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vladimir2022 [97]
3 years ago
8

A long distance runner starts at the beginning of a trail and runs at a rate of 4 miles per hour. One hour later, a cyclist star

ts at the beginning of the trail and travels at a rate of 20 miles per hour. What is the amount of time that the cyclist travels before overtaking the runner? Do not do any rounding.
Mathematics
1 answer:
Scrat [10]3 years ago
7 0
T = 1/4 hour will be the answer
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What is the value of this expression 4to the power of 2 times 4 to the power of negative 3
AleksandrR [38]
4^2*4^-3

16- .016 (taken from a fraction into a decimal and rounded to the nearest tenth)

16.984 is your answer.

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Laura shades 60 squares on her hundredths grid And Billy shades 50 squares on his hundredths grid. Write the decimal number that
Andre45 [30]

Answer:

Laura = 0.60

Billy = 0.50

0.60 > 0.50

Step-by-step explanation:

Given

Laura = 60\ shades

Billy = 50\ shades

Required

Represent using decimal number and compare

From the question, we understand that there are 100th grids;

So:

Laura = \frac{60}{100}

Laura = 0.60

Billy = \frac{50}{100}

Billy = 0.50

Comparing both decimals;

Since 0.60 is greater than 0.50, we have:

0.60 > 0.50

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3 years ago
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.

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I need help finding the answers for all of these, I've been stuck on it for the last 30 minutes ​
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Answer:

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