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Andrews [41]
2 years ago
13

A 500 yard train travels at a constant speed. A motorcyclist rides at a constant speed on the highway parallel to the train trac

ks. The motorcyclist starts at the rear of the train and drives to the very front of the train, and then falls back to the rear of the train. As the motorcycle completes this cycle, the train travels 1200 yards. How far did the motorcyclist travel?
Mathematics
1 answer:
garik1379 [7]2 years ago
7 0

Answer:

120/2 = x/5....120 miles to 2 hrs = x miles to 5 hrs

cross multiply

(2)(x) = (120)(5)

2x = 600

x = 600/2

x = 300....the motorcyclist would travel 300 miles in 5 hrs

or u could do it this way..

120/2 = 60 miles per hr

60 * 5 = 300 miles

Step-by-step explanation:

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Sin theta=-1/2 then cos theta=​
zepelin [54]

Answer:

<h2>cos 30°= 0.866</h2>

Step-by-step explanation:

Step one:

Applying the SOH CAH TOA principle

assuming all dimensions are in cm

Step two:

Given data

opposite= 1 cm

hypotenuse= 2 cm

<h3>we can now solve for θ</h3>

Sin(θ)= opp/hyp

Sin(θ)= 1/2

Sin(θ)= 0.5

θ= sin-1 0.5

θ= 30°

hence  from tables cos 30°= 0.866

4 0
3 years ago
10. Contacts. Assume that 30% of students at a university
jonny [76]

Using the <em>normal distribution and the central limit theorem</em>, we have that:

a) A normal model with mean 0.3 and standard deviation of 0.0458 should be used.

b) There is a 0.2327 = 23.27% probability that more than one third of this sample wear contacts.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
  • By the Central Limit Theorem, for a <u>proportion p in a sample of size n</u>, the sampling distribution of sample proportion is approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1 - p)}{n}}, as long as np \geq 10 and n(1 - p) \geq 10.

In this problem:

  • 30% of students at a university wear contact lenses, hence p = 0.3.
  • We randomly pick 100 students, hence n = 100.

Item a:

np = 100(0.3) = 30 \geq 10

n(1 - p) = 100(0.7) = 70 \geq 10

Hence a normal model is appropriated.

The mean and the standard deviation are given as follows:

\mu = p = 0.3

s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.3(0.7)}{100}} = 0.0458

Item b:

The probability is <u>1 subtracted by the p-value of Z when X = 1/3 = 0.3333</u>, hence:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.3333 - 0.3}{0.0458}

Z = 0.73

Z = 0.73 has a p-value of 0.7673.

1 - 0.7673 = 0.2327.

0.2327 = 23.27% probability that more than one third of this sample wear contacts.

To learn more about the <em>normal distribution and the central limit theorem</em>, you can take a look at brainly.com/question/24663213

5 0
3 years ago
A student is building a parallelogram- shaped deck with a base of (4x + 3) feet and a height of (3x - 2) feet. Which polynomial
timurjin [86]

Answer:

F

Step-by-step explanation:

see attached image above

8 0
3 years ago
Read 2 more answers
Mark spends $36 at a basketball game. He buys a T-shirt for $22. He then buys a bottle of water for $4 and 2 tacos. How much is
Arturiano [62]

Answer:

each taco is $7.

Step-by-step explanation:

In total he spent $36. He bought a shirt for $22 and a bottle of water for $4.

22+4= 26

36-22= 14

14 divided by 2= 7

5 0
3 years ago
Read 2 more answers
Really confused and am on final attempt!
Flura [38]

Answer:

C

Step-by-step explanation:

the legs of a 30-60-90 triangle are 1 and \sqrt{3}, while the hypotenuse is 2.

the ratio of the legs is therefore 1 : \sqrt{3} → C



3 0
3 years ago
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