1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Helen [10]
3 years ago
14

Find the exact sum of the arithmetic series 6+3.8+⋯−29.2

Mathematics
1 answer:
matrenka [14]3 years ago
5 0

Answer:

-197.2

Step-by-step explanation:

Since it is arithmetic series, first find the difference d between the two know series.

3.8 - 6 = - 2.2

d = -2.2

a = 6

Tn = -29.2

Looking for the n term, use the linear method.

Tn = a+( n - 1)d

Substitute all the parameters

-29.2 = 6+( n - 1 ) -2.2

-29.2 = 6 - 2.2n + 2.2

- 29.2 = 8.2 - 2.2n

-29.2 - 8.2 = - 2.2n

-37.4 = -2.2n

n = 37.4/ 2.2

n = 17 terms.

To Find the exact sum of the arithmetic series, use the sum formula below

Sm = n/2( 2a + (n - 1)d)

Sm = 17/2( 2 × 6 + ( 17 - 1 ) -2.2

Sm = 17/2(12 - 35.2)

Sm = 8.5( - 23.2)

Sm = - 197.2

Therefore, the exact sum of the arithmetic series is -197.2

You might be interested in
Need to know the population in 2015
Margarita [4]
\bf P=1110.9e^{kt}\quad 
\begin{cases}
P=1200 &\textit{in thousands}\\
t=2 &\textit{in 2002}
\end{cases}\implies 1200=1110.9e^{k2}
\\\\\\
\cfrac{1200}{1110.9}=e^{2k}\implies ln\left( \frac{1200}{1110.9} \right)=ln(e^{2k})\implies ln\left( \frac{1200}{1110.9} \right)=2k
\\\\\\
\cfrac{ln\left( \frac{1200}{1110.9} \right)}{2}=k\implies 0.0385755\approx k\implies 0.0386\approx k\\\\
-------------------------------\\\\

\bf P=1110.9e^{0.0386t}\qquad 
\begin{cases}
t=14\\
\textit{year 2015}
\end{cases}\implies P=1110.9e^{0.0386\cdot 14}
\\\\\\
P\approx 1907.0747\implies about\ 1,907,075\textit{ once rounded up}
3 0
2 years ago
In a random sample of 400 residents of Boston, 320 residents indicated that they voted for Obama in the last presidential electi
coldgirl [10]

Answer:

C.I =  0.7608   ≤ p ≤   0.8392

Step-by-step explanation:

Given that:

Let consider a  random sample n = 400 candidates where  320 residents indicated that they voted for Obama

probability \hat p = \dfrac{320}{400}

= 0.8

Level of significance ∝ = 100 -95%

= 5%

= 0.05

The objective is to  develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.

The confidence internal can be computed as:

=\hat p  \pm Z_{\alpha/2} \sqrt{\dfrac{ p(1-p)}{n } }

where;

Z_{0.05/2} = Z_{0.025} = 1.960

SO;

=0.8  \pm 1.960 \sqrt{\dfrac{ 0.8(1-0.8)}{400 } }

=0.8  \pm 1.960 \sqrt{\dfrac{ 0.8(0.2)}{400 } }

=0.8  \pm 1.960 \sqrt{\dfrac{ 0.16}{400 } }

=0.8  \pm 1.960 \sqrt{4 \times 10^{-4}}

=0.8  \pm 1.960 \times 0.02}

=0.8  \pm 0.0392

= 0.8 - 0.0392     OR   0.8 + 0.0392  

= 0.7608    OR    0.8392

Thus; C.I =  0.7608   ≤ p ≤   0.8392

3 0
2 years ago
John’s friend told him that he could earn $49 for handing out flyers at a local concert John wants to.m calculate the hourly rat
oee [108]
Dat boi gonna get scammed.
7 0
2 years ago
Read 2 more answers
Which of the following is equivalent to this expression?
Aliun [14]

Answer:

121

Step-by-step explanation:

6 0
3 years ago
The volume of a rectangular prism is represented by the function x3 + 11x2 + 20x – 32. The width of the box is x – 1 while the h
Oksi-84 [34.3K]

we know that

the volume of a rectangular prism is equal to

V=L*W*H

where

L is the length of the box

W is the width of the box

H is is the height of the box

in this problem we have

V=x^{3\ }+11x^2+20x-32

W=x-1

H=x+8

L=?

<u>Find the length of the box</u>

Using a graph tool-------> we will determine the roots of the equation of volume

see the attached figure

the roots are

x=-8\\x=-4\\ x=1

so

x^{3\ }+11x^2+20x-32=(x+8)*(x+4)*(x-1)

therefore

<u>the answer is</u>

the length of the box is equal to (x+4)

8 0
2 years ago
Read 2 more answers
Other questions:
  • Factor:<br> 4b2 - 12b + 9
    11·1 answer
  • Suppose that a car normally sells for $16,500 and is now on sale for $14,000. What is the percent of discount?
    6·1 answer
  • Dexter rides his bike 3 1/4 miles each day on Monday, Wednesday, and Friday. On Tuesday and Thursday he rides 7 3/8 miles each d
    5·1 answer
  • Need help really bad
    8·1 answer
  • Evaluate 9.5v + 8.9w when v=6 and w=7
    6·1 answer
  • PLEASE HELP, WILL MARK BRAINILEST
    7·1 answer
  • Which quadratic equation has roots –2 and 1/5?
    8·1 answer
  • Find f(3) ahahahahah
    13·1 answer
  • You are taking a quiz that has 12 multiple-choice questions. If each question has 5 possible answers, how many different ways ar
    12·1 answer
  • When I did it I didn't get any of the answer choices so I know i'm Incorrect please help me find the correct answer
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!