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exis [7]
3 years ago
9

The top of the cylindrical can shown below has a diameter of 7 centimeters (cm).

Mathematics
1 answer:
Sidana [21]3 years ago
5 0

Answer:

Circumference of the can is 21.98 cm.

Step-by-step explanation:

Since, top of the cylinder can shown in the figure is in the shape of a circle

Circumference of a circle is given by the formula,

Circumference 'C' = π × Diameter

Where r = radius of the circle

Therefore, circumference of a circle with diameter 7 centimeters will be,

C = 7π

   = 7 × 3.14

   = 21.98 cm

Therefore, circumference of the can is 21.98 cm.

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The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation
Wewaii [24]

Answer:

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.

This means that \mu = 14, \sigma = 2

Sample of 100:

This means that n = 100, s = \frac{2}{\sqrt{100}} = 0.2

What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?

This is 1 subtracted by the p-value of Z when X = 14.2. So

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

By the Central Limit Theorem

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

Z = \frac{14.2 - 14}{0.2}

Z = 1

Z = 1 has a p-value of 0.8413.

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

6 0
3 years ago
.(3x+1)(x-3)<br> Binomial
Dafna11 [192]

Answer:

3x^2−8x−3

Step-by-step explanation:

(3x+1)(x−3)

=(3x+1)(x+−3)

=(3x)(x)+(3x)(−3)+(1)(x)+(1)(−3)

=3x^2−9x+x−3

=3x^2−8x−3

5 0
3 years ago
A survey of 500 college students moving into their dorm revealed that 425 brought a microwave, 380 brought a video game console,
tia_tia [17]

Answer:

0.90

Step-by-step explanation:

I’m doing the unit test

5 0
2 years ago
The wrestling team wants to sell pies for a fundraiser. The cafeteria helped out by donating 2 pies. Each pie will be cut into 4
Eduardwww [97]

Answer:

The answer would be 8

Step-by-step explanation:

4x8=32

4 is the pieces of each pie

8 is how many pies

32 is how many pieces they need

8 0
3 years ago
Find the earnings for giving a haircut to m men and w women. Justify your answer
Ratling [72]
Woman and men would be the same price, if the haircuts are very popular, each gender got the same haircut, then they also would be the same price, it is mostly about the prices, interestingness, and popularity or each barbershop, go by your nearest barbershop and see what prices they have. :))
3 0
3 years ago
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