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2 years ago

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A small bus charges $3.50 per person for a ride from the train station to a concert. The bus will run if at least 3 people take

it, and it cannot fit more than 10 people. Function B gives the amount of money that the bus operator earns when n people ride the bus.

1 answer:

Luden [163]2 years ago

6 0

Can you help me pleaseeeeeeeee

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How many terms are there in the sequence 1, 8, 28, 56, ..., 1 ?

BabaBlast [244]

Answer:

9 terms

Step-by-step explanation:

Given:

1, 8, 28, 56, ..., 1

Required

Determine the number of sequence

To determine the number of sequence, we need to understand how the sequence are generated

The sequence are generated using

$\left[\begin{array}{c}n&&r\end{array}\right] = \frac{n!}{(n-r)!r!}$

Where n = 8 and r = 0,1....8

When r = 0

$\left[\begin{array}{c}8&&0\end{array}\right] = \frac{8!}{(8-0)!0!} = \frac{8!}{8!0!} = 1$

When r = 1

$\left[\begin{array}{c}8&&1\end{array}\right] = \frac{8!}{(8-1)!1!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8$

When r = 2

$\left[\begin{array}{c}8&&2\end{array}\right] = \frac{8!}{(8-2)!2!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} =2 8$

When r = 3

$\left[\begin{array}{c}8&&3\end{array}\right] = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56$

When r = 4

$\left[\begin{array}{c}8&&4\end{array}\right] = \frac{8!}{(8-4)!4!} = \frac{8!}{4!3!} = \frac{8 * 7 * 6 * 5 * 4!}{4! *4*3* 2 *1} = \frac{8 * 7 * 6*5}{4*3 *2 *1} = 70$

When r = 5

$\left[\begin{array}{c}8&&5\end{array}\right] = \frac{8!}{(8-5)!5!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56$

When r = 6

$\left[\begin{array}{c}8&&6\end{array}\right] = \frac{8!}{(8-6)!6!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} = 28$

When r = 7

$\left[\begin{array}{c}8&&7\end{array}\right] = \frac{8!}{(8-7)!7!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8$

When r = 8

$\left[\begin{array}{c}8&&8\end{array}\right] = \frac{8!}{(8-8)!8!} = \frac{8!}{8!0!} = 1$

The full sequence is: 1,8,28,56,70,56,28,8,1

And the number of terms is 9

3 0

3 years ago

Help plz anyone plz help me !!!!!!!!

scZoUnD [109]

Check the attachment for the answers. Click on it again to make it bigger.

8 0

3 years ago

The test scores on a 100-point test were recorded for 20 students:71 93 91 86 7573 86 82 76 5784 89 67 62 7277 68 65 75 84a. Can

Dafna11 [192]

Answer: a. Yes

b. mean = 76.65

standard deviation = 10.04

c. 76.65 ± 4.4

Step-by-step explanation:

a. <u>Stem</u> <u>and</u> <u>leaf</u> <u>Plot</u> shows the frequencies with which classes of value occur. To create this plot, we divide the set of numbers into 2 columns: <u>stem</u>, the left column, which contains the tens digits; <u>leaf</u>, the right column, which contains the unit digits.

<u>Normal</u> <u>distribution</u> is a type of distribution: it's a bell-shaped, symmetrical, unimodal distribution.

A stem and leaf plot displays the main features of the distribution. If turned on its side, we can see the shape of the data.

The figure below shows the stem and leaf plot of the 100-point test score. As we can see, when turned, the plot resembles bell-shaped distribution. So, this test scores were selected from a normal population.

b. <u>Mean</u> is the average number of a data set. It is calculated as the sum of all the data divided by the quantity the sample has:

mean = $\frac{\Sigma x}{n}$

For the 100-point test score:

mean = $\frac{71+93+91+...+65+75+84}{20}$

mean = 76.65

<u>Standard</u> <u>Deviation</u> determines how much the data is dispersed from the mean. It is calculated as:

$s=\sqrt{\frac{\Sigma (x-mean)^{2}}{n-1} }$

For the 100-point test score:

$s=\sqrt{\frac{[(71-76.65)+(93-76.65)+...+(84-76.65)]^{2}}{20-1} }$

s = 10.04

The mean and standard deviation of the scores are 76.65 and 10.04, respectively.

c. <u>Confidence</u> <u>Interval</u> is a range of values we are confident the real mean lies.

The calculations for the confidence interval is

mean ± $z\frac{s}{\sqrt{n} }$

where

z is the z-score for the 95% confidence interval, which is equal 1.96

Calculating interval

76.65 ± $1.96.\frac{10.04}{\sqrt{20} }$

76.65 ± 4.4

The 95% confidence interval for the average test score in the population of students is between 72.25 and 81.05.

7 0

2 years ago

If Anna walked 13/3 of a mile how many whole miles did she walk

Anuta_ua [19.1K]

Answer: 4 Whole Miles

Step-by-step explanation:

If she walked 13/3 of a mile

13/3 = 4.3333333

4 is the closest whole mile.

3 0

3 years ago

Read 2 more answers

2 plus 3 plus 8 plus 2

xeze [42]

Answer:

15

Step-by-step explanation:

2+3+8+2

2+3= 8+2=

5 + 10=

15

5 0

3 years ago