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3 years ago

Shawna and her best friend Keisha go shopping.

Mathematics

1 answer:

amid [387]3 years ago

4 0

Answer:

138

Step-by-step explanation:

p(x) = 3x^4 + 2x^3 − 4x^2 + 21

Let x = 2

p(2) = 3*(2)^4 + 2*(2)^3 − 4*(2)^2 + 21

= 3*16+2*8-4*4+21

=48+16-16+21

= 69

This is per girl

There are 2 girls

2 * 69

138

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Find a formula for the sum of n terms. Use the formula to find the limit as n → [infinity]. lim n → [infinity] n 2 + i n 8 n i =

Masteriza [31]

Complete Question

Find a formula for the sum of n terms. $\sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )$

Use the formula to find the limit as $n \to \infty$

Answer:

$K_n = \frac{n + 73 }{n}$

$\lim_{n \to \infty} K_n = 1$

Step-by-step explanation:

So let assume that

$K_n = \sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )$

=> $K_n = \sum\limits_{i=1}^n ( \frac{16}{n} + \frac{2i}{n^2} )$

=> $K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)$

Generally

$\sum\limits_{i=1}^n (k) = \frac{1}{2} n (n + 1)$

$\sum\limits_{i=1}^n (8) = \frac{1}{2} * 8* (8 + 1)$

$\sum\limits_{i=1}^n (8) = 36$

$K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)$

and

$\sum\limits_{i=1}^n (i) = \frac{1}{2} n (n + 1)$

Therefore

$K_n = \frac{72}{n} + \frac{2}{n^2} * \frac{1}{2} n (n + 1 )$

$K_n = \frac{72}{n} + \frac{1}{n} (n + 1 )$

$K_n = \frac{72}{n} + 1 + \frac{1}{n}$

$K_n = \frac{72 + 1 + n }{n}$

$K_n = \frac{n + 73 }{n}$

Now $\lim_{n \to \infty} K_n = \lim_{n \to \infty} [\frac{n + 73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [\frac{n}{n} + \frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 + \frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 ] + \lim_{n \to \infty} [\frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = 1 + 0$

Therefore

$\lim_{n \to \infty} K_n = 1$

5 0

3 years ago

At a school. Number of boys:number of girls=11:9. There are 124 more boys than girl. Work out the total number of students at th

JulsSmile [24]

Answer:

Total students = 1240

Step-by-step explanation:

Given that,

Number of boys: number of girls=11:9

$\dfrac{x}{y}=\dfrac{11}{9}\\\\9x=11y$ ......(1)

There are 124 more boys than girls i.e.

x = 124+y .....(2)

Put the value of x from equation (2) in equation (1). So,

9(124+y) = 11y

1116 +9y = 11y

1116 = 2y

y = 558

Put the value of y in equation (2).

x = 124+558

x = 682

Total students = x+y

= 682+558

= 1240

So, there are 1240 students at the school.

5 0

3 years ago

Hi please help i’ll give brainliest

Harman [31]

Answer:

1)8

2)25

3)20

Step-by-step explanation:

I hope this helps :)

Let me know if you have any questions

7 0

3 years ago

Read 2 more answers

What is the slope of a line that is perpendicular to the line whose equation is 2y = 3x - 1?

alexandr1967 [171]

Answer:

The slope of the line is $-\frac{2}{3}$

Step-by-step explanation:

For any line $y=mx+b$ , a line that is perpendicular to it is $y_\perp =-\frac{1}{m} x+b$ .

Therefore the slope of the perpendicular line is $-\frac{1}{m}$ .

For our case $y=\frac{3}{2}x-\frac{1}{2}$ therefore the slope of the prependicular is the reciprocal of $\frac{3}{2}$ multiplied by $-1.$

$\therefore\:slope=-\frac{2}{3}.$

4 0

3 years ago

Explain how counting number of girls in five children family can be treated as a binomial experiment. What assumptions are neces

Juliette [100K]

This is a binomial experiment and you'll use the binomial probability distribution because:

There are two choices for each birth. Either you get a girl or you get a boy. So there are two outcomes to each trial. This is where the "bi" comes from in "binomial" (bi means 2).
Each birth is independent of any other birth. The probability of getting a girl is the same for each trial. In this case, the probability is p = 1/2 = 0.5 = 50%
There are fixed number of trials. In this case, there are 5 births so n = 5 is the number of trials.

Since all of those conditions above are met, this means we have a binomial experiment.

Some textbooks may split up item #2 into two parts, but I chose to place them together since they are similar ideas.

8 0

3 years ago