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aksik [14]
3 years ago
13

A rectangle has length 127.3 cm and width 86.5 cm, both correct to 1 decimal place. Calculate the upperbound and the lowerbound

for the perimeter of the rectangle. pls answer fast. i need all the workings.
Mathematics
1 answer:
Mnenie [13.5K]3 years ago
8 0

Answer:

Correct to 1dp

127.3 cm = 127.0 cm

86.5 cm = 87.0 cm

Upper limits:

127.0 cm = 127.05 cm

87.0 cm = 87.05 cm

Lower Limits:

127.0 cm = 126.95 cm

87.0 cm = 86.95 cm

upper limit of perimeter of rectangle:

P = 2(l+w)

= 2(127.05 + 87.05)

= 2(214.1)

= 428.2 cm

lower limit of perimeter of rectangle:

P = 2(l+w)

= 2(126.95 + 86.95)

= 2(213.9)

= 427.8 cm

therefore;

427.8 cm \leqslant perimeter < 428.2cm

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Step-by-step explanation:

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Step-by-step explanation:

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The manufacturer of Pepsi claims that its 2-liter bottles contain, on average, no more than 250 calories. A sample of 20 2-liter
Stels [109]

Answer:

Yes, Sample information does indicate that a 2-liter bottle of Pepsi contains more than 250 calories  

Step-by-step explanation:  

Null Hypothesis [H0] : u < 250  

Alternate Hypothesis [H1] : u > 250 {One Tail}  

t = (x' - u) / [ sd / √n ]  

= (255 - 250) / (5.6 / √20)  

5 / (5.6 /√20)  

= 3.99  

As t ie 3.99 > t value 1.65 ie for one tail 95% confidence level. So, we reject the null hypothesis & conclude that it contains more than 250 calories.  

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The mean annual cost of an automotive insurance policy is normally distributed with a mean of $1140 and standard deviation of $3
DerKrebs [107]

Using the normal distribution, it is found that the probabilities are given as follows:

a) 0.8871 = 88.71%.

b) 0.0778 = 7.78%.

c) 0.8485 = 84.85%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

The parameters in this problem are given as follows:

\mu = 1140, \sigma = 310, n = 16, s = \frac{310}{\sqrt{16}} = 77.5

Item a:

The probability is the <u>p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1000</u>, hence:

X = 1250:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{1250 - 1140}{77.5}

Z = 1.42

Z = 1.42 has a p-value of 0.9222.

X = 1000:

Z = \frac{X - \mu}{s}

Z = \frac{1000 - 1140}{77.5}

Z = -1.81

Z = -1.81 has a p-value of 0.0351.

0.9222 - 0.0351 = 0.8871 = 88.71% probability.

Item b:

The probability is <u>one subtracted by the p-value of Z when X = 1250</u>, hence:

1 - 0.9222 = 0.0778 = 7.78%.

Item c:

The probability is the <u>p-value of Z when X = 1220</u>, hence:

Z = \frac{X - \mu}{s}

Z = \frac{1220 - 1140}{77.5}

Z = 1.03

Z = 1.03 has a p-value of 0.8485.

0.8485 = 84.85% probability.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

3 0
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