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Andrew [12]
3 years ago
11

Part a: what is the initial value of the function? what does it mean in the context of the situation?

Mathematics
1 answer:
ser-zykov [4K]3 years ago
4 0

Answer:

Initial value = 10, slope = 4

Step-by-step explanation:

Initial value is the point where x takes its lowest value. In this case it is x = 0 and y = 10. Rate of change is the slope at a given point. Because this is a first order equation graph the slope is always the same. And in this case it is 4 as for every 1 unit of x the y goes 4.

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The owner of Matt’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.

4 0
3 years ago
If a population of 300 cells doubles every hour, which function represents the population after (h) hours
tangare [24]
I say y=300(2x) X=hours Y=population
Y=600x
8 0
3 years ago
Please Help Waiting 1 hour Please!!
mezya [45]

Step-by-step explanation:

yes the are similar because of AA Theorem

EAB is similar to ECD

4 0
3 years ago
The in center is the center of the circle of a triangle
Lana71 [14]

Answer:

inscribed

Step-by-step explanation:

For any given triangle, the circle inside of it is called the Inscribed circle

4 0
3 years ago
Determine the relationship between the number of desks in the classroom and
mash [69]

30 + 8 = 38 desks

38 x 4 = 152 legs

If you did not add those eight desks then you will have 120 legs.

So, the amount of legs will go up by 32 if you add 8 more desks.

7 0
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