Ask question

Ask question

All categories

3 days ago

9

While driving home for the holidays, you can’t seem to get Little’s Law out of your mind. You note that your average speed of tr

avel is about 60 miles per hour. Moreover, the traffic report from the WXPN traffic chopper states that there is an average of 24 cars going in your direction on a one-quarter mile part of the highway. What is the flow rate of the highway (going in your direction) in cars per hour?

1 answer:

Svet_ta [4.3K]3 days ago

7 0

Answer:

1,200 cars per hour

Step-by-step explanation:

Assuming a steady flow of vehicles, as noted in the scenario.

If we imagined a counter at your position, there would be 25 cars within a quarter-mile, including your vehicle, all traveling at your speed.

Next, let's determine how long it takes to cover that quarter-mile distance. With your velocity at 60 mph, we can set up a proportion:

60 miles -----------> 1 hour

¼ of a mile --------> x hours

Then we can calculate:

60/ (¼) = 1/x ---------> x = 1/240 hours.

This indicates that in 1/240 hours, all 25 cars pass by the counter.

Now, let's find how many cars pass the counter in one hour. By cross-multiplying, we get:

1/240 hours -------> 25 cars

1 hour --------------> x cars

Thus, we have 1/240 = 25/x -------> x = 25*240 = 1,200 cars.

The highway's flow rate in the direction you are heading is 1,200 cars per hour.

You might be interested in

A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of awriting

tester [3916]

Answer:

a) Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

b) $p_v =P(t_{17}$

Given that the p-value is lower than the significance threshold in this situation, we have sufficient grounds to reject the null hypothesis.

c) $p_v =P(t_{17}$

In this case, since the p-value exceeds the significance threshold, we have adequate evidence to FAIL to reject the null hypothesis.

d) $p_v =P(t_{17}$

Here again, with the p-value being less than the significance level, we can reject the null hypothesis.

Step-by-step explanation:

1) Provided data and references

$\bar X$ represents the average of the samples

$s$ denotes the standard deviation of the samples

$n=18$ indicates the number of samples

$\mu_o =10$ is the value we are examining

$\alpha$ defines the significance level for the test.

t represents the specific statistic of interest

$p_v$ indicates the p-value relevant to the test (the variable of concern)

Define the null and alternative hypotheses.

To assess if the true mean is at least 10 hours, we must set up a hypothesis:

Part a

Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

If we consider the sample size being less than 30 and the population deviation unknown, it’s more appropriate to use a t-test to compare the actual mean with the reference value, calculated as:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Part b

In this scenario t=-2.3, $\alpha=0.05$

Initially, we need to calculate the degrees of freedom $df=n-1=18-1=17$

Since this is a left-tailed test, the p-value is determined by:

$p_v =P(t_{17}$

In this instance, with the p-value being less than the significance level, we have sufficient evidence to reject the null hypothesis.

Part c

For this situation t=-1.8, $\alpha=0.01$

We need to find the degrees of freedom $df=n-1=18-1=17$

For the left-tailed test, the p-value is given by:

$p_v =P(t_{17}$

In this case, since the p-value is above the significance level, we have enough grounds to FAIL to reject the null hypothesis.

Part d

For this case t=-3.6, $\alpha=0.05$

Firstly, we find the degrees of freedom $df=n-1=18-1=17$

Since we are conducting a left-tailed test, the p-value is calculated as:

$p_v =P(t_{17}$

Here, with the p-value being lower than the significance threshold, we can reject the null hypothesis.

5 0

6 days ago

Write the set of points from -5 to 4 but excluding -1 and 4 as a union of intervals

babunello [3635]

We need to specify the interval for numbers ranging from -5 to 4.

Moreover, we must exclude the values -1 and 4 from this range.

First, let’s note some crucial guidelines regarding interval notation.

It’s essential to identify which values are included and which ones are not in the specified range.

An open interval (or) indicates excluded numbers, while a closed interval [or] shows included numbers.

In this scenario, we notice three key numbers: -5, -1, and 4.

It is explicit that -1 and 4 are excluded, though -5 is not indicated as excluded, hence it remains included.

-1 lies between -5 and 4 on the number line.

Consequently, we can represent the interval notation from -5 to -1. (Note: -5 is included and -1 is not).

Thus, we write a closed interval " [ " on the left side of -5 and an open interval " ( " on the right side of -1. This gives us,

[-5, -1 ).

Next, we represent the interval from -1 to 4.

Since both endpoints are excluded, we will use open intervals ( ) on both sides of -1 and 4.

This results in the interval being

(-1,4).

We combine the two interval notations using the union symbol. So, the final interval representation is

[-5, -1 ) ∪ (-1,4).

5 0

4 days ago

Ms. Gallegos burns 236 calories riding her bike each hour. She wants to burn more than 590 calories riding her bike at the same

Svet_ta [4321]

Response:

354

Detailed explanation:

5 0

4 days ago

A real estate agent sells two sites for Rs. 18000 each. On one he gains 25% and on the other he loses 25 %. What is his loss or

zzz [4022]

ESPERO QUE ESTO TE SEA ÚTIL

3 0

13 days ago

Sabas dance class is 3 miles from her home. Her music class is 12 miles from her home. Write an equation that shows the number o

Zina [3914]

Answer:

3x = 12

x = 4

Step-by-step explanation:

The equation indicates that the distance to the dance class is three times that to her home, and when multiplied by "x", it reveals how much farther 3 is from 12. Consequently, if you evaluate the expression, the distance to the dance class is four times greater than that to her music class.

5 0

12 days ago