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lara31 [8.8K]
1 year ago
15

The sum of the squares of two consecutive even integers is 884. find the integers

Mathematics
1 answer:
andriy [413]1 year ago
3 0
2x + 2x +2 are the integers
4x^2 + 4x^2 +8x +4 =884 (The sum of the integers squared)
8 x^2 +8x -880 = 0

x = 10
Therefore, the integers are:
20 and 22




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Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?
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For x∈ {-∞,-3} y<0, below x-axis

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Step-by-step explanation:

f(x)=2x^{3}-26x-24

2x^{3}-26x-24=0

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=> 2x^{2} -2x-24=0\\=>2(x^{2} -x-12)=0\\=> x^{2} -x-12=0\\=> x^{2} -4x+3x-12=0\\=> x(x-4)+3(x-4)=0\\=> (x-4)(x+3)=0\\

=> x-4=0\\=> x_{2}=4\\=> x+3=0\\=>x_{3}=-3\\

For x∈ {-∞,-3} y<0, below x-axis

x∈ {-3,-1} y>0, above x-axis

x∈ {-1,4} y<0, below x-axis

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Michelle exercises for half an hour every day. How minutes in total does she exercise for over 5 days?
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A library buys 36 English books, 48 Science books and 72 Mathematics books. The thickness of each book is the same. Now, the lib
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13

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A committee of 15 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the pr
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Answer:

0.006% probability that the final vote count is unanimous.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

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So 50% of voting yes, 50% no, so p = 0.5

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This means that n = 15

What is the probability that the final vote count is unanimous?

Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So

p = P(X = 0) + P(X = 15)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003

P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003

So

p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006

0.006% probability that the final vote count is unanimous.

7 0
1 year ago
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