A quality control expert at a drink bottling factory took a random sample of bottles from a batch and measured

From a shipment of 65 transistors, 6 of which are defective, a sample of 5 transistors is selected at random.

Vladimir79 [104]

Answer:

a) 8259888

b) 34220

c) 45057474

Step-by-step explanation:

Given,

The total number of transistor = 65,

In which, the defective transistor = 6,

So, the number of non defective transistor = 65 - 6 = 59,

Since, out of these transistor 5 are selected,

a) Thus, the number of ways = the total possible combination of 5 transistors = ${65}C_ 5$

$=\frac{65!}{(65-5)!5!}$

$=8259888$

b) The number of samples that contains exactly 3 defective transistors = the possible combination of exactly 3 defective transistors = ${6}C_3\times {59}C_2$

$=\frac{6!}{(6-3)!3!}\times \frac{59!}{(59-2)!\times 2!}$

$=20\times 1711$

$=34220$

c) The number of sample without any defective transistor = The possible combination of 0 defective transistor = $^6C_0\times ^{59}C_5$

$=1\times 45057474$

$=45057474$

5 0

3 years ago

Rationalise:<br>(1) 4/(2+root3+root7)<br>(2) 4/(2root3+root5)

Temka [501]

$\frac{4}{2+\sqrt3+\sqrt7}\cdot\frac{2-(\sqrt3+\sqrt7)}{2-(\sqrt3+\sqrt7)}=\frac{8-4\sqrt3-4\sqrt7}{2^2-(\sqrt3+\sqrt7)^2}=\frac{8-4\sqrt3-4\sqrt7}{4-3-2\sqrt{3\cdot7}-7}\\\\=\frac{8-4\sqrt3-4\sqrt7}{-6-2\sqrt{21}}=\frac{-2(2\sqrt3+2\sqrt7-4)}{-2(3+\sqrt{21})}=\frac{2\sqrt3+2\sqrt7-4}{3+\sqrt{21}}\cdot\frac{3-\sqrt{21}}{3-\sqrt{21}}\\\\=\frac{6\sqrt3-2\sqrt{63}+6\sqrt7-2\sqrt{147}-12+4\sqrt{21}}{3^2-(\sqrt{21})^2}=\frac{6\sqrt3-2\sqrt{9\cdot7}+6\sqrt7-2\sqrt{49\cdot3}-12+4\sqrt{21}}{9-21}$

$=\frac{6\sqrt3-6\sqrt7+6\sqrt7-14\sqrt3-12+4\sqrt{21}}{-12}=\frac{-8\sqrt3+4\sqrt{21}-12}{-12}=\frac{-4(2\sqrt3-\sqrt{21}+3)}{-12}\\\\=\frac{2\sqrt3-\sqrt{21}+3}{3}$

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$\frac{4}{2\sqrt3+\sqrt5}\cdot\frac{2\sqrt3-\sqrt5}{2\sqrt3-\sqrt5}=\frac{8\sqrt3-4\sqrt5}{(2\sqrt3)^2-(\sqrt5)^2}=\frac{8\sqrt3-4\sqrt5}{4\cdot3-5}=\frac{8\sqrt3-4\sqrt5}{12-5}\\\\=\frac{8\sqrt3-4\sqrt5}{7}$

4 0

4 years ago

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Will require a less costly investment in

Alexxandr [17]

Answer:

The Shoe Hut

Star's Coffee and Coffee

Step-by-step explanation:

3 0

3 years ago

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Are their always the same number of prime numbers between 2 consecutive multiples of 10

Harlamova29_29 [7]

Yes there are. Its just the way they work out!

3 0

3 years ago

Which pair of numbers is relatively prime?

Leno4ka [110]

Two numbers are relatively prime if they have no factors in common. In other words, if their greatest common divisor is 1.
7 and 42- both divisible by 7
66 and 77- both divisible by 11
90 and 891- both divisible by 9
Answer would be 16 and 39

4 0

3 years ago

Read 2 more answers