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3 years ago

Ben is spending his summer driving across the country. He is going to spend the first day

Mathematics

1 answer:

KengaRu [80]3 years ago

4 0

Answer:

The graph of the data presented is shown in the attached image to this solution.

It shows that the relationship between distance travelled in miles and the time take in hours is D = 55t

Step-by-step explanation:

The distance travelled with the corresponding time taken are presented in the table

Note: D - Distance travelled (miles)

t - Time (hours)

D | t

55 | 1

110 | 2

165 | 3

220 | 4

275 | 5

330 | 6

We are then told to plot these distance travelled on a graph with the time taken.

The distance travelled is plotted on the y-axis and the time in hours is plotted on the x-axis.

The image of the graph of this function will be attached to this answer

It is evident that the graph shows the relationship between the distance travelled and time taken to be D = 55t

Hope this Helps!!!

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3 years ago

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This is a classic example of Scientific Notation.
5.3 x 10^5 actually equals 530,000
3.8 x 10^4 actually equals 38,000
Since it is asking for the sum of the numbers you are adding.
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3 years ago

The owner of Mattâ€™s Gas Station wants to study gasoline purchases of customers at his station. In 2017, the mean amount of gas

gulaghasi [49]

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 9

For the alternative hypothesis,

µ ≠ 9

This is a 2 tailed test

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 9

x = 9.9

σ = 2.5

n = 50

z = (9.9 - 9)/(2.5/√50) = 2.55

Looking at the normal distribution table, the probability corresponding to the area above the z score is 1 - 0.99461 = 0.00539

Recall, population mean is 9

The difference between sample sample mean and population mean is 9.9 - 9 = 0.9

Since the curve is symmetrical and it is a two tailed test, the x value for the left tail is 9 - 0.9 = 8.1

the x value for the right tail is 9 + 0.9 = 9.9

These means are higher and lower than the null mean. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area. We already got the area above the z score as z = 0.00539

We would double this area to include the area in the left tail of z = - 2.55. Thus

p = 0.00539 × 2 = 0.01078

Since alpha, 0.01 < 0.01078, we would reject the null hypothesis

But we are told to use the critical value approach, then

Since α = 0.01, the critical value is determined from the normal distribution table.

For the left, α/2 = 0.01/2 = 0.005

The z score for an area to the left of 0.005 is - 2.575

For the right, α/2 = 1 - 0.005 = 0.995

The z score for an area to the right of 0.995 is 2.575

In order to reject the null hypothesis, the test statistic must be smaller than - 2.575 or greater than 2.575

Since - 2.55 > - 2.575 and 2.55 < 2.575, we would reject the null hypothesis. This corresponds to our previous decision.

b) we would assume normal distribution because the sample size is sufficiently large and the population standard deviation is known.

c) Confidence interval is written in the form,

(Sample mean ± margin of error)

Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.

Margin of error = z × σ/√n

The z score for confidence level of 99% is 2.58

Margin of error = 2.58 × 2.5/√50 = 0.91

Confidence interval = 9.9 ± 0.91

The lower end of the confidence interval is

9.9 - 0.91 = 8.99

Therefore, p = 9 will be contained in the interval.

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Vikentia [17]

Answer:

A) The model exists: f(x) = -3x^2 +4x -4

Step-by-step explanation:

A quadratic model will always exist for 3 given points, provided they are not on a line. In that case, a linear model is appropriate.

Here, the slope between -1 and 0 is positive, and the slope between 0 and 3 is negative. Thus, we know these points are not collinear, and a model must exist.

The model is most easily found using a quadratic regression tool. Such is shown in the attachment. It tells us that ...

f(x) = -3x^2 +4x -4

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Answer:

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