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Varvara68 [4.7K]

2 years ago

5

Mrs. chill has 26 yards of ribbon. She places equal amounts on 3 different spools to sell. How much ribbon in yards are on each

spool

1 answer:

den301095 [7]2 years ago

6 0

8.6 yards are on each spool

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A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021

egoroff_w [7]

The sum of the given series can be found by simplification of the number

of terms in the series.

A is approximately <u>2020.022</u>

Reasons:

The given sequence is presented as follows;

A = 1011 + 337 + 337/2 + 1011/10 + 337/5 + ... + 1/2021

Therefore;

$\displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}$

The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;

$\displaystyle a_{n+1} = \mathbf{\frac{n^2 + 3 \cdot n + 2}{2}}$

Therefore, for the last term we have;

$\displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}$

2 × 2043231 = n² + 3·n + 2

Which gives;

n² + 3·n + 2 - 2 × 2043231 = n² + 3·n - 4086460 = 0

Which gives, the number of terms, n = 2020

$\displaystyle \frac{A}{2} = \mathbf{ 1011 \cdot \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460} \right)}$

$\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2} +\frac{1}{2} - \frac{1}{3} + \frac{1}{3}- \frac{1}{4} +...+\frac{1}{2021}-\frac{1}{2022} \right)$

Which gives;

$\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2022} \right)$

$\displaystyle A = 2 \times 1011 \cdot \left(1 - \frac{1}{2022} \right) = \frac{1032231}{511} \approx \mathbf{2020.022}$

A ≈ <u>2020.022</u>

Learn more about the sum of a series here:

brainly.com/question/190295

8 0

1 year ago

Read 2 more answers

Solve the system of equations. If a system has one unique solution, write the solution set. Otherwise, determine the number of s

Sauron [17]

The value of x, y and z from the system of equation are -1, -8 and 5 respectively.

Data;

-2x + 6y + 3z = -31
-3y + 7z = 59
2z = 10

<h3>System of Equation</h3>

To solve this problem, we have to solve the system of equation using substitution method.

From equation (iii)

$2z = 10\\z = 5$

let us substitute the value of z into equation (ii)

$-3y + 7z = 59\\z = 5\\-3y + 7(5) = 59\\-3y + 35 = 59\\-3y = 59 - 35\\-3y = 24\\y = -8$

Let's substitute the value of x and y into equation (i)

$-2x + 6y + 3z = -31\\y = -8, z = 5\\-2x + 6(-8) + 3(5) = -31\\-2x - 48 + 15 = -31\\-2x - 33 = -31\\-2x = -31 + 33\\-2x = 2\\x = -1$

From the calculation above, the value of x, y and z are -1, -8 and 5 respectively.

Learn more on system of equations here;

brainly.com/question/14323743

6 0

1 year ago

Describe the one basic move you need to change the equation

bixtya [17]

Answer:

Step-by-step explanation: 2x+17=36 ⇒ 2x= -17+36 ⇒ x=8.5+18

so your answer is E

8 0

2 years ago

A man who has lost $37 playing roulette in Las Vegas wins $43 playing blackjack. He then loses $44 playing wheel of fortune. Wri

Rina8888 [55]

Answer:

(-37+43)-44=x

Step-by-step explanation:

i put the parentheses only because of PEMDAS. it's a pretty straightfoward question. To put it in an expression however, I'm not sure. Best of luck!

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2 years ago

One beaver can chew though a tree that is 15 cm thick in 20 min if it works at the same pase how long will it tack one beaver to

Vesna [10]

It takes 8 trees to make a stack 1.2 metres tall, so if ut takes 20 minutes per tree, then it will take 8 × 20 or 160 minutes, or 2 hours 40 minutes.

4 0

2 years ago