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2 years ago

Colin is skateboarding and is riding a rail. The rail is attached to two poles. The first pole is 80 cm tall and the

Mathematics

1 answer:

Vinvika [58]2 years ago

5 0

Answer:

$\sqrt{4.49m}$

Step-by-step explanation:

the unit of length is meter,

so, 80cm=0.8cm, 10cm=0.1m

the length of the rail= $\sqrt{(0.8-0.1)^2+2^2}$

= $\sqrt{4.49m}$

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How do you find pi?

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to calculate pi you can use the Nilakantha Series.

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3 years ago

The amount of money spent on textbooks per year for students is approximately normal.

Ostrovityanka [42]

Answer:a

$336.04 < \mu < 443.96$

The margin of error will increase

The margin of error will decreases

The 99% confidence interval is $0.4107 < p < 0.4293$

Step-by-step explanation:

From the question we are told that

The sample size $n = 19$

The sample mean is $\= x = \$\ 390$

The standard deviation is $\sigma = \$ \ 120$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table

$Z_{\frac{\alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 1.96 * \frac{120}{\sqrt{19} }$

=> $E = 53.96$

The 95% confidence interval is

$\= x - E < \mu < \= x + E$

=> $390 - 53.96 < \mu < 390 - 53.96$

=> $336.04 < \mu < 443.96$

When the confidence level increases the $Z_{\frac{\alpha }{2} }$ also increases which increases the margin of error hence the confidence level becomes wider

Generally the sample size mathematically varies with margin of error as follows

$n \ \ \alpha \ \ \frac{1}{E^2 }$

So if the sample size increases the margin of error decrease

The sample proportion is mathematically represented as

$\r p = \frac{210}{500}$

$\r p = 0.42$

Given that the confidence level is 0.99 the level of significance is $\alpha = 0.01$

The critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }$

=> $E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }$

=> $E = 0.0093$

The 99% confidence interval is

$\r p - E < p < \r p + E$

$0.42 - 0.0093 < p < 0.42 + 0.0093$

$0.4107 < p < 0.4293$

4 0

4 years ago

Which graph shows the solution to the following inequality? 4d- 6 < 18 PLEASE HELP

kenny6666 [7]

Answer:

answer a

Step-by-step explanation:

$4d-6$ < $18$

Let's isolate $d$ on one side of the equation. Ignore the inequality for now. We'll deal with that later.

$4d-6=18\\4d-6+6=18+6\\4d=24\\\frac{4d}{4}=\frac{24}{4}\\ d=6$

Now, I'm going to bring back the inequality or < symbol. I only removed it when simplifying and isolating $d$ , but if this confuses you, just do your math and keep the inequality there.

$d$ < $6$

On a number line, this would include every number less than $6$ , due to the < (less than) symbol. This disqualifies answers b and d because they are showing every number greater than $6$ . But, how do we decide between answers a and c?
If a line has point at its beginning, $6$ , then that means that every number less than or equal to [ ≤ ] 6 is being shown, but our equation just says less than [ < ] 6, so answer a is our correct answer.

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4 years ago

Read 2 more answers

Estela and Gavin make a poster together. Estela asks Gavin to draw a quadrilateral with a 45° angle between side lengths of 5 in

Aleks [24]

Ggbccghjcdtyjbcbnjhxffcnjjj

4 0

3 years ago

The sum of three consecutive terms of an arithmetic sequence is 27, and the sum of their squares is 293. What is the absolute di

Ber [7]

The absolute difference between the greatest and the least of these three numbers in the arithmetic sequence is 10.

The sequence is an arithmetic sequence. Therefore,

d = common difference

let

a = centre term

Therefore, the 3 consecutive term will be as follows

a - d, a, a + d

a - d + a + a + d = 27

3a = 27

a = 27 / 3

a = 9

Therefore,

(a-d)² + (a)² + (a + d)² = 293

(a²-2ad+d²) + 9² + (a² + 2ad + d²) = 293

(81 - 18d + d²) + 81 + (81 + 18d + d²) = 293

243 + 2d² = 293

2d² = 50

d² = 50 / 2

d = √25

d = 5

common difference = 5

Therefore, the 3 numbers are as follows

9 - 5 , 9, 9 + 5 = 4, 9, 14

The difference between the greatest and the least of these 3 numbers are as follows:

14 - 4 = 10

learn more on Arithmetic progression: brainly.com/question/25749583?referrer=searchResults

7 0

3 years ago