I need help , I don't understand

Which expression is equivalent to *picture attached*

DiKsa [7]

Answer:

The correct option is;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$

Step-by-step explanation:

The given expression is presented as follows;

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right )$

Which can be expanded into the following form;

$\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3 \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left n^2 + 3 \times\sum\limits _{n = 1}^{50} n$

From which we have;

$\sum\limits _{k = 1}^{n} \left k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}$

$\sum\limits _{k = 1}^{n} \left k = \dfrac{n \times (n+1) }{2}$

Therefore, substituting the value of n = 50 we have;

$\sum\limits _{n = 1}^{50} \left k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}$

$\sum\limits _{k = 1}^{50} \left k = \dfrac{50 \times (50+1) }{2}$

Which gives;

$4 \times \sum\limits _{n = 1}^{50} \left n^2 = 4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}$

$3 \times\sum\limits _{n = 1}^{50} n = 3 \times \dfrac{n \times (n+1) }{2} = 3 \times \dfrac{50 \times (51) }{2}$

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3 \times \dfrac{50 \times (51) }{2}$

Therefore, we have;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$ .

4 0

2 years ago

DeAndre downloaded 8 apps onto his tablet in 12 seconds. At this rate, how many apps could he download in one minute? (12 second

ale4655 [162]

40 apps.

Explanation:
60 divided by 12 is 5. That’s how many downloading sessions could fit in a minute. Multiply 5 by the number of apps, which is 8. Your answer is 40 apps.

7 0

1 year ago

Kathryn is 1.6 meters tall. Convert her height to feet. Round to the nearest tenth.

Andrej [43]

Answer:

1.6 m = 5.3 ft

4 0

2 years ago

A hat contains slips of paper with the names of the 26 other students in Eduardo’s class on them, 10 of whom are boys. To determ

Yuki888 [10]

Answer:

The probability that both of Eduardo’s partners for the group project will be girls is

Step-by-step explanation:

Given : A hat contains slips of paper with the names of the 26 other students in Eduardo’s class on them, 10 of whom are boys. To determine his partners for the group project, Eduardo has to pull two names out of the hat without replacing them.

To find : What is the probability that both of Eduardo’s partners for the group project will be girls?

Solution :

Total number of students = 26

Number of boys = 10

Number of girls = 26-10=16

Eduardo has to pull two names out of the hat without replacing them.

For the first hat,

Favorable outcome of getting girl = 16

Total number of outcome = 26

For the second hat, without replacement

Favorable outcome of getting another girl = 15

Total number of outcome = 25

The probability that both of Eduardo’s partners for the group project will be girls is

Hope This Helps :D

5 0

2 years ago

Read 2 more answers

Can I get help with both or one. please and thank you!!!

Pavlova-9 [17]

14. The answer is A; 8 is the opposite reciprocal of -1/8, which is what you need for perpendicular slope.
15. The answer is C; you can guess and check by plugging points into the equation.

3 0

2 years ago