Is (8,-44) a solution to y=-7x+6

Mathematics

1 answer:

NARA [144]3 years ago

8 0

No

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let a,b,c,d be four integers (not necessarily distinct) in the set {1,2,3,4,5}. the no. of polynomials x^4+ax^3+bx^2+cx+d which

Eddi Din [679]

By either long or synthetic division, it's easy to show that

$\dfrac{x^4+ax^3+bx^2+cx+d}{x+1}=x^3+(a-1)x^2+(-a+b+1)x+(a-b+c-1)-\dfrac{a-b+c-d-1}{x+1}$

The quartic will be exactly divisible by $x+1$ when the numerator of the remainder term vanishes, or for those values of $a,b,c,d$ such that

$a-b+c-d-1=0$

I'm not sure how to count the number of solutions (software tells me it should be 80), but hopefully this is a helpful push in the right direction.

8 0

3 years ago

The probability of a randomly selected adult in one country being infected with a certain virus is 0.005. In tests for the viru

myrzilka [38]

Answer:

The probability is 12.66%.

This is a low probability, so it is unlikely for such a combined sample to test positive.

Step-by-step explanation:

If the probability of being infected is 0.005, the probability of not being infected is 0.995.

Then, to find the probability of at least one of the 27 people being infected P(A), we can find the complementary case: all people are not infected: P(A').

$P(A') = 0.995^{27}$