answers

Answer:

504ft3

Step-by-step explanation:

V=Bh

V=(18x2) 14

V=36x14

V= 504

Answer:

volume = height × length ×width

volume =18×14×2

volume =504ft³

Please help I don't understand this

Answers

-9 is least -3 is greatest

Which triangles are similar to AED? Please help!!!

Answers

I’ve had this question before and the answers were ABE and EFA

Answer:

DEF, EAD, or DEA

Step-by-step explanation:

this is because you can mix up the letters and still be a different combination with the same answer

What is the area of the following circle?
Either enter an exact answer in terms of 7 or use 3.14 for a
and enter your answer as a decimal.
T=4
units
HELP ME

Answers

Answer:

16pi or 50.24

Step-by-step explanation:

Solve |3x – 2| = |x + 1| Question 12 options: A) x = 3∕2 or x = 1∕4 B) No solutions C) x = 3 or x = –4 D) x = 1∕4

Answers

Answer:

x = 3/2

Step-by-step explanation:

Step (1) :

We should put like term togther:

3x - x = 2 +1

2x = 3

Step (2) :

Divide bothe side by 2:

2x/2 = 3/2

x = 3/2

PLS ANSWER GIVING 15 POINTS!!!

Answers

Answer:

Instead of adding the exponents of 2 to get four you should just leave the exponent as two in the final answer.

the set of natural numbers x that satisfy x + 2= 1​

Answers

Answer:

x = -1

x + 2 = 1

x = 1 - 2

x = -1

Hope that helps!

-Sabrina

Step-by-step explanation:

What is the equation of the line in slope-intercept form?

Answers

I belive it would be y=-5/1x+6?

But im only like 90% sure so dont take my word for it but i hope that right?

Answer:

y=-5x+6

Step-by-step explanation:

To find your slope (or m value), you must identify 2 points that your line crosses through (I used (1,1) and (0,6). You can either count up and over to the point (0,6) from (1,1), or you can use the formula y2-y1/x2-x1 (it would look like 6-1/0-1). This will give you -5 for your slope.

Your x-intercept (or b value) is 6 because you can see from the graph that that is where your line intercepts y.

I hope this helped :)

List all multiples of 10 up to 100.

Answers

keep adding 10 starting from 0 until u get to 100:
10
20
30
40
50
60
70
80
90
100

Hey so can someone do my delta math for me



like i give u the questions and u answer yeah ok thanks

Answers

both x=62 and y=62 have a good night
Nobody likes deltamath

Select all the expressions that are equivalent to 4x+2.

A 8x+48 x plus 4

B 12(8x+4)1 half times open paren 8 x plus 4 close paren

C 12(2x+1)1 half times open paren 2 x plus 1 close paren

D 2(2x+1)2 times open paren 2 x plus 1 close paren

E 2x+2x+1+1
and one brainleiss

Answers

okay so your answers are

D and E!!

Help me plz will mark branialist

Answers

Answer:

8

Step-by-step explanation:

Find the equation of a line parallel to 3x-4y=24 that contains the point (-4,2). ​

Answers

Put the equation is slope intercept form so you can find the slope.

3x - 4y = 24
-4y = 24 - 3x
y = -6 + (3/4)x

The slope is 3/4, which will be the slope for the parallel line. Now use point-slope form to find the equation for the line:

y-y1 = m(x-x1) —> y - 2 = (3/4)(x + 4)

An airplane takes off 200 yards in front of a 60 foot building. At what angle of elevation must the plane
take off in order to avoid crashing into the building?

Answers

Answer:

16.69°

Step-by-step explanation:

Given that,

Height of the building, h = 60 foot

Distance from the base of the building, b = 60 foot

We need to find the angle of elevation must the plane takes off in order to avoid crashing into the building. So,

[tex]\tan\theta=\dfrac{60}{200}\\\\\theta=\tan^{-1}\dfrac{60}{200}\\\\=16.69^{\circ}[/tex]

So, the required angle is 16.69°.

find the area points

Answers

Answer:

The entire trapezoid is 48 units sq

the cut out part is 30

the trapezoid without the cutout is 18

Step-by-step explanation:

Find the value of X and Y in the triangle

Answers

9514 1404 393

Answer:

  x ≈ 7.00

  y ≈ 12.21

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships ...

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

__

Translated to the figure at hand, these are ...

  cos(35°) = 10/y   ⇒   y = 10/cos(35°) ≈ 12.21

  tan(35°) = x/10   ⇒   x = 10·tan(35°) ≈ 7.00

The points in the table lie on a line. Find the slope of the line. Then draw its
graph.
3.
4.
0
-3
3
х
6
-2
х
-1
0
1
3
y
2
1
-7
0
y
1
-3
5
y
o
0
I need help on number 3 and 4

Answers

Answer: I need a better picture to solve the problem

Step-by-step explanation:

express as a difference.


a.) 7+3

b.) a+5

c.) a+b
First correct answer is Brainliest.

Answers

10

b: 5+5
c: 5+5

thats thw andeer

Answer:

Step-by-step explanation:

15-5

a-(-5)

a-(-b)

you pick a card, roll a die, and find the sum. How many different sums are possible?​

Answers

answer : 6

step by step: there’s six sides to a dice

If we pick a card, roll a die, and find the sum , the different sums possible is 17.

What is Permutation and Combination ?

A permutation is an act of arranging the objects or numbers in order.

Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter.

If we pick any card and roll a die

The sum possible is

The highest it can be would be  13(card) + 6(die)  =19

the Lowest it can be would be 1(card) + 1 (die)  = 2

So the different sums possible is 19-2 = 17.

To know more about Permutation and Combination

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Helpppppp hurry and no links

Answers

Step-by-step explanation:

6.3%

that is the correct answer

6.3 % is your

Hope I was of some help.
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