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2 years ago

A spool of thread contains 150 revolutions of thread. the diameter of the spool is 3 centimeters. find the length of the thread

1 answer:

4 0

The circumference is given by:
C = 2 * pi * r
Where,
r: radio
Substituting we have:
C = 2 * (3.14) * (3/2)
C = 9.42 cm
Then, the length is given by the product of the circumference and the number of revolutions.
We have then:
L = (150) * (9.42)
L = 1413 cm
Answer:
the length of the thread is:
L = 1413 cm

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D. There is not enough evidence at the 5% significance level to indicate that one route gets Katy to work faster, on average, since 0 falls within the bounds of the confidence interval.

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A friend of mine is giving a dinner party. His current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabe

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a) 720, b) 475020, c) 69300, d) 0.146, e) 0.001

Step-by-step explanation:

It is given that my friend has 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet.

If he wants to serve 3 bottles of zinfandel and serving order is important, then the total number of ways is

$10\times 9\times 8=720$

Therefore if he wants to serve 3 bottles of zinfandel and serving order is important, then the total number of ways are 720.

The total number of bottles is

$10+8+11=29$

Combination is defined as

$^nC_r=\frac{n!}{r!(n-r)!}$

where, n is total possible outcomes and r is selected outcomes.

we have to select 6 bottles out of 29. so,

$^{29}C_{6}=475020$

Therefore ff 6 bottles of wine are to be randomly selected from the 29 for serving, then the total number of ways are 475020.

If we want to select 2 bottles of each variety, then total number of ways are

$^{10}C_{2}\times ^{8}C_{2}\times ^{11}C_{2}=69300$

Therefore if 6 bottles are randomly selected with two bottles of each variety, then the total possible ways are 69300.

Probability is defined as

$P=\frac{\text{Total outcomes}}{\text{Favorable outcomes}}$

$\frac{^{10}C_{2}\times ^{8}C_{2}\times ^{11}C_{2}}{^{29}C_{6}}=\frac{69300}{475020}\approx 0.146$

Therefore the probability that two bottles of each variety being chosen is 0.146.

If 6 bottles are randomly selected, then the probability that all of them are the same variety is

$\frac{^{10}C_{6}+^{8}C_{6}+^{11}C_{6}}{^{29}C_{6}}=\frac{700}{475020}\approx 0.001$

Therefore if 6 bottles are randomly selected, then the probability that all of them are the same variety is 0.001.

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2 years ago