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Naya [18.7K]
3 years ago
10

An Eastbound train (E) traveling 95 mph and a Westbound train (W) traveling 110 mph leave the same train station at different ti

mes. After 4 hours, they are 4 00 miles apart. Which system of linear equations can be used to determine the time that each of the trains has been traveling?
Mathematics
1 answer:
Simora [160]3 years ago
8 0

Answer:

The system of linear equations that can be used to determine the time that each of the trains has been traveling is:

E + W = 4 ....... Equation 1

95 E + 110W = 400  ......Equation 2

Hence,

An Eastbound train has been travelling for =  (E) = 2.67 hours

A Westbound train has been travelling for =  (W) = 1.33 hours

Step-by-step explanation:

An Eastbound train (E) traveling 95 mph and a Westbound train (W) traveling 110 mph leave the same train station at different times. After 4 hours, they are 4 00 miles apart. Which system of linear equations can be used to determine the time that each of the trains has been traveling?

Speed = Distance/Time

Distance = Speed × Time

Let the time

An Eastbound train =  (E)

A Westbound train =  (W)

E + W = 4 hours ....... Equation 1

95mph × E + 110mph × W = 400 miles

95 E + 110W = 400 miles ......Equation 2

The system of linear equations that can be used to determine the time that each of the trains has been traveling is:

E + W = 4 ....... Equation 1

95 E + 110W = 400  ......Equation 2

E = 4 - W

We substitute 4 - W for E in Equation 2

95 (4 - W) + 110W = 400  

380 - 95W + 110W = 400

Collect like terms

95W - 110W = 400 - 380

15W = 20

W = 20/15

W = 1.3333333333 hours

≈ 1.33 hours

E = 4 - W

E = 4 - 1.33 hours

E = 2.67 hours

Therefore,

An Eastbound train has been travelling for =  (E) = 2.67 hours

A Westbound train has been travelling for =  (W) = 1.33 hours

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Tennis Replay In the year that this exercise was written, there were 879 challenges made to referee calls in professional tennis
tiny-mole [99]

Answer:

a. 0.0209 = 2.09% probability that among the 879 challenges, the number of overturned calls is exactly 231.

b. 231 is less than 2.5 standard deviations above the mean, which means that 231 overturned calls among 879 challenges is not a significantly high result.

Step-by-step explanation:

For each challenge, there are only two possible outcomes. Either it was overturned, or it was not. The probability of a challenge being overturned is independent of any other challenge. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Significantly high:

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

If a value is more than 2.5 standard deviations above the mean, this value is considered significantly high.

25% of the challenges are successfully upheld with the call overturned.

This means that p = 0.25

879 challenges

This meas that n = 879

a. If the 25% rate is correct, find the probability that among the 879 challenges, the number of overturned calls is exactly 231.

This is P(X = 231). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 231) = C_{879,231}.(0.25)^{231}.(0.75)^{648} = 0.0209

0.0209 = 2.09% probability that among the 879 challenges, the number of overturned calls is exactly 231.

b. If the 25% rate is correct, find the probability that among the 879 challenges, the number of overturned calls is 231 or more. If the 25% rate is correct, is 231 overturned calls among 879 challenges a result that is significantly high

The mean is:

E(X) = np = 879*0.25 = 219.75

The standard deviation is:

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{879*0.25*0.75} = 12.84

219.75 + 2.5*12.84 = 251.85 > 231

231 is less than 2.5 standard deviations above the mean, which means that 231 overturned calls among 879 challenges is not a significantly high result.

5 0
3 years ago
Maria's book is longer than Brandon's. The difference in the two book lengths is 56
Bingel [31]

Answer:

Maria's book is 202 pages long, Brandon's book is 146 pages long

Step-by-step explanation:

We can set this up with 2 variables: lets say that Maria's book length is x and Brandon's is y.

We can see that Maria's book is 56 pages longer than Brandon's and can come up with an equation:

x=y+56

We also see that their booklengths add up to 348, and can get:

x+y=348

From here, we solve for x and y. We can use substitution to find y.

x+y=348

(y+56)+y=348

2y=292

y=146

Here we plug in for x:

x=y+56

x=(146)+56

x=202

Therefor we get that Maria's book is 202 pages long, Brandon's book is 146 pages long

7 0
2 years ago
Omar owns a small business selling ice-cream. He knows that in the last week 32
vekshin1

Answer:

500

Step-by-step explanation:

Hope this helps.

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2 years ago
What is one and two thirds times two and three fourths
andrey2020 [161]
The answer is 2 and two twelfths.
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Read 2 more answers
A sector of a circle has a central angle of 100 degrees. If the area of the sector is 50pi, what is the radius of the circle
MrMuchimi

The radius of the circle having the area of the sector 50π, and the central angle of the radius as 100° is <u>6√5 units</u>.

An area of a circle with two radii and an arc is referred to as a sector. The minor sector, which is the smaller section of the circle, and the major sector, which is the bigger component of the circle, are the two sectors that make up a circle.

Area of a Sector of a Circle = (θ/360°) πr², where r is the radius of the circle and θ is the sector angle, in degrees, that the arc at the center subtends.

In the question, we are asked to find the radius of the circle in which a sector has a central angle of 100° and the area of the sector is 50π.

From the given information, the area of the sector = 50π, the central angle, θ = 100°, and the radius r is unknown.

Substituting the known values in the formula Area of a Sector of a Circle = (θ/360°) πr², we get:

50π = (100°/360°) πr²,

or, r² = 50*360°/100° = 180,

or, r = √180 = 6√5.

Thus, the radius of the circle having the area of the sector 50π, and the central angle of the radius as 100° is <u>6√5 units</u>.

Learn more about the area of a sector at

brainly.com/question/22972014

#SPJ4

8 0
1 year ago
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