What is the slope of the line shown below?

Sara’s little brother is getting ready to color the picture of a rainbow that Sara drew for him. To make the task easier for her

Zina [12379]

There are seven rainbow colors: red, orange, yellow, green, blue, indigo, and violet, so 7 possible choices. When two events occur in sequence, multiply their probabilities. With replacement: P(violet)=1/7 and P(orange)=1/7, so P(violet then orange)=1/7 * 1/7 = 1/49. Without replacement: after picking violet, P(orange)=1/6, so P(violet then orange)=1/7 * 1/6 = 1/42.

8 0

1 month ago

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Sanjit drives the 45 km distance between York and Leeds he then drives a further 42 km from Leeds to Blackpool

Leona [12618]

The average speed for his entire journey from York to Blackpool is about 61.41 km/h.

Here’s a breakdown of how we arrive at this:

$\text{ The average speed}=\frac{\text{Total distance covered}}{\text{Total time taken}}$

The distance he travelled from York to Leeds is 45 km,

and the speed during that section was 54 km/h.

Therefore, the time taken to travel from York to Leeds is 45/54 hours (since Time = Distance/Speed).

Next, the distance from Leeds to Blackpool is 42 km,

and the time for that leg of the journey is 35 minutes, which is 35/60 hours.

This leads to the total duration for his trip as

$=\frac{45}{54}+\frac{35}{60}=\frac{450+315}{540}=\frac{765}{540}=\frac{17}{12}$ hours.

The cumulative distance covered equals 45 + 42 = 87 km.

Thus, his average speed is calculated as:

$=\frac{87}{17/12}= \frac{12\times 87}{17}=\frac{1044}{17}=61.4117647\approx 61.41\text{ km per hour}$

3 0

3 months ago

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Sandy takes a day off once every 4 days, and Morgan takes a day off once every 10 days. Today, both of them have taken the day o

Zina [12379]

Assuming that the departure day for both is day 0, Sandy's next day off occurs on day 4, while Morgan's falls on day 10. Sandy's days off will be on days 4, 8, 12, 16, and 20. Meanwhile, Morgan's days off will be on days 10, 20, 30, 40, and 50. Thus, both of them will share a day off on day 20, meaning they will next have a joint day off in 20 days.

4 0

2 months ago

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Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers have maintained careful records

Leona [12618]

Response:

Regarding this scenario, we have the following details about the timeframe to organize a return

$\mu =90, \sigma =14$

And we select a sample size =49>30, and we aim to find the standard deviation for the sample mean. Based on the central limit theorem, we understand that the sample mean distribution $\bar X$ is represented by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

The standard deviation would then be:

$\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2$

Therefore, the most accurate response would be

b. 2 minutes

Step-by-step explanation:

Prior concepts

Normal distribution, defines a probability distribution that is symmetric around the mean, showing that occurrences near the mean are more frequent than those that are further away.

The central limit theorem states that "when we have a population with mean μ and standard deviation σ and draw sufficiently large random samples from the population with replacement, then the distribution of the sample means will resemble a normal distribution. This applies regardless of whether the original population is normal or skewed, given that the sample size is large enough".

Solution to the problem

For this case, we have the following information about the time to prepare a return

$\mu =90, \sigma =14$

A sample size =49>30 also indicates that we are focused on determining the standard deviation for the sample mean. Based on the central limit theorem, we recognize that the sample mean distribution $\bar X$ is described by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And subsequently, the standard deviation will be:

$\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2$

Hence, the most accurate answer would be

b. 2 minutes

3 0

2 months ago