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zaharov [31]
3 years ago
14

Daphne has a rope that is 60 meters long. She wants to use it to mark the boundary of a circle whose radius is an integer. What'

s the largest possible radius for her circle, in meters?
Mathematics
1 answer:
Elan Coil [88]3 years ago
3 0

9514 1404 393

Answer:

  9 m

Step-by-step explanation:

The relationship between radius and circumference is ...

  C = 2πr

Daphne wants r an integer such that ...

  60 m ≥ 2πr

  r ≤ (60 m)/(2π)

  r ≤ (30/π) m ≈ 9.549 m

The largest integer radius Daphne can use is 9 meters.

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Dave’s Automatic Door, referred to in Exercise 29, installs automatic garage door openers. Based on a sample, following are the
HACTEHA [7]

The question is not complete and the full question says;

Calculate the (a) range, (b) arithmetic mean, (c) mean deviation, and (d) interpret the values. Dave’s Automatic Door installs automatic garage door openers. The following list indicates the number of minutes needed to install a sample of 10 door openers: 28, 32, 24, 46, 44, 40, 54, 38, 32, and 42.

Answer:

A) Range = 30 minutes

B) Mean = 38

C) Mean Deviation = 7.2

D) This is well written in the explanation.

Step-by-step explanation:

A) In statistics, Range = Largest value - Smallest value. From the question, the highest time is 54 minutes while the smallest time is 24 minutes.

Thus; Range = 54 - 24 = 30 minutes

B) In statistics,

Mean = Σx/n

Where n is the number of times occurring and Σx is the sum of all the times occurring

Thus,

Σx = 28 + 32 + 24 + 46 + 44 + 40 + 54 + 38 + 32 + 42 = 380

n = 10

Thus, Mean(x') = 380/10 = 38

C) Mean deviation is given as;

M.D = [Σ(x-x')]/n

Thus, Σ(x-x') = (28-38) + (32-38) + (24-38) + (46-38) + (44-38) + (40-38) + (54-38) + (38-38) + (32-38) + (42-38) = 72

So, M.D = 72/10 = 7.2

D) The range of the times is 30 minutes.

The average time required to open one door is 38 minutes.

The number of minutes the time deviates on average from the mean of 38 minutes is 7.2 minutes

4 0
2 years ago
A 20 cm long thin wire is used to form a square. What is the area of the square?
sergij07 [2.7K]

Answer:

25cm^2

Step-by-step explanation:

A square has 4 equal sides so each side will be 20/4 = 5cm

Easily calculate the area by taking 5 x 5 = 25cm^2

6 0
2 years ago
There are four nickels, three dimes, and three quarters in your pocket. You randomly pick three coins and place them on a counte
kupik [55]

Total coins = 10 ( 4 + 3 + 3 = 10).

The probability of picking a nickel first = 4/10 = 2/5 ( 4 nickels out of 10 total).

The probability of picking a dime second = 3/9 = 1/3 ( 3 dimes out of 9 coins left).

The probability of picking the third coin as a quarter = 3/8 ( 3 quarters out of 8 coins left).

The probability of picking all three in that order = 2/5 x 1/3 x 3/8 = 1/20

3 0
3 years ago
Type a digit that makes this statement true.<br><br> 81,583,74_ is divisible by 6.
grigory [225]

Answer:

81583746

Step-by-step explanation:

It will be divisible by 6 if it ends in 6; when you divide you get 13,597,291‬.

7 0
2 years ago
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Ben earns an annual income of $12,800 a year. The income tax he has to pay is 15%. What is the amount of income tax in dollars a
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Answer:

Step-by-step explanation:

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