the arithmetic sequence ai is defined by the formula: a1= 2 ai= ai - 1 -3 find the sum of the first 335 terms in the sequence

Answers

Answer 1

Given:

In an arithmetic sequence,

[tex]a_1=2[/tex]

[tex]a_i=a_{i-1}-3[/tex]

To find:

The sum of the first 335 terms in the given sequence.

Solution:

The recursive formula of an arithmetic sequence is:

[tex]a_i=a_{i-1}+d[/tex]         ...(i)

Where, d is the common difference.

We have,

[tex]a_i=a_{i-1}-3[/tex]          ...(ii)

On comparing (i) and (ii), we get

[tex]d=-3[/tex]

The sum of first i terms of an arithmetic sequence is:

[tex]S_i=\dfrac{i}{2}[2a+(i-1)d][/tex]

Putting [tex]i=335,a=2,d=-3[/tex], we get

[tex]S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)][/tex]

[tex]S_{335}=\dfrac{335}{2}[4+(334)(-3)][/tex]

[tex]S_{335}=\dfrac{335}{2}[4-1002][/tex]

[tex]S_{335}=\dfrac{335}{2}(-998)[/tex]

On further simplification, we get

[tex]S_{335}=335\times (-499)[/tex]

[tex]S_{335}=-167165[/tex]

Therefore, the sum of the first 335 terms in the given sequence is -167165.


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Use the Pythagorean Theorem.

h² = 5² - 3² = 4²

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Answer:

x=6

Step-by-step explanation:

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I wrote the wrong answer so I erased it

solve the system of equations-6x+7y=9 and 2x-2y=-4

Answers

Answer:

y = -3 and x = -5

Step-by-step explanation:

Hi,

-6x + 7y = 9

2x - 2y = -4

Multiply the bottm equation by 3...

-6x + 7y = 9

6x - 6y = -12

Add...

y = -3

Now...

2x - 2 (-3) = -4

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Answer...

y = -3 and x = -5

Solve for h. What is h?
Problem 20h=2

Answers

Answer:

h=1/10

Step-by-step explanation:

Find the measure of 61.
{
839
41
{ K
41 = [?]
Enter

Answers

Answer:

m<1 = 97°

Step-by-step explanation:

<1 and 83° are same-side interior angles. Same-side interior angles are supplementary. This implies that:

m<1 + 83° = 180°

Therefore:

m<1 + 83° - 83° = 180° - 83° (subtraction property of equality)

m<1 = 97°

Answer:

<1=97°

steps:

<1+83=180 co interior angle

<1=180-83=97°

The stem-and-leaf plot shows the distances, in miles, that a group of owners of new cars drove one weekend.

How many of the owners drove between 50 and 65 miles?

Answers

6 people drove between 50 and 65 miles because the stem-and-leaf plot show 55, 56, 58, 58, 63, 63

If Sheyenne walked 8 miles in 2 hours what was her speed?

Answers

Answer:

4 miles per hour

Step-by-step explanation:

Answer:

4mph

Step-by-step explanation:

8 divided by 2 and boom the answer.Hope this helps.

what is the value of k if - 2/3(k - 6) = 3/2(k+6)​

Answers

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer:  -30/13

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

60 points 90 % of my grade

Answers

Answer:

5/6 x 4 = 20/6 as simplified as 10/3 in fraction form. 5/6 x 4 = 3.3333 in decimal form.

Step-by-step explanation:

Answer:

5/6 × 4 = ?

5/6 × 4

= 5/6 × 4/1

= 5×4/6×1

= 20/6

= 10/3

= 3.33

Please help cus I don’t know

Answers

Answer:

D) 53°

Step-by-step explanation:

All interior angles of any triangle add up to 180°

? = 180° - 43° - 84°

? = 53°

Answer:

Its B. 53

Step-by-step explanation:

To find the unknown angel you need to add the number you already have AKA 43 and 84 you need to add up to 180 so 43+84+53= 180

In a recent survey in a Statistics class, it was determined that only 70% of the students attend class on Fridays. From past data it was noted that 88% of those who went to class on Fridays pass the course, while only 20% of those who did not go to class on Fridays passed the course. a. What percentage of students is expected to pass the course? b. Given that a person passes the course, what is the probability that he/she attended classes on Fridays? (Hint: the above problem is based on conditional probability concept and the Bayes theorem)

Answers

Answer:

a) 67.6% of students is expected to pass the course

b) 0.9112 = 91.12% probability that he/she attended classes on Fridays

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

a. What percentage of students is expected to pass the course?

88% of 70%(attended class)

20% of 100 - 70 = 30%(did not attend class). So

[tex]p = 0.88*0.7 + 0.2*0.3 = 0.676[/tex]

0.676*100% = 67.6%

67.6% of students is expected to pass the course.

b. Given that a person passes the course, what is the probability that he/she attended classes on Fridays?

Here, we use conditional probability:

Event A: Passed the course

Event B: Attended classes on Fridays.

67.6% of students is expected to pass the course.

This means that [tex]P(A) = 0.676[/tex]

Probability that passed and attended classes on Friday.

88% of 70%

This means that:

[tex]P(A \cap B) = 0.88*0.7 = 0.616[/tex]

Then

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.616}{0.676} = 0.9112[/tex]

0.9112 = 91.12% probability that he/she attended classes on Fridays

Dawn bought 12 grams of chocolate. She ate half of the chocolate. How many grams of chocolate did she eat​

Answers

Dawn would have ate 6 grams of chocolate

Explanation: if you divide 12 by 2 it equals 6

2. A student measured the mass of an object
to be 56 g, but the actual mass was 53 g.
What is the absolute error?
Quickkkkkk

Answers

There answer .......

The absolute Error is 5.66%.

What is absolute Error?

The discrepancy between a quantity's measured or inferred value and its actual value is known as the absolute error.

The absolute error is insufficient because it provides no information about the significance of the error. An inaccuracy of a few centimetres when estimating the kilometres between cities is insignificant and unimportant. A measurement mistake of a few centimetres when measuring tiny machine parts is a highly important defect. Although both inaccuracies are in the centimetre range, the second one is more serious than the first.

Given:

Actual Mass = 53g

and, Measure mass= 56 g

So, Absolute Error = | 56- 53 / 56| x 100

Absolute Error = |3 / 56| x 100

Absolute Error = 0.056603 x 100

Absolute Error = 5.66%

Hence, the absolute Error is 5.66%.

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What is the y value in solution the following system?
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(Worth 10 points)

Answers

4x+3y=7......……(i)
X+2y=-2………....(ii)
Multiplying eqn (ii) by 4
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Solving eqn ( i) and (iii)

Here are five statements.


For each statement, say whether it is TRUE or FALSE.
The first one has been done for you.

Note: Please make sure you follow the format of the answers, e.g.
2) ....
3) ...

Answers

Answer:

Step-by-step explanation:

2) False.

3) True. It could be 50°-65°-65°.

4) True. It could be 35°-35°-110°.

5) True. It could be 40°-50°-90°.

what is an outlier number?

Answers

Answer:

an outlier is a number that is at least 2 standard deviations away from the mean for example in the set 1,1,1,1,1,1,1,1,1,7,7,7 would be the outlier

Step-by-step explanation:

watashi wa sore ga tadashī koto o negatte imasu

arigatozaimasu!!

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IGNORE THE PERSON THAT PUT THE LINK IN HE OR SHE IS PUTTING THAT FOR EVERYONE BUT YOU NEED TO GO SEARCH math-way it’s a algebra calculator and it gives u answer hope it helps

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Answers

Answer:

[tex]\frac{5^3s^3t^6}{s^4 x 50t}[/tex]

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I need help with this

Answers

Answer:

1/5

Step-by-step explanation:

because u divied

Which of the following is the correct way to state the similarity between these two figures?

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B.) ABCDE ~ VWXYZ


C.) ABCDE ~ VZWYX


D.) ABCDE ~ ZWYXV

Answers

Answer:

ABCDE is similar to the ZWYXV

(help?)
Look at the model.
Which of the following statements of equality is true? [png]

Answers

Answer:

H

Step-by-step explanation:

Answer:

H

Step-by-step explanation:

3 times 2 and x in each row

which equals to 6 and 3x

Angel and Kellie each have the same amount of money in their wallet. Angel buys two juice drinks and receives $1.10 in change after she pays. Kellie buys 1 juice drink and receives $3.05 in change after she pays. Which equation shows how to find the cost of a juice drink, j?

Answers

Answer:

y= 2x+1.10

y=x+3.05

Step-by-step explanation:

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Answers

Answer:

11) m<8

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15) g<-18

16) y< or equal to -16

17) a> or equal to 16

Step-by-step explanation:

hope this helps

what is -6.77626358E-21 written in scientific notion with three significant digits ​

Answers

Answer:

-6.78 x 10^-21

Step-by-step explanation:

-6.77626358E-21

= -6.78 x 10^-21

NO LINKS PLEASE HELP ME ​

Answers

Answer

angle 5 = 31°

Step-by-step explanation:

Answer:

31 degrees

Step-by-step explanation:

Angles 1, 5, and 6 combine to form a straight line, which is 180 degrees, so add 56 and 93 and subtract that from 180

A graduate student conducted a study of field mice in rural Kansas. The student obtained a sample of 100 field mice and recorded the weight, in grams, of each mouse. The mean and standard deviation of the recorded weights are 35 grams and 2.4 grams, respectively. After the measurements were taken, it was discovered that the scale was not calibrated correctly. The student adjusted the 100 measurements by subtracting 3 grams from each measurement. What are the values of the mean and standard deviation of the corrected measurements

Answers

Subtracting 3 from all measurements, it is found that:

The mean will decrease by 3.The standard deviation will remain constant.

What are the mean and the standard deviation of a data-set?

The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.

From this, we have that:

When 3 is subtracted from all measures, the sum of all observations will be subtracted by 3 x 100 = 300, hence the mean will decrease by 3.The mean decreases by 3, as does each observation, hence the sum of the differences squared between each observation and the mean remains constant, as does the standard deviation.

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The sum of a number times 8 and 23 is at most 26.
Use the variable b for the unknown number

Answers

Answer:

b ≤ 3/8

Step-by-step explanation:

Let the unknown number be b.

Translating the word problem into an algebraic expression, we have;

8b + 23 ≤ 26

Rearranging the equation, we have;

8b ≤ 26 - 23

8b ≤ 3

Dividing both sides by 8, we have;

b ≤ 3/8

keiko has bought 36pounds of dog food, she feed the dog 3/4 pound of food each meal. how many meals would this last

Answers

Answer:

48 meals

Step-by-step explanation:

36lbs ÷ 3/4lbs = 48

If PQRS is a rhombus, find m

Answers

Answer:

m<PQR = 82°

Step-by-step explanation:

In a Rhombus, the diagonals bisect its angles. This means that they divide each the four angles into two equal parts.

Therefore:

(4x - 27)° = (2x + 7)°

Solve for x

4x - 27 = 2x + 7

Collect like terms

4x - 2x = 27 + 7

2x = 34

Divide both sides by 2

2x/2 = 34/2

x = 17

✔️m<PQR = (4x - 27) + (2x + 7)

Plug in the value of x

m<PQR = (4*17 - 27) + (2*17 + 7)

m<PQR = 41 + 41

m<PQR = 82°

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