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1 year ago

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What is the shortest strip of fiber from which five pieces of the following lengths can be cut: 9 1/2 inches, 10 11/16 inches, 6

9/16 inches, 7 1/2 inches, and 1 5/8 inches? No allowance is made for waste.

1 answer:

Allushta [10]1 year ago

3 0

Answer:

<u>35 7/8 inches</u>

Step-by-step explanation:

<u>Shortest strip</u>

9 1/2 + 10 11/16 + 6 9/16 + 7 1/2 + 1 5/8
9 8/16 + 10 11/16 + 6 9/16 + 7 8/16 + 1 10/16
9 + 10 + 6 + 7 + 1 + (46/16)
33 + 2 7/8
<u>35 7/8 inches</u>

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Suppose the diameter of a circle is 6 units What is its circumference?

Kipish [7]

Answer:

18.84 estimated, 6π exactly

Step-by-step explanation:

Hi!

<u>The formula for finding the circumference of a circle is 2πr:</u>

In that case, all we need to do <em>first </em>is to divide the diameter by 2, so we can substitute that into the equation.

6 ÷ 2 = 3

So we have 2π × 3 to solve.

2π × 3 = 6π

We can estimate the circumference by multiplying by 3.14.

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(actually multiplying by π gives 18.849... which is pretty close!)

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Hope this helps!

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2 years ago

In an international film festival, a penal of 11 judges is formed to judge the best film. At last two films FA and FB were consi

valentina_108 [34]

Answer:

The answer is "0.4329 ".

Step-by-step explanation:

P( three in favor of FA)

Select 3 out of 6 FA supporters then select 2 out of 5 FB supportive judges

$=\frac{^{6}_{C_{3}}\times ^{5}_{C_{2}}}{^{11}_{C_{5}}}\\\\=\frac{\frac{6!}{3!(6-3)!}\times \frac{5!}{2!(5-2)!}}{\frac{11!}{5!(11-5)!}}\\\\=\frac{\frac{6!}{3! \times 3!}\times \frac{5!}{2! \times 3!}}{\frac{11!}{5! \times 6!}}\\\\=\frac{\frac{6 \times 5 \times 4 \times 3!}{3 \times 2 \times 1\times 3!}\times \frac{5 \times 4 \times 3!}{2 \times 1 \times 3!}}{\frac{11 \times10 \times 9 \times 8 \times 7 \times 6! }{5 \times 4 \times 3 \times 2 \times 1 \times 6!}}\\\\$

$=\frac{ (5 \times 4) \times(5 \times 2)}{(11 \times 3 \times 2 \times 7 )}\\\\=\frac{ 20 \times 10 }{(11 \times 42)}\\\\=\frac{ 200 }{462}\\\\=\frac{100 }{231}\\\\=0.4329$

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2 years ago

At a financial institution, a fraud detection system identifies suspicious transactions and sends them to a specialist for revie

labwork [276]

Answer:

a. E(X) = 54.4

b. E(X) = 2.5

c. P(Y=2) = .0116

Step-by-step explanation:

a.

E(X) = np = .40 probability * 136 trials = 54.4 blocked transmissions

To get the expected value, we simply multiply probability times number of trials. You can look at it in simple terms by thinking if there's a 50% chance of flipping heads and you flip a coin twice, in an ideal world you will have .5*2 = 1 head.

b.

i. Let X represent the number of suspicious transmissions reviewed until finding the first blocked one. We will use a geometric distribution to model the "first" transmission. Whenever we're looking for the "first" time something happens, we use geometric.

ii. E(X) = 1/p , according to the geometric model.

= 1/.4 = 2.5.

We expect that the specialist will review 2.5 suspicious transactions <em>on average </em>before finding the first transmission that will be blocked.

c.

i. Let Y represent the exact number of blocked transmissions out of 10. We will use a binomial distribution to model the "fixed" number of transmissions. Whenever we're looking for a "fixed" number of times something happens, we use binomial.

ii. P(Y=k) = (n choose k)(p^k)(q^n-k)

P(Y=2) = (¹⁰₂)(.4^2)(.6^10-2)

= 45 (.4^2)(.6^10-2) = .0016

As for calculator notation, the n choose k can be accessed on a TI-84 via MATH -> PRB -> nCr. It looks like 10 nCr 2 on the display.

Hence the probability that two transactions out of ten will be blocked is .0016 by the binomial model.

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3 years ago