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tekilochka [14]
1 year ago
9

How many different ways are there to choose a subset of the set {1,2,3,4,5,6} so that the product of the members of the subset i

s even
Mathematics
1 answer:
zvonat [6]1 year ago
3 0

You have to pick at least one even factor from the set to make an even product.

There are 3 even numbers to choose from, and we can pick up to 3 additional odd numbers.

For example, if we pick out 1 even number and 2 odd numbers, this can be done in

\dbinom 31 \dbinom 32 = 3\cdot3 = 9

ways. If we pick out 3 even numbers and 0 odd numbers, this can be done in

\dbinom 33 \dbinom 30 = 1\cdot1 = 1

way.

The total count is then the sum of all possible selections with at least 1 even number and between 0 and 3 odd numbers.

\displaystyle \sum_{e=1}^3 \binom 3e \sum_{o=0}^3 \binom 3o = 2^3 \sum_{e=1}^3 \binom3e = 8 \left(\sum_{e=0}^3 \binom3e - \binom30\right) = 8(2^3 - 1) = \boxed{56}

where we use the binomial identity

\displaystyle \sum_{k=0}^n \binom nk = \sum_{k=0}^n \binom nk 1^{n-k} 1^k = (1+1)^n = 2^n

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MrRa [10]

Answer:

The  equation for a line that is parallel to y + 5 = 3(x - 1) and goes through the point (3,-4) will be:

  • y = 3x-13

Step-by-step explanation:

Given the equation

y + 5 = 3(x - 1)

Writing in the slope-intercept form

y=mx+b

where m is the slope and b is the y-intercept

y = 3(x-1) -5

y  = 3x-3-5

y = 3x - 8

Thus, the slope = m = 3

We know that the parallel lines have equal slopes.

So, the slope of a parallel line is also 3

Using the point-slope form of the line equation

y-y_1=m\left(x-x_1\right)

substituting the values m = 3 and the point (3, -4)

y-(-4)=3(x-3)

y+4 = 3x-9

y = 3x-9-4

y = 3x-13

Thus, the  equation for a line that is parallel to y + 5 = 3(x - 1) and goes through the point (3,-4) will be:

  • y = 3x-13
5 0
3 years ago
Find the prime factorization: 49 i am stuck
ollegr [7]

Answer:

49 can be broken down into 7 * 7 so the prime factorization is simply 7².

8 0
3 years ago
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RoseWind [281]

Answer:

(f•g)(4) = 45

Step-by-step explanation:

f(x)=4x+1

g(x)=x^2-5

(f•g)(x) = 4(x^2 -5)+1

(f•g)(4) = 4(4^2 -5)+1

(f•g)(4) = 4(16-5)+1

(f•g)(4) = 4(11)+1

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VikaD [51]

Answer:

The ray that goes parallel to the main axis after passing through the lens should also be parallel from the object to the lens

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1) Light rays are drawn from the object incidented on the lens and parallel to the principal axis. The incident light refracts (bends) through the lens and converges at the focal point at the other side of the lens.

2) Another incident light passes through the optical centre undeflected and intersect with the refracted ray at the other side of the lens.

Based on the above points, Roshan made an error by drawing the ray that goes parallel to the main axis and after passing through the lens made the same ray to be parallel from the object to the lens instead of refracting (bending) after passing through the lens.

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Think about it this way:

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