is the sum of two polynomials of degree 5 always a polynomial of degree 5? Give an example to explain your answer

1 answer:

7 0

An example to consider is

f(x)=5x^5+2x^3+3x
g(x)=-5x^5-x^4+x^2-4

Consequently, f(x)+g(x) results in -x^4+2x^3+x^2+3x-4, which classifies as a polynomial of degree 4.

Thus, the conclusion is negative. A counter-example is illustrated above.

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A business manager who needs to make many phone calls has estimated that when she calls a client, the probability that she will

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Answer:

a. 0.68 or 68%

b. 0.08 or 8%

c. 0.32 or 32%

Step-by-step explanation:

The probability of contacting the client on the first call is 60%

The likelihood of reaching the client on the second call is 20%

a. The chance of the manager successfully connecting with her client within two calls is the sum of the chances for one or two calls:

$P(X\leq2) = P(X=1) +P(X=2)\\P(X\leq2) = 0.60+(1-0.60)*0.2\\P(X\leq2) = 0.68 = 68\%$

b. The probability that the manager connects during the second call but not the first is:

$P(X=2) = (1-0.6)*0.2 =0.08 = 8\%$

c. The probability that the manager fails to connect in two consecutive calls (requiring more calls) is P(X>2):

$P(X>2) = 1-P(X\leq2) = 1-0.68\\P(X>2) = 0.32 = 32\%$

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