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3 years ago

Plz help, I don't understand this.

Mathematics

1 answer:

Oksanka [162]3 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

consecutive even integers have a difference of 2 between them

for example 2, 4, 6 are 3 consecutive even integers

In general if we let the first integer be k then the next 2 integers are

k + 2 and k + 4

the sum of these equals 4 times the first integer, that is 4k, hence

k + k + 2 + k + 4 = 4k

3k + 6 = 4k ( subtract 3k from both sides )

6 = k

the 3 consecutive integers are

k = 6

k + 2 = 6 + 2 = 8

k + 4 = 6 + 4 = 10

that is 6, 8 and 10

note that sum = 6 + 8 + 10 = 24

and 4 × 6 = 24

confirming the sum of the 3 integers equals 4 times the first integer

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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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3 years ago

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romanna [79]

Answer:

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3 years ago

A circle has its center at (1, 4) and a radius of 2 units. Find the equation of the circle using the Pythagorean Theorem.

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3 years ago

Three apple pies, all the following shape, are left on a counter. How much total pie has been left?

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2 years ago

Researchers at the Centers for Disease Control and Prevention have been studying the decay pattern of a new virus with a decay r

koban [17]

The Researcher will find 69 viruses, because 231 viruses are decayed in 7 hours, if a virus with a decay rate of 19% per hour and they start with 300 viruses.

Step-by-step explanation:

The given is,

A new virus with a decay rate of 19% per hour

They start with 300 viruses

Step:1

Formula to calculate the viruses at decay rate,

$y = A(1-r)^{t}$ ............................(1)

Where, y - No of viruses after given time

A - Viruses at initial stage

r - Decay rate

t - No. of hours

From the given,

A = 300

r = 19% per hour

t = 7 hours

Equation (1) becomes,

$y = 300(1-0.19)^{7}$

$= 300(0.81)^{7}$

$= 300(0.228767)$

$= 68.63$

Viruses of 7 hours ≅ 69 viruses

( or )

Step:1

For 1st hour,

= (No.of viruses in hour) - (No,of viruses in last hour × Decay rate )

= (300)-(300 × 0.19)

= 300 - 57

= 243

For 2nd hour,

= (243)-(243 × 0.19)

= 243 - 46.17

= 196.83

For 3rd hour,

= (196.83)-(196.83 × 0.19)

= 196.83 - 37.39

= 159.4323

For 4th hour,

= (159.4323)-(159.4323 × 0.19)

= 159.4323 - 30.2921

= 129.1402

For 5th hour,

= (129.1402)-(129.1402 × 0.19)

= 129.1402 - 24.5366

= 104.6035

For 6th hour,

= ( 104.6035)-( 104.6035 × 0.19)

= 104.6035 - 19.8747

= 84.7288

For 7th hour,

= (84.7288)-(84.7288 × 0.19)

= 84.7288 - 16.0984

= 68.63 viruses

Result:

The Researcher will find 69 viruses, because 231 viruses are decayed in 7 hours, if a virus with a decay rate of 19% per hour and they start with 300 viruses.

7 0

3 years ago