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irina1246 [14]
2 years ago
12

A bag contains four red marbles, two green ones, one lavender one, three yellows, and one orange marble. HINT (See Example 7.] H

ow many sets of four marbles include none of the red ones?
Mathematics
1 answer:
Murljashka [212]2 years ago
4 0

Answer:  35

Step-by-step explanation:

Given : A bag contains four red marbles, two green ones, one lavender one, three yellows, and one orange marble.

Total = 4+2+1+3+1=11

To find sets of four marbles include none of the red ones, we need to exclude red marbles when we count the total number of marbles.

Then, the total marbles(exclude red) =11-4=7

Now, the combination of 7 marbles taking 4 at a time is given by :-

^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!3!}=35

Hence, the number of sets of four marbles include none of the red ones = 35

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this is the best thing i could find for you, good luck with your question,

5x is greater than or equal to -25

The product of 5 and a number is at least –25

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product of 5 and a number is 5x

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for word at least we use >=

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Does the series converge or diverge? If it converges, what is the sum? Show your work. ∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1
Mekhanik [1.2K]

Answer:

Step-by-step explanation:

Given the series,

∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1

I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)

So,

∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞

There are different types of test to show if a series converges or diverges

So, using Ratio test

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Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))

Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))

Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)

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a is first term

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So, first term is

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S∞ = -4 / 1--½

S∞ = -4 / 1 + ½

S∞ = -4 / 3/2 = -4 × 2 / 3

S∞ = -8 / 3 = -2⅔

The sum to infinity is -2.67 or -2⅔

Check attachment for better understanding

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3 years ago
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