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natali 33 [55]
3 years ago
14

An increase in walking has been shown to contribute to a healthier life-style. A sedentary American takes an average of 5000 ste

ps per day (and 65% of Americans are overweight). A group of health-conscious employees of a large health care system volunteered to wear pedometers for a month to record their steps. It was found that a random sample of 40 walkers took an average of 5430 steps per day, and the population standard deviation is 600 steps. At = 0.05 can it be concluded that they walked more than the mean number of 5000 steps per day?
Mathematics
1 answer:
Zielflug [23.3K]3 years ago
6 0

Answer:

Step-by-step explanation:

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,

H0: µ = 5000

For the alternative hypothesis,

H1: µ > 5000

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 = 5000

x = 5430

σ = 600

n = 40

z = (5430 - 5000)/(600/√40) = 4.53

Looking at the normal distribution table, the probability corresponding to the z score is < 0.0001

Since alpha, 0.05 > than the p value, then we would reject the null hypothesis. Therefore, at a 5% level of significance, it can be concluded that they walked more than the mean number of 5000 steps per day.

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Find the numerical coefficient of 7x^3​
Travka [436]

Answer:

7

Step-by-step explanation:

4 0
3 years ago
Pearl's Biking Company manufactures and sells bikes. Each bike costs £40 to make, and the company's fixed costs are £5000. In ad
____ [38]

Answer:

R(x) =300·x - 2·x²

C(x) = £5000 + £40 × x

The break even points are 23.47 and 106.53 or 23 and 107 bikes

Step-by-step explanation:

Given that the price function P(x) = 300 -2·x

Cost per bike = £40

The revenue function R(x) is given by  bike price × total number of bikes manufactured and sold

∴ R(x)  = P(x)×x = (300 - 2·x)×x = 300·x - 2·x²

The company's cost function, C(x) is Fixed cost + cost to produce each bike × total number of bikes produced

∴ C(x) = £5000 + £40 × x

The break even point is given by the relation;

Total revenue - total cost = 0

That is, break even point is R(x) - C(x) = 0

300·x - 2·x² - (5000 + 40·x) = 0

-2·x²+260·x-5000 = 0 or 2·x²- 260·x + 5000 = 0

Factorizing, we have;

(x - (65 -5√69))(x - (65 +5√69))

Solving gives x = 23.47 or 106.53

Therefore, the break even points are 23.47 and 106.53.

That is the company is profitable when they produce less than 23 bikes or more than 107 bikes.

3 0
3 years ago
Two students walk in the same direction along a straight path, at a constant speed - one at .90 m/s and the other at 1.90 m/s.a.
anyanavicka [17]

Answer:

a)The second student arrive 7 minutes and 36 seconds sooner

b)They have to walk 598,51 m

Step-by-step explanation:

Speed= Distance/Time

We are looking for time now

Time = Distance/Speed

First student

Time = 780 m/0.90 m/s=866,66 seconds

Second student

Time = 780 m/1.90 m/s=410,52 seconds

Difference=866,66-410,52= 456,14 seconds

In minutes

Difference= 456,14 seconds /60=7 minutes 36 seconds

Distance=Speed x Time

Speed¹ x Time¹ =Speed² x Time²

Time¹= Time² + 5.50 min

5.50 min =350 seconds

Time²  =Speed¹ x Time¹ /Speed²

Time²  =Speed¹ x (Time² + 350 seconds  ) /Speed²

Time²  =0.9 x (Time² + 350 seconds  ) /1.9

Time²  =0,4737 x (Time² + 350 seconds  )

Time²  =0,4737 Time² + 165,79 seconds

Time²  - 0,4737 Time² = 165,79 seconds

0,5263 Time² = 165,79 seconds

Time² = 165,79 seconds/0,5263 =315,01 seconds

Distance=1,9 x 315,01 seconds = 598,51 m

5 0
3 years ago
-2 + 3n&lt; 28 and 6n - 7 &gt; 17
sveta [45]

Answer:

N< 10 and N>4

Step-by-step explanation:

-2+3n< 28. =. 3n < 30. =. N < 10

+2. +2 ÷3. ÷3

6n - 7 > 17. =. 6n > 24. =. N > 4

+7. +7. ÷ 6. ÷ 6

8 0
3 years ago
Please help, I’ll mark your answer as brainliest.
timama [110]

Already answered here: brainly.com/question/26919792

5 0
3 years ago
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