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m_a_m_a [10]
3 years ago
8

Lyra and Donna are testing the two-way radios they built for their high school science project. Lyra goes to the top of a buildi

ng that is 22 meters high with one of the radios and stands directly above the building’s entrance. Donna walks out of the entrance, perpendicular to the building, with the other radio. If Donna is more than 50 meters from the entrance, the connection between the radios breaks. What is the range of communication for the two radios to the nearest meter? A) 50 meters B) 55 meters C) 62 meters D) 72 meters

Mathematics
1 answer:
nata0808 [166]3 years ago
5 0
This question is far easier to understand if we draw it out. I've included an image attachment to help show the relationships of the measurements. As we can see from the image, their positioning helps form a triangle that we can use the Pythagorean Theorem to find the connection range.
The Theorem is a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse.

22^2 + 50^2 = c^2
484 + 2500 = c^2
2984= c^2
\sqrt{2984} = c
54.63 = c
So the answer to the nearest meter is 55 meters.

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At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen
guajiro [1.7K]

Answer:

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

p1 -> 1993

20 out of 100, so:

p_1 = \frac{20}{100} = 0.2

s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04

p2 -> 1997

10 out of 100, so:

p_2 = \frac{10}{100} = 0.1

s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03

Distribution of p1 – p2:

p = p_1 - p_2 = 0.2 - 0.1 = 0.1

s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05

Confidence interval:

p \pm zs

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.  

The lower bound of the interval is:

p - zs = 0.1 - 1.645*0.05 = 0.01775


The upper bound of the interval is:

p + zs = 0.1 + 1.645*0.05 = 0.18225


The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

6 0
3 years ago
en un maratòn participan corredores de todos los continentes 5/6 de los corredores son europeos se sabe que los americanos son l
Marysya12 [62]

Usando proporciones, se encuentra que 400 africanos han participado.

En total, hay x participantes.

\frac{5}{6} de los corredores son europeos, o sea:

E = \frac{5x}{6}

Los americanos son la dècime parte de los europeos, o sea:

Am = \frac{1}{10}E = \frac{5x}{60} = \frac{x}{12}

Los africanos son la quinta parte de los americanos, o sea:

Afr = \frac{1}{5}Am = \frac{x}{60}

En la carrera han inscritos 24 000 participantes, o sea, x = 24000. Por eso, la cantidad de africanos es:

Afr = \frac{x}{60} = \frac{24000}{60} = 400

Para obtener más información sobre las proporciones, puedes visitar a brainly.com/question/24615636

8 0
2 years ago
CAN SOMEONE HELP ME​
ANTONII [103]

Answer:

C is the answer

you can also see

7 0
2 years ago
NEED HELP ASAP
Lostsunrise [7]

Answer:

0.09

step by step explanation

7 0
2 years ago
A pyramid at a museum has a height of 21 meters and a square base with side lengths of 30 meters. 21 m 30 m What is the approxim
Orlov [11]

Answer: 6,300 m^3

Step-by-step explanation:

Put numbers into calculator

5 0
2 years ago
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