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fgiga [73]
3 years ago
7

Use the remainder theorem to find the remainder of 2x^4 + x^2 - 10x -1 divided by x +2.

Mathematics
1 answer:
Svetllana [295]3 years ago
8 0

Remainder Theorem says that if there is any Polynomial equation P(x), which is to be divided by (x - a) then remainder can be calculated by substituting value of a in equation P(x).  

2x^{4} +x^{2}-10x-1 = P(x)   divided by   (x+2)

Step 1: Find a

To find a we will have to convert (x+2) into (x - a) form

i.e.  (x+2) = (x - (-2))

therefore, a = -2

Step 2: Substitute value of a in P(x),

By substitution we get,

2(-2)^{4}+(-2)^{2}-10(-2)-1

= 2(16) + 4 +20 -1

= 32 +4 + 20 - 1

= 55 = Remainder

Hence, Remainder is 55.

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The graph shows the relationship between hours worked and total earnings for a store clerk. Let h represent hours worked and e r
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The answer is C.

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y = kx → e =

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Although cities encourage carpooling to reduce traffic congestion, most vehicles carry only one person. For example, 64% of vehi
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Answer:

a) 0.7291 is the probability that more than half out of 10 vehicles carry just 1 person.

b) 0.996 is the probability that more than half of the vehicles  carry just one person.    

Step-by-step explanation:

We are given the following information:

A) Binomial distribution

We treat vehicle on road with one passenger as a success.

P(success) = 64% = 0.64

Then the number of vehicles follows a binomial distribution, where

P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 10

We have to evaluate:

P(x \geq 6) = P(x =6) +...+ P(x = 10) \\= \binom{10}{6}(0.64)^6(1-0.64)^4 +...+ \binom{10}{10}(0.64)^{10}(1-0.79)^0\\=0.7291

0.7291 is the probability that more than half out of 10 vehicles carry just 1 person.

B) By normal approximation

Sample size, n = 92

p = 0.64

\mu = np = 92(0.64) = 58.88

\sigma = \sqrt{np(1-p)} = \sqrt{92(0.64)(1-0.64)} = 4.60

We have to evaluate the probability that more than 47 cars carry just one person.

P(x \geq 47)

After continuity correction, we will evaluate

P( x \geq 46.5) = P( z > \displaystyle\frac{46.5 - 58.88}{4.60}) = P(z > -2.6913)

= 1 - P(z \leq -2.6913)

Calculation the value from standard normal z table, we have,  

P(x > 46.5) = 1 - 0.004 = 0.996 = 99.6\%

0.996 is the probability that more than half out of 92 vehicles carry just one person.

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